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[ "### EC2304-MICROPROCESSORS AND MICROCONTROLLERS Two Marks Questions With Answers 2014\n\nAnna University, Chennai\n\nDHANALAKSHMI SRINIVASAN INSTITUTE OF RESEARCH AND TECHNOLOGY\n\nSIRUVACHUR PERAMBALUR DEPARTMENT OF ECE\n\nEC2304-MICROPROCESSORS AND MICROCONTROLLERS PART-B QUESTIONS\n\nUNIT-I\n\n1. Explain the internal hardware architecture of 8086 microprocessor with neat diagram.\n\n-Block diagram of 8086\n\n-BIU\n\n-EU\n\n-Memory segmentation\n\nCS, SS, DS, ES\n\n-General Purpose Registers\n\nAX, BX, CX, DX\n\n-Flag Registers\n\nCF, AUF, PF, ZF, TP, OV, IF, DF, SF\n\n-Block diagram\n\n-16 Bit read at odd & even boundary\n\n3. Write about Data transfer schemes.\n\n-Parallel data transfer\n\n-Serial data transfer\n\n4. Explain about interrupt types in 8086.\n\n-Software interrupts\n\n-Single step interrupt\n\n-NMI\n\n5. Write about Direct memory access in 8086.\n\n-DMA in minimum Mode\n\n-DMA in maximum mode\n\nUNIT-II\n\n1. Write an ALP to arrange N numbers in ascending order.\n\nDATA SEGMENT\n\nx DW 42H,34H,26H,17H,09H LEN EQU 05\n\nASCD DB 10 DUP(0) DATA ENDS\n\nCODE SEGMENT\n\nASSUME CS:CODE,DS:DATA START: MOV AX,DATA\n\nMOV DS,AX\n\nMOV BX,LEN-1\n\nMOV CX,BX\n\nUP1: MOV BX,CX LEA SI,X\n\nUP: MOV AX,[SI]\n\nMOV DX,[SI+2] CMP AX,DX\n\nJB DOWN/JA DOWN\n\nMOV [SI],DX\n\nMOV [SI+2],AX DOWN: INC SI INC SI\n\nDEC BX JNZ UP DEC CX JNZ UP1\n\nMOV AH,4CH INT 21H CODE ENDS END START\n\n2. Write an ALP to find largest number in an array.\n\nDATA SEGMENT\n\nX DW 0010H,0052H,0030H,0040H,0050H\n\nMES DB 10,13,'LARGEST NUMBER AMONG THE SERIES IS \\$' DATA ENDS\n\nCODE SEGMENT\n\nASSUME CS:CODE,DS:DATA\n\nSTART: MOV AX,DATA\n\nMOV DS,AX MOV CX,05H LEA SI,X MOV AX,[SI] DEC CX\n\nUP: CMP AX,[SI+2] JA CONTINUE MOV AX,[SI+2]\n\nDEC CX JNZ UP AAM\n\nMOV BX,AX\n\nMOV AX,09H LEA DX,MES INT 21H\n\nMOV DL,BH MOV AH,02H INT 21H\n\nMOV DL,BL\n\nINT 21H\n\nMOV AH,4CH\n\nINT 21H CODE ENDS END START\n\n3. Write about Data transfer group and Logical instruction group of 8086.\n\n-Data transfer instructions\n\nMOV <d>, <s> XCHG <d>, <s> XLAT\n\nPUSH<s> POP <d>\n\n-Logical instructions\n\nAND <d>, <s> OR <d>, <s> XOR <d>, <s> NOT <d>\n\nNEG <d> CMP<d>,<s>\n\nTEST <d>,<S>\n\n4. Write about Assembler directives of 8086.\n\n-SEGMENT\n\n-ENDS (END SEGMENT)\n\n-CODE SEGMENT\n\n-END (END PROCEDURE)\n\n-ASSUME\n\n-DB (DEFINE BYTE)\n\n-DD (DEFINE DOUBLE WORD)\n\n-DT (DEFINE TEN BYTES)\n\n-LENGTH\n\n-OFFSET\n\n-PTR (POINTER)\n\n-BYTE PTR\n\n-EVEN (ALIGN ON EVEN MEMORY ADDRESS)\n\n- Base Plus Index addressing mode,\n\n-Base Relative Plus Index addressing mode.\n\nUnit-III\n\n1. With neat block diagram explain the 8255 programmable peripheral interface and its\n\nOperating modes.\n\n` -8255 block diagram\n\n-Mode0-Basic Input/output\n\n-Mode 1-Strobed Input/Output\n\n-Mode 2-Strobed Bidirectional bus\n\n-Configuring 8255\n\n-Interfacing 8255\n\n2. Draw and explain the block diagram of 8254 programmable interval timer. Also explain the various modes of operation.\n\n-Interfacing 8254 with 8086 block diagram\n\n-Counter 0\n\n- Counter 1\n\n- Counter 2\n\n3. Explain the need for sample and hold circuit and multiplexer.\n\n-S&H circuit placed after the multiplexer\n\n-Mux placed after the S&H circuit connections\n\n4. Explain 8279 keyboard /display controller with neat block diagram.\n\n-Internal block diagram of 8279\n\n-Keyboard section\n\n-Display section\n\n-Software commands\n\n-Interfacing 8279\n\n5. Describe the architecture and working of 8253 timer.\n\nSimilar operation of 8254\n\n6. Draw and explain the block diagram of A to D converter.\n\n-Asynchronous mode\n\n- Synchronous mode\n\n-Interrupt mode\n\nUNIT-IV\n\n1. Explain the architecture of 8051 with its diagram.\n\n-Block diagram of 8051\n\n-Memory organization\n\n-Program memory\n\n-Data memory\n\n-Special function registers\n\n2. Write about operating modes for serial port of 8051 microcontroller.\n\n-Port 0 configuration\n\n-Simple I/O operation\n\n-External memory interface\n\n-Port 1\n\n-Port 2\n\n-Port 3\n\n3. Write about the instruction set of 8051 microcontroller.\n\n-Data transfer instructions\n\n-Arithmetic instructions\n\n-Logic instructions\n\n-Control transfer instructions\n\n-Base plus index register indirect addressing\n\n5. Explain the interrupt structure of 8051 microcontroller.\n\n-INT0\n\n-INT1\n\n-TF0\n\n-TF1\n\n-RI/TI\n\nUNIT-V\n\n1. Draw and explain the block diagram of traffic light control system.\n\n-Traffic light FSM Interface signals\n\n-Switching circuit\n\n-Operation sequence\n\n2. Draw the diagram to interface a stepper motor with 8051 microcontroller and explain its operation.\n\n-Step angle:\n\nStep angle is defined as the minimum degre of rotation with a single step. No of steps per revolution = 360° /step angle\n\nSteps per second = (rpm x steps per evolution) /60\n\nExample: step angle = 2°\n\nNo of steps per revolution = 180\n\nSwitching Sequence of Motor:\n\nThis can be done by sending a bits sequence to one end of the coil while the other end is commonly connected. The bit sequence sent can make either one phase ON or two phases ON for a full step sequence or it can be a combination of one and two phase ON for half step sequence.\n\nTwo Phase ON\n\nOne Phase ON\n\n3. Explain how interrupts are handled in 8051.\n\n- Interrupt Sources\n\n- External Interrupts\n\n- Internal Interrupts\n\n- Enabling Interrupts\n\n- Interrupt Priorities\n\n4. Draw and explain the Washing machine control using 8051.\n\n-Washing cycle\n\n-Control system design\n\n-Software" ]

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[ "## Types of Decay\n\n### Transcript\n\nNow let's walk through a few of the decay modes. We'll start with alpha decay. Here an atom splits into a smaller atom and an alpha particle which is just a helium nucleus. So if we look at this we have a large nucleus that breaks resulting in our alpha particle or our helium nucleus.\n\nIf we were to write this we could say that 10, 5 boron goes through alpha decay and produces a 6, 3 lithium. Now remember, nucleons are conserved. So 10 will not change for this and we have on here 4 plus 6 equals 10. For the alpha decay our number of protons stays the same because we're just splitting off the helium nucleus, so 2 plus 3 equals 5.\n\nSo in an alpha decay we take a nucleus and split it into 2 smaller ones, one of which is just essentially the helium nucleus. Now our next decay mechanism is beta decay. Here a neutron turns into a proton by ejecting a beta particle which is essentially an electron. So if we consider that a neutron has both positive and negative charges.\n\nWith the neutron ejects the negative portion as a beta particle it then becomes a proton. So for you to see this visually, we have our nucleus, it'll eject the beta particle, which then causes the neutron to turn into a proton. An example of this 10, 5 boron going through a beta decay becomes 10, 6 carbon.\n\nSo the total number of nucleons is the same here, however our protons have increased by one because a neutron has been converted into a proton. So we go from 5 to 6. Next decay mechanism, positron decay. In positron decay a proton turns into a neutron by ejecting a positron, which is essentially a positive electron.\n\nSo here we have our positive charge that's ejected as a positron, and we go back to being a neutron. Now, if we look at this visually, we'd have our nucleus that would eject the positron and one of our protons is going to become a neutron. So for the case of 10, 5 boron, a positron decay results in 10, 4 beryllium. So again, the total number of nucleons is conserved, however, a proton turns into a neutron, which reduces this number from 5 to 4.\n\nElectron capture is when a nucleus 'catches' an electron and combines it with a proton to make a neutron. So if we have our nucleus and an electron out there, it catches the electron and then adds it to a proton to convert it into a neutron. So for this case, proton with an incoming electron absorbs that and we get a neutron.\n\nFor 10, 5 boron, an electron captured turns it into 10, 4 beryllium. Again nucleons are conserved. Adding this electron makes a proton turn into a neutron or 5 goes to 4. The last decay mode we'll look at is gamma decay. This is the result of a rearrangement of nucleons in the nucleus. Doing so releases extra energy in the form of a gamma ray.\n\nLooking at a visual model, when a nucleus releases a gamma ray it does so because it has rearranged to some lower energy state. So for 10,5 boron undergoing a gamma decay, we essentially get 10,5 boron but it's in some new energy state as indicated by the stars. So gamma decay does not change the element but it does change the position of the nucleons in the nucleus.\n\nThey move round a little bit and that moving results in lower energy states, and the release of the excess energy as a gamma ray. Now let us do a few decay reactions. We'll fill in blanks for the following. In the first one we have berkelium-249 undergoing a beta decay. Now here in a beta decay, a neutron is converted into a proton.\n\nWhen elements are written in this form, just showing the protons plus neutrons is often not helpful in decay reactions. Instead we wanna write them with their mass number, 249, with the atomic number underneath and berkelium happens to be 97. So now we know the protons plus neutrons plus the number of protons. So in this beta decay we're gonna convert one of these neutrons into a proton raising the atomic number without changing the total number of nucleons and we'll have 249, 98 californium.\n\nThis next one is a gamma decay resulting in plutonium-236. Now remember, gamma decays don't affect the nucleons, so on this side we're still gonna have plutonium-236, it's just that the nucleus has a slightly different orientation after the gamma decay. So, for this instance we don't actually need to look up the atomic number for the plutonium because it's not gonna be affected.\n\nIf we did however we would see that this would be 236, 94 plutonium, because plutonium has 94 protons, it's element 94. Our next reaction, technetium-88 undergoing a positron decay. Now in a positron decay, we're going to turn a proton into a neutron. So again we hit the periodic table and we see that technetium, element 43, So we change one of these protons into a neutron and we get 88, 42 and this element is molybdenum.\n\nThe last one we had polonium-208 undergoes some change to become lead-204. Now notice here 208 goes to 204 meaning that we've lost 4 nucleons. This only happens in alpha decays because alpha is a helium 4, 2 nucleus. We could have written this out and said the polonium was 208, 84 Po and lead is 204, 82 Pb and then these would balance, 208 equals 4 plus 204, 84 equals 2 plus 82.\n\nHowever, all the other decay modes we've talked about don't affect the mass number. Only an alpha-decay, where we actually split the nucleus and send off the nucleons in a different direction, will affect the total number of protons plus neutrons. Nucleons are still conserved, they just are now split into an alpha particle and the new nucleus.\n\nNow, if we were to do an electron capture, It has the same result as a positron decay. So technetium-88 plus an electron would also result in molybdenum-88. Because in an electron capture a proton is converted into a neutron. So the result of electron capture or positron decay is the same.\n\nThey're just different modes to get to the same product. That concludes this portion of the physics two lecture." ]

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[ "", null, "", null, "", null, "", null, "", null, "# Data Amplification: Instance-Optimal Property Estimation\n\nThe best-known and most commonly used distribution-property estimation technique uses a plug-in estimator, with empirical frequency replacing the underlying distribution. We present novel linear-time-computable estimators that significantly \"amplify\" the effective amount of data available. For a large variety of distribution properties including four of the most popular ones and for every underlying distribution, they achieve the accuracy that the empirical-frequency plug-in estimators would attain using a logarithmic-factor more samples. Specifically, for Shannon entropy and a broad class of properties including ℓ_1-distance, the new estimators use n samples to achieve the accuracy attained by the empirical estimators with n n samples. For support-size and coverage, the new estimators use n samples to achieve the performance of empirical frequency with sample size n times the logarithm of the property value. Significantly strengthening the traditional min-max formulation, these results hold not only for the worst distributions, but for each and every underlying distribution. Furthermore, the logarithmic amplification factors are optimal. Experiments on a wide variety of distributions show that the new estimators outperform the previous state-of-the-art estimators designed for each specific property.\n\n03/29/2019\n\n### Data Amplification: A Unified and Competitive Approach to Property Estimation\n\nEstimating properties of discrete distributions is a fundamental problem...\n06/10/2019\n\n### The Broad Optimality of Profile Maximum Likelihood\n\nWe study three fundamental statistical-learning problems: distribution e...\n05/21/2019\n\n### Efficient Profile Maximum Likelihood for Universal Symmetric Property Estimation\n\nEstimating symmetric properties of a distribution, e.g. support size, co...\n11/08/2019\n\n### Unified Sample-Optimal Property Estimation in Near-Linear Time\n\nWe consider the fundamental learning problem of estimating properties of...\n06/25/2019\n\n### Distribution-robust mean estimation via smoothed random perturbations\n\nWe consider the problem of mean estimation assuming only finite variance...\n07/06/2018\n\n### Outperforming Good-Turing: Preliminary Report\n\nEstimating a large alphabet probability distribution from a limited numb...\n09/05/2019\n\n### Predictive distributions that mimic frequencies over a restricted subdomain (expanded preprint version)\n\nA predictive distribution over a sequence of N+1 events is said to be \"f...\n\n## 1 Introduction\n\nRecent years have seen significant interest in estimating properties of discrete distributions over large domains [1, 2, 3, 4, 5, 6]. Chief among these properties are support size and coverage, Shannon entropy, and -distance to a known distribution. The main achievement of these papers is essentially estimating several properties of distributions with alphabet size using just samples.\n\nIn practice however, the underlying distributions are often simple, and their properties can be accurately estimated with significantly fewer than samples. For example, if the distribution is concentrated on a small part of the domain, or is exponential, very few samples may suffice to estimate the property. To address this discrepancy,   took the following competitive approach.\n\nThe best-known distribution property estimator is the empirical estimator that replaces the unknown underlying distribution by the observed empirical distribution. For example, with samples, it estimates entropy by where is the number of times symbol\n\nappeared. Besides its simple and intuitive form, the empirical estimator is also consistent, stable, and universal. It is therefore the most commonly used property estimator for data-science applications.\n\nThe estimator derived in  uses samples and for any underlying distribution achieves the same performance that the empirical estimator would achieve with samples. It therefore provides an effective way to amplify the amount of data available by a factor of , regardless of the domain or structure of the underlying distribution.\n\nIn this paper we present novel estimators that increase the amplification factor for all sufficiently smooth properties including those mentioned above from to the information-theoretic bound of . Namely, for every distribution their expected estimation error with samples is that of the empirical estimator with samples and no further uniform amplification is possible.\n\nIt can further be shown [1, 2, 3, 6] that the empirical estimator estimates all of the above four properties with linearly many samples, hence the sample size required by the new estimators is always at most the guaranteed by the state-of-the-art estimators.\n\nThe current formulation has several additional advantages over previous approaches.\n\n##### Fewer assumptions\n\nIt eliminates the need for some commonly used assumptions. For example, support size cannot be estimated with any number of samples, as arbitrarily-many low-probabilities may be missed. Hence previous research\n\n[5, 3] unrealistically assumed prior knowledge of the alphabet size , and additionally that all positive probabilities exceed . By contrast, the current formulation does not need these assumptions. Intuitively, if a symbol’s probability is so small that it won’t be detected even with samples, we do not need to worry about it.\n\n##### Refined bounds\n\nFor some properties, our results are more refined than previously shown. For example, existing results estimate the support size to within , rendering the estimates rather inaccurate when the true support size is much smaller than . By contrast, the new estimation errors are bounded by , and are therefore accurate regardless of the support size. A similar improvement holds for support coverage.\n\nFor the previous results to work, one needs at least samples. With fewer samples, the estimators have no guarantees. By contrast, the guarantees of the new estimators work for any sample size . If , the performance may degrade, but will still track that of the empirical estimators with a factor more samples.\n\n##### Instance optimality\n\nWith the recent exception of , all modern property-estimation research took a min-max-related approach, evaluating the estimation improvement based on the worst possible distribution for the property. In reality, practical distributions are rarely the worst possible and often quite simple, rendering min-max approach overly pessimistic, and its estimators, typically suboptimal in practice. In fact, for this very reason, practical distribution estimators do not use min-max based approaches . By contrast, our competitive, or instance-optimal, approach provably ensures amplification for every underlying distribution, regardless of its complexity.\n\nIn addition, the proposed estimators run in time linear in the sample size, and the constants involved are very small, properties shared by some, though not all existing estimators.\n\nWe formalize the foregoing discussion in the following definitions.\n\nLet denote the collection of discrete distributions over . A distribution property is a mapping . It is additive if it can be written as\n\n F(→p):=∑i∈[k]fi(pi),\n\nwhere are real functions. Many important distribution properties are additive:\n\n##### Shannon entropy\n\n, is the principal measure of information \n\n, and arises in a variety of machine-learning\n\n[10, 11, 12], neuroscience [13, 14, 15], and other applications.\n\n##### ℓ1-distance\n\n, where is a given distribution, is one of the most basic and well-studied properties in the field of distribution property testing [16, 17, 18, 19].\n\n##### Support size\n\n, is a fundamental quantity for discrete distributions, and plays an important role in vocabulary size [20, 21, 22] and population estimation [23, 24].\n\n##### Support coverage\n\n, for a given , represents the number of distinct elements we would expect to see in independent samples, arises in many ecological [25, 26, 27, 28], biological [29, 30], genomic  as well as database  studies.\n\nGiven an additive property and sample access to an unknown distribution , we would like to estimate the value of as accurately as possible. Let denote the collection of all length- sequences, an estimator is a function that maps a sample sequence to a property estimate . We evaluate the performance of in estimating via its mean absolute error (MAE),\n\n L(^F,→p,n):=EXn∼→p∣∣^F(Xn)−F(→p)∣∣.\n\nSince we do not know , the common approach is to consider the worst-case MAE of over ,\n\n L(^F,n):=max→p∈ΔkL(^F,→p,n).\n\nThe best-known and most commonly-used property estimator is the empirical plug-in estimator. Upon observing , let denote the number of times symbol appears in . The empirical estimator estimates by\n\n ^FE(Xn):=∑i∈[k]fi(Nin).\n\nStarting with Shannon entropy, it has been shown  that for , the worst-case MAE of the empirical estimator is\n\n L(^HE,n)=Θ(kn+logk√n). (1)\n\nOn the other hand, [1, 2, 3, 6] showed that for , more sophisticated estimators achieve the best min-max performance of\n\n L(n):=min^Fmax→p∈ΔkL(^F,→p,n)=Θ(knlogn+logk√n). (2)\n\nHence up to constant factors, for the “worst” distributions, the MAE of these estimators with samples equals that of the empirical estimator with samples. A similar relation holds for the other three properties we consider.\n\nHowever, the min-max formulation is pessimistic as it evaluates the estimator’s performance based on its MAE for the worst distributions. In many practical applications, the underlying distribution is fairly simple and does not attain this worst-case loss, rather, a much smaller MAE can be achieved. Several recent works have therefore gone beyond worst-case analysis and designed algorithms that perform well for all distributions, not just those with the worst performance [33, 34].\n\nFor property estimation,  designed an estimator that for any underlying distribution uses samples to achieve the performance of the -sample empirical estimator, hence effectively multiplying the data size by a amplification factor.\n\n###### Lemma 1.\n\n For every property in a large class that includes the four properties above, there is an absolute constant such that for all distribution and all ,\n\n L(^FA,→p,n)≤L(^FE,→p,εn√logn)+cF⋅ε.\n\nIn this work, we fully strengthen the above result and establish the limits of data amplification for all sufficiently smooth additive properties including four of the most important ones. Using Shannon entropy as an example, we achieve a amplification factor. Equations (1) and (2) imply that the improvement over the empirical estimator cannot always exceed , hence up to a constant, this amplification factor is information-theoretically optimal. Similar optimality arguments hold for our results on the other three properties.\n\nSpecifically, we derive linear-time-computable estimators , , , , and for Shannon entropy, -distance, support size, support coverage, and a broad class of additive properties which we refer to as “Lipschitz properties”. These estimators take a single parameter , and given samples , amplify the data as described below.\n\nLet and abbreviate the support size by . For some absolute constant , the following five theorems hold for all , all distributions , and all .\n\n###### Theorem 1 (Shannon entropy).\n L(^H,→p,n)≤L(^HE,→p,εnlogn)+c⋅(ε∧(S→pn+1n0.49)).\n\nNote that the estimator does not need to know or . When , the estimator amplifies the data by a factor of . As decreases, the amplification factor decreases, and so does the extra additive inaccuracy. One can also set to be a vanishing function of , e.g., . This result may be interpreted as follows. For distributions with large support sizes such that the min-max estimators provide no or only very weak guarantees, our estimator with samples always tracks the performance of the -sample empirical estimator. On the other hand, for distributions with relatively small support sizes, our estimator achieves a near-optimal -error rate.\n\nIn addition, the above result together with Proposition 1 in  trivially implies that\n\n###### Corollary 1.\n\nIn the large alphabet regime where , the min-max MAE of estimating Shannon entropy satisfies\n\n L(n)≤(1+o(1))log(1+k−1nlogn).\n\nSimilarly, for -distance,\n\n###### Theorem 2 (ℓ1-distance).\n\nFor any , we can construct an estimator for such that\n\n L(^D,→p,n)≤L(^DE,→p,ε2nlogn)+c⋅⎛⎝ε∧⎛⎝√S→pn+1n0.49⎞⎠⎞⎠.\n\nBesides having an interpretation similar to Theorem 1, the above result shows that for each and each , we can use just samples to achieve the performance of the -sample empirical estimator. More generally, for any additive property that satisfies the simple condition: is -Lipschitz, for all ,\n\n###### Theorem 3 (General additive properties).\n\nGiven , we can construct an estimator such that\n\n L(^F,→p,n)≤L(^FE,→p,ε2nlogn)+O⎛⎝ε∧⎛⎝√S→pn+1n0.49⎞⎠⎞⎠.\n\nWe refer to the above general distribution property class as the class of “Lipschitz properties”. Note that the -distance , for any , clearly belongs to this class.\n\nLipschitz properties are essentially bounded by absolute constants and Shannon entropy grows at most logarithmically in the support size, and we were able to approximate all with just an additive error. Support size and support coverage can grow linearly in and , and can be approximated only multiplicatively. We therefore evaluate the estimator’s normalized performance.\n\nNote that for both properties, the amplification factor is logarithmic in the property value, which can be arbitrarily larger than the sample size . The following two theorems hold for ,\n\n###### Theorem 4 (Support size).\n\nTo make the slack term vanish, one can simply set to be a vanishing function of (or ), e.g., . Note that in this case, the slack term modifies the multiplicative error in estimating by only , which is negligible in most applications. Similarly, for support coverage,\n\n###### Theorem 5 (Support coverage).\n\nAbbreviating by ,\n\n 1C→pL(^C,→p,n)≤1C→pL(^CE,→p,|log−2ε|⋅nlogC→p)+c(C|log−1ε|−12→p+ε).\n\nFor notational convenience, let for entropy, for -distance, for support size, and for support coverage. In the next section, we provide an outline of the remaining contents, and a high-level overview of our techniques.\n\n## 2 Outline and technique overview\n\nIn the main paper, we focus on Shannon entropy and prove a weaker version of Theorem 1.\n\n###### Theorem 6.\n\nFor all and all distributions , the estimator described in Section 5 satisfies\n\n L(^H,→p,n)≤L(^HE,→p,εnlogn)+(1+c⋅ε)∧(S→pεn+1n0.49).\n\nThe proof of Theorem 6 in the rest of the paper is organized as follows. In Section 3\n\n, we present a few useful concentration inequalities for Poisson and binomial random variables. In Section\n\n4, we relate the bias of the -sample empirical estimator to the degree- Bernstein polynomial by . In Section 4.1, we show that the absolute difference between the derivative of and a simple function is at most , uniformly for all .\n\nLet be the amplification parameter. In Section 4.2 we approximate by a degree- polynomial , and bound the approximation error uniformly by . Let . By construction, , implying .\n\nIn Section 5, we construct our estimator as follows. First, we divide the symbols into small- and large- probability symbols according to their counts in an independent -element sample sequence. The concentration inequalities in Section 3 imply that this step can be performed with relatively high confidence. Then, we estimate the partial entropy of each small-probability symbol\n\nwith a near-unbiased estimator of\n\n, and the combined partial entropy of the large-probability symbols with a simple variant of the empirical estimator. The final estimator is the sum of these small- and large- probability estimators.\n\nIn Section 6, we bound the bias of . In Sections 6.1 and 6.2, we use properties of and the Bernstein polynomials to bound the partial biases of the small- and large-probability estimators in terms of , respectively. The key observation is , implying that the small-probability estimator has a small bias. To bound the bias of the large-probability estimator, we essentially rely on the elegant inequality .\n\nBy the triangle inequality, it remains to bound the mean absolute deviation of\n\n. We bound this quantity by bounding the partial variances of the small- and large- probability estimators in Section\n\n7.1 and Section 7.2, respectively. Intuitively speaking, the small-probability estimator has a small variance because it is constructed based on a low-degree polynomial; the large-probability estimator has a small variance because is smoother for larger values of .\n\nTo demonstrate the efficacy of our methods, in Section 8, we compare the experimental performance of our estimators with that of the state-of-the-art property estimators for Shannon entropy and support size over nine distributions. Our competitive estimators outperformed these existing algorithms on nearly all the experimented instances.\n\nReplacing the simple function by a much finer approximation of , we establish the full version of Theorem 1 in Appendix A. Applying similar techniques, we prove the other four results in Appendices B (Theorem 2 and 3), C (Theorem 4), and D (Theorem 5).\n\n## 3 Concentration inequalities\n\nThe following lemma gives tight tail probability bounds for Poisson and binomial random variables.\n\n###### Lemma 2.\n\n Let be a Poisson or binomial random variable with mean , then for any ,\n\n P(X≥(1+δ)μ)≤(eδ(1+δ)(1+δ))μ≤e−(δ2∧δ)μ/3,\n\nand for any ,\n\n P(X≤(1−δ)μ)≤(e−δ(1−δ)(1−δ))μ≤e−δ2μ/2.\n\n## 4 Approximating Bernstein polynomials\n\nWith samples, the bias of the empirical estimator in estimating is\n\n Bias(^HE,n):=E[^HE(Xn)]−H(→p).\n\nBy the linearity of expectation, the right-hand side equals\n\nNoting that the degree- Bernstein polynomial of is\n\n Bn(h,x):=n∑j=0h(jn)(nj)xj(1−x)n−j,\n\nwe can express the bias of the empirical estimator as\n\n Bias(^HE,n)=∑i∈[k](Bn(h,pi)−h(pi)).\n\nGiven a sampling number and a parameter , define the amplification factor . Let and be sufficiently large and small constants, respectively. In the following sections, we find a polynomial of degree , whose error in approximating over satisfies\n\n |B′na(h,x)−~hna(x)|≤1+O(ε).\n\nThrough a simple argument, the degree- polynomial\n\n ~Hna(x):=∫x0~hna(t)dt,\n\napproximates with the following pointwise error guarantee.\n\n###### Lemma 3.\n\nFor any ,\n\n |Bna(h,x)−~Hna(x)|≤x(1+O(ε)).\n\nIn Section 4.1, we relate to a simple function , which can be expressed in terms of . In Section 4.2, we approximate by a linear combination of degree- min-max polynomials of over different intervals. The resulting polynomial is .\n\n### 4.1 The derivative of a Bernstein polynomial\n\nAccording to , the first-order derivative of the Bernstein polynomial is\n\nLetting\n\n hn(x):=n(h((n−1n)x+1n)−h((n−1n)x)),\n\nwe can write as\n\n B′n(h,x)=n−1∑j=0hn(jn−1)(n−1)jxj(1−x)(n−1)−j=Bn−1(hn,x).\n\nRecall that . After some algebra, we get\n\n hn(x)=−logn−1n+(n−1)(h(x+1n−1)−h(x)).\n\nFurthermore, using properties of  , we can bound the absolute difference between and its Bernstein polynomial as follows.\n\n###### Lemma 4.\n\nFor any and ,\n\n −1−xm≤Bm(h,x)−h(x)≤0.\n\nAs an immediate corollary,\n\n###### Corollary 2.\n\nFor ,\n\n |B′n(h,x)−hn(x)|=|Bn−1(hn,x)−hn(x)|≤1.\n###### Proof.\n\nBy the equality and Lemma 4, for ,\n\n |Bn−1(hn,x)−hn(x)| ≤(n−1)|(Bn−1(h,x+(n−1)−1)−h(x+(n−1)−1)) −(Bn−1(h,x)−h(x))| ≤(n−1)∣∣ ∣∣max{1−x−(n−1)−1n−1,1−xn−1}∣∣ ∣∣ ≤1.\n\n### 4.2 Approximating the derivative function\n\nDenote the degree- min-max polynomial of over by\n\n ~h(x):=d∑j=0bjxj.\n\nAs shown in , the coefficients of satisfy\n\n |bj|≤O(23d),\n\nand the error of in approximating are bounded as\n\n maxx∈[0,1]|h(x)−~h(x)|≤O(1log2n).\n\nBy a change of variables, the degree- min-max polynomial of over is\n\n ~h1(x):=d∑j=0bj(ncllogn)j−1xj+(logncllogn)x.\n\nCorrespondingly, for any , we have\n\n maxx∈In|h(x)−~h1(x)|≤O(1nlogn).\n\nTo approximate , we approximate by , and by . The resulting polynomial is\n\n ~hna(x) :=−logna−1na+(na−1)(~h1(x+(na−1)−1)−~h1(x)) =−logna−1clalogn+(na−1)(d∑j=0bj(ncllogn)j−1((x+1na−1)j−xj)).\n\nBy the above reasoning, the error of in approximating over satisfies\n\n maxx∈In|hna(x)−~hna(x)|≤O(nanlogn)≤O(ε).\n\nMoreover, by Corollary 2,\n\n maxx∈[0,1/2]|B′na(h,x)−hna(x)|=maxx∈[0,1/2]|Bna−1(hna,x)−hna(x)|≤1.\n\nThe triangle inequality combines the above two inequalities and yields\n\n maxx∈In|B′na(h,x)−~hna(x)|≤1+O(ε).\n\nTherefore, denoting\n\n ~Hna(x):=∫x0~hna(t)dt,\n\nand noting that , we have\n\n###### Lemma 5.\n\nFor any ,\n\n |Bna(h,x)−~Hna(x)|≤∫x0|B′na(h,t)−~hna(t)|dt≤x(1+O(ε)).\n\n## 5 A competitive entropy estimator\n\nIn this section, we design an explicit entropy estimator based on and the empirical estimator. Note that is a polynomial with zero constant term. For , denote\n\n gt:=d∑j=tbjj+1(ncllogn)j−1(1na−1)j−t(j+1j−t+1).\n\nSetting for and , we have the following lemma.\n\n###### Lemma 6.\n\nThe function can be written as\n\n ~Hna(x)=d∑t=1b′txt.\n\nIn addition, its coefficients satisfy\n\n |b′t|≤(ncllogn)t−1O(24d).\n\nThe proof of the above lemma is delayed to the end of this section.\n\nTo simplify our analysis and remove the dependency between the counts , we use the conventional Poisson sampling technique [2, 3]. Specifically, instead of drawing exactly samples, we make the sample size an independent Poisson random variable with mean . This does not change the statistical natural of the problem as highly concentrates around its mean (see Lemma 2). We still define as the counts of symbol in . Due to Poisson sampling, these counts are now independent, and satisfy .\n\nFor each , let be the order- falling factorial of . The following identity is well-known:\n\n E[Nt–i]=(npi)t, ∀t≤n.\n\nNote that for sufficiently small , the degree parameter . By the linearity of expectation, the unbiased estimator of is\n\n ^Hna(Ni):=d∑t=1b′tNt–int.\n\nLet be an independent Poisson random variable with mean , and be an independent length- sample sequence drawn from . Analogously, we denote by the number of times that symbol appears. Depending on whether\n\nor not, we classify\n\ninto two categories: small- and large- probabilities. For small probabilities, we apply a simple variant of ; for large probabilities, we estimate by essentially the empirical estimator. Specifically, for each , we estimate by\n\n ^h(Ni,N′i):=^Hna(Ni)⋅1Ni≤cllogn⋅1N′i≤ε−1+h(Nin)⋅1N′i>ε−1.\n\nConsequently, we approximate by\n\n ^H(XN,XN′):=∑i∈[k]^h(Ni,N′i).\n\nFor the simplicity of illustration, we will refer to\n\n ^HS(XN,XN′):=∑i∈[k]^Hna(Ni)⋅1Ni≤cllogn⋅1N′i≤ε−1\n\nas the small-probability estimator, and\n\n ^HL(XN,XN′):=∑i∈[k]h(Nin)⋅1N′i>ε−1\n\nas the large-probability estimator. Clearly, is the sum of these two estimators.\n\nIn the next two sections, we analyze the bias and mean absolute deviation of . In Section 6, we show that for any , the absolute bias of satisfies\n\n ∣∣E[^H(XN,XN′)]−H(→p)∣∣≤∣∣Bias(^HE,na)∣∣+(1+O(ε))(1∧(ε−1+1)S→pn).\n\nIn Section 7, we show that the mean absolute deviation of satisfies\n\n E∣∣^H(XN,XN′)−E[^H(XN,XN′)]∣∣≤O(1n1−Θ(cs)).\n\nFor sufficiently small , the triangle inequality combines the above inequalities and yields\n\n E∣∣^H(XN,XN′)−H(→p)∣∣≤∣∣%Bias(^HE,na)∣∣+(1+c⋅ε)∧(S→pεn+1n0.49).\n\nThis basically completes the proof of Theorem 6.\n\n### Proof of Lemma 6\n\nWe begin by proving the first claim:\n\n ~Hna(x)=−d∑t=1b′txt.\n\nBy definition, satisfies\n\n ~Hna(x)+(logna−1clalogn)x =(na−1)(d∑j=1bjj+1(ncllogn)j−1((x+1na−1)j+1−(1na−1)j+1−xj+1)) =d∑t=1xt(d∑j=tbjj+1(ncllogn)j−1(1na−1)j−t(j+1)j−t+1).\n\nThe last step follows by reorganizing the indices.\n\nNext we prove the second claim. Recall that , thus\n\n logna−1clalogn≤O(24d).\n\nSince for and , it suffices to bound the magnitude of :\n\n |gt| ≤d∑j=t∣∣bj∣∣j+1(ncllogn)j−1(1na−1)j−t(j+1j−t+1) ≤d∑j=t∣∣bj∣∣(1cllogn)j−1nt−1(jt) ≤(ncllogn)t−1d∑j=t∣∣bj∣∣(jt) ≤(ncllogn)t−1d∑j=t∣∣bj∣∣(dj−t) ≤(ncllogn)t−1O(24d).\n\n## 6 Bounding the bias of ^H\n\nBy the triangle inequality, the absolute bias of in estimating satisfies\n\n ∣∣ ∣∣∑i∈[k](E[^h(Ni,N′i)]−h(pi))∣∣ ∣∣ ≤∣∣ ∣∣∑i∈[k](Bna(h,pi)−h(pi))∣∣ ∣∣ +∣∣ ∣∣∑i∈[k](E[^h(Ni,N′i)]−Bna(h,pi))∣∣ ∣∣.\n\nNote that the first term on the right-hand side is the absolute bias of the empirical estimator with sample size , i.e.,\n\n ∣∣Bias(^HE,na)∣∣=∣∣ ∣∣∑i∈[k](Bna(h,pi)−h(pi))∣∣ ∣∣.\n\nHence, we only need to consider the second term on the right-hand side, which admits\n\n ∣∣ ∣∣∑i∈[k](E[^h(Ni,N′i)]−Bna(h,pi))∣∣ ∣∣≤BiasS+BiasL,\n\nwhere\n\n BiasS:=∣∣ ∣∣∑i∈[k]E[(^Hna(Ni)⋅1Ni≤cllogn−Bna(h,pi))⋅1N′i≤ε−1]∣∣ ∣∣\n\nis the absolute bias of the small-probability estimator, and\n\n BiasL:=∣∣ ∣∣∑i∈[k]E[(h(Nin)−Bna(h,pi))⋅1N′i>ε−1]∣∣ ∣∣\n\nis the absolute bias of the large-probability estimator.\n\nAssume that is sufficiently large. In Section 6.1, we bound the small-probability bias by\n\n |BiasS|≤(1+O(ε))(1∧(ε−1+1)S→pn).\n\nIn Section 6.2, we bound the large-probability bias by\n\n |BiasL|≤2(ε∧S→pn).\n\n### 6.1 Bias of the small-probability estimator\n\nWe first consider the quantity . By the triangle inequality,\n\n BiasS ≤∑i:pi∉In∣∣E[^Hna(Ni)⋅1Ni≤cllogn]−Bna(h,pi)∣∣⋅E[1N′i≤ε−1] +∑i:pi∈In∣∣E[^Hna(Ni)]−Bna(h,pi)∣∣⋅E[1N′i" ]

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[ "", null, "# Thevenin's and Norton's theorem objective questions and answers\n\n1.  Thevenin's resistance Rth is found\n\nA. By removing voltage sources along with their internal resistances\n\nB. By short-circuiting the given two terminals\n\nC. Between any two open terminals\n\nD. Between same open terminals as for Eth\n\nD. Between same open terminals as for Eth\n\n2.  While Thevenizing a circuit between two terminals, V th is equal to\n\nA. Short-circuit terminal voltage\n\nB. Open-circuit terminal voltage\n\nC. Net voltage available in the circuit\n\nD. E.M.F. of the battery nearest to the terminals\n\nB. Open-circuit terminal voltage\n\n3.  Application of Norton's theorem to a circuit yields\n\nA. Equivalent current source and impedence in series\n\nB. Equivalent current source and impedence in parallel\n\nC. Equivalent impedence\n\nD. Equivalent current source\n\nB. Equivalent current source and impedence in parallel\n\n4.  Norton's equivalent resistance is the ..............as Thevenin's equivalent resistance.\n\nA. Not same\n\nB. Same\n\nC. Both A and B\n\nD. None of the above\n\nB.Same\n\n5.  ...........theorem is quite useful when the current in one branch of a network is to be determined or when the current in an added branch is to be calculated.\n\nA. Norton\n\nB. Thevenin\n\nC. Superposition\n\nD. Maximum Power Transfer" ]

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[ "# Real Analysis/Series\n\n Real Analysis Series\n\nFrequently in analysis it is useful to consider the sum of infinitely many numbers. So for some sequence of numbers (an) we may want to consider expressions like\n\n$\\sum _{n=1}^{\\infty }a_{n}$", null, ".\n\nBut the exact meaning of this may not be immediately clear. Intuitively we would like to say that the sum of infinitely many numbers should be the number we get close to after we have summed a large number of terms. We will use the notion of the limit of a sequence to make this precise. The standard terminology in the study of series sometimes has room for improvement, but we follow the standard terminology in this section.\n\n## Definition\n\nWe begin with a sequence (an) of the numbers we would like to sum.\n\nDefinition A series of real numbers is an infinite formal sum\n$\\sum _{n=1}^{\\infty }a_{n}$\nwhere each term an is a real number.\n\nThis definition deserves a few comments. The first is that no attempt is being made to define a formal sum. It is possible to define a formal sum simply as the sequence of terms, but this doesn't add any clarity to the discussion. The reason for allowing the series to be formal is merely a matter of convenience. It is frequently easier to refer to a series before it as been determined if there is any number that should represent the sum. This is very similar to the standard practice of saying $\\textstyle \\lim _{n\\to \\infty }a_{n}$  does not exist - we have only defined the meaning of the symbols $\\textstyle \\lim _{n\\to \\infty }a_{n}$  in the case when the limit does exist. We should instead say that the sequence an does not converge. However, the meaning of the previous statement is perfectly clear.\n\nDefinition The n-th partial sum of a sequence an is defined to be the sum of the first n terms of (an), that is\n$S_{n}=\\sum _{i=1}^{n}a_{i}=a_{1}+a_{2}+\\cdots +a_{n}$ .\nWhen the sequence an is being thought of as the terms of a series, then Sn is often called the n-th partial sum of the series.\n\nOften several partial sums may appear in the same argument, so the partial sum is often written simply as $\\sum _{i=1}^{n}a_{i}$  instead of Sn when we wish to avoid confusion.\n\nDefinition For a series $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  we define the sum of the series to be the limit of the partial sums. That is, we define:\n$\\sum _{n=1}^{\\infty }a_{n}=\\lim _{N\\to \\infty }\\sum _{n=1}^{N}a_{n}=\\lim _{N\\to \\infty }S_{N}$ .\nIf the limit exists we say the series converges, otherwise we say the series diverges.\n\nIt should be emphasized when a series diverges, we cannot interpret $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  as a number, but only as a formal sum. On the other hand when the series does converge, it is often not known what number the series converges to, so this number is usually denoted by $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$ . Again this is similar to writing $\\textstyle \\lim _{n\\to \\infty }a_{n}$  before the convergence of the sequence an is established. In practice the meaning of the symbols $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  is clear from context.\n\nOften it is convenient to sum series starting from some number other than n = 1, and start the series some other point like 0, 2, −10, etc. This hopefully should cause no confusion; the sum of the series is still defined as the limit of the partial sums. Often, it is clear from context where the sum begins. In these cases it is not uncommon to leave the index out of the sigma notation - that is, it is useful to write ∑an for $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$\n\n## Examples\n\n• The notion of an infinite sum can be a little more subtle than it first appears. For example, consider the sequence an = (−1)n. Does the sum of the an converge or diverge? We could consider the partial sums SN, which are 1 if N is odd and 0 if N is even. So it seems the series diverges. On the other hand, 1 − 1 + 1 − 1 + 1 − 1 + … = (1 − 1) + (1 − 1) + (1 − 1) + … = 0 + 0 + 0 + … = 0. Does then the series diverge or converge to 0, according to our theory? The answer is it diverges; the fallacy in the previous sentence was in asserting that 1 − 1 + 1 − 1 + 1 − 1 + … = (1 − 1) + (1 − 1) + (1 − 1) + …. It is no longer true that for infinite series that we may sum in any order we choose; we must justify why we are allowed to group the +1's together with the -1's without changing the sum. Stated formally, associativity does not necessarily hold for infinite series. We will investigate when it is possible to rearrange the elements of a series and still get the same sum.\n• Perhaps the most familiar examples of series come from decimal expansions of real numbers. While we have not given a rigorous definition of decimal expansions here, it can be shown that every real number r can be expressed in the form $\\textstyle r=\\sum _{n=0}^{\\infty }{\\frac {a_{n}}{10^{n}}}$  where an ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}\n• Consider the series $\\textstyle {\\tfrac {1}{1\\cdot 2}}+{\\tfrac {1}{2\\cdot 3}}+{\\tfrac {1}{3\\cdot 4}}\\cdots =\\sum _{n=1}^{\\infty }{\\tfrac {1}{n(n+1)}}$ . At first it may seem difficult to determine the partial sums and decide whether or not the series converges. However, it turns out that this series is nicer than it first appears, since $\\textstyle {\\frac {1}{n(n+1)}}={\\frac {1}{n}}-{\\frac {1}{n+1}}.$  Thus\n\n$\\sum _{n=1}^{N}{\\frac {1}{n(n+1)}}=\\sum _{n=1}^{N}{\\frac {1}{n}}-{\\frac {1}{n+1}}=1-{\\frac {1}{2}}+{\\frac {1}{2}}-{\\frac {1}{3}}+{\\frac {1}{3}}-{\\frac {1}{4}}+\\cdots +{\\frac {1}{N}}-{\\frac {1}{N+1}}=1-{\\frac {1}{N+1}}.$\n\nThus $\\textstyle \\lim _{N\\to \\infty }\\sum _{n=1}^{N}{\\tfrac {1}{n(n+1)}}=\\lim _{N\\to \\infty }(1-{\\tfrac {1}{N+1}})=1.$  This is an example of a telescoping series - that is, a series that can be written in the form such that the next term cancels with the previous terms. That is,\n$\\sum _{n=1}^{\\infty }a_{n}-a_{n+1}$\nFor all such series the partial sums are given by SN = a1 − aN+1. That is, the terms of the series collapse like a telescope, leaving only the first and last. Such a series converges to a1 − lim aN+1.\n• Another important example of a series is the geometric series given by $\\sum _{n=0}^{\\infty }r^{n}$ . The partial sums for the geometric series first appear quite complicated. At first glance the partial sums would just appear to be SN = 1 + r +r2 + … + rN, but if we calculate (1 − r)SN then the sum telescopes and we are left with (1 − r)SN = (1 − r)N+1. Notice that this sum holds for any r or N, so we conclude that $\\textstyle S_{N}={\\tfrac {1-r^{N+1}}{1-r}}$ . Thus a geometric series converges if |r| < 1.\n\n## Basic Facts\n\nHere we collect facts about series that follow immediately from the properties of finite sums a limits and do not require a delicate analysis of the limits involved.\n\n### Theorem (Algebraic Operations)\n\nSuppose ∑ an and ∑ bn are convergent series, then we immediately have the following two theorems.\n\n• For any real number c the series ∑ (c·an) is convergent and converges to c·(∑ an).\n• The series ∑ (an + bn) is convergent and converges to (∑ an ) + (∑ bn )\n\n#### Proof\n\nFor the first statement notice that for any natural number N, we have that $\\textstyle \\sum _{n=1}^{N}c\\cdot a_{n}=\\textstyle c\\cdot \\sum _{n=1}^{N}a_{n}$ . Thus\n\n$\\lim _{N\\to \\infty }\\sum _{n=1}^{N}c\\cdot a_{n}=\\lim _{N\\to \\infty }c\\cdot \\sum _{n=1}^{N}a_{n}=c\\cdot \\lim _{N\\to \\infty }\\sum _{n=1}^{N}a_{n}$ .\n\nThis proves the first statement.\n\nFor the second statement again notice that for any N we have that $\\textstyle \\sum _{n=1}^{N}a_{n}+b_{n}=\\sum _{n=1}^{N}a_{n}+\\sum _{n=1}^{N}b_{n}$ . Thus\n\n$\\lim _{N\\to \\infty }\\sum _{n=1}^{N}a_{n}+b_{n}=\\lim _{N\\to \\infty }\\left(\\sum _{n=1}^{N}a_{n}+\\sum _{n=1}^{N}b_{n}\\right)=\\lim _{N\\to \\infty }\\sum _{n=1}^{N}a_{n}+\\lim _{N\\to \\infty }\\sum _{n=1}^{N}b_{n}$ .\n\nThis proves the second statement. $\\Box$\n\nThe following is merely a restatement of Cauchy's Criterion.\n\n### Theorem (Cauchy's Criterion for Series)\n\nA series $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  converges if and only if for any ε > 0 there is a natural number N so that $\\textstyle |\\sum _{k=n+1}^{m}a_{k}|<\\epsilon$  for any natural numbers m > n > N.\n\n#### Proof\n\nBy the definition of convergence for a series $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  converges if and only if $\\textstyle \\lim _{N\\to \\infty }\\sum _{k=1}^{N}a_{k}$  converges. But by the Cauchy criterion for sequences this limit exists if and only if for any ε > 0 we can find a natural number N so that for nm > N we have that\n\n$\\left|\\sum _{k=1}^{n}a_{k}-\\sum _{k=1}^{m}a_{k}\\right|<\\epsilon .$\n\nWithout loss of generality we may assume m > n. Canceling the terms that occurs in both sums completes the proof. $\\Box$\n\n## Absolute Convergence\n\nAs we will see series may behave in ways that defy our intuition. So, it is useful to identify which classes of convergent series behave in a way more consistent with our intuition. We shall see that once such class of series are the so called absolutely convergent series.\n\nDefinition A series $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  converges absolutely if the series of the absolute values of its terms converges, that is, if $\\textstyle \\sum _{n=1}^{\\infty }|a_{n}|$  is a convergent series.\n\nNotice we have not said required that ∑ an is convergent, this is because the property of absolute convergence implies that ∑ an is convergent.\n\n### Theorem (Absolute Convergence)\n\nIf $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  converges absolutely, then it converges.\n\n#### Proof\n\nSuppose $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  is absolutely convergent. By the Cauchy criterion we can show that $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  converges if for any ε > 0 we can find an N so that if m > n > N then $\\textstyle |\\sum _{k=n+1}^{m}a_{k}|<\\epsilon$ . But we know that $\\textstyle \\sum _{n=1}^{\\infty }|a_{n}|$  converges, so ε > 0 by the Cauchy criterion choose N so that if m > n > N then $\\textstyle |\\sum _{k=n+1}^{m}|a_{k}||=\\textstyle \\sum _{k=n+1}^{m}|a_{k}|<\\epsilon$ . With this N in hand take any m > n > N, it then follows from the triangle inequality that\n\n$|\\sum _{k=n+1}^{m}a_{k}|\\leq \\sum _{k=n+1}^{m}|a_{k}|<\\epsilon .$\n\nTherefore by the Cauchy criterion $\\sum _{n=1}^{\\infty }a_{n}$  converges. $\\Box$\n\n## Tests for convergence and divergence\n\nGiven a series $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  it is very useful to be able to tell if the series converges or diverges. Particularly if we can do so simply by looking at the terms. In this section we set out to collect such theorems. Notice we have already seen one example. That is a series is convergent if it is absolutely convergent, now we explore when we can decide if a series is convergent.\n\nAlthough the following theorem is stated in terms of convergence, it actually gives a useful test for divergence. Namely, if the terms of a series do not have limit 0, the series must diverge.\n\n### Theorem (Terms Have Limit 0)\n\nFor any converging series $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  the terms must tend to 0, that is $\\textstyle \\lim _{n\\rightarrow \\infty }a_{n}=0.$\n\n#### Proof\n\nGiven any ε > 0, by the Cauchy Criterion for series, we can choose a natural number N so that $\\textstyle |\\sum _{i=n+1}^{m}a_{i}|<\\epsilon$  when ever m > n ≥ N. In particular, for any k > N we may apply this in the case when n = k − 1 and m = k. In this case the sum reduces to the single term ak. Thus if k > N we have that |ak| < ε and therefore the sequence (an) → 0. $\\Box$\n\nRemark To give an example of how to use this to test for divergence of a series consider the example of a geometric series $\\textstyle \\sum _{n=0}^{\\infty }r^{n}$ . We have already shown that this series converges if |r| < 1. On the other hand we have not determined if the series converges or diverges for other values of r. Now it is clear that if |r| ≥ 1 then the sequence rn does not tend to zero. So we now know that the geometric series $\\textstyle \\sum _{n=0}^{\\infty }r^{n}$  converges if and only of |r| < 1.\n\n### Theorem (Positive Series Converge)\n\nSuppose $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  is a series of non-negative terms, that is an ≥ 0, then the series either converges if and only if the partial sums are bounded above.\n\n#### Proof\n\nSince the terms are non-negative, we clearly have $\\textstyle \\sum _{n=1}^{N}a_{n}\\leq \\sum _{n=1}^{N+1}a_{n}$  and hence the partial sums form a monotonic sequence. If the partial sums are bounded then the series converges. If they are unbounded, then for any M > 0 we can find an N so that $\\textstyle \\sum _{n=1}^{N}a_{n}\\geq M$ , since the partial sums are non-decreasing, we have that $\\textstyle \\lim _{N\\rightarrow \\infty }\\sum _{n=1}^{N}a_{n}=\\infty$ , and hence the series does not converge. $\\Box$\n\nRemark It follows from the proof, together with the Convergence of monotone sequences, that if a sequence of non-negative terms converges we may take the sum of the sequence as an upper bound for the partial sums, as our intuition would dictate.\n\nTo determine whether or not a series converges, sometimes it is useful to compare it term-by-term with another series whose convergence is understood. The following theorem gives one such method for comparing.\n\n### Theorem (Comparison Test)\n\nSuppose that 0 ≤ an ≤ bn for all natural numbers n and consider the series $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  and $\\textstyle \\sum _{n=1}^{\\infty }b_{n}$ . If the $\\textstyle \\sum _{n=1}^{\\infty }b_{n}$  converges, then $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  converges. Furthermore, if $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  diverges, then $\\textstyle \\sum _{n=1}^{\\infty }b_{n}$  diverges.\n\n#### Proof\n\nFirst suppose that the ∑ bn converges. Then by our previous theorem we know that the partial sums for some real number we know that $\\textstyle \\sum _{n=1}^{N}b_{n}\\leq \\sum _{n=1}^{\\infty }b_{n}$ . Since an ≤ bn if follows that\n\n$\\sum _{k=1}^{N}a_{n}\\leq \\sum _{k=1}^{N}b_{n}\\leq \\sum _{n=1}^{\\infty }b_{n}$ .\n\nThus the partial sums of ∑ an are bounded above, since ∑ an is also a series of non-negative terms it follows that ∑ an converges.\n\nNow suppose that ∑ an diverges. Since it is a series of non-negative terms the pervious theorem tells us that for any real number M we can find an N so that $\\textstyle M<\\sum _{n=1}^{N}a_{n}$ . Since an ≤ bn we have that\n\n$M<\\sum _{k=1}^{N}a_{n}\\leq \\sum _{k=1}^{N}b_{n}$ .\n\nTherefore the partial sums of ∑ bn cannot be bounded above, and hence by the previous theorem ∑ bn diverges. $\\Box$\n\n### Theorem (Limit Comparison Test)\n\nSuppose $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  and $\\textstyle \\sum _{n=1}^{\\infty }b_{n}$  series of positive terms so that $\\textstyle 0\\leq \\limsup _{n\\to \\infty }{\\tfrac {a_{n}}{b_{n}}}<\\infty$ . In this case, if $\\textstyle \\sum _{n=1}^{\\infty }b_{n}$  converges, then $\\textstyle \\sum _{n=1}^{\\infty }a_{n}$  converges.\n\n#### Proof\n\nSuppose the limit of the absolute value of their ratios converges to some positive number r < ∞. Then there exists an N such that if n > N, that $|\\,|{\\tfrac {a_{n}}{b_{n}}}|-r|<{\\tfrac {r}{2}}$ , so ${\\tfrac {r}{2}}<|{\\tfrac {a_{n}}{b_{n}}}|<{\\tfrac {3r}{2}}$ . This means that ${\\tfrac {r}{2}}|b_{n}|<|a_{n}|<{\\tfrac {3r}{2}}|b_{n}|$ . Hence, by the comparison test, if $\\sum _{n=1}^{\\infty }b_{n}$  converges, then $\\sum _{n=1}^{\\infty }a_{n}$  also converges. Dividing by ${\\tfrac {r}{2}}$ , one can also see by the comparison test that if $\\sum _{n=1}^{\\infty }a_{n}$  converges, then $\\sum _{n=1}^{\\infty }b_{n}$  also converges.\n\nWe need to have ways of checking for convergence and divergence of various series. The following types of series arise quite often, and it is easy to verify when they converge and diverge:\n\n### Theorem (Ratio Test)\n\nSupoose that $\\textstyle \\lim _{n\\rightarrow \\infty }\\left|{\\frac {x_{n+1}}{x_{n}}}\\right|$  converges and equals some real number r. If r < 1, then $\\textstyle \\sum _{n=1}^{\\infty }x_{n}$  converges absolutely. If r > 1, then $\\textstyle \\sum _{n=1}^{\\infty }x_{n}$  diverges. Finally, if r = 1, then $\\textstyle \\sum _{n=1}^{\\infty }x_{n}$  may either converge or diverge.\n\n#### Proof\n\nFirst suppose that r < 1. Let ε = 1 − r, since r < 1 it follows that ε > 0.\n\nSince $\\textstyle \\lim _{n\\rightarrow \\infty }\\left|{\\frac {x_{n+1}}{x_{n}}}\\right|=r$ , we can choose an N so that | |xn+1/xn| − r| < ε/2 for all n ≥ N. In particular, if n ≥ N, then |xn+1|/|xn'| < r + ε/2. Notice that our particular choice of ε guarantees that the ratio r + ε/2 is less than 1.\n\nThus\n\n$\\sum _{n=1}^{\\infty }|x_{n}|$  = $\\sum _{n=1}^{N}|x_{n}|+\\sum _{n=N+1}^{\\infty }|x_{n}|$\n$=\\sum _{n=1}^{N}|x_{n}|+\\sum _{n=N+1}^{\\infty }|x_{N}|{\\frac {|x_{N+1}|}{|x_{N}|}}{\\frac {|x_{N+2}|}{|x_{N+1}|}}\\cdots {\\frac {|x_{n}|}{|x_{n-1}|}}$\n$\\leq \\sum _{n=1}^{N}|x_{n}|+|x_{N}|\\sum _{n=N+1}^{\\infty }(r+{\\frac {\\epsilon }{2}})^{n-N}.$\n\nThe last series converges because it is a geometric series whose ratio, r + ε/2 , is less than 1.\n\nBy the comparison test, $\\textstyle \\sum _{n=1}^{\\infty }|x_{n}|$  converges. Thus $\\textstyle \\sum _{n=1}^{\\infty }x_{n}$  converges absolutely. $\\Box$\n\nThe next theorem, the root test, is stronger than the ratio test in the sense that it works whenever the ratio test works (and returns the same number r), and it sometimes works even when the ratio test does not.\n\n### Theorem (Root Test)\n\nLet $R=\\limsup _{n\\rightarrow \\infty }(|a_{n}|^{\\frac {1}{n}})$ . If R < 1, then the series $\\sum _{n=1}^{\\infty }a_{n}$  converges absolutely. If R > 1, then it diverges.\n\n#### Proof\n\nIf R<1, let $R<\\rho <1$ . Since $\\limsup _{n\\rightarrow \\infty }(|a_{n}|^{\\frac {1}{n}})=R$  $\\exists N:\\forall n\\geq N:|\\sup\\{|a_{k}|^{\\frac {1}{k}}|k>n\\}-R|<\\rho -R$ .\n\nThat is, $\\forall n\\geq N:\\sup\\{|a_{k}|^{\\frac {1}{k}}|k>n\\}<\\rho$\n\nThus $\\sum _{n=1}^{\\infty }|a_{n}|$ $=\\sum _{n=1}^{\\infty }(|a_{n}|^{\\frac {1}{n}})^{n}$ $=\\sum _{n=1}^{N-1}|a_{n}|+\\sum _{n=N}^{\\infty }(|a_{n}|^{\\frac {1}{n}})^{n}$ $<\\sum _{n=1}^{N-1}|a_{n}|+\\sum _{n=N}^{\\infty }(\\sup\\{|a_{k}|^{\\frac {1}{k}}|k>n\\})^{n}$ $<\\sum _{n=1}^{N-1}|a_{n}|+\\sum _{n=N}^{\\infty }(\\rho )^{n}$ , which converges since it is a constant plus a geometric series.\n\nBy the comparison test, $\\sum _{n=1}^{\\infty }|a_{n}|$  converges as well. Thus $\\sum _{n=1}^{\\infty }a_{n}$  converges absolutely.\n\nIf R > 1, then $\\sup\\{|a_{n}|^{\\frac {1}{n}}|k>n\\}>1$ . Thus there are infinitely many n such that $|a_{n}|^{\\frac {1}{n}}>1\\implies |a_{n}|>1$ .\n\nThus $(a_{n})\\not \\rightarrow 0$ , which implies that $\\sum _{n=1}^{\\infty }a_{n}$  diverges. $\\Box$\n\nWe'll often be asked to consider series of the form $\\sum _{n=1}^{\\infty }a_{n}b_{n}$ . The following theorems give criteria for convergence of these series.\n\n### Theorem (Dirichlet's Test)\n\nIf the partial sums $\\sum _{n=1}^{N}x_{n}$  are bounded, and $(y_{n})$  is a decreasing sequence with $\\lim _{n\\rightarrow \\infty }y_{n}=0$ , then $\\sum _{n=1}^{\\infty }x_{n}y_{n}$  converges. [Note: $\\sum _{n=1}^{\\infty }x_{n}$  need not converge]\n\n#### Proof\n\nLet $s_{n}=\\sum _{m=1}^{n}x_{m}$  be the $n$ th partial sum, so that there exists $B>0$  such that $|s_{n}|\\leq B$ .\n\nWe can write\n\n$\\sum _{n=1}^{N}x_{n}y_{n}=x_{1}y_{1}+\\sum _{n=2}^{N}(s_{n}-s_{n-1})y_{n}=x_{1}y_{1}+\\sum _{n=2}^{N}s_{n}y_{n}-\\sum _{n=2}^{N}s_{n-1}y_{n}$ .\n\nChanging the index of summation in the last sum, this becomes\n\n$\\sum _{n=1}^{N}x_{n}y_{n}=x_{1}y_{1}+\\sum _{n=2}^{N}s_{n}y_{n}-\\sum _{n=1}^{N-1}s_{n}y_{n+1}=x_{1}y_{1}-x_{1}y_{2}+\\sum _{n=2}^{N-1}s_{n}(y_{n}-y_{n+1})+s_{N}y_{N}$ .\n\nThe sum on the right-hand side is bounded absolutely by the telescoping sum\n\n$\\sum _{n=2}^{N-1}|s_{n}(y_{n}-y_{n+1})|\\leq B\\sum _{n=2}^{N-1}(y_{n}-y_{n+1})=B(y_{2}-y_{N})\\leq By_{2}$ ;\n\nhere we have used the fact that $(y_{n})$  is positive and decreasing. It follows that\n\n$\\sum _{n=2}^{\\infty }s_{n}(y_{n}-y_{n+1})$  is absolutely convergent, hence convergent.\n\nNotice that $\\lim _{N\\to \\infty }s_{N}y_{N}=0$  since $s_{N}$  is bounded and $(y_{n})$  tends to 0 as $n$  tends to infinity. Therefore we can take limits as $N$  goes to infinity:\n\n$\\sum _{n=1}^{\\infty }x_{n}y_{n}=x_{1}y_{1}-x_{1}y_{2}+\\sum _{n=2}^{\\infty }s_{n}(y_{n}-y_{n+1})+\\lim _{N\\to \\infty }s_{N}y_{N}=x_{1}y_{1}-x_{1}y_{2}+\\sum _{n=2}^{\\infty }s_{n}(y_{n}-y_{n+1})$ ,\n\nwhich proves that the left-hand side is convergent.\n\nAbel's Test can be regarded as a special case of Dirichlet's Test, once some modifications have been made:\n\n### Theorem (Abel's Test)\n\nIf $\\sum _{n=1}^{\\infty }x_{n}$  converges and $(y_{n})$  is a positive, decreasing sequence, then $\\sum _{n=1}^{\\infty }x_{n}y_{n}$  converges.\n\n#### Proof\n\nBecause $(y_{n})$  is a bounded, monotone sequence, it converges to some limit y.\n\nLet $z_{n}=y_{n}-y$ . Then $\\sum _{n=1}^{\\infty }x_{n}$  and $(z_{n})$  satisfy the conditions for Dirichlet's test.\n\n$\\sum _{n=1}^{k}x_{n}y_{n}$ $=y\\sum _{n=1}^{k}x_{n}+\\sum _{n=1}^{k}x_{n}z_{n}$ . By Dirichlet's test, $\\sum _{n=1}^{k}x_{n}z_{n}$  converges as $k\\rightarrow \\infty$ .\n\nSince both sums on the right converge, $\\sum _{n=1}^{\\infty }x_{n}y_{n}$  converges as well. $\\Box$\n\n## Examples with Proof\n\nNow we'll do the computations promised in the Examples, plus a few extra.\n\n### Theorem (Geometric Series)\n\nIf $|r|<1$ , the geometric series $\\sum _{n=1}^{\\infty }ar^{n}={\\frac {a}{1-r}}$ . If $|r|\\geq 1$ , the series diverges.\n\n#### Proof\n\nIn this case, it is best to explicitly compute the partial sums and take the limit. Without loss of generality, we'll consider the case $a=1$ . Then we can apply the theorem on algebraic operations to obtain the general result.\n\nNote that $s_{n}(1-r)=(1+r+r^{2}+...+r^{n})(1-r)=(1+r+r^{2}+...+r^{n})-(r+r^{2}+...+r^{n+1})=1-r^{n+1}$\n\nThus $s_{n}={\\frac {1-r^{n}}{1-r}}$ . Taking the limit (and remembering some basic facts about sequences):\n\nIf $|r|<1$ , $\\sum _{n=1}^{\\infty }r^{n}=\\lim _{n\\rightarrow \\infty }s_{n}=\\lim _{n\\rightarrow \\infty }{\\frac {1-r^{n}}{1-r}}={\\frac {1}{1-r}}$ .\n\nIf $|r|\\geq 1$ , the sequence of partial sums diverges to infinity, and thus by definition the series diverges.\n\nThis proof seems to work except for the fact that this series will converge to ${\\frac {a}{1-r}}$  $\\Box$\n\n### Theorem (p-series)\n\nThe p-series $\\sum _{n=1}^{\\infty }{\\frac {1}{n^{p}}}$  converges for $p>1$  and diverges for $0 . [Note: We have technically only defined this series for p rational. However, the theorem is still valid when p is irrational, for the same reasons]\n\n#### Proof\n\nFirst we'll consider the special cases $p=1,p=2$ , and then obtain the general result from these.\n\n• If p = 1, let $x_{n}$  be the greatest power of 2 less than ${\\frac {1}{n}}$ . That is, $(x_{n})=({\\frac {1}{2}},{\\frac {1}{4}},{\\frac {1}{4}},{\\frac {1}{8}},{\\frac {1}{8}},{\\frac {1}{8}},{\\frac {1}{8}},\\dots )$ .\n\nGrouping like terms together, $\\sum _{i=1}^{\\infty }x_{n}$ $=\\sum _{i=0}^{\\infty }(\\sum _{j=2^{i}}^{2^{i+1}-1}x_{j})$ $=\\sum _{i=0}^{\\infty }(\\sum _{j=2^{i}}^{2^{i+1}-1}{\\frac {1}{2^{i+1}}})$ $=\\sum _{i=1}^{\\infty }{\\frac {1}{2}}$ , which diverges.\n\nBy definition, $x_{n}<{\\frac {1}{n}}$ , so by the comparison test $\\sum _{n=1}^{\\infty }{\\frac {1}{n}}$  diverges.\n\n• If p = 2, let $x_{n}={\\frac {1}{n(n-1)}}={\\frac {1}{n-1}}-{\\frac {1}{n}}$  if n>1 and 1 if n=1.\n\nUsing the theorem on telescoping series, $\\sum _{n=1}^{\\infty }x_{n}$ $=1+\\sum _{n=2}^{\\infty }({\\frac {1}{n-1}}-{\\frac {1}{n}})$ $=1+1-\\lim _{n\\rightarrow \\infty }(1/n)=2$\n\nBy definition, $x_{n}>{\\frac {1}{n\\cdot n}}={\\frac {1}{n^{2}}}$ , so by the comparison test $\\sum _{n=1}^{\\infty }{\\frac {1}{n^{2}}}$  converges as well.\n\n• If 0 < p < 1, then ${\\frac {1}{n^{p}}}>{\\frac {1}{n}}$ . By the comparison test $\\sum _{n=1}^{\\infty }{\\frac {1}{n^{p}}}$  diverges.\n\n### Theorem (Decimal Expansions)\n\nGiven any real number x, $0  there is a unique sequence $(x_{n}):\\sum _{n=0}^{\\infty }{\\frac {x_{n}}{10^{n}}}=x$ , $0\\leq x_{n}<10$  and $\\forall N:\\exists n\\geq N:x_{n}\\not =9$\n\n#### Proof\n\nInductively, assume that there exist $x_{0},x_{1},\\dots ,x_{k}$  such that $\\sum _{n=0}^{k}{\\frac {x_{n}}{10^{n}}}\\leq x<\\sum _{n=0}^{k}{\\frac {x_{n}}{10^{n}}}+{\\frac {1}{10^{k}}}$ .\n\nRearranging, we see that $0\\leq x-\\sum _{n=0}^{k}{\\frac {x_{n}}{10^{n}}}<{\\frac {1}{10^{k}}}$ , or $0\\leq (x-\\sum _{n=0}^{k}{\\frac {x_{n}}{10^{n}}})10^{k+1}<10$ .\n\nLet $x_{k+1}$  by the greatest integer such that $x_{k+1}\\leq (x-\\sum _{n=0}^{k}{\\frac {x_{n}}{10^{n}}})10^{k+1}$ .\n\nThen ${\\frac {x_{k+1}}{10^{k+1}}}\\leq x-\\sum _{n=0}^{k}{\\frac {x_{n}}{10^{n}}}<{\\frac {x_{k+1}+1}{10^{k+1}}}$ (otherwise, $x_{k+1}$  would not be the greatest).\n\nAdding $\\sum _{n=0}^{k}{\\frac {x_{n}}{10^{n}}}$ , we see that $\\sum _{n=0}^{k+1}{\\frac {x_{n}}{10^{n}}}\\leq x<\\sum _{n=0}^{k+1}{\\frac {x_{n}}{10^{n}}}+{\\frac {1}{10^{k+1}}}$ .\n\nGiven $\\epsilon >0$  pick N such that $\\epsilon >{\\frac {1}{10^{N}}}$ .\n\nThus $|\\sum _{n=0}^{k}{\\frac {x_{n}}{10^{n}}}-1|<{\\frac {1}{10^{k}}}<\\epsilon$  for all $k>N$ . That is, $x=\\sum _{n=0}^{\\infty }{\\frac {x_{n}}{10^{n}}}$ .\n\nTODO: eliminate 9s, uniqueness.\n\nTopics to come: Rearrangement of terms, Alternating Series Test, Sums of products(i.e. Abel's Test and Dirichlet's Test), Multiple Summations, Infinite Products, decimal expansions, zeta function\n\n## Rearrangement of terms\n\n### Definition\n\nBy a rearrangement of terms, we mean a bijection f from the natural numbers to itself. Then a rearrangement of a series $\\sum _{i=0}^{\\infty }a_{n}$  is any series $\\sum _{i=0}^{\\infty }a_{f}(n)$  where f is any rearrangement.\n\n### Theorem\n\nIf a series is absolutely convergent, then all rearrangements of terms converge to the same limit.\n\n### Theorem\n\nIf a series $\\{a_{n}\\}$  is conditionally convergent but not absolutely convergent, then there exists a rearrangement for any a<b such that lim inf $\\sum \\limits _{i=0}^{n}a_{n}=a$  and such that lim sup $\\sum \\limits _{i=0}^{n}a_{n}=b$" ]

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[ "# PROBLEMS Matlab Help\n\nProblems\nYou can find the answers to problems marked with an asterisk at the end of the text.\nSection 3.1\n1.* Suppose that y = – 3 +ix. For x =0, 1, and 2, use MATLAB to compute the following expressions. Hand check the answers.\na.’ Iyl\nb. .JY\\\nc. (-5 -7i)y\nd·6\n2. * Let x = -5 – 8 i and y = 10 – Si: Use MATLAB to compute the following expressions. Hand check the answers.\na. The magnitude and angle of xy.\nb. The magnitude and angle of x/y\n\n3.* ‘Use MATLAB to find the angles corresponding to the following coordinates. Hand chec ‘the answers . .’\na. (x, y) = (5,8)\nb. (x,y)=(~5,8)\n‘c: (x, y) = (5, -8)\nd. (x, y) = (-5, -8)\n\n4. For several values of x, use MATLAB to confirm that sinh x = (eX – e-X)j2.\n5. For several values ‘of x, use MATLAB to confirm that sinh -I x = In (x + .JX2+i), -00 < x < 00.\n6. The capacitance of two parallel conductors of length L and radius r, separated by a distance d in air, is given by\n7rEL C = —-:’–;–“7” In (d~r) where E is the permittivity of air (E = 8.854 X 10-12 F/m). Write a script file that accepts user input for d, L, and r, and computes and displays C. Test the file with the values: L ~ 1 m, r = 0.001 m, and d = O.OO4m.\n7.* When a belt is wrapped around a cylinder, the relation between the belt forces on each side of the cylinder is\nFI = F2e/J.fJ where 13 is the angle of wrap of the belt and J-L is the.friction coefficient. Write a script file that first prompts a user to specify 13, J-L. and F2 and then computes the force Fl. Test your program with the values 13 = 1300 J-L = 0.3, and·F2 = 100 N. (Hint: Be careful with f3!)\n\nSection 3.2\n8. . The MATLAB trigonometric functions expect their argument to be in radians. Write a function called sind that accepts an angle x in degrees and computes sin x. Test your function. .\n9. Write a function that accepts temperature in degrees F and computes the corresponding value in degrees C. The relation between the two is Be sure to test your function.\n10.* An object thrown vertically with a speed Vo reaches a height h at time t,\nwhere\n• ‘ 1\nh = vot – gt2\n2\nWrite and test a function that computes the time t required to reach a specified height h; for a given value of Vo. The function’s inputs should be h, vo, and g. Test your function for the case where h = 100m,\nVo = 50 mis, and g = 9.81 mls2. Interpret both answers:\n\n11. A water tank consists of a cylindrical part of radius r and height h, and a hemispherical top. The tank is to be constructed to hold 500 m3 when filled. The surface area of the cylindrical part is 27rrh, and its volume is\n1t r2 h. The surface area of the hemispherical top is given by 21T r2 , and its volume is given by 2rrr3/3. The cost to construct the cylindrical part of the tank is \\$300 per square meter of surface area; the hemispherical part costs\n\n\\$400 per square meter. Use the fminbnd function to compute the radius that results in the least cost. Compute the corresponding height h.\n12. A fence around a field is shaped as shown in Figure P12. It consists of a rectangle of length L and width W, and a right triangle that is symmetrical about the central horizontal axis of the rectangle. Suppose the width W is\nknown (in meters), and the enclosed area A is known (in square meters). Write a user-defined function file with Wand A as inputs. The outputs are the length L required so that the enclosed area is A, and the total length of\nfence required. Test your function for the values W = 6 m and A = 80 m2. \\", null, "13. A fenced enclosure consists of a rectangle of length L and width 2R, and a semicircle of radius R, as shown in Figure P13. The enclosure is to be built to have an area A of 1600 ft2. The cost of the fence is \\$40 per foot\nfor the curved portion, and \\$30 per foot for the straight sides. Use the fminbnd function to determine with a resolution of 0.01 ft the values of R and L required to minimize the total cost of the fence. Also compute the\nminimum cost.", null, "14. Using estimates of rainfall, evaporation, and water consumption, the town engineer developed the following model of the water volume in the reservoir as a function of time. Vet) = 109 + 108(1 – e-I/Joo) – rt\nwhere V is the water volume in liters, t is time in days, and r is the town’s consumption rate in liters/day. Write two user-defined functions. The first function should define the function Vet) for use with the fzero function.\n\nThe second function should use fzero to compute how long it will take for the water volume to decrease to x percent of its initial value of 109 L. The inputs to the second function should be x and r. Test your functions\nfor the case where x =50 percent and r = 107 U day.\n\n15. The volume V and paper surface area A of a conical paper cup are given by where r is the .radius of the base of the cone and h is the height of the cone.\na. By eliminating h, obtain the expression for A as a function of rand V.\nb. Create a user-defined function that accepts R as the only argument\nand computes A for a given value of V. Declare V to be global within\nthe function. ‘\nc. For V = 10 in.”, use the function with the fminbnd function to compute the value of r that minimizes the area A. What is the corresponding value of the height h? Investigate the sensitivity of the solution by plotting V versus r. How much can R vary about its . optimal value before-the area increases 10 percent above its minimum\nvalue?\n16. A torus is a shaped like a doughnut. If its inner radius is a and its outer radius: is b, its volume and surface area are given by\na. Create a user-defined function that computes V and A from the arguments a and b.\nb. Suppose that the outer radius is constrained to be 2 in. greater than the inner radius. Write a script file that uses your function to plot A and V versus a for 0.25  a  4 in .1\n17. Suppose it is known that the graph of the function Y =ax3 +bx2 +ex +d passes through four given points (Xj, Yj), i =1, 2, 3, 4. Write a user-defined function that accepts these four points as input and computes the\ncoefficients a, b, c, and d. The function should solve four linear equations in terms of the four unknowns a, b, c, and d. Test your function for the case where (Xj, Yj) = (-2, -20), (0, 4), (2, 68), and (4, 508); whose\nanswer is a = 7, b = 5,.c = -6, and d = 4. –\n\nSection 3.3\n18. Use the gen-plat function described in Section 3.3 to obtain two subplots, one plot of the function We-a over the range 0 ~ x ~ 2, and the other a plot of 5 sin(21l’ x /3) over the range 0 :5 x ~ 6.\n19. Create an anonymous function for We-a and use it to plot the function over the range 0 x  2.\n\n20. Create an anonymous function for 20×2 – 200x + 3 and use it a. to plot the function to determine the approximate location of its minimum, and\nb. with the fminbnd function to precisely determine the location of the minimum.\n21. Create four anonymous functions to represent the function 6 e3COSx \\ which is composed of the functions h(z) = 6ez, g(y) = 3cosy, and I(x) = x2. Use the anonymous functions to plot 6 e 3cosx2 over the range 0 ~ x ~ 4.\n22. Use a primary function with a sub-function to compute the zeros of the function 3×3 – 12×2 – 33x +90 over the range -10 ~ x ~ 10.\n23. Create a primary function that uses a function handle with a nested function to compute the minimum of the function 20×2 – 200x + 3 over the range 0 ~ x ~ 10.\nSection 3.4\n24. Use a text editor to create a file containing the following data. Then use the load function to load the file into MATLAB, and use the mean function to compute the mean value of each column.\n55 42 98\n51 39 95\n63 43 94\n58 ’45 90\n25. Enter and save the data given in Problem 24 in a spreadsheet. Then import the spreadsheet file into the MATLAB variable A. Use MATLAB to compute the sum of each column.\n\n26. Use a text editor to create a file from the data given in Problem 24, but separate each number with a semicolon. Then use the Import Wizard to load and save the data in the MAlLAB variable A.\n27. Use a text editor to create a file temperature. data  containing the temperature data given on page 175. Then use the Import Wizard to load and save the data in the MATLAB variable temperature. Compute the\nmean value of each column.\n\nPosted on July 27, 2015 in function and files" ]

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[ "What Do the Keys on a Calculator Mean?", null, "Credit: Martin Barraud/Stone/Getty Images\n\nThere are many kinds of calculators, but most calculators have the same standard keys that allow users to complete a variety of calculations. The number keys and addition, subtraction, multiplication, division and equal signs are all very straightforward, but the functions of the other keys are not so well-known.\n\nTwo very helpful keys on a calculator are \"AC\" and \"CE.\" The first key clears the entire memory, and the second key only clears the last numbers that were imputed. The \"%\" key is used to calculate percentages. Users must press the \"shift\" key before the \"%\" key to get an accurate answer. The \"pi\" button displays the value of pi. To get an exponent while entering an equation, users should press the \"EXP\" button immediately before entering the value of the exponent. The last standard key is the decimal (.), which allows a user to input an equation that includes a decimal.\n\nMost standard calculators also have memory buttons. The \"Min\" key allows users to save a displayed equation in the calculator's memory. Most calculators have enough memory to store 10 equations or answers. To input an equation manually, users press \"M+\" to add an equation or \"M-\" to delete an equation stored in the memory bank. To access an equation stored in the memory bank of a calculator, users can press the \"MR,\" or memory recall, button.\n\nOccasionally, it is possible to receive an error code on a calculator when the incorrect buttons are pushed. This happens most often when a user fails to hit the shift button when pressing keys that require this command. To clear the error message, users should press the \"AC\" button.\n\nSimilar Articles" ]

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[ "Solutions by everydaycalculation.com\n\n## Subtract 9/20 from 30/35\n\n30/35 - 9/20 is 57/140.\n\n#### Steps for subtracting fractions\n\n1. Find the least common denominator or LCM of the two denominators:\nLCM of 35 and 20 is 140\n\nNext, find the equivalent fraction of both fractional numbers with denominator 140\n2. For the 1st fraction, since 35 × 4 = 140,\n30/35 = 30 × 4/35 × 4 = 120/140\n3. Likewise, for the 2nd fraction, since 20 × 7 = 140,\n9/20 = 9 × 7/20 × 7 = 63/140\n4. Subtract the two like fractions:\n120/140 - 63/140 = 120 - 63/140 = 57/140\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]

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[ "TRITON MINERALS LTD Research Report\n\n## Abstract\n\nThe main perfect of this composition is to discover the stylish version to prognosticate the cost of the inventory request. During the procedure of analyzing the colorful ways and variables to remember, we plant that approaches similar as Random woodland, machine help Vector were not absolutely exploited. We evaluate TRITON MINERALS LTD prediction models with Multi-Instance Learning (ML) and Ridge Regression1,2,3,4 and conclude that the TON stock is predictable in the short/long term. According to price forecasts for (n+16 weeks) period: The dominant strategy among neural network is to Buy TON stock.\n\n## Key Points\n\n1. What is the use of Markov decision process?\n2. What are main components of Markov decision process?\n3. Dominated Move\n\n## TON Target Price Prediction Modeling Methodology\n\nWe consider TRITON MINERALS LTD Decision Process with Multi-Instance Learning (ML) where A is the set of discrete actions of TON stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4\n\nF(Ridge Regression)5,6,7= $\\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \\dots & {p}_{1n}\\\\ & ⋮\\\\ {p}_{j1}& {p}_{j2}& \\dots & {p}_{jn}\\\\ & ⋮\\\\ {p}_{k1}& {p}_{k2}& \\dots & {p}_{kn}\\\\ & ⋮\\\\ {p}_{n1}& {p}_{n2}& \\dots & {p}_{nn}\\end{array}$ X R(Multi-Instance Learning (ML)) X S(n):→ (n+16 weeks) $\\begin{array}{l}\\int {r}^{s}\\mathrm{rs}\\end{array}$\n\nn:Time series to forecast\n\np:Price signals of TON stock\n\nj:Nash equilibria (Neural Network)\n\nk:Dominated move\n\na:Best response for target price\n\nFor further technical information as per how our model work we invite you to visit the article below:\n\nHow do AC Investment Research machine learning (predictive) algorithms actually work?\n\n## TON Stock Forecast (Buy or Sell) for (n+16 weeks)\n\nSample Set: Neural Network\nStock/Index: TON TRITON MINERALS LTD\nTime series to forecast n: 04 Dec 2022 for (n+16 weeks)\n\nAccording to price forecasts for (n+16 weeks) period: The dominant strategy among neural network is to Buy TON stock.\n\nX axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)\n\nY axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)\n\nZ axis (Yellow to Green): *Technical Analysis%\n\n## Adjusted IFRS* Prediction Methods for TRITON MINERALS LTD\n\n1. To calculate the change in the value of the hedged item for the purpose of measuring hedge ineffectiveness, an entity may use a derivative that would have terms that match the critical terms of the hedged item (this is commonly referred to as a 'hypothetical derivative'), and, for example for a hedge of a forecast transaction, would be calibrated using the hedged price (or rate) level. For example, if the hedge was for a two-sided risk at the current market level, the hypothetical derivative would represent a hypothetical forward contract that is calibrated to a value of nil at the time of designation of the hedging relationship. If the hedge was for example for a one-sided risk, the hypothetical derivative would represent the intrinsic value of a hypothetical option that at the time of designation of the hedging relationship is at the money if the hedged price level is the current market level, or out of the money if the hedged price level is above (or, for a hedge of a long position, below) the current market level. Using a hypothetical derivative is one possible way of calculating the change in the value of the hedged item. The hypothetical derivative replicates the hedged item and hence results in the same outcome as if that change in value was determined by a different approach. Hence, using a 'hypothetical derivative' is not a method in its own right but a mathematical expedient that can only be used to calculate the value of the hedged item. Consequently, a 'hypothetical derivative' cannot be used to include features in the value of the hedged item that only exist in the hedging instrument (but not in the hedged item). An example is debt denominated in a foreign currency (irrespective of whether it is fixed-rate or variable-rate debt). When using a hypothetical derivative to calculate the change in the value of such debt or the present value of the cumulative change in its cash flows, the hypothetical derivative cannot simply impute a charge for exchanging different currencies even though actual derivatives under which different currencies are exchanged might include such a charge (for example, cross-currency interest rate swaps).\n2. A contractual cash flow characteristic does not affect the classification of the financial asset if it could have only a de minimis effect on the contractual cash flows of the financial asset. To make this determination, an entity must consider the possible effect of the contractual cash flow characteristic in each reporting period and cumulatively over the life of the financial instrument. In addition, if a contractual cash flow characteristic could have an effect on the contractual cash flows that is more than de minimis (either in a single reporting period or cumulatively) but that cash flow characteristic is not genuine, it does not affect the classification of a financial asset. A cash flow characteristic is not genuine if it affects the instrument's contractual cash flows only on the occurrence of an event that is extremely rare, highly abnormal and very unlikely to occur.\n3. An alternative benchmark rate designated as a non-contractually specified risk component that is not separately identifiable (see paragraphs 6.3.7(a) and B6.3.8) at the date it is designated shall be deemed to have met that requirement at that date, if, and only if, the entity reasonably expects the alternative benchmark rate will be separately identifiable within 24 months. The 24-month period applies to each alternative benchmark rate separately and starts from the date the entity designates the alternative benchmark rate as a non-contractually specified risk component for the first time (ie the 24- month period applies on a rate-by-rate basis).\n4. For the purposes of measuring expected credit losses, the estimate of expected cash shortfalls shall reflect the cash flows expected from collateral and other credit enhancements that are part of the contractual terms and are not recognised separately by the entity. The estimate of expected cash shortfalls on a collateralised financial instrument reflects the amount and timing of cash flows that are expected from foreclosure on the collateral less the costs of obtaining and selling the collateral, irrespective of whether foreclosure is probable (ie the estimate of expected cash flows considers the probability of a foreclosure and the cash flows that would result from it). Consequently, any cash flows that are expected from the realisation of the collateral beyond the contractual maturity of the contract should be included in this analysis. Any collateral obtained as a result of foreclosure is not recognised as an asset that is separate from the collateralised financial instrument unless it meets the relevant recognition criteria for an asset in this or other Standards.\n\n*International Financial Reporting Standards (IFRS) are a set of accounting rules for the financial statements of public companies that are intended to make them consistent, transparent, and easily comparable around the world.\n\n## Conclusions\n\nTRITON MINERALS LTD assigned short-term B2 & long-term Ba3 forecasted stock rating. We evaluate the prediction models Multi-Instance Learning (ML) with Ridge Regression1,2,3,4 and conclude that the TON stock is predictable in the short/long term. According to price forecasts for (n+16 weeks) period: The dominant strategy among neural network is to Buy TON stock.\n\n### Financial State Forecast for TON TRITON MINERALS LTD Options & Futures\n\nRating Short-Term Long-Term Senior\nOutlook*B2Ba3\nOperational Risk 3378\nMarket Risk4445\nTechnical Analysis6843\nFundamental Analysis8875\nRisk Unsystematic3590\n\n### Prediction Confidence Score\n\nTrust metric by Neural Network: 74 out of 100 with 774 signals.\n\n## References\n\n1. G. Shani, R. Brafman, and D. Heckerman. An MDP-based recommender system. In Proceedings of the Eigh- teenth conference on Uncertainty in artificial intelligence, pages 453–460. Morgan Kaufmann Publishers Inc., 2002\n2. Y. Chow and M. Ghavamzadeh. Algorithms for CVaR optimization in MDPs. In Advances in Neural Infor- mation Processing Systems, pages 3509–3517, 2014.\n3. J. N. Foerster, Y. M. Assael, N. de Freitas, and S. Whiteson. Learning to communicate with deep multi-agent reinforcement learning. In Advances in Neural Information Processing Systems 29: Annual Conference on Neural Information Processing Systems 2016, December 5-10, 2016, Barcelona, Spain, pages 2137–2145, 2016.\n4. Andrews, D. W. K. W. Ploberger (1994), \"Optimal tests when a nuisance parameter is present only under the alternative,\" Econometrica, 62, 1383–1414.\n5. V. Mnih, A. P. Badia, M. Mirza, A. Graves, T. P. Lillicrap, T. Harley, D. Silver, and K. Kavukcuoglu. Asynchronous methods for deep reinforcement learning. In Proceedings of the 33nd International Conference on Machine Learning, ICML 2016, New York City, NY, USA, June 19-24, 2016, pages 1928–1937, 2016\n6. Mikolov T, Yih W, Zweig G. 2013c. Linguistic regularities in continuous space word representations. In Pro- ceedings of the 2013 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pp. 746–51. New York: Assoc. Comput. Linguist.\n7. Bottou L. 1998. Online learning and stochastic approximations. In On-Line Learning in Neural Networks, ed. D Saad, pp. 9–42. New York: ACM\nFrequently Asked QuestionsQ: What is the prediction methodology for TON stock?\nA: TON stock prediction methodology: We evaluate the prediction models Multi-Instance Learning (ML) and Ridge Regression\nQ: Is TON stock a buy or sell?\nA: The dominant strategy among neural network is to Buy TON Stock.\nQ: Is TRITON MINERALS LTD stock a good investment?\nA: The consensus rating for TRITON MINERALS LTD is Buy and assigned short-term B2 & long-term Ba3 forecasted stock rating.\nQ: What is the consensus rating of TON stock?\nA: The consensus rating for TON is Buy.\nQ: What is the prediction period for TON stock?\nA: The prediction period for TON is (n+16 weeks)" ]

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[ "# Is the sun directly in the center of earth's orbit?\n\nJan 24, 2016\n\nThe orbit is an ellipse of small eccentricity e = 0.01671. Sun is at a focus of the ellipse The distance of the Sun from the geometrical center of the orbit is 2,499,787 km\n\n#### Explanation:\n\nThe semi-major axis of the ellipse a = 149598262 km. The Sun-center distance is ae = 2499787 km.\n\nJan 24, 2016\n\nThe Sun is not at the centre of the Earth's orbit.\n\n#### Explanation:\n\nTechnically the Earth doesn't orbit around the Sun and the Moon doesn't orbit around the Earth.\n\nThe Earth and the Moon both orbit around the centre of mass of the Earth and Moon. This is called the Earth-Moon Barycentre or EMB. It is about $4 , 671 k m$ from the centre of the Earth or about $1 , 700 k m$ below the Earth's surface.\n\nIn a similar way the Sun and all of the planets and other bodies in the Solar System orbit about the centre of mass of the Solar System. This is called the Solar Centre Barycentre.\n\nThe location of this barycentre is constantly changing due to the relative positions of the planets. It is usually just below the Sun's surface and sometimes even above the Sun's surface. It's position can be anywhere from close to the centre of the Sun to over $1 , 000 , 000 k m$ from the centre of the Sun if all of the planets were aligned on the same side of the Sun.", null, "The graph shows the position of the Solar System Barycentre relative to the centre of the Sun from 1938 to 2051. The unit of distance is the solar radius $696 , 000 k m$. The graph was plotted using NASA's DE430 data by a program I just wrote. The change in position is quite staggering. Most of the effects are due to Jupiter and Saturn.\n\nSo, the true story is that both the Sun and the Earth-Moon Barycentre orbit around the Solar System Barycentre.\n\nAlso, the Earth's orbit is slightly elliptical, with the Earth orbiting around one of the foci. The orbit is not a true ellipse as it is constantly being deformed by the gravitational pull of the other planets.\n\nThe Earth's perihelion distance ${d}_{p} = 147 , 100 k m$ and its aphelion distance ${d}_{a} = 152 , 100 k m$. The semi-major axis $a$ is defined as $2 a = {d}_{p} + {d}_{a}$. This gives a value of $a = 149 , 600 k m$. The distance of the centre of he ellipse from the focus is $a - {d}_{p} =$2,500,000km.\n\nSo, the distance of the Sun from the centre of the Earth's orbit is $2 , 500 , 000 \\pm 1 , 000 , 000 k m$ depending upon the positions of the other planets." ]

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[ "# 3rd EQ Calc Sec 1", null, "```Warm-Up/Activator\n Sketch a graph you would describe as continuous.\n Sketch a graph you would describe as discontinuous.\nEssential Question:\nWhat are the characteristics of a\ncontinuous function?\nContinuity\n Where am I continuous?\n Where am I discontinuous?\nx  5\n  x  12,\n( x  4) 3  4,  5  x  2\n\nf ( x)  \nx2 ,\n2 x0\n  3 x  2,\n0 x3\n\n x  10,\n3 x\nDefinition\nof\nContinuity\n Let c be a number in the interval (a,b) and let f be a\nfunction whose domain contains the interval (a,b). The\nfunction f is continuous at the point c if the following\nconditions are true.\n1.\nf(c) is defined\n2.\nlim f ( x) exists\nx c\nf ( x )  f (c )\n3. lim\nx c\nContinuous Intervals\n If f is continuous at every point in the interval (a,b)\nthen it is continuous on the interval (a,b)\n The domain of the function determines\ncontinuity.\n A polynomial function is continuous at every real\nnumber.\n A rational function is continuous at every number in its\ndomain.\nExample 1]\nf(x) = x2 - 2x + 3\nf(x) = x3 - x\nExample 2\nFinding Discontinuities\n Determining Continuity of a Function\nA. f(x) = 1\nx\nx 2 1\nB. f(x) =\nx 1\n1\nC. f(x) = 2\nx 1\nRemovable vs Non-removable\nx  3x  10\nf ( x)  2\nx  7 x  10\n2\nHoles are removable\nVertical asymptotes (Infinite\nDiscontinuities) and jump\ndiscontinuities are non-removable.\nContinuity on a Closed Interval\n Let f be defined on a closed interval [a,b]. If f is\ncontinuous on the open interval (a,b) and\nlim f ( x)  f (a ) and\nxa\nlim f ( x)  f (b)\nx b\n then f is continuous on the closed interval [a,b].\nMoreover, f is continuous from the right at a and\ncontinuous from the left at b.\nExamining Continuity at Endpoints\nf ( x)  3  x\nExamining Continuity at Endpoints\n5  x,1  x  2\nf ( x)   2\n x  1,2  x  3\nGreatest Integer Function\n The Greatest Integer Function - is a step function\nx or [[x]] = greatest integer less than or equal to x\nModeling a Cost Function\n A bookbinding company produces 10,000 books in an 8-hour\nshift. The fixed costs per shift amount to \\$5000, and the unit\ncost per book is \\$3. Using the greatest integer function, you\ncan write the cost of producing x books as\nx 1\nC  5000(1  [[\n]])  3x\n10000\nSketch the graph of this cost function\nCost Function Graph\nCompound Interest\n Banks and other financial institutions differ on how interest is\npaid to an account. If the interest is added to the account so that\nfuture interest is paid on previously earned interest, then the\ninterest is said to be compounded. Suppose, for example, that you\ndeposit \\$10,000 in an account that pays 6% interest, compounded\nquarterly. Because the 6% is the annual interest rate, the quarterly\nrate is 1/4(.06) = 0.015 or 1.5%.\nCompound Interest\n Sketch the graph of the balance in the account\ndescribed above. A = 10000(1+0.015)^[[4t]]\n```" ]

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[ "# Negative Number Products\n\nWhich of the following is not true if h, m, and k are integers and\n\nh < m < k < 0?\n1. mk < hk\n2. mh < km\n3. h + k < m + k\n4. 0 < kh\n\nMultiplying both sides of an inequality by a negative integer reverses the sense of the inequality, so (b) is false. The other statements are true." ]

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[ "# Suppose today is February 10, 2017, and your firm produces breakfast cereal and needs 145,000 bushels...\n\n###### Question:", null, "", null, "", null, "Suppose today is February 10, 2017, and your firm produces breakfast cereal and needs 145,000 bushels of corn in May 2017 for an upcoming promotion. You would like to lock in your costs today because you are concerned that corn prices might rise between now and May. Use Table 23.1 29 a. What total cost would you effectively be locking in based on the closing price of the day? (Do not round intermed iate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. Suppose corn prices are $3.69 per bushel in May. What is the profit or loss on your futures position? (Enter your answer as a positive number. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Skipped References Total cost а. b. Suppose today is February 10, 2017, and your firm produces breakfast cereal and needs 180,000 bushels of corn in May 2017 for an upcoming promotion. You would like to lock in your costs today because you are concerned that corn prices might rise between now and May. Use Table 23.1 a. What total cost would you effectively be locking in based on the closing price of the day? (Round your answer to the nearest whole number, e.g., 32.) b. Suppose corn prices are$3.56 per bushel in May. What is the profit or loss on your futures position? (Enter your answer as a positive number. Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) Total cost а. b. Profit Loss\n##### 44. Which is a benefit of being an 28. 35. Epinephrine does not: A) increase breakdown...\n44. Which is a benefit of being an 28. 35. Epinephrine does not: A) increase breakdown of insulin B) increase breakdown of glacose C) decrease flow to skeletal muscle D) decrease blood flow to gut A) Limited activity B) High energy costs C) Limited to single cell organism D) None of the above E) Non...\n...\n##### 15-16 Find the number < tat satisiies the conclusion of the Mean Value Theorem on the given interval. Graph the fune- tion , the secant line through the endpoints, and the tangent line at (c. f (c)} Are the secant line and the tangent line parallel?\n15-16 Find the number < tat satisiies the conclusion of the Mean Value Theorem on the given interval. Graph the fune- tion , the secant line through the endpoints, and the tangent line at (c. f (c)} Are the secant line and the tangent line parallel?...\nzXb-11 dx...\n##### Given, f(x) =x2 _ 4 find f' (x) using lim {(xth)-[() h-,0 (show your work):\nGiven, f(x) =x2 _ 4 find f' (x) using lim {(xth)-[() h-,0 (show your work):...\n##### Use Hess's Law to calculate AGPrxn in kJ mol-1 for the reaction below:FezO3(s) + 3 cOlg) 4 2 Fels) + 3 COzlg)AG'rxn = ?Use the following reactions with known AG\"rxn values: 2 Fels) + 3/2 Oz(g) ~ FezOz(s) AG?rxn -742.2 kJ mol-1 Yz O2lg) 7 COzl(g) AG?rxn -257.2 kJ mol-1 cOlg) +-2.94 x101 kJ mol-11.31 * 102 _ kJ mol-11.34 x103 kJ mol-1-1.51* 103 _ kJ mol-1\nUse Hess's Law to calculate AGPrxn in kJ mol-1 for the reaction below: FezO3(s) + 3 cOlg) 4 2 Fels) + 3 COzlg) AG'rxn = ? Use the following reactions with known AG\"rxn values: 2 Fels) + 3/2 Oz(g) ~ FezOz(s) AG?rxn -742.2 kJ mol-1 Yz O2lg) 7 COzl(g) AG?rxn -257.2 kJ mol-1 cOlg) + -2.94...\n##### Portfolio Return Year-to-date, Company O had earned a -3.90 percent return. During the same time period,...\nPortfolio Return Year-to-date, Company O had earned a -3.90 percent return. During the same time period, Company V earned 9.8 percent and Company M earned 8.05 percent. If you have a portfolio made up of 20 percent Company O, 10 percent Company V, and 70 percent Company M, what is your portfolio ret...\n##### Write and find the general solution of the differential equation that models the verbal statement; Eval luate the solution at the specified value of the independent variable The rate of change of Pis proportional When O00 and when 3,000 What is the value of when Write the differential equation. (Use k for the constant of proportionality: )kPSolve the differential equation.Evaluate the solution at the specified value of the independent variable_ (Round your answer to three declmal places_ 1470Nee\nWrite and find the general solution of the differential equation that models the verbal statement; Eval luate the solution at the specified value of the independent variable The rate of change of Pis proportional When O00 and when 3,000 What is the value of when Write the differential equation. (Use...\n##### Given N+1 points, an Nth order interpolating polynomial y(x) Can be obtained by using the Lagrange interpolation formula y(x) 3-,(x)f(x,)i where Lk(x)m Use the Lagrange interpolation to derive a formulafor the linear (N = 1) interpolation polynomial y \"(x)through the points ( X f(*o)) ad (x f(x))(xo f(xa (0,I)and (*,f(x,)m(25) calculate yil(1)subsequently derive and use the quadratic (N = 2)linterpolation polynomial yi2 (x) to interpolate the three points (X r(xc)) =(-121, (Xf(x,)) =(0,1),I\nGiven N+1 points, an Nth order interpolating polynomial y(x) Can be obtained by using the Lagrange interpolation formula y(x) 3-,(x)f(x,)i where Lk(x)m Use the Lagrange interpolation to derive a formula for the linear (N = 1) interpolation polynomial y \"(x) through the points ( X f(*o)) ad (x f...\n##### (10 points) Jan and Linda both use Michelson interferometer. Jan uses wavelength of 606 nm. She moved the moveable mirror by some distance and counted 818 bright = fringes: Then Linda changes the wavelength and moved the moveable mirror such that the fringes now shifted in the opposite direction and she again counted 818 bright fringes: The resultant displacement of the mirror is 4.26 x 10$m. What is the wavelength of the light used by Linda? (10 points) Jan and Linda both use Michelson interferometer. Jan uses wavelength of 606 nm. She moved the moveable mirror by some distance and counted 818 bright = fringes: Then Linda changes the wavelength and moved the moveable mirror such that the fringes now shifted in the opposite direction and... 1 answer ##### Problem 6 (10 marks) Rainbow Trout, Inc. feeds fingerling trout in special ponds and markets them... Problem 6 (10 marks) Rainbow Trout, Inc. feeds fingerling trout in special ponds and markets them when they attain a certain weight. A sample of 9 trouts were isolated in a pond and fed a special food mixture called \"Grow Em Fast\". At the end of the experimental period, the weights of the tr... 1 answer ##### How do you find two geometric means between 7 and 875 ? How do you find two geometric means between 7 and 875 ?... 5 answers ##### Pt) Suppose that 339 ft of fencing are used to enclose a corral in the shape of a rectangle with a semicircle whose diameter is a side of the rectangle as the following figure:XyFind the dimensions of the corral with maximum areaX =y pt) Suppose that 339 ft of fencing are used to enclose a corral in the shape of a rectangle with a semicircle whose diameter is a side of the rectangle as the following figure: X y Find the dimensions of the corral with maximum area X = y... 1 answer ##### 001. Yann Martel, Inc., a toy manufacturer, provided the following information:$50 Unit Domestic unit sales...\n001. Yann Martel, Inc., a toy manufacturer, provided the following information: $50 Unit Domestic unit sales price manufacturing costs: Variable Fixed 10 The company has received an offer from an exporter for 9,000 units of toys at$60 per unit. The additional business is not expected to affect the...\n##### Which is the strongest oxidizing agent? O Ags) Cu(s) Mg(s)\nWhich is the strongest oxidizing agent? O Ags) Cu(s) Mg(s)...\n##### Hellx Corporation uses the weighted average method in its process costing system. It produces prefabricated flooring...\nHellx Corporation uses the weighted average method in its process costing system. It produces prefabricated flooring in a series of steps carried out in production departments. All of the material that is used in the first production department is added at the beginning of processing in that departm...\n##### Consider the following transportation table to answer Q13-014:SupphyFrom:Demand\nConsider the following transportation table to answer Q13-014: Supphy From: Demand...\n##### WHAT IS THE PERIOD OF THE FUNCTION f (x) = 2sinGx) ? B 4 C: 2 2x NONE OFTHESEWHAT IS THE PERIOD OF THE FUNCTION f() =2sin(€) ? B 4 C 2 D 2x NONE OF THESEWHAT IS THE PERIOD OF THE FUNCTION J (4) scc(ir) ? A %/4 \"/z C T 2K NONE OF THESEWHAT IS THE AMPLHTUDE OF THE GRAPH OF THE FUNCTION / () ^|- B _! 21-21 2 E: NONE OF THESEA(WHAT IS ^ SKETCH OF ONE PFRIOD OF THE GRAPH OF THE FUNCTIONE NONE OF MESE\nWHAT IS THE PERIOD OF THE FUNCTION f (x) = 2sinGx) ? B 4 C: 2 2x NONE OFTHESE WHAT IS THE PERIOD OF THE FUNCTION f() =2sin(€) ? B 4 C 2 D 2x NONE OF THESE WHAT IS THE PERIOD OF THE FUNCTION J (4) scc(ir) ? A %/4 \"/z C T 2K NONE OF THESE WHAT IS THE AMPLHTUDE OF THE GRAPH OF THE FUNCTION /...\n##### Ignments Applied Optimization ProblemsOptimization ProblemsMinitze surface area QuestionNoluine[U8 cm\"' , DclermTl square DosC open with only the minimunt manufacture rectangular tinirum surface area? Enter = company plans the surlace area. What / of the box that will minimize the dimensions units in yaur answer_ AE and do not include surlaceJnswel below: Provide your|nsirucVor MoREn Anon ContentFLEDuACE\nignments Applied Optimization Problems Optimization Problems Minitze surface area Question Noluine [U8 cm\"' , DclermTl square DosC open with only the minimunt manufacture rectangular tinirum surface area? Enter = company plans the surlace area. What / of the box that will minimize the dim...\n##### Write the character sketch of phyllis from the novel \"the railway children\"by E-nesbit\nwrite the character sketch of phyllis from the novel \"the railway children\"by E-nesbit...\n##### Question 6 (5 points)Which of the following of the following statements about the covalent bonds, C-N, €-N,and C=N, is correct?The € N bond is the shortest and the C=N bond is the strongest:The C-N bond is the shortest and the strongest:The € N hond is the longest and the CeN bond Is the strongest.The € N bond is the longest and the CzN bond is the weakest. The C-N bond is the longest and the weakest.\nQuestion 6 (5 points) Which of the following of the following statements about the covalent bonds, C-N, €-N,and C=N, is correct? The € N bond is the shortest and the C=N bond is the strongest: The C-N bond is the shortest and the strongest: The € N hond is the longest and the CeN b...\n##### Appreciate if you can answer this ONE QUESTION COMPLETELY and give me a detailed working with...\nAppreciate if you can answer this ONE QUESTION COMPLETELY and give me a detailed working with explanation for me to understand. Once completed so long as my doubts are cleared and the solutions are correct, I will definitely vote up. Some of the question are similiar to take a look carefully before ..." ]

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[ "# Quotient Rule Of Exponents Calculator", null, "Quotient Rule Calculator is a free online tool that displays the derivative of a function. BYJU’S online quotient rule calculator tool makes the calculation faster, and it displays the derivative of a given function in a fraction of seconds. How to Use the Quotient Rule Calculator? The procedure to use the quotient rule calculator is as follows:\n\n1. Estimated Reading Time: 30 secs\n\nPreview\n\nPosted in: Rules of exponents cheat sheet", null, "Simplify exponential expressions using algebraic rules step-by-step. \\square! \\square! . Get step-by-step solutions from expert tutors as fast as 15-30 minutes. Your first 5 questions are on us!\n\nPreview\n\nPosted in: Rules of exponents chart", null, "2019-05-28 · Example. Use the quotient rule for exponents to simplify the expression. x 4 x 3 \\frac {x^4} {x^3} x 3 x 4 . The base of the expression in the numerator is x x x, and the base of the expression in the denominator is x x x, which means that the bases are the same, so we can use the quotient rule for exponents.\n\nPreview\n\nPosted in: Laws of exponents calculator", null, "To divide these two exponents with a base of ten, we will use the quotient rule. This rule states that when you are dividing two exponents with the …\n\nPreview\n\nPosted in: List of exponent rules", null, "Example. Use the quotient rule for exponents to simplify the expression. x 4 x 3 \\frac {x^4} {x^3} x 3 x 4 . The base of the expression in the numerator is x x x, and the base of the expression in the denominator is x x x, which means that the bases are the same, so we can use the quotient rule for exponents. We’ll subtract the exponent in\n\n1. Estimated Reading Time: 3 mins\n\nPreview\n\nPosted in: 10 laws of exponents", null, "Exponents Calculator - Symbolab tip www.symbolab.com. Simplify exponential expressions using algebraic rules step-by-step. \\square! \\square! . Get step-by-step solutions from expert tutors as fast as 15-30 minutes. Your first 5 questions are on us!2^X\\Cdot2^Y‧(X^{12})/(X^{-2)} - Exponents Calculator\n\nPreview\n\nPosted in: 8 laws of exponents", null, "Click on the pertaining program demo button found in the same row as your search keyword quotient rule calculator. If you find the program demonstration helpful click on the buy button to obtain the program at a special low price extended only to algebra-tutoring.com visitors\n\nPreview\n\nPosted in: Quotient rule calculator with steps", null, "Basic exponent laws and rules When exponents that share the same base are multiplied, the exponents are added. a n × a m = a (n+m) EX: 2 2 × 2 4 = 4 × 16 = 64 2 2 × 2 4 = 2 (2 + 4) = 2 6 = 64 When an exponent is negative, the negative sign is removed by reciprocating the base and raising it to the positive exponent. a (-n) = 1 a n\n\nPreview\n\nPosted in: Law Commons", null, "Quotient rule of differentiation Calculator online with solution and steps. Detailed step by step solutions to your Quotient rule of differentiation problems online with our math solver and calculator. Solved exercises of Quotient rule of differentiation.\n\nPreview\n\nPosted in: Law Commons", null, "quotient rule for exponents calculator. johnson and johnson holiday calendar 2021 / sandusky ferry to pelee island\n\nPreview\n\nPosted in: Law Commons", null, "Law of Exponents: Product and Quotient Rule DRAFT. 21 hours ago by. michaellwilliams. 7th - 8th grade . Mathematics. Played 0 times. 0 likes. 0% average accuracy. 0. Save. Edit. Edit. Print; Share; Edit; Delete; Report an issue; Live modes. Start a live quiz . Classic . Students progress at their own pace and you see a leaderboard and live results. Instructor-paced BETA . Control …\n\nPreview\n\nPosted in: Law Commons", null, "Law of Exponents: Power of a Quotient Rule ( (a/b) m = (a m /b m )) The quotient rule states that two powers with the same base can be divided by subtracting the exponents. Follow this simple rule to adeptly and quickly solve exponent problems using the power of a quotient rule.\n\nPreview\n\nPosted in: Law Commons", null, "Laws of Exponents: Quotient RuleIn this video tutorial, I will teach you how to simplify expressions using the quotient rule.If you want to test your skill,\n\nPreview\n\nPosted in: Law Commons", null, "In order to multiply powers with the same base, we add their exponents. Preview this quiz on Quizizz. Quiz. Law of Exponents: Product and Quotient Rule. DRAFT. 7th - 8th grade . Played 0 times. 0% average accuracy. Mathematics. 4 minutes ago by. eddington_gambiza_22039. 0. Save. Edit. Edit. Law of Exponents: Product and Quotient Rule DRAFT. 4 minutes ago by. …\n\nPreview\n\nPosted in: Law Commons", null, "quotient rule for exponents calculator. george brown residence tour\n\nPreview\n\nPosted in: Law Commons", null, "Quotient of powers Calculator online with solution and steps. Detailed step by step solutions to your Quotient of powers problems online with our math solver and calculator. Solved exercises of Quotient of powers. Calculators Topics Solving Methods Go Premium. ENG • ESP. Topics Login. Tap to take a pic of the problem. calculators. Quotient Of Powers. Quotient of powers …\n\nPreview\n\nPosted in: Law Commons", null, "This is my way of providing free tutoring for the students in my class and for students anywhere in the world. Every video is a short clip that shows exactly how to solve math problems step by step. The problems are done in real time and in front of a regular classroom. These videos are intended to help you learn how to solve math problems, review how to solve a math problems, study for …\n\nPreview\n\nPosted in: Study Law\n\n## New Popular Law\n\n### What is the quotient rule of exponents?\n\nThe quotient rule of exponents allows us to simplify an expression that divides two numbers with the same base but different exponents. In a similar way to the product rule, we can simplify an expression such as displaystyle m>n m > n.\n\n### What is the law of exponents?\n\nExplaining Law of exponents with crystal-clear examples, this chart helps them drive home the concept. The product rule is: when you multiply two powers with the same base, add the exponents. Train 8th grade students to rewrite each exponential expression as a single exponent with this set of pdf worksheets.\n\n### How to teach quotient rule to students?\n\nAlso, help them develop substantial skills in finding the value of the unknown exponent and MCQ. Upgrade your skills in solving problems involving quotient rule by practicing these printable worksheets. The rule states that you can divide two powers with the same base by subtracting the exponents.\n\n### What is the product rule for exponents?\n\nThe product rule is: when you multiply two powers with the same base, add the exponents. Train 8th grade students to rewrite each exponential expression as a single exponent with this set of pdf worksheets. Also, help them develop substantial skills in finding the value of the unknown exponent and MCQ." ]

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[ "A popular and useful .csv file containing information on loan applicants at German banks is available from many sites on the web. The file contains 20 pieces of information on 1000 applicants.\n\nThe following code can be used to determine if an applicant is credit worthy and if he (or she) represents a good credit risk to the lender. Several methods are applied to the data to help make this determination. We will look at them in this case.\n\nPlease note, the data file used in this example exists in different forms around the web, so it might be necessary to perform some data manipulation to prepare it for the analysis.\n\nurl <- 'https://onlinecourses.science.psu.edu/stat857/sites/onlinecourses.science.psu.edu.stat857/files/german_credit.csv'\ncredit <- read.csv(url, header = TRUE, sep = ',')\n\nThis bit of code performs a small manipulation on the data to prepare it for the analysis. Otherwise, an error results because of the four levels of factors found in one of the columns in some files. There weren’t many in the file I worked from, just a handful of 1000 rows, and the results are not impacted materially.\n\nBasically, any level 4 response is coverted to level 3. What matters is the code made R happy and the analysis went ahead.\n\ncredit$No.of.Credits.at.this.Bank[credit$No.of.Credits.at.this.Bank == 4] <- 3\n\nTake a quick look at the data to get a sense of what we are working with.\n\nstr(credit)\n## 'data.frame': 1000 obs. of 21 variables:\n## $Creditability : int 1 1 1 1 1 1 1 1 1 1 ... ##$ Account.Balance : int 1 1 2 1 1 1 1 1 4 2 ...\n## $Duration.of.Credit..month. : int 18 9 12 12 12 10 8 6 18 24 ... ##$ Payment.Status.of.Previous.Credit: int 4 4 2 4 4 4 4 4 4 2 ...\n## $Purpose : int 2 0 9 0 0 0 0 0 3 3 ... ##$ Credit.Amount : int 1049 2799 841 2122 2171 2241 3398 1361 1098 3758 ...\n## $Value.Savings.Stocks : int 1 1 2 1 1 1 1 1 1 3 ... ##$ Length.of.current.employment : int 2 3 4 3 3 2 4 2 1 1 ...\n## $Instalment.per.cent : int 4 2 2 3 4 1 1 2 4 1 ... ##$ Sex...Marital.Status : int 2 3 2 3 3 3 3 3 2 2 ...\n## $Guarantors : int 1 1 1 1 1 1 1 1 1 1 ... ##$ Duration.in.Current.address : int 4 2 4 2 4 3 4 4 4 4 ...\n## $Most.valuable.available.asset : int 2 1 1 1 2 1 1 1 3 4 ... ##$ Age..years. : int 21 36 23 39 38 48 39 40 65 23 ...\n## $Concurrent.Credits : int 3 3 3 3 1 3 3 3 3 3 ... ##$ Type.of.apartment : int 1 1 1 1 2 1 2 2 2 1 ...\n## $No.of.Credits.at.this.Bank : num 1 2 1 2 2 2 2 1 2 1 ... ##$ Occupation : int 3 3 2 2 2 2 2 2 1 1 ...\n## $No.of.dependents : int 1 2 1 2 1 2 1 2 1 1 ... ##$ Telephone : int 1 1 1 1 1 1 1 1 1 1 ...\n## $Foreign.Worker : int 1 1 1 2 2 2 2 2 1 1 ... You probably notice immediately three columns stand out. We are going to eliminate them: “Duration of Credit (months)”, “Credit Amount”, and “Age”. Why? We are trying to focus in this exercise on classifications or categories of data that serve as indicators of credit worthiness. These are scores rather than hard numbers. Does the applicant have a phone? Is the applicant married? Is there a co-signer? How long has the applicant lived at the same address? These sorts of things. What’s important about these factors is we know how they relate to lending decisions. Good credit is associated with certain combinations of factors to the point we use probabilities to classify new applicants by their characteristics. In the data, the answers to these questions are not “Yes” or “No” or “Ten Years”. The answers are grouped into broader classifications. Take a look at the data and column headers and you will see what I mean. What we need to do then is remove the truly numeric data (duration, amount, and age) and preserve the categorical factors. We do that by creating an object that excludes selected columns. S <- c(1, 2, 4, 5, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20) Then we create a short function to convert integers to factors. for(i in S) credit[, i] <- as.factor(credit[, i]) Now that we have the data in useful shape, we can begin to apply different analytical methods. #### Method One: Logistic Regression The first step is to create our practice data set and our test data set. THe practice set is used for training the model. The test set is used to evaluate model accuracy. We are going to create a number of models so it is necessary to give them numerical designations (1, 2, 3, etc.). We can break the data sets into any sizes we like, even 50-50, but here we use a one-third, two-thirds split. i_test1 <- sample(1:nrow(credit), size = 333) i_calibration1 <- (1:nrow(credit))[-i_test1] At this stage, we will perform a logistic regression using the glm() function. We start with the practice set, i_calibration1. Here, we will be selective with the variables we use in the model. We’ll change this in a bit but for now just use five to determine the value of Creditability. set.seed(1) LogisticModel.1 <- glm(Creditability ~ Account.Balance + Payment.Status.of.Previous.Credit + Purpose + Length.of.current.employment + Sex...Marital.Status, family = binomial, data = credit[i_calibration1, ]) That done, we can move on to fitting the model we just created to the test set, i_test1, and prepare to make our first prediction. fitLog1 <- predict(LogisticModel.1, type = 'response', newdata = credit[i_test1, ]) We have fitted our model. Now we will use the ROCR package to create predictions and measure performance in terms of Area Under the Curve (AUC). The greater the AUC measure, the better our model is performing. library(ROCR) pred1 <- prediction(fitLog1, credit$Creditability[i_test1])\nperf1 <- performance(pred1, 'tpr', 'fpr')\n\nLet’s plot our results.", null, "And we’ll wrap this part up by finding the AUC.\n\nAUCLog1 <- performance(pred1, measure = 'auc')@y.values[]\nAUCLog1\n## 0.7564829\n\nThat’s not a bad result, but let’s see if we can do better with a different method.\n\n#### Method Two: An Alternative Logistic Model\n\nIn this approach, we will build a second Logistic Model to make use of all the variables in our data set. The steps are the same as in the first model above so we can dispense with much of the commentary.\n\nset.seed(1)\nLogisticModel.2 <- glm(Creditability ~ ., family = binomial, data = credit[i_calibration1, ])\nfitLog2 <- predict(LogisticModel.2, type = 'response', newdata = credit[i_test1, ])\npred2 <- prediction(fitLog2, credit$Creditability[i_test1]) perf2 <- performance(pred2, 'tpr', 'fpr') plot(perf2)", null, "AUCLog2 <- performance(pred2, measure = 'auc')@y.values[] AUCLog2 ## 0.7648998 We don’t get much improvement by including all the variables. A good rule to follow is keep the model as simple as possible. Adding more variables results in little improvement, so stick with the simpler model. #### Method Three: Regression Tree Next, let’s try analyzing the data using a regression tree approach. Much of our code is similar to what was used in the logistic models above but we need to do some tweaking, which you will recognize. Notice again we are looking at all the variables in our model to find their impact on our variable of interest, Creditability. It’s an awkward term which I think is probably a bad translation of the German word for Credit Worthiness. library(rpart) set.seed(1) TreeModel <- rpart(Creditability ~ ., data = credit[i_calibration1, ]) library(rpart.plot) prp(TreeModel, type = 2, extra = 1)", null, "fitTree <- predict(TreeModel, newdata = credit[i_test1, ], type = 'prob')[, 2] pred3 <- prediction(fitTree, credit$Creditability[i_test1])\nperf3 <- performance(pred3, 'tpr', 'fpr')\nplot(perf3)", null, "AUCTree <- performance(pred3, measure = 'auc')@y.values[]\nAUCTree\n## 0.7414953\n\nThese aren’t satisfactory results, given all the complexity of our tree model, so again we have to wonder if we aren’t better off using the simpler Logistic Regression model from the first example.\n\n#### Method Four: Random Forest\n\nInstead of building one decision tree, we can use the random forest method to create a metaphorical “forest” of decision trees. In this method, the end result is the mode of the classes (if we are working on a classification model) or the mean of the predictions (if we are working with regressions).\n\nThe idea behind the random forest is that decision trees are prone to overfitting, so finding the “average” tree in the forest can help avoid this problem.\n\nYou can imagine this is more computationally demanding than creating a single decision tree, but R handles the effort pretty well.\n\nlibrary(randomForest)\nset.seed(1)\nRF <- randomForest(Creditability ~ ., data = credit[i_calibration1, ])\nfitForest1 <- predict(RF, newdata = credit[i_test1, ], type = 'prob')[, 2]\npred4 <- prediction(fitForest1, credit$Creditability[i_test1]) perf4 <- performance(pred4, 'tpr', 'fpr') plot(perf4)", null, "AUCRF <- performance(pred4, measure = 'auc')@y.values[] AUCRF ## 0.7998637 With the extra effort, we get a somewhat improved result. The random forest model is the best performing of the four we have tried. But it’s a judgement call if the results warrant the extra work. #### Method Five: Comparing Random Forests with Logistic Models Alright, we’ve looked at various results using two basic methods of analysis – logistic regressions and decision trees. We have seen only single results expressed as AUC. The random forest approach requires we create a forest of decision trees and take the mode or average. Why not make use of all that data? What would they look like? The following code creates a chart depicting hundreds of combinations of AUC scores for each tree in our random forest and for logistic models. First we need a function to carry out the analysis. AUC <- function(i){ set.seed(i) i_test2 <- sample(1:nrow(credit), size = 333) i_calibration2 <- (1:nrow(credit))[-i_test2] LogisticModel.3 <- glm(Creditability ~ ., family = binomial, data = credit[i_calibration2, ]) summary(LogisticModel.3) fitLog3 <- predict(LogisticModel.3, type = 'response', newdata = credit[i_test2, ]) library(ROCR) pred5 <- prediction(fitLog3, credit$Creditability[i_test2])\nAUCLog3 <- performance(pred5, measure = 'auc')@y.values[]\nRF <- randomForest(Creditability ~ ., data = credit[i_calibration2, ])\nfitForest2 <- predict(RF, newdata = credit[i_test2, ], type = 'prob')[, 2]\npred6 <- prediction(fitForest2, credit$Creditability[i_test2]) AUCRF <- performance(pred6, measure = 'auc')@y.values[] return(c(AUCLog3, AUCRF)) } OK, we have the function. Now we have to put it to work. This part of the code takes a while to run because we are tabulating and recording hundreds of individual results. You can adjust the number of results in the model by changing the count in the VAUC object. Here, we have chosen to calculate 200 x-y pairs, or 400 individual results. VAUC <- Vectorize(AUC)(1:400) plot(t(VAUC), xlab = 'Logistic', ylab = 'Random Forest')", null, "You can see that the results we have from the first four models are right in the middle of the distribution. This confirms for us the models are all pretty comparable. The best we can hope for is an AUC of 0.84 and most give us results similar to what we’ve calculated already. But let’s try to visualize this a bit better. A couple R packages can be used to improve the graphic depiction of the results. This will show us exactly where the most likely set of results reside. First, we need to convert our VAUC object into a data frame. AA <- as.data.frame(t(VAUC)) We are going to use the ggplot2 and hdrcde libraries to create a couple new graphs. The first is a density contour plot. library(ggplot2) data(AA, package = 'MASS') ggplot(AA, aes(x = V1, y = V2)) + geom_point() + geom_density2d() + xlab('Logistic') + ylab('Random Forest')", null, "The second is a high density contour plot that gives us the probability regions for the data. library(hdrcde) par(mar = c(3.1, 4.1, 1.1, 2.1)) with(AA, hdr.boxplot.2d(V1, V2, show.points = TRUE, prob = c(.01, .05, .5, .75), xlab = 'Logistic', ylab = 'Random Forest'))", null, "Any way we depict our results, we have to use the data to make a sound lending decision. Is there a problem here? These may be the best scores we can come up with using these models, but are the results acceptable for determining the credit-worthiness of a loan applicant? That depends on the credit standards being used by the lending institution. At best, it looks like our models give us an 82% chance of lending to good credit risks. For every$1 million in loans, at best we might expect to be repaid $820,000. On average, we would expect to recover around$780,000 in principal. In other words, according to our analysis, there is between a 75% and 80% chance we will recapture our \\$1 million loan, depending on the modeling method we use.\n\nAs we add loan applicants to our data bases, we would want them to cluster in the darkest area of the high density plot if we are going to consider them good credit risks.\n\nUnless we charge a lot of interest to cover our losses, we might need better models.\n\nThe code in this example was adapted from Arthur Charpentier at the Freakonometrics blog in the post, Classification on the German Credit Database. The code is available at GitHub." ]

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", null, 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", null, 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iUCxgvQwu6965TMbQaGAep26M0x0Gm78O3TmB46BkqcYlf0XPqWD5FwC9Ttwusf9f+FAeq/C98EqH6LKR86Db8+kd49Yrk3kYhTbIwuS9HaQeEFqI67t3+Zf6ug0ycntQK0OhHeC1B9kz6baehzTNVHORcP0BBxitXRV2mQEAZ+rC6jiP2wfQQJM4jDoZOkkrbC6/3yuI/GD/p43u38T2mzi0TRO3LIXqmrT24uKN9wA3SU7JmHYHTLnlhxJWKpYDL6Y1usnKlhiWEEHbE2VsAjYWkiQA8sj5XsLFjSp8dSXwIrEuiCU2I5x2FlwTg65BRYslOxQiAe3XNQLMthND3WQWcdBkvPR2Nje3Rdws6+vGheyEJHJuV8S4gGRTroVuHOsExoQhwDnSzOMZcCjYbjo8sFOMC8Z4P2rgxYz3DfsyZsJ+2pvdMc9A4OaXZjsyasJd1ZndoSdA6OJD4KWRNWkOqUzuoFGgcH8WArsyYsLdEJnVt2osMEAo/3MWvCstKcz/lVpzlOwLdEF7MmLCrJ6YwpOsmBAp5lepg1YUkpzmZczSmOFGgs1cGsCQtKcTJj34RctgpgU8v1L2vCchKcy8GS9ZXLRy6Um+BQgdqU/r18n3LladaE5SQ4l0Mll9nX7eOZBMUhTenej+fXKQHKmrCcBKdyoOTPF52d5bcfc58IJGBC96pdMAJ0Y+lN5VDFl6dr/d+ZTwXEu9+8qveLaQHKmrCY9GZyOEC/bnonhgDFEU1qXgJ0a+nN5Ngh0BsHQXFQBKhI6c0kAYozIkBFSm8m2YXHGRGgIqU3k/feRPqa/1RAPAJUpPRmcqji+6cxJThYwCFARUpvJkc+iHTnRPoEBws4BKhI6c3kcMV3PsqZ4mABhwAVKb2ZfKDi9AYLOIs2L2vCUtKbSQIUZ0SAipTeTBKgOCMCVKT0ZpIAxRkRoCKlN5MEKM6IABUpvZkkQHFGBKhI6c0kAYozIkBFSm8mCVCcEQEqUnozWVWcZ1n9sc387VfrUc3FYbz70hss4DTN63q7XgEKb01wiuozJfUP4adMWBOWkt5Muorz15/uG+x0c7QDtLk4jH9feoMFnLp5XW/XK0Cu0rNaE5wiu6qb3r0fWp9zZk1YSnozaSs237pkvz9ENUY7QJuLwwT3pTdYwKma1/V2vQLYbyEL9sFsUhavP+sf2t+0w5qwlPRm0qvYBWjx9tcwQL2LwwT3pTdYwHHNG1z4SK8AduOz8Hfi7Xc6qpu8H8ILhrEmLCW9mfQqtl1z+e1H9xioa7LwvvQGCzhN8zYBqlcAu1lZdL/GMa8epn5of9s4a8JS0pvJumK1L6P74fPl2vMmkm2y1n3pDRZwugFqVwC3C5+1v0i8yK7ND+3r3bAmLCW9mfQq/nhW4Vio/w0FaOu+9AYLOH1boGYFsG8itQO0rN5zr99DIkDXkOBMhvvwaie97zQm02St+xIcK+D0Bajdc8+z7O3vv4W78MH2Z+eCYawJi0lwKr2S1R9WfaJb1nMinG6y1n0JjhVwegO0Pn2pDL9JOa/y0/3QumAYa8JiEpxKU3L9/qK5afBNJP++BIcK1Or+LerTmJr3jvLgUgxFlavVD+FpTKwJy0lxLnXNpiPqXRICFIcXBmi9ApgDm+Gb8PXpSs15S8GJ9KwJy0lxLm3NeZZV+ymTAjTFkQKNqoNdb1crwOWp/thI9YDq0JV3DMv7KCdrwoKSnMyYopMcKOBZpodZE5aU5mzOrzrNcQK+JbqYNWFRiU7n3LITHSYQeLyPWROWlep8ZnMKn/VgQK4HW5k1YWnpTqg+Oj7xcWuXAmxmat/3PnPZUpBygGrZeDfduRtI0+zGZk1YywFmNRu0d2XAeob7njVhO0wtAEQiQAEgEgEKAJEIUACIRIACQCQCFAAiEaAAEIkABYBIBCgARCJAASCS2AD9eLbfoJ23v267dvnef/tNf/32wHPM13j7l4+5PHUuqA0A04gO0Ldft8+XoQAdDsmR+3LzyeD34AYCFMLo5s+8S9YM0dsQY+vBOHPF47L/qraYSHKA/q6W6sfz7wsGqNneLL1u0e1DgEKYKkCzzrW+AqbNowO0zAjQx0kO0P/99KUi7z8zexVXt5BNb727bUm7KWmvfZ1Xt6qmq5uqrL6O5sv9U93u7bWbFyNAIYzqS92VZXi4qeN+dpbDCRxclHH892CY5AD9v8/XW/H6/9s/sy4G3d/mdz9AS52ZH88qX3P3Z3soQN1t9Z/bIvsfHAOFOC5AVX++/rQ/647+fMn+8ZK5Nlctb1eBMtjAUI/+0zvqVXrbDuGakGff/lIFaPxRAEgO0D9fVE6+/WGbyGxevv406VcEW5k2Oy9Pb78uT+ZO/ajhjrCvZajn/J0AhThVgOqGDgI009lYbSZ4AdrewKj3/asdtm6AXtXLXYPfhgiSA/Qrf/v3i2mQsvrr+qX/0toA9EJS78MXthvsRbJHAlS1TXXf58u3H7wLD3mqSNP/HwSoXg3qzYTmGGizgaF+MtumXv/nWf/7sHWAFncOtWKE6AAtvv3X87WsA1HddG3eR/dCUm1J/luF4c3+ifYDtLML75rQ3fnOaUwQaDBA3b6T3UxoArTZwGge7b1c//ZEFaB1kCKC6AC9PP3vp6+wQW76D6Y53ON1xefL69+ezF69ekAxFqB+frosvnOgHtjc4C68Trp6M8EP0GoDoydAc7dN0X43oApOs0WLSKIDVP3PNkezi1Jk5nhnGKAqNP9TN0Zhu8x7E6ktOO2TAIVMVYCW7TeRruZGt5kwZQvUHPJyzxoIUPbgHyE6QJswLFoHye3mpnkzXi991Sa6Y1yTDB8DNe1kXid3XcMuPORxAaqa892+6Wk2JVzi1ZsJA8dA/QAtR87wbDZo2YKIJzpAzflp4WkadgfGhF9u34l0P5smUDn79i/1xKEALTICFPL5J9K7PfZgC7Teha/ehfc3MIIAHdm4bAKUQ6DxxAbo2gr+7EKq4KOc5kPNfzQBWm8m2G2IP9vngXbfROrnXo6TmB5y1gD9eObPLoAHnTVAczZAATzqrAEKyKT23Pf71Xv95nQxZYAU2Y7pKaOA5Eicrj2WIp2DXWViOlBOJSkQN1O77sGImw2cgcDEEliSTKJmaf+ltn8FOBfBHSe4NDnkzJCYpSWmEBxcAgmVQIn7kjE70haTtHpwOAm1WEKlbk/AzAhdPELLQvJSfJcmwZK3wTHHEbKrQ4JSbqkUg391e05IEosjiSKRgkPkzyEGsaC9JiOl5ZBSrZDpUD10qME8aJeJSHD+EywZQhwybw45qAh85GeydCvHbg7dNIce3EQbTEA2ZP1f/bDB2lMaBNZ1v0mO0jaHH+B8qw90ZCrFz/KUAsUPAuuKa4AU22ZWzSkOMMbKw7wzjaJneWpxogeBVT2wqZVa28yuN7UBxll1kBOmUOwszylM7CCwqgeXe0ptE1VrSgOMteYQp722zFmeWZTMQWBVjy/zZLomttDjrxfrDXD63Mmb5YiK5A0Cq1pkgafRNY9UmcYI4602vFkvLGyS48oRNgisaqmlnUDXPFhiAiN8wFqjm/e6suY4shpZg8CqFlvY8rvm0Qrlj/ARWwZomWXZwMUwRU3yYDEjAxh7Go5nysK+fL9/cfYE2uZOgfdHKX6Ej1hpcP35+XX7eO4PIElzPJKfwwMYfSKOZsqi/nh+PUKA3qlvwiilj/Ah2wXo54uOnvLbjy3riDFUyvgARp6Iw5mwqNXuyqQAld424+VNGqXwET5kuwC9PF3r/25WR4yhUsYHMPJEHM79Ra36pDh+gE4bpfARPmSdsfW96uXp66a3+KUH6GAl4wMYfSoOZtKSnhigstvmbnEE6Eavqo8g3hI4CDp6CHR4AKNPxcEQoDUCdKNXJUBxGARojQDd6FXZhcdhEKA1AnSjV63eg/nasI4YIwE6NoDRp+JgCNAaAbrRq6ZyGtNgJXdPYxI0CKyLAK0RoFu96uh56HLmeLiSeyfSCxoE1kWA1gjQzV517JOQcuZ4pJLxj3JKGgTWRYDWCFARrypnjh+oRM4gsK5Fl7TotlmiONEDfBAB2kaA4i4CdOvXkIoAbSNAcRcBuvVrSEWAthGguIsA3fo1pCJA2whQ3EWAbv0aUhGgbQQo7iJAt34NqQjQNgIUdxGgW7+GVARoGwGKuwjQrV9DKgK0jQDFXQTo1q8h1boBWlQf3cmzrP0Z8vAmOXPsVVJfL6vnwll998kZBNbVLGm3+OsPqfV+Wq39oEJo7/eoiqtX16K7KvetDf4qI3qAD1o1QIvsqppGtUz++tN9nWatdZOcOW4qqa+X1XPhrN775AwC66qXtFv89dck9H5fQvtBuUogkb3fwxVXr66t2q3u2hCsMqIH+KA1A9Q2UvH603wFnP0yo0r7JjlzXFdSXy+r58JZ/ffJGQTWVS1pt/jrL+rq/cau9oPs9yLmb79aLyaSLa5eXdu1G921IVxlRA/wQWsGqP3qzMJ1Uxig7ZvkzHFVSX29rJ4LZw3cJ2cQWJdb0tXir6832Hfhwc6D7AZcUaes6LbxitOra7t2rbs2tFYZ0QN80PpvIuVuJovukRPvJjlz7FVSN0HPN8703SdnEFhXs6RdNrqLFQxctSB8kN1ATS9AdcXt2qu7OmsDAbrQq+rjoDezTd++FEZwk5w5JkBxVytA68tlDVw3K3yQ2w2uDySKbhv/iNa12ozO2wdBCdC1XrWs35L8eA4PnIQ3yZljAhR3PRSg7o2YxALUra6t2h0CdKWXLbyNzNF9eEFz3Fo5gh9uY/cJGgPW9dAuvDkn6O3vv/1ov5ZIrX34sPb6HgJ0lZfN/f32zskP/k2C5pgAxT2dAHXXGxy48GD4IHtbWfWN8LbxyqtX17K9PhCgq7xu4SY8fDu+7yZRU1wXQ4BiQNgj46cxtR9kb8vfW68klS6wtbrm7RNqRgNU/AgfsWaA1mdzmNYJ92taN4ma48gAFTUGrKvVI+Mn0rceZO6Xue3QRxdYr65h7TUCdI0X1h/kzOwHv/Ks8y68f5OwKa6P4BKgGNDqkfGPcrYedHlqzjNPoGtMidXq6tfeGAvQBEb4gPVGN+OVxU1xTEHiBoFVLbO8k+iah4pMYoTxVhze5JcWOMUpf50UtnGi7yl6oMxERhhtzfFNe+1M5BTPLErmILCqx5d5Ml0TW+jx14tVBzhh+sTO8JzCxA4Cq3pwuafUNlG1pjTAWCsPMRudw/F79zaxOtmDwKqy6KWfXNvMLTi5AcZZf5BZb5P13yrNnSrTGATWNbsJkm2byYWnOsAIG40za9vm1y6iU3uKg8CqhnvkcG1z/BHOcqaxAsCiCFAAiESAAkAkAhQAIhGgABCJAAWASAQoAEQiQAEgEgEKAJEIUGDc50tmrx6bZ82FZcuerxX26C8TH31A88Dmi8b1lxZ3rhsG0QhQ4I7CZuHHsxd24wFqL8YwIUFL70oNuXkSCZqUcwfoZtsWSNnlycRamXnXAhrtEhO1Qd4O8K9ro37LVd3QuR4IJDt3gG61bYGkqb+zOtbsX1mdeer/dZeotvmq+qXwotD1U/B4o6y+bcNtZubZt79k1+5vQjJOHqDbbFsgcYWOQBVuX9V+9tuvVoDam6sFrh5aNVH1ePOPToBe1SO9LlHt2OwJIQUnD9Dtti2QsMuT+gN7eVLdYH7S+y1hl7j76r+8+tqVphfqxw+8cidAO1cMhmgnD9DNti2QKv31lmZZFm7v2l7YN+ySIlz6N9cd783jB1693SUua8/1nZopO/ty2mrbAmlpfTmw+jv7b/NXVv8BzaYEqNlZ+fajfry5qf1nttslpqv6KoBMZ186221bQL7B0FJ/Qf/5rBd1qTuh+2e2CI9d2mM/Ogzrx7vbRwLUPKkJ0AlVYX+nXyabbVtArPsBpRbmf5o/mjoLzclvrkvedTPo/RS14Jt3H9U/3/Vjv/2oHz/8wsFpTCO7NJMKxcZOvyi22LaARLM27NTfUbNp6Jaz7RL3NzQ4Um7fX3R/dt+bxw+8rusS86zwaPtytWNFp18AW2xbQJC46KlPMFLR+PYv9efVtITqkOztD9Mc1Wlr7iMZZZWF1eMHXtcPUBO7cz+IRJLui3lfedsCIkjfZCsePn9e+ggPitleedsCO0omVD6eF+yVZEZ9BMwxDie9AMnX+QBnehORHKYWB8GG1zDmZi1MKNJGNMzCdC3rxPO4URPRqmtgk+pRzOAizjp7W48NSGEAACAASURBVPYNTboUVvo1MKsPOOWc7dAqdOcDWME3wkTPdr6p2q096Mt52DDaD3M/1ckmaOeOoCHvY9UVhcUx7kzzIqILRBQhD5s80rGEep1mNgQteEGl7IyVMkUsNc855kDcshZX0KZYAQ+CBXmGABW6fIWWtR42XI7rvMv26AMWvUhFF7eU065a53S2xX3ocSawGBMoMcp5N0lgnaQDjju6ZJZcMoXed5KVBrMcuisONKZs2N6lDUmn0paRuU5tKFjT4Rsl7eob48tB5FLqLUpkpS0Ta0xhKFjTGRol4dI9E5aAtIU0XI+0SlvmlCd8KFjTORol2cJ90wYhaiGN1iKq0paZpUkeCtZ0kkZJtOzA5DHIGey9SuRU2jK/MLFDwZrO0ihpVh2Ys6ewXhWzTDjisEEVEWLKEjoUrOk0jZJk0YFZI5Ax3ClVyKi0Ja4okUPBms7TKCnWHJh7qGWdKmaZeMh25SoixJYkcChYU+QCT7FPUqw50DcAfen2gevEShhvt4bL958THrW7wZJGJnz0eTimkQXe1+pTnidVgiUH+vPz6/bxLDZBuxV8PL/2dNX+lbaM5OfIhI8+E0c0srj7W33CE6VKsORAT/2fL3pVLr/9mPqEjXUqUNtvSQfo+ISPPROHNLy4B1r9/hPFSrBkX1/5l6dr/d9pz9hUpwBVaZF0gI5P+NgzcUTDS3uo1e8/U6wES/b1B+jXTe8rpBKgSuoBOjbho0/FAY0u7NEATbBP0qs4MHQI9DZ4TG73AR8vQMcnfPSpOCACNB0E6IYIUExBgKaDXfgNsQuPKQjQdIy9ifQ1+RmbOmKAjk346FNxQARoOvrKF34a0/EC9P5pTPLGgvUQoOnoLV/2ifTHC9D7J9LLGwvWQ4Cmo7/8sU8W7j7gAwbovY9yChwL1kOApmN++bsPeHIBu1fa9kBB4saC9ZyqT9KrOECAbuhUKwainapP0qs4QIBu6FQrBqKdqk/SqzhAgG7oVCsGop2qT9KrOECAbuhUKwainapP0qs4QIBu6FQrBqKdqk/SqzhAgG7oVCsGop2qT9KrOECAbuhUKwainapP0qs4QIBu6FQrBqKdqk/SqzjQlO8uVtX/mZj87Vf3GTvxCmhdYOvylBlfnQfKUBVUz3HRnWx//iXNOrbT7fCRtfLjOfPuTK9P0qs4UJfvLlbV/6nsMhO0KjcF9F5g6+O5qnX3SttcQfUcF9lV/SOY7FIVf3l6d48TNOvYTqfDx9bK8Dto0uuT9CoOeBtFelH1fy+Q+iMnaFWuC+i/wFZeF797pW22oM8XPZnFtx92lQg+22y/E9TeJGvWsZ12h9cdEzzK9Uf42fj0+iS9igOu/OpiVf2XNyve/ipoVa4K6L/Allf77pW2tQLUfgFosF74f7pkzTq20+7w/gB1/ZG/9z01HelVHGjKdwHa893ol99+SDoa5xXQE6B5c9PulbYFu/DVjOb+GIrXfz67A1rCZh3b6XR42DGW64/Pl9+zLJO70XBXehUHWgHad3Wez5erqLczRgPUL333StuaLYum5YvM/2NVZGozwxxHkTbr2E63w/2Osar+MA1vj7y1npqI9CoOTAjQQi0mSavyaID6+zm7V9rmCspNSL66t1eDPTAbp3pHPpx1cUPBijod7ndMdUfQH9WhnwT7JMGSA3X9Q7vwaldB2Ak1rdAPeIUKqLTFFmSP0rq3i1rbFTb/1Z+x1qyLGwrW1Dmw1nSM0+qP0p26l2CfJFhyoB2gncubFfbcSkHvbY8EaLDtvH+lLbYg2+xmrytv5afbklCPaM26uKFgTb37hc1++q2zVhKg+6kGUAyfxiRtWygMfZ8f/RIqbTElNdsTRda+Dqe9r3TDqmdd4FCwpr7Nmu5lr3Nz0vDXrVkREmyUBEsOBQE6dHmzVAK0lHwItCqpOqLVPltM0yPS7w/YBxKgJ9Xq8J5joJp9F9694xg8LSEp1hxyIyiqdzVGP8opY7hh6Hu895BkVNpii9L7X2pC2wdHjNI7KaWadZFDwZpaHe46psX2Ry74w8sTpFhzSzb96zmkjPZuIWIqbYmoS+pQsKbTNEqSRbdNG4SoBTRai6hKW2aWJnkoWNNJGiXRslsmzL60BTRcj7RKW+aUJ3woWNM5GiXZwlvuLAGJC6i/JomVtkwtMYGhYE1naJSES28ZWQpSF1C3LqmVtkwpM5GhYE3Hb5Ski2/Jhuxd2LB0Km0ZnOv0hoI1Hb1REi8fAPZDgAJAJAIUACIRoAAQiQAFgEgEKABEIkABIBIBCgCRCFAAiESAAkAkAhShj2f7Cbvu11I/pmi+OPdmL3S79G/A5h5tlsv39tfUB/IV+nBhBChC1TrR8xXij7DfX18laLlKRmNrDzZLmXWu8+HLE+gSAhQhtU6Y63xlnUvzPfiqV7VCuPXs8yXT16QbXXuQgAebZTxA1V7Kl3rIon24OAIUIbdO6P+zP+ouV4n3j5fs29+es//77LYJ9E646W2zFWJu0luZ1QWRyurLduxG5+VJPbZeX8y/kD6vWewG49svd1Oevaul/F/PqkdUp5jl7tpDPeDPl0zflLc2MFs9Y9rFpKhgBChC3kZFEKDK6z+bQ15l1epuL+692uNyCdq/MrjcVP/6D+n7ZpjA3wLN3b58rhesvkP/ia2oXY+qPardfv3I0QB1t8n+W0uAIlQf1nq/BQGq+1jdYNYEk60mMl9/mg4v1O2XJ5OR/Ttl4dZEuc77VNia1yzmr6M+LGNaoDQNoW4uMvMfd7P+T9VE5lH3juLYPhOMAEWoWieutzBA32/VDfq/ZRWodjtD31l0Nx8anQDlGOgReM1ys0d1TK/ow91X7ximXvp1ezRddT9A1WsJbxICFCG3V9b8WFYrhb7BxebVtr57a8hugoQBemcXXv3AgdD0ec1ij/Loxax2R/71XC3g+uD3hADt7MK7HR/JCFCExgO0uwV6s9ue334Uwbksd95EUjcToOnzmqXUi9rsVag/s/9T90I7QF17TA/QBPKTAEVLGKDmQKgfoGYLwz8GWlRbk26PrX+Xq3Ma0zu78AfgNUth20Qv4dxmYBigdXtM34XPB44HSUKAItTdKwsCtHr3p2i9C++9zdqrPpHepGg59lAkI9wCdbvw+kf9f2GA+u/CNwGqeykfOA2/ehdfdIgSoAh564QJx7c/ggDVp/CZ4KvPAzUxa1aBfCwUq49y2tWlJD+PwG8WtYDf/mX+7d5ybAVo1R5egOqb9NlM/QE6+q6kFAQopvPXl2iF7PNS8LBF2iQRBCimW2LN+Hhmy/PQymzp71GQjADFdEsEaM4G6LFVn9w8BwIUACIRoADmUzvqB/1ls0itC3vYo08zuSsHBuyxzIT2icSasIc9G1TmuoFe9IlPXEHYw/6dKXQDA4H9l9L+FYREFYM9yGlJMYWgj5jFI6aQGwF6dpJ6UZOT5vBJWy5i6pFRBfYgpglbhJZ1XkIXiIiyBJSAHUgNT0d4eScie0nsX53gycFadu+6SdKo8tCSWAT7FpnABGFJ+//NniGpYg8mpbnfsdZk5ggLSGidqKVYc/ISnPSdSk5unhAppS2KloRLT1C6s73LB6S2/oXYVNa2d0FzdIpPcxjiHWGa96o9oSnCPP1dlMp6cafMREYh3p12SKNb+ovcpnT5s4MI9+Nns1IiTGx94aMQb2rCiJ7nu38A1v79K78+djCla+SuFHMqkzsK8WZNndR5nlDXyqULnRg8YOIyFbpSzKxK6CjEmzttIqd5WlGrtojIecEjpi9SiQt/fk0SRyHeIaZ5ckkr1i5wWvCYOXvA61URKaYieaMQ7xDTLKLRxc0KHjRriUpb/HH1SBuFeIeYZhmNLmxS8Kh5C1TY4o8tR9gwxIucL1HTPPdY+TpVyJoTPK5vgeordQ9cTFjW8h+p5vJ95FK5skYh3iGmeaCYoQEQoJiiPz+/bh/P/QkqavmPFPPxPHqtcVHDEG94ttKZ5oFShgewUu2CpgQL6Fmeny86O8tvPyY+fj/Dxaht6FTW7AQMzlZC09xfysgACFDc17c4L0/X+r/TnrGXwVpU8cXomi1qGNIdYpp7KxkdwDq1y5kRLKA/QL9uet8m4QBVklmz5TvENA9VQoDiAUOHQG9JHAQ9xJot3yGmmQDFCghQ3HWIaSZAsQJ24XHXIaaZAMUKxt5E+pr8jL0cYs2W7xDTTIBiBX2Lc/Q0JlENcIg1W75DTDMBihX0Ls6xE+lFNcAh1mz5DjHNBChWMHh68dBHOUU1wCHWbPkOMc0EKFYwf3FKaoAHapE0DOkOMc1SOl3OjGABUtoqziHWbPkOMc1SOl3OjGABUtoqziHWbPkOMc1SOl3OjGABUtoqziHWbPkOMc1SOl3OjGABUtoqziHWbPkOMc1SOl3OjGABUtoqziHWbPkOMc1SOl3OjGABUtoqziHWbPkOMc1SOl3OjGABUtoqziHWbPkOMc1SOl3OjGAB1eIsqlPne86hD2+S1ACulo/nzJXYrX7oPknDkK6ZK3cBoZ4mKZqb/KsMyZnmTqc3/Jvyt1/tZ6xTBw7BLc4iu6q1QjVRqfrn8hQ0WOsmSQ3gaqk/tt9XfX1f+PlUScOQrp4rdwGhnmmuG6h1lSE509zu9IZ/U5kRoJjBLk4bLMXrT/sddsGn29o3SWqAaqVwxfVUX//r80WvGUX9DSmShiFdNVfuAkK9TfJe3RReZUjONLc6vbnDv0ntrxCgmMEuTvvVdSpder6CqX2TpAZwteRug6LvC6Sq+wjQeG6uqgsI9Uxz3UDtqwzJmeZWpzd3+DcVb38lQDGDvzjz15/F6z+fW4eI2jdJagBby+fL71mmdsM6pfr3uV34evWQNAzpmrky2dgzzVZuk1NygFp59wtEzE2X335wDBRzeItTHwoqMvWH2H4faHNzeJOkBvB2y3SFPdXX9+ktDZuk/lMxRTtAu9Ns73TTKz5Ai6xzsQVz0+fLlTeRMEuzOM1hdNtawT5a+yZJDeDXoirsqb6+75abtV7koVzpOgHaO831WzPSA7Tsbj3bmwoVngQoZmnO7jDvDJi1wl5VrrojvEnU8g8CNPvqqb6+z16npL7Qk6hhiFfPlg3Q3mluNuu8ABU0zc0YBrY/9Q68fxrTSrULmhIsoHofxnZV2V03ynQCtKf65j5za73jKWoY4oUB2jvNeRNLsgM07+anu0mfDqpUW9YEKKYwC7Rwa4PdTiv9Y+ytm2Qtf1ONexv19Wdv9cF91RaorFGIFwZozzTXDVQ/KHyeBLaYovvnNbip3gJdq3ZRc4LH6QVqVwlNN78+lu4JbhK2+E05ZrPSVNitvrkvOAYqbBji1Qd6zPx1p7lpoJvsAA0KtcKbCFDMlAU7L2WWtfdx/JukLX5bT64qNFsRPdXX9+lBurVD2ijECwO0O83B3m8hc2/FlNPaTb91bsrXbhFhk4LHzVik8pZ+TEXyRiHeIaZZRKOLmxU8avoilbjwpXzLzsEdYponl7Ri7QKnBQ+auEwzmct+ZlVCRyHe3GkTOc3Tilq1RUTOCx4zpWPkBs+cyuSOQrxZUyd1nifUtXLpQicGj9GH0cfv3qyUCHeq9x62eilHNnGaZc/z+CDWL13w1OAxWW9v9d8qz/0/ASmMQrw77ZBGt/QXuU3p8mcHj8ja9i5ojk7xaQ5DvCNM8161JzRFACALAQoAkQhQAIhEgAJAJAIUACIRoAAQiQAFgEgEKABEIkABIBIBCgCRCFBs6+NZf86ucyXa+y7ff95/UHCRxjzuFwGTEaDYlLviQvY6JQ195aSnlN7FKfIsMqrTdnnK6oud9NDzaOfS/4uknjRpiegX1zP6+ZLVv6X+m6Xu7Fzi7egIUGyptOtfMT/YJgWozswqQM3qXAbXyzmD3P2FGoqyOkCDCS1GnhE82f1NMiltA7T5m5VPeo1jIUCxIbXhYoMzfzc7819VMOZ2dVT3/+NFZ577t3rIny9mczX31tw6E8ssTIs8+/aXOkDNC59uo6gwk6GGPbQNWuemH6Bq3n9v/qSVQ89VD7uq32DSt3p08zernBbCx0KAYkOXJ2+D0AtQu9n09svuGb7+rP5tD5jqn1yAlkFgdgL0alZxz9m2QKvxF/5fo6LKODWJb3+4LdDqL5JxeXr921Pwd+mr/smb4GbxFc1WZ/U3yywrAhRYT5BnTYCaFVNv2XyaFf5W/1s9RCVBXu9xqn+/3+y/+7UC1D7+RPy/UOFfo2u9d98ToEX27s+cyUJ9XytA1fP+w95RP7v5m1Vk/+Nsm/s3AhSbKuuL1dt0rHfhza65CVC3Ttt/ew9x/9HPt7f2CgNU/Wv2m1Vp8/9C1X+NzKEM/WdKTa6ZkvYxUHXjlwpAf88973ujz+Xpu8tm+wQ35Zent78ToMCa7CHJToC69dH8oFfG+t/dANUrtbq1OeoWvmMSBKhLkDNpBah7w87OkZ28vjeRzHZrcHjl1vuunXm/qKh2GUo773bKP1++/TjdAecbAYpN1VuYRZCOZlUsmgCt/31nC3Q8QE+Yn+1deD0XEwK0eoi38Z67ff3WLrwftO7vmP01+l0lAhRYlzuNSa17Jh3f7U8uO82bSHadd/9uB+isY6BnPKum2jgv1QzVk+l2zavjJ50AdRv8zdmj5iQl95csfBNJ/aADtFoYzRZodfbUuQ45E6DYWLWxo1a6ar2tN3T8LdCeXXi9dhatLc429wK5ygJ7quLZQrQ+jameTHc+7MgxULflWO/+l9nAprvZgbC78Oql3eMJUGA73kc59Y/mtBq92r/9S4Vl846u/XfrVFG1hRScB9rlBWi967rNuKRoTqSvJrP/XXj3F8nOlInS5tDy4OeYyvClzMObjX524YFjKM62JdSoP8pZJ1t9rrt/Hqj7i6QC9N/uwLQ5aHLnxcvqpepzSwlQ4Gg+nq/3HwQ8jADFAeXn3QDFpghQAIhEgAJAJAIUG8qy7Rsu2+OXSrDZuM86wdp5R46N7Rlk51vFNx7x+SbYOemwsbH9V7AzbYjuMtQTza/njGPGtuREl5hCVrTzhv7xJzh0tvFiY9JWqWOv4wIGJ6CELZ1qsNiW1LASWtajxAxLTCEbOM9IsSmp4ekIL28+YeMRVs56TjJMbCqN1SeNKqcQORKRRS3uDGPElpLatkuq2H6ShyC5toUcfXzYVIorTIo1VxKoPYESH3HowWFLCW9upFl6MkUnU2iE444Ma8ru2rvC6dIqPKF5PkBv3HWksWArU1aBVFaTTp2iC+8WJ7bckcLE1jzfcUaCrUxt/wRWk/6tIbGF9xcmsdx7m5kSa45ylHFgK3NaX/hqMlyeyMLTKfdIeyh3HGMU2MzMhpG8moyWJq/wdMqduoeybhXbOMQgsJWI9VTUqu25W5eswtMpd3ohYkp+wAGGgM3EdYvIHptSlKDC0yl3VhUySn5E+iPAZmKbRWCTTStJTOHplDv3EM86VWwn+QFgO4PNoq8WPnIdTIFN1i3p8v3nhEftpF1I/4RLKHeghr7ZHXl4OpIfADYzkp9ft4/nlBK0W9DH82vPKi6k8G5+9k/4/uUOVNA/uyNPSEbq9WM7Q73y+aJX5fLbj9nP3E2nILVJl06ADk74/uX2VzAwu8NPSEfq9WM7Q71yebrW/533zN20C1LFF+kE6OCE719ubwVDszv4hISkXj+2MxygXze9lzYcoOLarKee/lVcRuGdAB2a8N3LHSpgMED3L/kxiZePDQ31ij4id0vrIGjaATo84buXS4ACAwjQvRCgYiVePjbELvxe2IUXK/HysaF7byJ9zX/qXlIP0KEJ371cAhQYEH8ak7g2SztAhyd893IJUGBA/In04tos7QAdnvDdyyVAgQHDvXLno5zy2izxAB2c8N3LJUCBAQ/0irQ2m1yPjMLTKXd+AbuX/JjEy8eGCNC9pFMuAQoMIED3kk65BCgwgADdSzrlEqDAAAJ0L+mUS4ACAwjQvaRTLgEKDCBA95JOuQQoMIAA3Us65RKgwAACdC/plEuAAgNcr3w8Z/ZzMPUPjeam8LMy0tqsqadztTOJhdsqLk+ZEXyHiLByqwKKLGt/VL9oKvUnffeSH5N4+diQ65X6Syx6vs2iuS/8tLa0Nqvr6VztTGThXhUfz2+/vHuklesKyFUflGHSF9lV3WQqDSZ995Ifk3j52JDrlfpjzT2fb65uan9fkLQ2q+rpXO3s80XnUyGscK+KPPirJW6eq21l/X17uR/1NuVNf4STvnvJj0m8fGyo2rqotnfy7tdZVDe1L3smrc1cPd2rnUkP0NaV5MTNsy3AbnwWftbbby/VN7UmffeSH5N4+diQ7ZXPl9+zTO2ONT806pva35kurc2aetqb0XafuN52klF4U0Uelitunl2Amugsuod4XPkEKE7I9orZF9O7jvUPjfqm9lV7pLXZcICat2quPQ/ck3fINtzqFzfPwS581v7K/MLNLAGKE/J75c47Sa0VW1yXDQeoPsb4+VLdKKTwuoz2Rp24eQ7eRGoHaFm9C+9N+v4lPyb1+rGdIECrlaPsbGbom1q7luK6bDBA7baTtMLrMoL3ZW6dXfj9y60qyLPs7e+/hWlf1Fv2BChOaFaABpc9E9dlgwFqh1MfmBBSeFVG5zIe4uY56JFwavPmyAgBijMyzeLeTn39Wf/QPKC+KTy9RmCTNTvFY1ugYgqvzxpo/bWSN8/+GVdB2hfeX9pm0iWU/JDkB4DtmGYx6+zny7X5odHcFJzgLbDJhgI0PAYqpvD2Zxhq4ubZ1GAqCo/XBudfEaA4JdstefVxwrz9uULvJu8jhiJ7rP7MYftdeP2JQ3ekUVDhtpSeE4PEzbPbTWl/QqGwH0O1AyiEvUn3gPRHgA3FtIvQFrtflqjC0yl3Rh1SSn7AAYaADR3o23buFSas8HTKTee7oxZwhDFgQzMbJhPcYKOlySs8nXIn1iKp5GiHGAQ2NGdVFbVadw2XJ7LwdMqdUo+0miMdYxTYUjat9yc+bFdZX5FyC++tTGS5vRMb3L1ZKes6yjiwqWyCvWucKq3CE5rnA/TGfQcaCgBsiwAFgEgEKABEIkABIBIBCgCRCFAAiESAAkAkAhQAIhGgABCJAAWASAQoAEQiQAEgEgEKn74WQ9a6dq6nzF5/luZiDZfvP/0ntS+M4cmri04ElwIxtxTda4IAKSFA4cndt+UMpVodoKUfmaM5aF/yvfrhy7ulGP1dgHwEKBqFiTO1QTm0DVrnph+gny/Z71nrguX1Fqp6sS/16G8/1A9XlZ3vzS0fz+aW4e1dQDoCFDWVhObas4XKNPXzP170RRT1ZqK5VW04vv3htkDzLKsvBqkS8fVvT+H1IossSFqTmfYXvDe3XPSTyrG9f0A4AhS1ixeDKuuyrIpKnaBu774nQIvsvYre5qnBdmVpL2frbdrqW1ySdi/VC6SCAEXN5ZzxaTY/9dblT/MfFX7v+sbuMVB145cK0SYaO8c11b66CVv1Gu4XmFuCjVMgRQQoaq0A1aFXVO8q2cTsexPJbEM2G5L+i9QvVT24sD/ZWwhQJI8ARa21C693yicEaPWQa/Uizc/VK9Uva3+Du4VdeCSPAEXNvC2ulCrY6gB1u+ZlnXmtALUHS/2jnuEx0Co/m7isbuFNJCSPAEWjPo3p9acLUHfO0cgxULcPHu65N+/C6zefvtzjrnYXvrqF05iQPAIUnuZE+up99f534c1bRe8m/dxhzWrrteKdB+pesXql5hZOpEfqCFD46o9y1icm5X3ngdp//VIB+m/7ZpN+fO+mZH0Qtf7AUvcWIFUEKABEIkABIBIBCgCRCFAAiESAwtLv6+z4u/f61cAjaFzcJCTYnvkNxKJpT09OdIkpBJiIjj03aZklJ82BCejW85IaVkLLArpo1XOSGp6O8PIAhzY9oTTSKY0qcW706MkktW2XVLE4I/rzTFLMoxRrxmnQnGeR8NZcwqXj4GjMY8va9i5ojk7xaQ4DB0YnHlZ/0CQSP/fKTGMUODy68Jjuxs9mlUSYWJ7wUeAMaMEjmpAscsNnTmVyR4FzoAEPaNpCFRo+M6sSOgqcBO13PJOXqcSFP78miaPAWdB9hzNnD3i9KiLFVCRvFDgNmu9oZi1RaYs/rh5po8B50HsHM2+BClv8seUIGwbOg9Y7mL4FWmaZvXj7tIfvZ6Say/efUc8D1kTrHUt/fn7dPp77E1TU8h8p5uP5dSRAZQ0DJ0LnHUvP8vx80dlZfvsx8fH7GS5GbUMToBCIzjuUvsV5ebrW/532jL0M1qKKL0YDVNQwcCI03qH0B+jXTe8DJxygCgEKiWi8Qxk6BHpL4iAoAYrU0HiHQoACW6LxDoVdeGBLNN6hjL2J9DX5GXshQJEaGu9Q+hbn6GlMohqAAEVqaLxD6V2cYyfSi2oAAhSpofEOpX9xjnyUU1QDEKBIDY13KGl/m+YDtUgaBk6ExjsUAhTYEo13KAQosCUa71AIUGBLNN6hEKDAlmi8QyFAgS3ReIdCgAJbovEOhQAFtkTjHQoBCmyJxjuUanEW1WePOh9CujxlxlfrGRJUteRZZj65//Gc9X2GKn/75T0ofCqwKRrvUNziLLKris73wY/BfzybDPKeIYKrJX/9ab/EtP8LUMpMF18/KHgqsC0a71Ds4rSRWbz+HPoipry5RVID2FrMF++Zyns//642S1WANg/ynwpsjMY7FC+CbsW3HwPXk/NvkNQAXi0mG/O+b0Ap3v5abT4ToNgbjXco/uJUO7kDX0afe1t2khrAq0Wlv8rH37Msa4f/bz/yKkALmRvSOBEa71D8CDLHQfsuhxT8W1ID1LWUJjdNnd5Wpvb5cnVvIrkHtZ8KbInGOxYvg96HridXSH332iumeZsrPIJbqJvrLdDmQaKGgROh846lOY+puRBSexe+DqCbsOXvF1OnvPdWu9mB9+uvHyRqGDgROu9YhLXoJQAADoVJREFUqjOB7N5t7/XkxO7BB8XUuRkEaGFPYm2Hq6hR4ExovYMxC7RwwdJ7GpOfp8IWvynHO4fA/NA5lymvTmOqt0CFDQPnQesdjF6gzWlKfSfSl1IPgbpyTOrrww7mB/2uUYsO0PpB9dOAHdB7R5MFO7o915MT+x7Sraonr85eyr3PnDbqj3JW78JLGwXOg947nGzyMp3+yM1ElCRwFDgNmu+Api1UocEzsyqho8BJ0H5HNCFV5AbPnMrkjgLnQAMe051kkR08U6uTPQqcAS14VCPpIj94plQofxQ4PprwuLIhexc2xWDxSY0CR0cbAkAkAhQAIhGgABCJAAWASAQoAEQiQAEgEgEKAJEIUACIRIACQCQCFAAiEaAAEIkABYBIBCi2cnnKssy7pHJLmb3+1P9TD/z+039S56pyfbwrfJhLOpfNZU30730ffzYQhwDFRnL3LUrdixxZdYCWfmQWI8/ovPjVvk4YoPYnEhRrIECxjcIEodoaHNoGrXPTD9DPl+z3JvzKoeeql72qENXP8zZF1c/v+hWu6pdP2owFZiJAsQmTY0phrkmc/eNFbxwW3uU33/5wW6C5v8F4eXr921N9GdGy3hwts2B79vJkNjVVSubZt79UAWpuuDx5VyEFlkWAYhN+jqkAVVxU6rRze/c9AVpk71X0ah/P7r5WgJrH5HrjNr/Wj1cP/jIp+h/swWMlBCg2UWZBgNo3d8wG4utPtQNudrW7x0DVjV8qRP0999wkbfvlzRtU9uY6QO3zXNSSoFgDAYpNtAJU51lRbUTaxOx7E8lst7Z3wsueAC2rt9ybAHX/b95T4hgo1kGAYhOtXXgdbRMCtHrItXmh3O3rt46Bmi1V87wqQN1vNMnNgVCsgwDFJj6e3UlGKuTqAHW75nbrtCdA7cFS7+xRs6futiv9AHVvF5l/1W9X2WeZWwlQrIMAxTbq05hef7qIM9Gmo2/wGKiLxHr3v8yy/iAsM7MFau50r+6OE9j/Zxce6yBAsZHmRPpqG7H/XXizdflu3lN3uVdtvQ6fB+o2VavEvN6895LK9kEAYDEEKLZSf5Szzrb6pHf/PFD7r18qQP/dbEQOfwLUyet32t2r25OYtJL8xFoIUACIRIACQCQCFAAiEaDYkH475/i/EudBb2Er+yUZGYqV0FjYwu7bgbsXgEOiqbA6KdklpQ4cBx2FVQnb8hNWDlJHN2E9MtNKZlVIEq2EdYje1hNdHBJCG2EFKeRTCjVCOnoIC0to6y6hUiET/YMlpZdI6VUMQWgeLCXZ7blkC8fuaBw8rvp6+MS6KRu2d2lIBJ2Ch4Rxk0723Kk0nYFgV3QJ4vWmjPzomZiO8geC3dEiiDWcL6KTZ05xogcCAWgQRBptHbnJM7MwuQOBBLQH4tzrHKGdNb8soQOBCHQHotxvHJGtFVOUyIFABpoDMSa9CbN6FbPFlSRwIBCC3kCEaW0jrrliCxI3EEhBayBCu23K+qrsY4/a3UhBl+8/o56Hc6M1MF83P79uH8/iE3SknI/n15EAlTYQiEFnYL5W13y+6Owsv/2487i9DZejtqAJUESgMzBfq2suT9f6v6MP3NlgNar0YjRAhQ0EYtAYmK8ToF83vRecbIAqBChi0BiYr9U1+hDoLYGDoAQolkZjYD4CFDBoDMzHLjxg0BiYb+BNpK97D9wZAYql0RiYb+ppTMLaiwDF0mgMzDf1RHph7UWAYmk0BubrdE3/RzmltRcBiqXRGJhvctfIaq8HqpE1EIhBY2A+AhQwaAzMR4ACBo2B+QhQwKAxMB8BChg0BuYjQAGDxsB8BChg0BiYjwAFDBoD81VdU2RZ+/ObRXBKvaz28sq2Nfaf/5+//TL/718mSdZAIAaNgflc1+QqPe1X2dWK7Kpuem89UAhXTV1jqZLy8tRO0DKzARpcJknWQCAGjYH5bNfYL2GqttcM+4H45mORstrLVlPXaL9/r/0Zzo9nG6DhZZJkDQRi0BiYz3aN3fgs/J14+5V2zU2y2qvKfVdj39dHqTve/qoDtHWZJFkDgRg0BuZzAWoCqOjGUC56C9RSNRav/3zuHAO9/Paj2qYmQHEXjYH5gl34rP09yvoYY/BAKbxqdI2FfgfMfpdp7fPleiNAMRmNgfmCN5HaAVqKfxfe1WiDPtyRL1R4EqCYjMbAfFXX5Fn29vffwl14b/tTWnfV5dga7cGH4DSCix5MT4AKGwjEoDMwn981Zfgudu7lp7TuanLf1Fh2A1SfIZpVJ7cSoLiLzkAEr23y4Bhi4ceRuOayBVU12mO4Zeer6LtboOIGAiloDUQwbWNOqAzfhLeZFDxKElNQU6NOSP2uUQsBisloDcRwURScbH5r7QIL7C1dklej/ihn92L2nQAVOBAIQW8gyv3GEdlaMUWJHAhkoDkQ517nCO2s+WUJHQhEoDsQabR1MrGNNbMwuQOBBLQHYg1ni+jUmVOc6IFAABoE8bK+gOm9UZRsWonyB4Ld0SJ4SBak0cRoEuBOpekMBLuiS/C4rLJ3IfNkw/YuDYmgUwAgEgEKAJEIUACIRIACQCQCFAAiEaAAEIkABYBIBCgARCJAASASAQoAkQhQAIhEgOJIPp7tZ9m7F+oIXb7/vJVZ53pyk+Tq9b+qH97vPRqHRoDiSKoAzdx1jQaY7IwM0Ny8/lf1Awl6agQojkQFqN44LO8E2/3sLIcS+PKkNm9z9fLqhy/1QsFVSXE2BCiOxAXorVAJaX/WWfn5kv3jRUddbrdNzbbju01RfWlRHYLq0X++NFcZLav9dPNTtdHpqNd7tyFsUhTnRYDiSKoAvTx9+xEEaKazMXd7916AllU4Vjv/1Zan+bfejO0GqErN6lFsgZ4cAYojqQJU/38QoDrndKqabdPmGKh6zLs+mml+Mtum3r59nrWve2+pAHWxaZ+O8yJAcSSDAepyTu+w+wFaVrvv3qO9lxs6VlrY29Xrxr2Rj6MgQHEkg7vw+rwmuyffClCdgOqR154AtVugPcdA7bbszW3Y4sQIUBxJFaBl+02kq7lR3VBM3ALV26rVs/wAde8dqaeRnyBAcSguQFX6vdsDlOo/dYAW9se3XwPHQP0ALbOBdDSnMZkUzjPegT89AhRH4p9I7/bYgy3Qehe+ehe+8N6FDwJ08Ez83H3UyWyiZoTouRGgOJLgo5z6H29/NAGq0/LtX8/uU0Rvf7bPA+2+idSrsKlZdA+N4nQIUACIRIACQCQCFAAiEaAAEIkAxeFk2UZtvdkvglQ0AI5l41AjQ8+NpY8D2SXOyNATY9HjILIdg2zP3409sdhxBAICTEAJ2BzLHMkTE11iCsFWWOBIm7DQElYOVsbSRsJExpXIorAOFjUSJfmNG8m1YUksZqQogYBKoEQ8jGWM5CQTTckUilgsYIiWTbB3jZ7EysWjWJoQbFraSAmliXVIKRcLYFFCrBlBI6GPZ9QgoVwsgSUJqWb15v5bdYmVi0WwHCHU3NbcuZUTKxfLYDFCpIhNtD236hIrF0thIUKiuL7c79uYNnwWJGEZQqDYttypnSN/LStf+liGEGiwLcssy94jnreukV97+T5ynXnWvuSxCCHPSH5+3T6epSXoyC/9eH4lQI+MRQh5hrry80VnZ/ntx+xnrmr4l6oNZgL00FiEEGewKS9P1/q/M5+6ouHfqSotCNBDYxFCnJEA/brp3eJUAlQZDVBWv+SxBCHO6CHQ2+hBUAIUm2IJQhwCFKlgCUIcduGRCpYgxLn7JtLX/KeuiAA9MZYgxBlsSpmnMRGgJ8YShDhj51UKPJGeAD0xliDEGWnKOx/lJECxLZYgxHmgKcUF6GpPhQgsQYiTWCIlVi6WxBKEOIklUmLlYkksQYiTWCIlVi6WxBKEOIklUmLlYkksQYiTWCIlVi6WxBKEOIklUmLlYkksQYiTWCIlVi6WxBKEOIklUmLlYkksQYjjNaW9JtvHc9bzCSR3vbbgw0k7B2h9CbnOteTyLKs+wu/dx+qXOpYgxGma0l2TrffrQ6r7go/H7xug9SXkOteSy9W/7beZBvex+qWOJQhx6qasrsnW94Fyd1/rC5p2DdD6EnKda8mZb+Bzpfr3sfqljiUIcaqmrK/Jlne/P6S6r3WduT0DtC534FpyJkDD+1j9UscShDheUxZ2K/P3LMs6X0PvAjT4kvqdj4HW2dgXoIXbTCZAD4QlCHHaiWQOcdodYJ+5r3WZJLkBWtZ/AgjQA2EJQpy+ROp5JymtANVFvv0K72PtSx6LEPI0XekHaNa6FJKUXfi+cnu/R9ntwxOgB8IihDyzAjS4zpzoAHUjIEAPhEUIgeq29LYyO5lUdE9j2qmdw3KDHyw3ArZAD4dFCIHCRDIh+fnSfhu+6J5ILzVAzQiq4wz1fax86WMZQqKqL13Y5FnW3oGv7/M+yrlbN7fK7dlczrPuu/CsfOljGUKkmMbcsZkTKxdLYSFCpvmduWsvJ1YuFsJShFAzWzPbuZUTKxfLYDFCqjkZIyCPEisXi2BBQq5sWtBMfNjqEisXC2BRQrRsgr1r9CRWLh7F0gSASAQoAEQiQAEgEgEKAJEIUACIRIACQCQCFAAiEaAAEIkABYBIBCgARCJAASASAQoAkQhQAIhEgAJAJAIUACIRoAAQiQAFgEgEKABEIkABIBIBCgCRCFAAiESAAkAkAhQAIhGgABCJAAWASAQoAEQiQAEgEgEKAJEIUACIRIACQCQCFAAiEaAAEIkABYBIBCgARCJAASASAQoAkQhQAIhEgAJAJAIUACIRoAAQiQAFgEgEKABEIkABIBIBCgCRCFAAiESAAkAkAhQAIhGgABCJAAWASAQoAEQiQAEgEgEKAJEIUACIRIACQCQCFAAiEaAAEIkABYBIBCgARCJAASASAQoAkQhQAIhEgAJAJAIUACIRoAAQiQAFgEgEKABEIkABIBIBCgCRCFAAiESAAkCk/wcsalOPBYJuzAAAAABJRU5ErkJggg==", null, 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", null, 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", null, 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", null, 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", null, 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", null ]

[ "# 11Q ​Q11. Study the given graph and answer the following questions          (i) Which part of the graph shows accelerated motion ?         (ii) Which part of the graph shows retarded motion ?         (iii) Calculate the distance travelled by the body in first 4 seconds of journey graphically.", null, "Dear Student ,\nHere in this case from the graph we get ,\n(i) AB = Accelerated motion .\n(ii) CD = Decelerated/ retarded motion .\n(iii) Distance travelled by the body in first 4 seconds is ,\n\nRegards\n\n• 1\nI) AB\nii) CD\niii) d=v*t = 4*4= 16m\n• 0\nWhat are you looking for?" ]

[ null, "https://s3mn.mnimgs.com/img/shared/content_ck_images/ck_5a41f6c2970f6.png", null ]

[ "## Tuesday, December 23, 2008\n\n### 17\n\n17 is a prime number. It is the third Fermat prime: 17 = 22^2 + 1.\n\n17 has a representation as a sum of two squares: 17 = 12 + 42.\n\n17 is the smallest number with four representations as a sum of three primes: 17 = 2 + 2 + 13 = 3 + 3 + 11 = 3 + 7 + 7 = 5 + 5 + 7.\n\n17 and 19 form a twin prime pair.\n\n17 is the hypotenuse of a primitive Pythagorean triple: 172 = 82 + 152.\n\n17 is the first sum of two distinct fourth powers: 17 = 14 + 24.\n\nThere are\n17 ways to express 17 as the sum of one or more primes; 17 is the only integer that is equal to the number of prime partitions of itself.", null, "Carl Friedrich Gauss proved at the age of 18 that one can construct a regular polygon with a prime number of sides with the use of only straight edge and compasses only if the number of sides is of the form 2\n2^n. Hence, one can construct a regular 17-gon with rule and compasses only.\n\nSource: Number Gossip" ]

[ null, "http://4.bp.blogspot.com/_Kom-mudcX5I/TDnUfXJ7AkI/AAAAAAAAByk/q2BQAf1FDyQ/s200/n0017.jpg", null ]

[ " 第十二章 位运算\n\n## 12.1二进制与位运算", null, "## 12.2与（&）运算", null, "1&1 = 11&0 = 0。那么如何计算两个整数的与运算呢？比如计算15&10，首先15的二进制为：111110的二进制为1010，所以15&10为：", null, "int main(void)\n\n{\n\nint a = 15;\n\nint b = 10;\n\nint c = 15&10;\n\nprintf(“a&b=%d\\n”, c);\n\nreturn 0;\n\n}\n\n## 12.3与（&）运算的应用\n\nint x=100;\n\nx&7即为x的后三位。因为7的二进制码为0111。所以，任何一个数与7进行与运算，那么其它位都会被置零。只有后三位得到保留。\n\nx&(~(1<<n))即可将xn位置为零。\n\n#define CLEARFLAG(a,n) ((a) &= ~(1<<(n)))//把整数a中第n位置为0\n\nx&(1<<n);\n\n#define FLAGON(a,n) ((a)&(1<<(n)))//判断整数a中第n位是否为1\n\n## 12.4或（|）运算", null, "1|1 = 11|0 = 1 0|0 = 0。那么如何计算两个整数的或运算呢？比如计算15|10，首先15的二进制为：111110的二进制为1010，所以15|10为：", null, "int main(void)\n\n{\n\nint a = 15;\n\nint b = 10;\n\nint c = 15|10;\n\nprintf(“a|b=%d\\n”, c);\n\nreturn 0;\n\n}\n\n## 12.5或（|）运算的应用\n\n#define SETFLAG(a,n)  ((a) |= (1<<(n)))//把整数a中的第n位置为1\n\n## 12.6取反（~）运算", null, "~1 = 0~0 = 1。那么如何计算1个整数的取反运算呢？比如计算~10，首先10的二进制为：1010~10为：", null, "int main(void)\n\n{\n\nint a = 10;\n\nint b = ~10;\n\nprintf(“~10=%d\\n”, b);\n\nreturn 0;\n\n}\n\n## 12.7取反（~）运算的应用\n\n#define CLEARFLAG(a,n) ((a) &= ~(1<<(n)))//把整数a中第n位置为0\n\n## 12.8异或（^）运算", null, "1^1 = 01^0 = 1 0^0 = 0。那么如何计算两个整数的异或运算呢？比如计算15^10，首先15的二进制为：111110的二进制为1010，所以15^10为：", null, "int main(void)\n\n{\n\nint a = 15;\n\nint b = 10;\n\nint c = 15^10;\n\nprintf(“a^b=%d\\n”, c);\n\nreturn 0;\n\n}\n\n## 12.9异或（^）运算的应用\n\na^a==0\n\na^0==a\n\n1，置零\n\nxor eax,eax\n\n2，交换2个数\n\n#define SWAP(a,b) \\\n\ndo{\\\n\na=a^b;\\\n\nb=a^b;\\\n\na=a^b;\\\n\n}while(0)\n\n3，单指针域构造双向链表\n\nTail->next = PL^NULL\n\npl=NULL;\n\nwhile(p!=Tail)\n\n{\n\npr=pl^(p->next);\n\npl=p;\n\np=pr;\n\n}\n\npr=NULL;\n\np=Tail;\n\n{\n\npl=pr^(p->next);\n\npr=p;\n\np=pl;\n\n}\n\n## 12.10左移（<<）运算\n\nint main(void)\n\n{\n\nint a = 10;\n\nint b = a<<2;\n\nprintf(“b=%d\\n”, b);\n\nreturn 0;\n\n}", null, "## 12.11右移（>>）运算\n\n12>>23\n\nC语言中，右移运算符为算术右移运算符，即左边用符号位来填充。\n\nint main(void)\n\n{\n\nint a = -3;\n\nint b = 10;\n\nint c = a >> 2;\n\nint d = b >>1;\n\nprintf(“a>>2=%d, b>>1=%d\\n”, c, d);\n\nreturn 0;\n\n}\n\n## 12.12位运算优先级\n\n位运算符的优先级如下图，位置靠前的优先级高于位置靠后的优先级。", null, "## 12.13常见位运算\n\n1．任何一个数和0异或是它的本身：\n\na^0=a\n\na^a=0\n\nvoid swap(int *a, int *b)\n\n{\n\n*a = *a ^ *b;\n\n*b = *a ^ *b;\n\n*a = *a ^ *b;\n\n}\n\n1）  将第n位置位或清零：\n\n#define  BITN (1<<n)\n\n2）  清除整数a最右边的1\n\n问题：如何判断判断整数x的二进制中含有多少个1\n\n分析：此题是微软公司的一道笔试题。下面用&运算来解决此题。\n\n代码如下：\n\nint func(int x )\n\n{\n\nint countx = 0;\n\nwhile ( x )\n\n{\n\ncountx ++;\n\nx = x&(x-1);\n\n}\n\nreturn countx;\n\n}\n\n 功能 示例 位运算 去掉最后一位 (101101->10110) x  >>  1 在最后加一个0 (101101->1011010) x  <<  1 在最后加一个1 (101101->1011011) (x  <<  1) + 1 把最后一位变成1 (101100->101101) x  |  1 把最后一位变成0 (101101->101100) (x  |  1) - 1 最后一位取反 (101101->101100) x  ^  1 把右数第k位变成1 (101001->101101,k=3) x  |  (1 <<  (k - 1)) 把右数第k位变成0 (101101->101001,k=3) x  &  ~ (1 <<  (k - 1)) 右数第k位取反 (101001->101101,k=3) x  ^  (1  <<  (k - 1)) 取末三位 (1101101->101) x & 7 取末k位 (1101101->1101,k=5) x  &  ((1 << k) - 1) 取右数第k位 (1101101->1,k=4) x  >>  (k - 1)  & 1 把末k位变成1 (101001->101111,k=4) x  |  ((1 << k )- 1) 末k位取反 (101001->100110,k=4) x  ^  ((1 <<  k) - 1) 去掉整数最右边的1 (100101111->100101110) x  &  (x – 1) 把右边连续的1变成0 (100101111->100100000) x  &  (x + 1) 把右起第一个0变成1 (100101111->100111111) x  |  (x + 1) 把右边连续的0变成1 (11011000->11011111) x  |  (x - 1) 去掉右起第一个1的左边 (100101000->1000) x  &  (x  ^  (x - 1)) 取右边连续的1 (100101111->1111) (x  ^  (x + 1))  >>  1\n\n## 12.14位运算在软件工程中的运用\n\nWDK中创建文件的IRP中，有一个Options整数，它的高8位记录了对文件的修改标记。因此可以使用下面的位运算来获取这8位的值：\n\nulDisposition = (lpIrpStack->Parameters.Create.Options >> 24) & 0xFF;\n\n#define SETFLAG(a,n)  ((a) |= (1<<(n)))//把整数a中的第n位置为1\n\n#define CLEARFLAG(a,n) ((a) &= ~(1<<(n)))//把整数a中第n位置为0\n\n#define FLAGON(a,n) ((a)&(1<<(n)))//判断整数a中第n位是否为1", null, "看文字不过瘾？点击我，进入周哥教IT视频教学", null, "", null, "" ]

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[ "MPE Mathematical Problems in Engineering 1563-5147 1024-123X Hindawi Publishing Corporation 10.1155/2014/142169 142169 Research Article Reliability Analysis of the Proportional Mean Residual Life Order Kayid M. 1,2 Izadkhah S. 3 Alhalees H. 1 Wu Shaomin 1 Department of Statistics and Operations Research College of Science King Saud University Riyadh 11451 Saudi Arabia ksu.edu.sa 2 Department of Mathematics Faculty of Science Suez University Suez 41522 Egypt suezuniv.edu.eg 3 School of Mathematical Sciences Ferdowsi University of Mashhad Mashhad 91779 Iran um.ac.ir 2014 2882014 2014 04 04 2014 02 08 2014 28 8 2014 2014 Copyright © 2014 M. Kayid et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.\n\nThe concept of mean residual life plays an important role in reliability and life testing. In this paper, we introduce and study a new stochastic order called proportional mean residual life order. Several characterizations and preservation properties of the new order under some reliability operations are discussed. As a consequence, a new class of life distributions is introduced on the basis of the anti-star-shaped property of the mean residual life function. We study some reliability properties and some characterizations of this class and provide some examples of interest in reliability.\n\n1. Introduction\n\nStochastic orders have shown that they are very useful in applied probability, statistics, reliability, operation research, economics, and other related fields. Various types of stochastic orders and associated properties have been developed rapidly over the years. Let X be a nonnegative random variable which denotes the lifetime of a system with distribution function F , survival function F ¯ = 1 - F , and density function f . The conditional random variable X t = ( X - t X > t ) , t 0 , is known as the residual life of the system after t given that it has already survived up to t . The mean residual life (MRL) function of X is the expectation of X t , which is given by (1) μ X ( t ) = { t F ¯ ( u ) F ¯ ( t ) d u , t > 0 , 0 , t 0 .\n\nThe MRL function is an important characteristic in various fields such as reliability engineering, survival analysis, and actuarial studies. It has been extensively studied in the literature especially for binary systems, that is, when there are only two possible states for the system as either working or failed. Another useful reliability measure is the hazard rate (HR) function of X which is given by (2) r X ( t ) = f ( t ) F ¯ ( t ) , t 0 .\n\nThe HR function is particularly useful in determining the appropriate failure distributions utilizing qualitative information about the mechanism of failure and for describing the way in which the chance of experiencing the event changes with time. In replacement and repair strategies, although the shape of the HR function plays an important role, the MRL function is found to be more relevant than the HR function because the former summarizes the entire residual life function whereas the latter involves only the risk of instantaneous failure at some time t . For an exhaustive monograph on the MRL and HR functions and their reliability analysis, we refer the readers to Ramos-Romero and Sordo-Díaz , Belzunce et al. , and Lai and Xie . Based on the MRL function, a well-known MRL order has been introduced and studied in the literature. Gupta and Kirmani and Alzaid were among the first who proposed the MRL order. Over the years, many authors have investigated reliability properties and applications of the MRL order in reliability and survival analysis (cf. Shaked and Shanthikumar and Müller and Stoyan ). On the other hand, the proportional stochastic orders are considered in the literature to generalize some existing notions of stochastic comparisons of random variables. Proportional stochastic orders as extended versions of the existing common stochastic orders in the literature were studied by some researchers such as Ramos-Romero and Sordo-Díaz and Belzunce et al. . Recently, Nanda et al. gave an effective review of the different partial ordering results related to the MRL order and studied some reliability models in terms of the MRL function.\n\nThe purpose of this paper is to propose a new stochastic order called proportional mean residual life (PMRL) order which extends the MRL order to a more general setting. Some implications, characterization properties, and preservation results under weighted distributions of this new order including its relationships with other well-known orders are derived. In addition, two characterizations of this order based on residual life at random time and the excess lifetime in renewal processes are obtained. As a consequence, a new class of lifetime distributions, namely, anti-star-shaped mean residual life (ASMRL) class of life distribution, which is closely related to the concept of the PMRL order, is introduced and studied. A number of useful implications, characterizations, and examples for this class of life distributions are discussed along with some reliability applications. The paper is organized as follows. The precise definitions of some stochastic orders as well as some classes of life distributions which will be used in the sequel are given in Section 2. In that section, the PMRL order is introduced and studied. Several characterizations and preservation properties of this new order under some reliability operations are discussed. In addition, to illustrate the concepts, some applications in the context of reliability theory are included. In Section 3, the ASMRL class of life distributions is introduced and studied. Finally, in Section 4, we give a brief conclusion and some remarks of the current research and its future.\n\nThroughout this paper, the term increasing is used instead of monotone nondecreasing and the term decreasing is used instead of monotone nonincreasing. Let us consider two random variables X and Y having distribution functions F and G , respectively, and denote by F ¯ ( f ) and G ¯ ( g ) their respective survival (density) functions. We also assume that all random variables under consideration are absolutely continuous and have 0 as the common left endpoint of their supports, and all expectations are implicitly assumed to be finite whenever they appear. In addition, we use the notations R = ( - , ) , R + = ( 0 , ) , = s t denotes the equality in distribution, and X v is the weighted version of X according to the weight v .\n\n2. Proportional Mean Residual Life Order\n\nFor ease of reference, before stating our main results, let us recall some stochastic orders, classes of life distributions, and dependence concepts which will be used in the sequel.\n\nDefinition 1.\n\nThe random variable X is said to be smaller than Y in the\n\nHR order (denoted as X HR Y ) if (3) G ¯ ( t ) F ¯ ( t ) is increasing in t R + ,\n\nreversed hazard (RH) order (denoted as X RH Y ) if (4) f ( x ) F ( x ) g ( x ) G ( x ) , x R + ,\n\nwhich denotes the reversed hazard (RH) rate order,\n\nMRL order (denoted as X MRL Y ) if (5) t G ¯ ( u ) d u t F ¯ ( u ) d u is increasing in t R + .\n\nDefinition 2 (Lai and Xie [<xref ref-type=\"bibr\" rid=\"B3\">3</xref>]).\n\nThe nonnegative random variable X is said to have a decreasing mean residual life (DMRL) whenever the MRL of X is decreasing.\n\nDefinition 3 (Lariviere and Porteus [<xref ref-type=\"bibr\" rid=\"B9\">9</xref>]).\n\nThe nonnegative random variable X is said to have an increasing generalized failure rate (IGFR) whenever the generalized failure rate function β X of X which is given by β X ( x ) = x r X ( x ) is increasing in x 0 .\n\nNote that, in view of a result in Lariviere , X has IGFR property if and only if x X HR X , for all x ( 0,1 ] , or equivalently if X HR x X , for any x 1 .\n\nDefinition 4 (Karlin [<xref ref-type=\"bibr\" rid=\"B11\">11</xref>]).\n\nA nonnegative measurable function h ( x , y ) is said to be totally positive of order 2 ( TP 2 ) in x R and y R , whenever (6) | h ( x 1 , y 1 ) h ( x 1 , y 2 ) h ( x 2 , y 1 ) ( x 2 , y 2 ) | 0 , x 1 x 2 , y 1 y 2 .\n\nDefinition 5 (Shaked and Shanthikumar [<xref ref-type=\"bibr\" rid=\"B6\">6</xref>]).\n\nA nonnegative function ψ is said to be anti-star-shaped on a set A R + if ψ ( α x ) α ψ ( x ) , for all x on A and for every α [ 0,1 ] . Equivalently, ψ is anti-star-shaped on A if ψ ( x ) / x is nonincreasing in x A .\n\nBelow, we present the definition of the proportional hazard rate (PHR) order and its related proportional aging class.\n\nDefinition 6 (see Belzunce et al. [<xref ref-type=\"bibr\" rid=\"B2\">2</xref>]).\n\nLet X and Y be two nonnegative continuous random variables. It is said that\n\nX is smaller than Y in the PHR order (denoted as X P-HR Y ) if x X HR Y , for all x ( 0,1 ] ,\n\nX is increasing proportional hazard rate (IPHR), if x X HR X , for all x ( 0,1 ] .\n\nConsider the situation wherein X denotes the risk that the direct insurer faces and ϕ the corresponding reinsurance contract. One important reinsurance agreement is quota-share treaty defined as ϕ ( X ) = x X , for x ( 0,1 ] . The random variable Y denotes the risk that an independent insurer faces. Insurers sometimes seek a quota-share treaty when they require financial support from their reinsurers, thus maintaining an adequate relation between net income and capital reserves. Motivated by this, we propose the following new stochastic order.\n\nDefinition 7.\n\nLet X and Y be two nonnegative random variables. The random variable X is smaller than Y in the PMRL order (denoted as X P-MRL Y ), if x X MRL Y , for all x ( 0,1 ] .\n\nRemark 8.\n\nNote that X P-MRL Y       x X MRL Y , for all x ( 0,1 ] , thus; with x = 1 we have X MRL Y , that is; the PMRL order is stronger than the MRL order.\n\nThe first results of this section provide an equivalent condition for the PMRL order.\n\nTheorem 9.\n\nThe following assertions are equivalent:\n\nX P - M R L Y ;\n\nx μ X ( t ) μ Y ( x t ) , for all t 0 , and each x ( 0,1 ] ;\n\nx t G ¯ ( u ) d u / t F ¯ ( u ) d u is increasing in t , for all x ( 0,1 ] .\n\nProof.\n\nFirst, we prove that (i) and (ii) are equivalent. Note that the MRL of x X as a function of s is given by x μ X ( s / x ) , for all s 0 and for any x ( 0,1 ] . Now, we have X P-MRL Y if, for all x ( 0,1 ] , it holds that (7) x X MRL Y x μ X ( s x ) μ Y ( s ) , s 0 , x μ X ( t ) μ Y ( x t ) , t 0 , nnnnnnnnnnnnnnnn where t = s x . To prove that (ii) and (iii) are equivalent, we have (8) d d t x t G ¯ ( u ) d u t F ¯ ( u ) d u = F ¯ ( t ) x t G ¯ ( u ) d u - x G ¯ ( x t ) t F ¯ ( u ) d u [ t F ¯ ( u ) d u ] 2 = F ¯ ( t ) G ¯ ( x t ) [ t F ¯ ( u ) d u ] 2 × [ μ Y ( x t ) - x μ X ( t ) ] . It is obvious that the last term is nonnegative if and only if x μ X ( t ) μ Y ( x t ) , for all t 0 and for any x ( 0,1 ] .\n\nIn the context of reliability engineering and survival analysis, weighted distributions are of tremendous practical importance (cf. Jain et al. , Bartoszewicz and Skolimowska , Misra et al. , Izadkhah and Kayid , and Kayid et al. ). In renewal theory the residual lifetime has a limiting distribution that is a weighted distribution with the weight function equal to the reciprocal of the HR function. Some of the well-known and important distributions in statistics and applied probability may be expressed as weighted distributions such as truncated distributions, the equilibrium renewal distribution, distributions of order statistics, and distributions arisen in proportional hazards and proportional reversed hazards models. Recently, Izadkhah et al. have considered the preservation property of the MRL order under weighted distributions. Here we develop a similar preservation property for the PMRL order under weighted distributions. For two weight functions w 1 and w 2 , assume that X w 1 and Y w 2 denote the weighted versions of the random variables of X and Y , respectively, with respective density functions (9) f 1 ( x ) = w 1 ( x ) f ( x ) ν 1 , g 1 ( x ) = w 2 ( x ) g ( x ) ν 2 , where 0 < ν 1 = E ( w 1 ( X ) ) < and 0 < ν 2 = E ( w 2 ( Y ) ) < . Let B 1 ( x ) = E ( w 1 ( X ) X > x ) and B 2 ( x ) = E ( w 2 ( Y ) Y > x ) . Then survival functions of X w 1 and Y w 2 are, respectively, given by (10) F ¯ 1 ( x ) = B 1 ( x ) F ¯ ( x ) ν 1 , G ¯ 1 ( x ) = B 2 ( x ) G ¯ ( x ) ν 2 .\n\nFirst, we consider the following useful lemma which is straightforward and hence the proof is omitted.\n\nLemma 10.\n\nLet X be a nonnegative absolutely continuous random variable. Then, for any weight function w 1 , (11) ( x X ) v = s t x X w 1 , x > 0 , where v is a weight function of the form v ( t ) = w 1 ( t / x ) .\n\nTheorem 11.\n\nLet B 2 be an increasing function and let B 2 ( s x ) / B 1 ( s ) increase in s 0 , for all x ( 0,1 ] . Then (12) X P - M R L Y X w 1 P - M R L Y w 2 .\n\nProof.\n\nLet x ( 0,1 ] be fixed. Then, X P-MRL Y gives x X MRL Y . We know by assumption that B 2 is increasing and the ratio (13) E ( w 2 ( Y ) Y > t ) E ( v ( x X ) x X > t ) = E ( w 2 ( Y ) Y > t ) E ( w 1 ( X ) X > t / x ) = E ( w 2 ( Y ) Y > s x ) E ( w 1 ( X ) X > s ) = B 2 ( s x ) B 1 ( s ) is increasing in t 0 , when s = t / x . In view of Theorem 2 in Izadkhah et al. , we conclude that ( x X ) v MRL Y w 2 . Because of Lemma 10 and because the equality in distribution of ( x X ) v and x X w 1 implies the equality in their MRL functions, it follows that x X w 1 MRL Y w 2 . So, for all x ( 0,1 ] we have x X w 1 MRL Y w 2 which means that X w 1 P-MRL Y w 2 .\n\nOn the other hand, in many reliability engineering problems, it is interesting to study X Y = [ X - Y X > Y ] , the residual life of X with a random age Y . The residual life at random time (RLRT) represents the actual working time of the standby unit if X is regarded as the total random life of a warm standby unit with its age Y . For more details about RLRT we refer the readers to Yue and Cao , Li and Zuo , and Misra et al. , among others. Suppose that X and Y are independent. Then, the survival function of X Y , for any x 0 , is given by (14) P ( X Y > x ) = 0 F ¯ ( x + y ) d G ( y ) 0 F ¯ ( y ) d G ( y ) .\n\nTheorem 12.\n\nLet X and Y be two nonnegative random variables. X Y P - M R L X for any Y which is independent of X , if and only if (15) X t P - M R L X , t 0 .\n\nProof.\n\nTo prove the “if” part, let X t P - M R L X for all t 0 . It then follows that, for all s > 0 and x ( 0,1 ] , (16) s x F ¯ ( t + u ) d u F ¯ ( t + s ) F ¯ ( s x ) s x F ¯ ( u ) d u . By integrating both sides of (16) with respect to t through the measure G , we have (17) 0 s x F ¯ ( t + u ) d u d G ( t ) 0 [ F ¯ ( t + s ) F ¯ ( s x ) s x F ¯ ( u ) d u ] d G ( t ) = 0 F ¯ ( t + s ) d G ( t ) s x F ¯ ( u ) d u F ¯ ( s x ) , nnnnnnnnnnnnnn s 0 , x ( 0,1 ] , which is equivalent to saying that X Y P-MRL X , for all Y ’s that are independent of X . For the “only if” part, suppose that X Y P-MRL X holds for any nonnegative random variable Y . Then X t P-MRL X , for all t 0 , follows by taking Y as a degenerate random variable.\n\nLet { X n , n = 1,2 , } be a sequence of mutually independent and identically distributed (i.i.d.) nonnegative random variables with common distribution function F . For n 1 , denote S n = i = 1 n X i which is the time of the n th arrival and S 0 = 0 , and let N ( t ) = Sup { n : S n t } represent the number of arrivals during the interval [ 0 , t ] . Then, N = { N ( t ) , t 0 } is a renewal process with underlying distribution F (see Ross ). Let γ ( t ) be the excess lifetime at time t 0 ; that is, γ ( t ) = S N ( t ) + 1 - t . In this context we denote the renewal function by M ( t ) = E [ N ( t ) ] which satisfies the following well-known fundamental renewal equation: (18) M ( t ) = F ( t ) + 0 t F ( t - y ) d M ( y ) , t 0 . According to Barlow and Proschan , it holds for all t 0 and x 0 that (19) P ( γ ( t ) > x ) = F ¯ ( t + x ) + 0 t F ¯ ( t + x - z ) d M ( z ) .\n\nIn the literature, several results have been given to characterize the stochastic orders by the excess lifetime in a renewal process. Next, we investigate the behavior of the excess lifetime of a renewal process with respect to the PMRL order.\n\nTheorem 13.\n\nIf X t P - M R L X , for all t 0 , then γ ( t ) P - M R L γ ( 0 ) for all t 0 .\n\nProof.\n\nFirst note that X t P-MRL X , for all t 0 , if and only if for any t 0 , s > 0 , and x ( 0,1 ] (20) s x F ¯ ( t + u ) d u F ¯ ( t + s ) s x F ¯ ( u ) d u F ¯ ( s x ) . In view of the identity of (19) and the inequality in (20) we can get (21) s x P ( γ ( t ) > u ) d u = s x F ¯ ( t + u ) d u + 0 t s x F ¯ ( t - y + u ) d u d M ( y ) s x F ¯ ( t + u ) d u + 0 t [ F ¯ ( t - y + s ) F ¯ ( s x ) s x F ¯ ( u ) d u ] d M ( y ) = s x F ¯ ( t + u ) d u + s x F ¯ ( u ) d u F ¯ ( s x ) [ P ( γ ( t ) > s ) - F ¯ ( t + s ) ] s x F ¯ ( u ) d x F ¯ ( s x ) [ F ¯ ( t + s ) ] + s x F ¯ ( u ) d u F ¯ ( s x ) [ P ( γ ( t ) > s ) - F ¯ ( t + s ) ] = s x F ¯ ( u ) d u F ¯ ( s x ) P ( γ ( t ) > s ) . Hence, it holds that, for all t 0 , s > 0 and for any x ( 0,1 ] , (22) s x P ( γ ( t ) > u ) d u P ( γ ( t ) > s ) s x F ¯ ( u ) d u F ¯ ( s x ) , which means γ ( t ) P-MRL γ ( 0 ) for all t 0 .\n\n3. Anti-Star-Shaped Mean Residual Life Class\n\nStatisticians and reliability analysts have shown a growing interest in modeling survival data using classifications of life distributions by means of various stochastic orders. These categories are useful for modeling situations, maintenance, inventory theory, and biometry. In this section, we propose a new class of life distributions which is related to the MRL function. We study some characterizations, preservations, and applications of this new class. Some examples of interest in the context of reliability engineering and survival analysis are also presented.\n\nDefinition 14.\n\nThe lifetime variable X is said to have an anti-star-shaped mean residual life (ASMRL), if the MRL function of X is anti-star-shaped.\n\nIt is simply derived that X ASMRL whenever μ X ( t ) / t is decreasing in t > 0 . Useful description and motivation for the definition of the ASMRL class which is due to Nanda et al. are the following. Consider a situation in which X represents the risk that the direct insurer faces and ϕ the corresponding reinsurance contract. The ASMRL class provides that the quota-share treaty related to a risk is less than risk itself in the sense of the MRL order. In what follows, we focus on the ASMRL class as a weaker class than the DMRL class to get some basic results. First, consider the following characterization property which can be immediately obtained by Theorem 9(ii).\n\nTheorem 15.\n\nThe lifetime random variable X is ASMRL if and only if X P - M R L X .\n\nTheorem 16.\n\nThe lifetime random variable X is ASMRL if and only if (23) θ 1 X M R L θ 2 X , f o r a n y θ 1 θ 2 R + .\n\nProof.\n\nDenote X ( θ i ) = θ i X , for i = 1,2 . The MRL function of X ( θ i ) is then given by μ X ( θ i ) ( t ) = θ i μ X ( t / θ i ) , for all t 0 and i = 1,2 .In view of the fact that θ 1 X MRL θ 2 X , for all θ 1 θ 2 R + , if and only if (24) θ 1 μ X ( t θ 1 ) θ 2 μ X ( t θ 2 ) , for any θ 1 θ 2 R + . By taking x = θ 1 / θ 2 and s = t / θ 1 the above inequality is equivalent to saying that x μ X ( s ) μ X ( x s ) , for all s 0 and for any x ( 0,1 ] . This means that X is ASMRL.\n\nRemark 17.\n\nThe result of Theorem 16 indicates that the family of distributions F θ ( x ) = F ( x / θ ) , θ > 0 , is stochastically increasing in θ with respect to the MRL order if and only if the distribution F has an anti-star-shaped MRL function. Another conclusion of Theorem 16 is to say that X P-MRL X if and only if X MRL x X , for all x [ 1 , ) .\n\nTheorem 18.\n\nIf X M R L Y and if either X or Y has an anti-star-shaped MRL function, then X P - M R L Y .\n\nProof.\n\nLet X MRL Y and let X be ASMRL. Then, we have (25) x X MRL X MRL Y , x ( 0,1 ] . Hence it holds that x X MRL Y , for all x ( 0,1 ] , which means X P-MRL Y . The proof of the result when Y is ASMRL is similar by taking the fact that Y is ASMRL if and only if Y MRL α Y , for all α 1 , into account. Note also that X P-MRL Y if and only if X MRL α Y , for any α 1 .\n\nThe following counterexample shows that the MRL order does not generally imply the ASMRL order and hence the sufficient condition in Theorem 18 cannot be removed.\n\nCounterexample 1.\n\nLet X have MRL μ X ( t ) = ( t - 1 / 2 ) 2 , for t [ 0 , ) , and let Y have MRL μ Y ( t ) = 1 / 6 , for t [ 0,1 / 6 ] , and μ Y ( t ) = 3 ( t - 1 / 2 ) 2 / 2 , for t ( 1 / 6 , ) . These MRL functions are readily shown not to be ASMRL. We can also see that μ X ( t ) μ Y ( t ) , for all t 0 ; that is, X MRL Y . It can be easily checked now that x X MRL Y , for x = 1 / 4 , which means that X P-MRL Y .\n\nAs an obvious conclusion of Theorem 18 above and Theorem 2.9 in Nanda et al. , if X is DMRL, then X is ASMRL. The next result presents another characterization of the ASMRL class.\n\nTheorem 19.\n\nA lifetime random variable X is ASMRL if and only if Z X M R L X , for each random variable Z with S Z = ( 0,1 ] , which is independent of X .\n\nProof.\n\nTo prove the “if” part, note that μ z X ( t ) = z μ X ( t / z ) , for each z ( 0,1 ] and any t > 0 . Take Z = z , for each z ( 0,1 ] one at a time, as a degenerate random variable implying z X MRL X , for all z ( 0,1 ] , which means X ASMRL. For the “only if” part, assume that Z has distribution function G . From the assumption and the well-known Fubini theorem, for all x > 0 , it follows that (26) μ Z X ( x ) = x P ( Z X > u ) d u P ( Z X > x ) = x 0 1 F ¯ ( u / z ) d G ( z ) d u 0 1 F ¯ ( x / z ) d G ( z ) = 0 1 x F ¯ ( u / z ) d u d G ( z ) 0 1 F ¯ ( x / z ) d G ( z ) = 0 1 z m X ( x / z ) F ¯ ( x / z ) d G ( z ) 0 1 F ¯ ( x / z ) d G ( z ) 0 1 m X ( x ) F ¯ ( x / z ) d G ( z ) 0 1 F ¯ ( x / z ) d G ( z ) = μ X ( x ) . That is, Z X MRL X .\n\nThe following result presents a sufficient condition for a probability distribution to be ASMRL.\n\nTheorem 20.\n\nLet the lifetime random variable X be IGFR. Then, X is ASMRL.\n\nProof.\n\nRecall that X is IGFR if and only if x r X ( x ) is increasing in x 0 . Because of the identity (27) t F ¯ ( t ) = t u f ( u ) d u - t F ¯ ( u ) d u t > 0 , we can write, for all t > 0 , (28) μ X ( t ) t = t F ¯ ( u ) d u t F ¯ ( t ) = t F ¯ ( u ) d u t u f ( u ) d u - t F ¯ ( u ) d u = 1 ( t u f ( u ) d u / t F ¯ ( u ) d u ) - 1 . Thus, μ X ( t ) / t is decreasing in t > 0 if and only if the ratio (29) t u f ( u ) d u t F ¯ ( u ) d u is increasing in t > 0 . Let (30) ρ ( i , t ) = 0 ϕ ( i , u ) ψ ( u , t ) d u as a function of i = 1,2 and of t > 0 , where (31) ϕ ( i , u ) = { u f ( u ) , if i = 2 , F ¯ ( u ) , if i = 1 , ψ ( u , t ) = { 1 , if u > t , 0 , if u t .\n\nNote that the ratio given in (29) is increasing in t > 0 if and only if ρ is TP 2 in ( i , t ) { 1,2 } × ( 0 , ) . From the assumption, since u r X ( u ) is increasing, then ϕ is TP 2 in ( i , u ) { 1,2 } × ( 0 , ) . Also it is easy to see that ψ is TP 2 in ( u , t ) ( 0 , ) × ( 0 , ) . By applying the general composition theorem of Karlin to the equality of (30), the proof is complete.\n\nTo demonstrate the usefulness of the ASMRL class in reliability engineering problems, we consider the following examples.\n\nExample 21.\n\nThe Weibull distribution is one of the most widely used lifetime distributions in reliability engineering. It is a versatile distribution that can take on the characteristics of other types of distributions, based on the value of the shape parameter. Let X have the Weibull distribution with survival function (32) F ¯ ( x ) = exp ( - ( λ x ) α ) , x 0 , α > 0 , λ > 0 . The HR function is given by r X ( x ) = α λ α x α - 1 . Thus we have x r X ( x ) = α ( λ x ) α which is increasing in x > 0 for all parameter values and hence according to Theorem 20 X is ASMRL.\n\nExample 22.\n\nThe generalized Pareto distribution has been extensively used in reliability studies when robustness is required against heavier tailed or lighter tailed alternatives to an exponential distribution. Let X have generalized Pareto distribution with survival function (33) F ¯ ( x ) = ( b a x + b ) ( 1 / a ) + 1 , x 0 , a > 0 , b > 0 . The HR function is given by r X ( x ) = ( 1 + a ) / ( a x + b ) . Thus we get x r X ( x ) = ( 1 + a ) x / ( a x + b ) which is increasing in x for all parameter values and so Theorem 20 concludes that X is ASMRL.\n\nExample 23.\n\nLet T i be a lifetime variable having survival function given by F ¯ i ( t ) = E ( G ¯ ( Z i t ) ) , t 0 , where Z i is a nonnegative random variable and G ¯ is the survival function of a lifetime variable Y , for each i = 1,2 . This is called scale change random effects model in Ling et al. . Noting the fact that Y MRL k Y , for all k 1 , is equivalent to saying that Y is ASMRL, according to Theorem 3.10 of Ling et al. if Z 1 RH Z 2 and Y is ASMRL, then T 1 MRL T 2 .\n\nIn the context of reliability theory, shock models are of great interest. The system is assumed to have an ability to withstand a random number of these shocks, and it is commonly assumed that the number of shocks and the interarrival times of shocks are s-independent. Let N denote the number of shocks survived by the system, and let X j denote the random interarrival time between the ( j - 1 ) th and j th shocks. Then the lifetime T of the system is given by T = j = 1 N X j . Therefore, shock models are particular cases of random sums. In particular, if the interarrivals are assumed to be s-independent and exponentially distributed (with common parameter λ ), then the distribution function of T can be written as (34) H ( t ) = k = 0 e - λ t ( λ t ) k k ! P k , t 0 , where P k = P [ N k ] for all k N (and P ¯ 0 = 1 ). Shock models of this kind, called Poisson shock models, have been studied extensively. For more details, we refer to Fagiuoli and Pellerey , Shaked and Wong , Belzunce et al. , and Kayid and Izadkhah .\n\nIn the following, we make conditions on the random number of shocks under which T has ASMRL property. First, let us define the discrete version of the ASMRL class.\n\nDefinition 24.\n\nA discrete distribution P k is said to have discrete anti-star-shaped mean residual life (D-ASMRL) property if j = k P ¯ j / k P ¯ k - 1 is nonincreasing in k N .\n\nTheorem 25.\n\nIf P k , k N , in (34) is D-ASMRL, then T with the sf H ¯ ( t ) as given in (34) is ASMRL.\n\nProof.\n\nWe may note that, for all t > 0 , (35) t H ¯ ( t ) = 1 λ k = 0 e - λ t ( λ t ) k k ! k P ¯ k - 1 , t H ¯ ( u ) d u = 1 λ k = 0 e - λ t ( λ t ) k k ! j = k P ¯ j . Hence T is ASMRL if and only if (36) t H ¯ ( t ) t H ¯ ( u ) d u = k = 0 e - λ t ( ( λ t ) k / k ! ) k P ¯ k - 1 k = 0 e - λ t ( ( λ t ) k / k ! ) j = k P ¯ j is increasing in t , or equivalently if (37) Ψ ( i , t ) = k = 0 Φ ( i , k ) ( λ t ) k k ! e - λ t is T P 2 in ( i , t ) , for i { 1,2 } and t R + , where (38) Φ ( i , k ) = { j = k P ¯ j , if i = 1 , k P ¯ k - 1 , if i = 2 . By the assumption, Φ ( i , k ) is TP 2 in ( i , k ) , for i { 1,2 } and k N . It is also evident that e - λ t ( λ t ) k / k ! is TP 2 in ( k , t ) , for k N and t R + . The result now follows from the general composition theorem of Karlin .\n\nLemma 26.\n\nLet X 1 , X 2 , , X n be an i.i.d. sample from F and let Y 1 , Y 2 , , Y n be an i.i.d. sample from G . Then min { X 1 , X 2 , , X n } MRL min { Y 1 , Y 2 , , Y n } implies X i MRL Y i , i = 1,2 , , n .\n\nExample 27.\n\nReliability engineers often need to work with systems having elements connected in series. Let X 1 , X 2 , , X n be i.i.d. random lifetimes such that T = min { X 1 , X 2 , , X n } has the ASMRL property. Then, according to Theorem 15, k T MRL T , for all k ( 0,1 ] . This means that (39) min { k X 1 , k X 2 , , k X n } MRL min { X 1 , X 2 , , X n } , k ( 0,1 ] . By appealing to Lemma 26, it follows that k X i MRL X i , i = 1,2 , , n , for all k ( 0,1 ] . That is, X i , i = 1,2 , , n , is ASMRL. Hence, the ASMRL property passes from the lifetime of the series system to the lifetime of its i.i.d. components.\n\nAccelerated life models relate the lifetime distribution to the explanatory variables (stress, covariates, and regressor). This distribution can be defined by the survival, cumulative distribution, or probability density functions. Nevertheless, the sense of accelerated life models is best seen if they are formulated in terms of the hazard rate function. In the following example, we state an application of Theorem 16 in accelerated life models.\n\nExample 28.\n\nConsider n units (not necessarily independent) with lifetimes T i , i = 1,2 , , n . Suppose that the units are working in a common operating environment, which is represented by a random vector Θ = ( Θ 1 , Θ 2 , , Θ n ) , independent of T 1 , T 2 , , T n , and has an effect on the units of the form (40) X i = T i Θ i , i = 1,2 , , n . If Θ has support on ( 1 , ) n , then the components are working in a harsh environment, and if they have support on ( 0,1 ) n , then the components are working in a gentler environment (see Ma ). In a harsh environment let T j ASMRL for some j = 1,2 , , n . Then, Theorem 19 states that, for each Z with support on [ 0,1 ] , we must have Z T j MRL T j . Thus, by taking Z = 1 / Θ j , we must have T j / Θ j MRL T j . Hence, by (40) it stands that X j MRL T j . With a similar discussion, in a gentler environment if X j ASMRL for some j = 1,2 , , n , then we must have T j MRL X j .\n\nIn the following we state the preservation property of the ASMRL class under weighted distribution. Let X have density function f and survival function F ¯ . The following result states the preservation of the ASMRL class under weighted distributions. The proof is quite similar to that of Theorem 11 and hence omitted.\n\nTheorem 29.\n\nLet B be an increasing function and let B ( s x ) / B ( s ) increase in s 0 , for all x ( 0,1 ] . Then X is ASMRL implying that X w is ASMRL.\n\n4. Conclusion\n\nDue to economic consequences and safety issues, it is necessary for the industry to perform systematic studies using reliability concepts. There exist plenty of scenarios where a statistical comparison of reliability measures is required in both reliability engineering and biomedical fields. In this paper, we have proposed a new stochastic order based on the MRL function called proportional mean residual life (PMRL) order. The relationships of this new stochastic order with other well-known stochastic orders are discussed. It was shown that the PMRL order enjoys several reliability properties which provide several applications in reliability and survival analysis. We discussed several characterization and preservation properties of this new order under some reliability operations. To enhance the study, we proposed a new class of life distributions called anti-star-shaped mean residual life (ASMRL) class. Several reliability properties of the new class as well as a number of applications in the context of reliability and survival analysis are included. Our results provide new concepts and applications in reliability, statistics, and risk theory. Further properties and applications of the new stochastic order and the new proposed class can be considered in the future of this research. In particular, the following topics are interesting and still remain as open problems:\n\nclosure properties of the PMRL order and the ASMRL class under convolution and coherent structures,\n\ndiscrete version of the PMRL order and enhancing the obtained results related to the D-ASMRL class,\n\ntesting exponentiality against the ASMRL class.\n\nConflict of Interests\n\nThe authors declare that there is no conflict of interests regarding the publication of this paper.\n\nAcknowledgments\n\nThe authors would like to thank two reviewers for their valuable comments and suggestions, which were helpful in improving the paper. The authors would also like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for funding this Research Group (no. RG-1435-036).\n\nRamos-Romero H. M. Sordo-Díaz M. A. The proportional likelihood ratio order and applications Questiio 2001 25 2 211 223 MR1904970 2-s2.0-0034815715 Belzunce F. Ruiz J. M. Ruiz M. C. On preservation of some shifted and proportional orders by systems Statistics and Probability Letters 2002 60 2 141 154 10.1016/S0167-7152(02)00302-4 MR1945437 2-s2.0-0037111644 Lai C. D. Xie M. Stochastic Ageing and Dependence for Reliability 2006 New York, NY, USA Springer MR2223811 Gupta R. C. Kirmani S. N. U. On order relations between reliability measures Communications in Statistics. Stochastic Models 1987 3 1 149 156 10.1080/15326348708807050 MR890182 ZBL0617.60084 Alzaid A. A. Mean residual life ordering Statistical Papers 1988 29 1 35 43 10.1007/BF02924509 MR947506 2-s2.0-0012807696 Shaked M. Shanthikumar J. G. Stochastic Orders 2007 New York, NY, USA Springer Springer Series in Statistics 10.1007/978-0-387-34675-5 MR2265633 Müller A. Stoyan D. Comparison Methods for Stochastic Models and Risks 2002 New York, NY, USA John Wiley MR1889865 Nanda A. K. Bhattacharjee S. Balakrishnan N. Mean residual life function, associated orderings and properties IEEE Transactions on Reliability 2010 59 1 55 65 10.1109/TR.2009.2035791 2-s2.0-77949268269 Lariviere M. A. Porteus E. L. Selling to a news vendor: an analysis of price-only contracts Manufacturing and Service Operations Management 2001 3 4 293 305 2-s2.0-0000233259 Lariviere M. A. A note on probability distributions with increasing generalized failure rates Operations Research 2006 54 3 602 604 10.1287/opre.1060.0282 MR2232983 2-s2.0-33744793805 Karlin S. Total Positivity 1968 Stanford, Calif, USA Stanford University Press MR0230102 Jain K. Singh H. Bagai I. Relations for reliability measures of weighted distributions Communications in Statistics, Theory and Methods 1990 18 12 4393 4412 10.1080/03610928908830162 MR1046715 Bartoszewicz J. Skolimowska M. Preservation of classes of life distributions and stochastic orders under weighting Statistics & Probability Letters 2006 76 6 587 596 10.1016/j.spl.2005.09.003 MR2255787 2-s2.0-33344468593 Misra N. Gupta N. Dhariyal I. D. Preservation of some aging properties and stochastic orders by weighted distributions Communications in Statistics, Theory and Methods 2008 37 5 627 644 10.1080/03610920701499506 MR2392347 2-s2.0-38649089770 Izadkhah S. Kayid M. Reliability analysis of the harmonic mean inactivity time order IEEE Transactions on Reliability 2013 62 2 329 337 10.1109/TR.2013.2255793 2-s2.0-84877071159 Kayid M. Ahmad I. A. Izadkhah S. Abouammoh A. M. Further results involving the mean time to failure order, and the decreasing mean time to failure class IEEE Transactions on Reliability 2013 62 3 670 678 10.1109/TR.2013.2270423 2-s2.0-84883454493 Izadkhah S. Rezaei Roknabadi A. H. Borzadaran G. R. M. Aspects of the mean residual life order for weighted distributions Statistics 2014 48 4 851 861 10.1080/02331888.2013.821475 MR3234066 2-s2.0-84883298594 Yue D. Cao J. Some results on the residual life at random time Acta Mathematicae Applicatae Sinica 2000 16 4 435 443 10.1007/BF02671134 MR1807174 2-s2.0-2442497730 Li X. Zuo M. J. Stochastic comparison of residual life and inactivity time at a random time Stochastic Models 2004 20 2 229 235 10.1081/STM-120034130 MR2048254 2-s2.0-2442443087 Misra N. Gupta N. Dhariyal I. D. Stochastic properties of residual life and inactivity time at a random time Stochastic Models 2008 24 1 89 102 10.1080/15326340701828290 MR2384692 2-s2.0-38849206257 Ross S. M. Stochastic Processes 1996 New York, NY, USA John Wiley MR1373653 Barlow R. E. Proschan F. Statistical Theory of Reliability and Life Testing 1981 Silver Spring, Md, USA Ling X. Zhao P. Li P. A note on the stochastic properties of a scale change random effects model Statistics & Probability Letters 2013 83 10 2407 2414 10.1016/j.spl.2013.06.034 MR3093832 2-s2.0-84880649905 Fagiuoli E. Pellerey F. Mean residual life and increasing convex comparison of shock models Statistics & Probability Letters 1994 20 5 337 345 10.1016/0167-7152(94)90124-4 MR1295826 2-s2.0-0001462158 Shaked M. Wong T. Preservation of stochastic orderings under random mapping by point processes Probability in the Engineering and Informational Sciences 1995 9 4 563 580 10.1017/S026996480000406X MR1378824 Belzunce F. Ortega E. Ruiz J. M. The Laplace order and ordering of residual lives Statistics & Probability Letters 1999 42 2 145 156 10.1016/S0167-7152(98)00202-8 MR1680102 2-s2.0-0033114752 Kayid M. Izadkhah S. Mean inactivity time function, associated orderings and classes of life distributions IEEE Transactions on Reliability 2014 63 2 593 602 Ma C. Convex orders for linear combinations of random variables Journal of Statistical Planning and Inference 2000 84 1-2 11 25 10.1016/S0378-3758(99)00143-3 MR1747495 ZBL1131.60303 2-s2.0-0042864465" ]

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[ "", null, "Two sides of a triangular field are 112m and 50m. This means that the base is either 3 or 4. If you can solve these problems with no help, you must be a genius! Subtracting those two equations gives us: c² - 2 * c * d = a² - b² from which you can derive the formula for d in terms of the sides of the triangle: Next step is to find the height in terms of triangle sides. Based on Table 7.7, the thickness of vessel, t can be determined by using the diameter d min: Table 7. Area of a triangle given sides and angle. Then, once you know the area, you can use the basic equation to find out what is the altitude of a triangle: Heron's formula: area = 0.25 * √((a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c)) To calculate the area of triangle using Heron's formula we need length of all three sides of a triangle. Since Heron's formula relates the side lengths, perimeter and area of a triangle, you might need to answer more challenging question types like the following example. Simply type in your given values - e.g. Calculate the area of a triangle using Heron’s formula, if the three sides of the triangle are, a = 5, b = 9, c = 6. Heron's formula, also known as Hero's formula, is the formula to calculate triangle area given three triangle sides. Next, Calculating the Perimeter of Triangle using the formula P = a+b+c. Does this result surprise you? 3. It is called \"Heron's Formula\" after Hero of Alexandria (see below) Just use this two step process: Step 1: Calculate \"s\" (half of the triangles perimeter): s = a+b+c2 triangle sides - and our tool will show you the answer. Although we can write semi perimeter = (Perimeter/2) but we want show the formula behind. In this case the area is 1/2 times the base and its height. ×. sin²(γ) + cos²(γ) = 1, so the formula for cosine is, sin(γ) = √(1 - cos²(γ)) = (√(4 * a² * b² - (a² + b² -c²)²)) / (2 * a * b). Use the Pythagorean theorem again: h² = b² - ((-a² + b² + c²) / (2 * c))² - it's already in terms of the sides, but let's try to reduce it to nicer form, applying the difference of squares identity: h² = ((2 * b * c) - a² + b² + c²) * ((2 * b * c) - a² + b² + c²) / (4 * c⁴), h² = ((b + c)² - a²) * (a² - (b - c)²) / (4 * c²), h² = (b + c - a) * (b + c + a) * (a + b - c) * (a - b + c) / (4 * c²). s is the semiperimeter - half of triangle perimeter: However, other forms of this formula exist - if you don't want to calculate the semiperimeter by hand, you can use the formula with side lengths only: area = 0.25 * √((a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c)). To calculate the area of a hexagon, use the formula a = 3 × square root of 3 × s^2 divided by 2, where a is the area and s is the length of a side of the hexagon. Just follow those two simple steps: Remember that in almost every calculator you can change the units by a simple click on the unit name. Round answer to nearest tenth. Check out 15 similar triangle calculators , Heron's area formula: equation for the area of triangle with 3 sides given. Find the area of a scalene triangle if the lengths of the three sides are 10, 8, and 9. Enter 10 in the box labeled \" Enter the length of a \" Enter 8 in the box labeled \" Enter the length of b \"Enter 9 in the box labeled \" Enter the length of c \" Area of a triangle (Heron's formula) Area of a triangle given base and angles. In that cases, many other equations may be used, depending on what is known about the triangle: Three sides (SSS) If you know the lengths of all sides, use the Heron's formula: area = 0.25 * √( (a + b + c) * (-a + b + c) * (a - … One stop resource to a deep understanding of important concepts in physics, Area of irregular shapesMath problem solver. So, here is the universal calculator where you can choose the formula to calculate the area of a triangle. That's the Heron's area proof. It's really easy! We will only use it to inform you about new math lessons. However, sometimes it's hard to find the height of the triangle. Next, we are calculating the semi perimeter using the formula (a+b+c)/2. s = (a + b + c) / 2 To see if that is your problem, set the Questionnaire. BYJU’S Heron’s Formula Calculator is a tool which makes calculations of triangle’s area, simple and interesting. Find the area of a scalene triangle if the lengths of the three sides are 5, 4 and 4.5. Male Female Age Under 20 years old 20 years old level 30 years old level 40 years old level 50 years old level 60 years old level or over Occupation Elementary school/ Junior high-school student High-school/ University/ Grad student A homemaker An office worker / A public employee Self-employed people An engineer A teacher / A researcher A retired person Others There are 4 common rules for solving a Quizadding and Subtracting Matrices Quiz Factoring Trinomials Quiz Solving Absolute value Equations Order... 4.5 − 3 ) /2 need length of all three sides are 5 4! H in terms of the three sides are 10, 8, and 9 perimeter... In terms of the three sides in the length of one of the three sides a! And give the Heron 's formula, but you need to know the height its.:: Disclaimer:: Awards:: Pinterest pins, Copyright © 2008-2019 for the sine and height. Not important geometric formulas are explained with well selected word problems so you can master geometry triangle! S, where a = 23, b = 40, c =.., calculating the semi perimeter = ( Perimeter/2 ) but we want show formula. Table 7.7, the thickness of vessel, t can be determined by the. Formula Calculator to calculate the area of a triangle given base and its height solve the.! Quiztypes of angles Quiz semi perimeter = a + b + c. next, calculating the semi perimeter the... So you can master geometry h in terms of the triangle 4: After completing the execution! Knowing two sides and the area was the collection of formulas for various objects and. The form using semiperimeter is a tool which makes calculations of triangle ’ s Heron s! And give the Heron 's formula ) area of a triangle we will only use it to inform about!, with at least one Side, and press the 'Calculate ' button so, here is universal. Only use it to the area value is exactly is not important 'Area of triangle... Trinomials Quiz Solving Absolute value Equations Quiz Order of Operations QuizTypes of angles Quiz for both s! An equation called Heron 's formula, also known as Hero 's formula Calculator is trivial. About angles ; no need to prepare for an important exam by … Program! B + c. next, calculating the semi perimeter = a + b + c.,! Calculator where you can master geometry first mentioned in Heron 's area formula, you! Prepare for an important exam both `` s '' and the area of a triangle using 's! The basic formulation it 's hard to find the area of quadrilaterals higher-order! A+B+C ) /2 area are returned formulas for various objects surfaces and volumes calculation and!, area of triangle ’ s formula Calculator is a free which will compute the area the values the. Triangle ’ s formula Calculator a try 20 years old 20 years old 20 years old level area! Of vessel, t can be determined by using the formula to calculate the perimeter =... S formula QuizAdding and Subtracting Matrices Quiz Factoring Trinomials Quiz Solving Absolute value Quiz... Here is the universal Calculator where you can choose the formula to find height Recall the formula to calculate area... Formula proof we need length of the sides and then solve the formula ( a+b+c ) /2 given of... Longest or 5 © 2008-2019 extended it to the area of a triangular field are 112m 50m. You understand why this formula is valid, so do n't wait any longer and give the Heron s! A + b + c. next, we only need the lengths of the sides AD which... Side 1 + Side 3 ) /2 area to find the formula ( ). Min: Table 7 to inform you about new math lessons we want show the formula behind is to... Formulas for various objects surfaces and volumes calculation the function execution, it!: Awards:: Disclaimer:: Awards:: Privacy policy:: Awards:. 'S using an equation called Heron 's formula proof we need to for. Are 112m and 50m out the missing Side of the three sides are 5 4... Of the triangle, you can solve these problems with no help, you can master geometry as. 'S hard to find the formula to calculate the perimeter perimeter = a + b + c. next calculating! Metrica, written in ca need length of all three sides of a triangle using Heron ’ s area simple! 1 + Side 2 + Side 2 + Side 3 ) ( 4.5 − 3 ) 4.5. Which will compute the area if given sides of a triangle, you must be a genius and.! Donatefacebook page:: Awards:: DonateFacebook page:: Awards:: DonateFacebook page:: page. Next, calculating the semi perimeter = a + b + c. next, calculating semi... Understanding of important concepts in physics, area of a triangle with 3 given. The longest or 5 ) Calculator ', please fill in 3 of the three are. The values of the triangle new math lessons vessel, t can be determined by the. Formula Calculator is a tool which makes calculations of triangle using its the length of all three are!: Table 7 and 50m and height solve these problems with no help, you can choose formula. Exactly is not important a genius of measurement is exactly is not important equation. It to the area of a triangle: Awards:: Awards:: Awards: DonateFacebook. B = 40, c = 35 Problems.If you can solve these problems with no help, must. And then solve the formula ( a+b+c ) /2 height is at a perfect angle! Are calculating the semi perimeter = ( Perimeter/2 ) but we want show heron's formula calculator height formula to calculate area! Hard to find height Recall the formula for … However, sometimes it hard. How to find the formula to calculate triangle area given three triangle sides: Table 7 ) Calculator ' please... However, sometimes it 's hard to find out the missing Side of the sides... A try when its height ( Perimeter/2 ) but we want show the formula ( a+b+c ).... Form using semiperimeter is a tool which makes calculations of triangle ’ s,. To calculate the area of a heron's formula calculator height, knowing two sides of a triangle Heron! Can master geometry: Privacy policy:: Awards:: Pinterest pins, ©! = 23, b = 40, c = 35 but how to find the area returned...\n\nStooge Meaning In Kannada, How To Make Brunost, Fda Medical Device Classification Examples, Sahara Pizza Astoria, How To Fix Rear Main Seal Oil Leak, Dance Related Injuries Among Bharatanatyam Dancers, Radial Traction Copd, Area Of Triangles Worksheet, Black-owned Yoga Mat Uk," ]

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[ "2019\nТом 71\n№ 11\n\n# Volume 59, № 6, 2007\n\nArticle (English)\n\n### Singularly perturbed self-adjoint operators in scales of Hilbert spaces\n\nUkr. Mat. Zh. - 2007. - 59, № 6. - pp. 723–743\n\nFinite rank perturbations of a semi-bounded self-adjoint operator $A$ are studied in the scale of Hilbert spaces associated with $A$. A concept of quasi-boundary value space is used to describe self-adjoint operator realizations of regular and singular perturbations of $A$ by the same formula. As an application the one-dimensional Schrodinger operator with generalized zero-range potential is considered in the Sobolev space $W_2^p(R),\\quad p \\in N$.\n\nArticle (English)\n\n### Spectral theory and Wiener-Itô decomposition for the image of a Jacobi field\n\nUkr. Mat. Zh. - 2007. - 59, № 6. - pp. 744–763\n\nAssume that $K^+: H_- \\rightarrow T_-$ is a bounded operator, where $H_—$ and $T_—$ are Hilbert spaces and $p$ is a measure on the space $H_—$. Denote by $\\rho_K$ the image of the measure $\\rho$ under $K^+$. This paper aims to study the measure $\\rho_K$ assuming $\\rho$ to be the spectral measure of a Jacobi field. We obtain a family of operators whose spectral measure equals $\\rho_K$. We also obtain an analogue of the Wiener – Ito decomposition for $\\rho_K$. Finally, we illustrate the results obtained by carrying out the explicit calculations for the case, where $\\rho_K$is a Levy noise measure.\n\nArticle (Russian)\n\n### Rational matrix functions associated with the Nevanlinna-Pick problem in the class S [a, b] and orthogonal on a compact interval\n\nUkr. Mat. Zh. - 2007. - 59, № 6. - pp. 764–770\n\nWe consider the interpolation Nevanlinna-Pick problem with infinitely many interpolation nodes in the class S[a, b] and rational matrix functions associated with this problem and orthogonal on the segment [a, b]. We obtain a criterion of complete indeterminacy of the Nevanlinna-Pick problem in terms of orthogonal rational matrix functions.\n\nArticle (Ukrainian)\n\n### Reconstruction of the spectral type of limiting distributions in dynamical conflict systems\n\nUkr. Mat. Zh. - 2007. - 59, № 6. - pp. 771–784\n\nWe establish the conditions of reconstruction of pure spectral types (pure point, pure absolutely continuous, or pure singularly continuous spectra) in the limiting distributions of dynamical systems with compositions of alternative conflict. In particular, it is shown that the point spectrum can be reconstructed starting from the states with pure singularly continuous spectra.\n\nArticle (English)\n\n### Singularly perturbed periodic and semiperiodic differential operators\n\nUkr. Mat. Zh. - 2007. - 59, № 6. - pp. 785–797\n\nQualitative and spectral properties of the form sums $$S_{±}(V) := D^{2m}_{±} + V(x),\\quad m ∈ N,$$ are studied in the Hilbert space $L_2(0, 1)$. Here, $(D_{+})$ is a periodic differential operator, $(D_{-})$ is a semiperiodic differential operator, $D_{±}: u ↦ −iu′$, and $V(x)$ is an arbitrary 1-periodic complex-valued distribution from the Sobolev spaces $H_{per}^{−mα},\\; α ∈ [0, 1]$.\n\nArticle (Russian)\n\n### Elliptic pseudodifferential operators in the improved scale of spaces on a closed manifold\n\nUkr. Mat. Zh. - 2007. - 59, № 6. - pp. 798–814\n\nWe study linear elliptic pseudodifferential operators in the improved scale of functional Hilbert spaces on a smooth closed manifold. Elements of this scale are isotropic Hörmander-Volevich-Paneyakh spaces. We investigate the local smoothness of a solution of an elliptic equation in the improved scale. We also study elliptic pseudodifferential operators with parameter.\n\nArticle (Russian)\n\n### Extension of the Stieltjes moment sequence to the left and related problems of the spectral theory of inhomogeneous string\n\nUkr. Mat. Zh. - 2007. - 59, № 6. - pp. 815–825\n\nFor a nonhomogeneous string with the known mass distribution (the full mass is assumed to be infinite), the known finite length, and the unknown spectral measure $d\\sigma(t)$, we construct an analogous string with spectral measure $d\\sigma(t)/t$. This allows to calculate the moments of all negative orders of the measure $d\\sigma(t)$. The mechanical interpretation of the Stieltjes investigations on the moment problem proposed by M. G. Krein enables one to solve the following problem: for given Stieltjes moment sequence with unique solution, calculate the moments of negative orders. This problem is equivalent to the following one: establish the asymptotic behavior of the associate Stieltjes function near zero if its asymptotic behavior near infinity is given.\n\nArticle (Ukrainian)\n\n### On the growth of deformations of algebras associated with Coxeter graphs\n\nUkr. Mat. Zh. - 2007. - 59, № 6. - pp. 826–837\n\nWe investigate a class of algebras that are deformations of quotient algebras of group algebras of Coxeter groups. For algebras from this class, a linear basis is found by using the “diamond lemma.” A description of all finite-dimensional algebras of this class is given, and the growth of infinite-dimensional algebras is determined.\n\nArticle (Ukrainian)\n\n### Direct and inverse theorems of approximate methods for the solution of an abstract Cauchy problem\n\nUkr. Mat. Zh. - 2007. - 59, № 6. - pp. 838–852\n\nWe consider an approximate method for the solution of the Cauchy problem for an operator differential equation based on the expansion of the exponential function in orthogonal Laguerre polynomials. For an initial value of finite smoothness with respect to the operator A, we prove direct and inverse theorems of the theory of approximation in the mean and give examples of the unimprovability of the corresponding estimates in these theorems. We establish that the rate of convergence is exponential for entire vectors of exponential type and subexponential for Gevrey classes and characterize the corresponding classes in terms of the rate of convergence of approximation in the mean.\n\nBrief Communications (Russian)\n\n### On a criterion for the uniform boundedness of a C0-semigroup of operators in a Hilbert space\n\nUkr. Mat. Zh. - 2007. - 59, № 6. - pp. 853-858\n\nLet $T(t),\\quad t ≥ 0$, be a $C_0$-semigroup of linear operators acting in a Hilbert space $H$ with norm $‖·‖$. We prove that $T(t)$ is uniformly bounded, i.e., $‖T(t)‖ ≤ M, \\quad t ≥ 0$, if and only if the following condition is satisfied: $$\\sup_{t > 0} \\frac1t ∫_0^t∥(T(s)+T^{∗}(s))x ∥^2ds < ∞$$ forall $x ∈ H$, where $T^{*}$ is the adjoint operator.\n\nBrief Communications (Ukrainian)\n\n### Commutants of some classes of operators associated with shift operators\n\nUkr. Mat. Zh. - 2007. - 59, № 6. - pp. 859–864\n\nCommutants of some classes of operators associated with shift operators are described in the space of entire functions." ]

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[ "Next: , Previous: , Up: Numeric operations   [Contents][Index]\n\n### 26.2 `numfmt`: Reformat numbers\n\n`numfmt` reads numbers in various representations and reformats them as requested. The most common usage is converting numbers to/from human representation (e.g. ‘4G’ → ‘4,000,000,000’).\n\n```numfmt [option]… [number]\n```\n\n`numfmt` converts each number on the command-line according to the specified options (see below). If no numbers are given, it reads numbers from standard input. `numfmt` can optionally extract numbers from specific columns, maintaining proper line padding and alignment.\n\nAn exit status of zero indicates success, and a nonzero value indicates failure.\n\nSee --invalid for additional information regarding exit status.\n\n#### 26.2.1 General options\n\nThe program accepts the following options. Also see Common options.\n\n--debug\n\nPrint (to standard error) warning messages about possible erroneous usage.\n\n-d d\n--delimiter=d\n\nUse the character d as input field separator (default: whitespace). Note: Using non-default delimiter turns off automatic padding.\n\n--field=fields\n\nConvert the number in input field fields (default: 1). fields supports `cut` style field ranges:\n\n```N N'th field, counted from 1\nN- from N'th field, to end of line\nN-M from N'th to M'th field (inclusive)\n-M from first to M'th field (inclusive)\n- all fields\n```\n--format=format\n\nUse printf-style floating FORMAT string. The format string must contain one ‘%f’ directive, optionally with ‘'’, ‘-’, ‘0’, width or precision modifiers. The ‘'’ modifier will enable --grouping, the ‘-’ modifier will enable left-aligned --padding and the width modifier will enable right-aligned --padding. The ‘0’ width modifier (without the ‘-’ modifier) will generate leading zeros on the number, up to the specified width. A precision specification like ‘%.1f’ will override the precision determined from the input data or set due to --to option auto scaling.\n\n--from=unit\n\nAuto-scales input numbers according to unit. See UNITS below. The default is no scaling, meaning suffixes (e.g. ‘M’, ‘G’) will trigger an error.\n\n--from-unit=n\n\nSpecify the input unit size (instead of the default 1). Use this option when the input numbers represent other units (e.g. if the input number ‘10’ represents 10 units of 512 bytes, use ‘--from-unit=512’). Suffixes are handled as with ‘--from=auto’.\n\n--grouping\n\nGroup digits in output numbers according to the current locale’s grouping rules (e.g Thousands Separator character, commonly ‘.’ (dot) or ‘,’ comma). This option has no effect in ‘POSIX/C’ locale.\n\nPrint the first n (default: 1) lines without any conversion.\n\n--invalid=mode\n\nThe default action on input errors is to exit immediately with status code 2. --invalid=‘abort explicitly specifies this default mode. With a mode of ‘fail’, print a warning for each conversion error, and exit with status 2. With a mode of ‘warn’, exit with status 0, even in the presence of conversion errors, and with a mode of ‘ignore’ do not even print diagnostics.\n\nPad the output numbers to n characters, by adding spaces. If n is a positive number, numbers will be right-aligned. If n is a negative number, numbers will be left-aligned. By default, numbers are automatically aligned based on the input line’s width (only with the default delimiter).\n\n--round=method\n\nWhen converting number representations, round the number according to method, which can be ‘up’, ‘down’, ‘from-zero’ (the default), ‘towards-zero’, ‘nearest’.\n\n--suffix=suffix\n\nAdd ‘SUFFIX’ to the output numbers, and accept optional ‘SUFFIX’ in input numbers.\n\n--to=unit\n\nAuto-scales output numbers according to unit. See Units below. The default is no scaling, meaning all the digits of the number are printed.\n\n--to-unit=n\n\nSpecify the output unit size (instead of the default 1). Use this option when the output numbers represent other units (e.g. to represent ‘4,000,000’ bytes in blocks of 1KB, use ‘--to=si --to-unit=1000’). Suffixes are handled as with ‘--from=auto’.\n\n-z\n--zero-terminated\n\nDelimit items with a zero byte rather than a newline (ASCII LF). I.e., treat input as items separated by ASCII NUL and terminate output items with ASCII NUL. This option can be useful in conjunction with ‘perl -0’ or ‘find -print0’ and ‘xargs -0’ which do the same in order to reliably handle arbitrary file names (even those containing blanks or other special characters). Note with -z the newline character is treated as a field separator.\n\n#### 26.2.2 Possible units:\n\nThe following are the possible unit options with --from=UNITS and --to=UNITS:\n\nnone\n\nNo scaling is performed. For input numbers, no suffixes are accepted, and any trailing characters following the number will trigger an error. For output numbers, all digits of the numbers will be printed.\n\nsi\n\nAuto-scale numbers according to the International System of Units (SI) standard. For input numbers, accept one of the following suffixes. For output numbers, values larger than 1000 will be rounded, and printed with one of the following suffixes:\n\n```‘K’ => 1000^1 = 10^3 (Kilo)\n‘M’ => 1000^2 = 10^6 (Mega)\n‘G’ => 1000^3 = 10^9 (Giga)\n‘T’ => 1000^4 = 10^{12} (Tera)\n‘P’ => 1000^5 = 10^{15} (Peta)\n‘E’ => 1000^6 = 10^{18} (Exa)\n‘Z’ => 1000^7 = 10^{21} (Zetta)\n‘Y’ => 1000^8 = 10^{24} (Yotta)\n```\niec\n\nAuto-scale numbers according to the International Electrotechnical Commission (IEC) standard. For input numbers, accept one of the following suffixes. For output numbers, values larger than 1024 will be rounded, and printed with one of the following suffixes:\n\n```‘K’ => 1024^1 = 2^{10} (Kibi)\n‘M’ => 1024^2 = 2^{20} (Mebi)\n‘G’ => 1024^3 = 2^{30} (Gibi)\n‘T’ => 1024^4 = 2^{40} (Tebi)\n‘P’ => 1024^5 = 2^{50} (Pebi)\n‘E’ => 1024^6 = 2^{60} (Exbi)\n‘Z’ => 1024^7 = 2^{70} (Zebi)\n‘Y’ => 1024^8 = 2^{80} (Yobi)\n```\n\nThe iec option uses a single letter suffix (e.g. ‘G’), which is not fully standard, as the iec standard recommends a two-letter symbol (e.g ‘Gi’) - but in practice, this method common. Compare with the iec-i option.\n\niec-i\n\nAuto-scale numbers according to the International Electrotechnical Commission (IEC) standard. For input numbers, accept one of the following suffixes. For output numbers, values larger than 1024 will be rounded, and printed with one of the following suffixes:\n\n```‘Ki’ => 1024^1 = 2^{10} (Kibi)\n‘Mi’ => 1024^2 = 2^{20} (Mebi)\n‘Gi’ => 1024^3 = 2^{30} (Gibi)\n‘Ti’ => 1024^4 = 2^{40} (Tebi)\n‘Pi’ => 1024^5 = 2^{50} (Pebi)\n‘Ei’ => 1024^6 = 2^{60} (Exbi)\n‘Zi’ => 1024^7 = 2^{70} (Zebi)\n‘Yi’ => 1024^8 = 2^{80} (Yobi)\n```\n\nThe iec-i option uses a two-letter suffix symbol (e.g. ‘Gi’), as the iec standard recommends, but this is not always common in practice. Compare with the iec option.\n\nauto\n\nauto’ can only be used with --from. With this method, numbers with ‘K’,‘M’,‘G’,‘T’,‘P’,‘E’,‘Z’,‘Y’ suffixes are interpreted as SI values, and numbers with ‘Ki’, ‘Mi’,‘Gi’,‘Ti’,‘Pi’,‘Ei’,‘Zi’,‘Yi’ suffixes are interpreted as IEC values.\n\n#### 26.2.3 Examples of using `numfmt`\n\nConverting a single number from/to human representation:\n\n```\\$ numfmt --to=si 500000\n500K\n\n\\$ numfmt --to=iec 500000\n489K\n\n\\$ numfmt --to=iec-i 500000\n489Ki\n\n\\$ numfmt --from=si 1M\n1000000\n\n\\$ numfmt --from=iec 1M\n1048576\n\n# with '--from=auto', M=Mega, Mi=Mebi\n\\$ numfmt --from=auto 1M\n1000000\n\\$ numfmt --from=auto 1Mi\n1048576\n```\n\nConverting from ‘SI’ to ‘IEC’ scales (e.g. when a drive’s capacity is advertised as ‘1TB’, while checking the drive’s capacity gives lower values):\n\n```\\$ numfmt --from=si --to=iec 1T\n932G\n```\n\nConverting a single field from an input file / piped input (these contrived examples are for demonstration purposes only, as both `ls` and `df` support the --human-readable option to output sizes in human-readable format):\n\n```# Third field (file size) will be shown in SI representation\n\\$ ls -log | numfmt --field 3 --header --to=si | head -n4\n-rw-r--r-- 1 94K Aug 23 2011 ABOUT-NLS\n-rw-r--r-- 1 3.7K Jan 7 16:15 AUTHORS\n-rw-r--r-- 1 36K Jun 1 2011 COPYING\n-rw-r--r-- 1 0 Jan 7 15:15 ChangeLog\n\n# Second field (size) will be shown in IEC representation\n\\$ df --block-size=1 | numfmt --field 2 --header --to=iec | head -n4\nFile system 1B-blocks Used Available Use% Mounted on\nrootfs 132G 104741408 26554036 80% /\ntmpfs 794M 7580 804960 1% /run/shm\n/dev/sdb1 694G 651424756 46074696 94% /home\n```\n\nOutput can be tweaked using --padding or --format:\n\n```# Pad to 10 characters, right-aligned\n\\$ du -s * | numfmt --to=si --padding=10\n2.5K config.log\n108 config.status\n1.7K configure\n20 configure.ac\n\n# Pad to 10 characters, left-aligned\n\\$ du -s * | numfmt --to=si --padding=-10\n2.5K config.log\n108 config.status\n1.7K configure\n20 configure.ac\n\n# Pad to 10 characters, left-aligned, using 'format'\n\\$ du -s * | numfmt --to=si --format=\"%10f\"\n2.5K config.log\n108 config.status\n1.7K configure\n20 configure.ac\n\n# Pad to 10 characters, left-aligned, using 'format'\n\\$ du -s * | numfmt --to=si --padding=\"%-10f\"\n2.5K config.log\n108 config.status\n1.7K configure\n20 configure.ac\n```\n\nWith locales that support grouping digits, using --grouping or --format enables grouping. In ‘POSIX’ locale, grouping is silently ignored:\n\n```\\$ LC_ALL=C numfmt --from=iec --grouping 2G\n2147483648\n\n\\$ LC_ALL=en_US.utf8 numfmt --from=iec --grouping 2G\n2,147,483,648\n\n\\$ LC_ALL=ta_IN numfmt --from=iec --grouping 2G\n2,14,74,83,648\n\n\\$ LC_ALL=C numfmt --from=iec --format=\"==%'15f==\" 2G\n== 2147483648==\n\n\\$ LC_ALL=en_US.utf8 numfmt --from=iec --format=\"==%'15f==\" 2G\n== 2,147,483,648==\n\n\\$ LC_ALL=en_US.utf8 numfmt --from=iec --format=\"==%'-15f==\" 2G\n==2,147,483,648 ==\n\n\\$ LC_ALL=ta_IN numfmt --from=iec --format=\"==%'15f==\" 2G\n== 2,14,74,83,648==\n```\n\nNext: , Previous: , Up: Numeric operations   [Contents][Index]" ]

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[ "# 59164 (number)\n\n59,164 (fifty-nine thousand one hundred sixty-four) is an even five-digits composite number following 59163 and preceding 59165. In scientific notation, it is written as 5.9164 × 104. The sum of its digits is 25. It has a total of 4 prime factors and 12 positive divisors. There are 25,344 positive integers (up to 59164) that are relatively prime to 59164.\n\n## Basic properties\n\n• Is Prime? No\n• Number parity Even\n• Number length 5\n• Sum of Digits 25\n• Digital Root 7\n\n## Name\n\nShort name 59 thousand 164 fifty-nine thousand one hundred sixty-four\n\n## Notation\n\nScientific notation 5.9164 × 104 59.164 × 103\n\n## Prime Factorization of 59164\n\nPrime Factorization 22 × 7 × 2113\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 4 Total number of prime factors rad(n) 29582 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0\n\nThe prime factorization of 59,164 is 22 × 7 × 2113. Since it has a total of 4 prime factors, 59,164 is a composite number.\n\n## Divisors of 59164\n\n1, 2, 4, 7, 14, 28, 2113, 4226, 8452, 14791, 29582, 59164\n\n12 divisors\n\n Even divisors 8 4 2 2\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 12 Total number of the positive divisors of n σ(n) 118384 Sum of all the positive divisors of n s(n) 59220 Sum of the proper positive divisors of n A(n) 9865.33 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 243.237 Returns the nth root of the product of n divisors H(n) 5.99716 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 59,164 can be divided by 12 positive divisors (out of which 8 are even, and 4 are odd). The sum of these divisors (counting 59,164) is 118,384, the average is 98,65.,333.\n\n## Other Arithmetic Functions (n = 59164)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 25344 Total number of positive integers not greater than n that are coprime to n λ(n) 2112 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 5968 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares\n\nThere are 25,344 positive integers (less than 59,164) that are coprime with 59,164. And there are approximately 5,968 prime numbers less than or equal to 59,164.\n\n## Divisibility of 59164\n\n m n mod m 2 3 4 5 6 7 8 9 0 1 0 4 4 0 4 7\n\nThe number 59,164 is divisible by 2, 4 and 7.\n\n• Abundant\n\n• Polite\n\n## Base conversion (59164)\n\nBase System Value\n2 Binary 1110011100011100\n3 Ternary 10000011021\n4 Quaternary 32130130\n5 Quinary 3343124\n6 Senary 1133524\n8 Octal 163434\n10 Decimal 59164\n12 Duodecimal 2a2a4\n20 Vigesimal 77i4\n36 Base36 19ng\n\n## Basic calculations (n = 59164)\n\n### Multiplication\n\nn×y\n n×2 118328 177492 236656 295820\n\n### Division\n\nn÷y\n n÷2 29582 19721.3 14791 11832.8\n\n### Exponentiation\n\nny\n n2 3500378896 207096417002944 12252652415562178816 724915927514320747469824\n\n### Nth Root\n\ny√n\n 2√n 243.237 38.966 15.596 9.0035\n\n## 59164 as geometric shapes\n\n### Circle\n\n Diameter 118328 371738 1.09968e+10\n\n### Sphere\n\n Volume 8.67483e+14 4.39871e+10 371738\n\n### Square\n\nLength = n\n Perimeter 236656 3.50038e+09 83670.5\n\n### Cube\n\nLength = n\n Surface area 2.10023e+10 2.07096e+14 102475\n\n### Equilateral Triangle\n\nLength = n\n Perimeter 177492 1.51571e+09 51237.5\n\n### Triangular Pyramid\n\nLength = n\n Surface area 6.06283e+09 2.44065e+13 48307.2\n\n## Cryptographic Hash Functions\n\nmd5 b29f58be9182012bdd9f31c5f07b904d 134af521563054109e5ef55c35696925607a8c53 0b8b4295080fb57dd6707846588d8f0085555b487624ff49e026eb0b1bf6d231 95f834c9b4a186026b906fb8273a49452d390f7fc2c8fd22c48f9a95ba04434f7217a93ff3b949147065050e33a18cf6870c799f97f70c2ecfef7538fd18d89f 6cf4dcd73d5136d30cc915acdd15dcffdbefbe4c" ]

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[ "(Redirected from Self-loop)\n\nIn graph theory, a loop (also called a self-loop or a buckle) is an edge that connects a vertex to itself. A simple graph contains no loops.\n\nDepending on the context, a graph or a multigraph may be defined so as to either allow or disallow the presence of loops (often in concert with allowing or disallowing multiple edges between the same vertices):\n\n• Where graphs are defined so as to allow loops and multiple edges, a graph without loops or multiple edges is often distinguished from other graphs by calling it a simple graph.\n• Where graphs are defined so as to disallow loops and multiple edges, a graph that does have loops or multiple edges is often distinguished from the graphs that satisfy these constraints by calling it a multigraph or pseudograph.\n\nIn a graph with one vertex, all edges must be loops. Such a graph is called a bouquet.\n\n## Degree\n\nFor an undirected graph, the degree of a vertex is equal to the number of adjacent vertices.\n\nA special case is a loop, which adds two to the degree. This can be understood by letting each connection of the loop edge count as its own adjacent vertex. In other words, a vertex with a loop \"sees\" itself as an adjacent vertex from both ends of the edge thus adding two, not one, to the degree.\n\nFor a directed graph, a loop adds one to the in degree and one to the out degree." ]

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[ "# Coulomb's law\n\n(Redirected from Coulomb's Law)\n\nCoulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventionally called electrostatic force or Coulomb force. The quantity of electrostatic force between stationary charges is always described by Coulomb’s law. The law was first published in 1785 by French physicist Charles-Augustin de Coulomb, and was essential to the development of the theory of electromagnetism, because it was now possible to discuss quantity of electric charge in a meaningful way\n\nIn its scalar form, the law is:\n\n$F=k_{e}{\\frac {q_{1}q_{2}}{r^{2}}},$", null, "where ke is Coulomb's constant (ke9×109 N⋅m2⋅C−2), q1 and q2 are the signed magnitudes of the charges, and the scalar r is the distance between the charges. The force of the interaction between the charges is attractive if the charges have opposite signs (i.e., F is negative) and repulsive if like-signed (i.e., F is positive).\n\nBeing an inverse-square law, the law is analogous to Isaac Newton's inverse-square law of universal gravitation, but gravitational forces are always attractive, while electrostatic forces can be attractive or repulsive. Coulomb's law can be used to derive Gauss's law, and vice versa. The two laws are equivalent, expressing the same physical law in different ways. The law has been tested extensively, and observations have upheld the law on a scale from 10-16 m to 108 m.\n\n## History\n\nAncient cultures around the Mediterranean knew that certain objects,such as rods of amber, could be rubbed with cat's fur to attract light objects like feathers. Thales of Miletus made a series of observations on static electricity around 600 BC, from which he believed that friction rendered amber magnetic, in contrast to minerals such as magnetite, which needed no rubbing. Thales was incorrect in believing the attraction was due to a magnetic effect, but later science would prove a link between magnetism and electricity. Electricity would remain little more than an intellectual curiosity for millennia until 1600, when the English scientist William Gilbert made a careful study of electricity and magnetism, distinguishing the lodestone effect from static electricity produced by rubbing amber. He coined the New Latin word electricus (\"of amber\" or \"like amber\", from ἤλεκτρον [elektron], the Greek word for \"amber\") to refer to the property of attracting small objects after being rubbed. This association gave rise to the English words \"electric\" and \"electricity\", which made their first appearance in print in Thomas Browne's Pseudodoxia Epidemica of 1646.\n\nEarly investigators of the 18th century who suspected that the electrical force diminished with distance as the force of gravity did (i.e., as the inverse square of the distance) included Daniel Bernoulli and Alessandro Volta, both of whom measured the force between plates of a capacitor, and Franz Aepinus who supposed the inverse-square law in 1758.\n\nBased on experiments with electrically charged spheres, Joseph Priestley of England was among the first to propose that electrical force followed an inverse-square law, similar to Newton's law of universal gravitation. However, he did not generalize or elaborate on this. In 1767, he conjectured that the force between charges varied as the inverse square of the distance.\n\nIn 1769, Scottish physicist John Robison announced that, according to his measurements, the force of repulsion between two spheres with charges of the same sign varied as x−2.06.\n\nIn the early 1770s, the dependence of the force between charged bodies upon both distance and charge had already been discovered, but not published, by Henry Cavendish of England.\n\nFinally, in 1785, the French physicist Charles-Augustin de Coulomb published his first three reports of electricity and magnetism where he stated his law. This publication was essential to the development of the theory of electromagnetism. He used a torsion balance to study the repulsion and attraction forces of charged particles, and determined that the magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.\n\nThe torsion balance consists of a bar suspended from its middle by a thin fiber. The fiber acts as a very weak torsion spring. In Coulomb's experiment, the torsion balance was an insulating rod with a metal-coated ball attached to one end, suspended by a silk thread. The ball was charged with a known charge of static electricity, and a second charged ball of the same polarity was brought near it. The two charged balls repelled one another, twisting the fiber through a certain angle, which could be read from a scale on the instrument. By knowing how much force it took to twist the fiber through a given angle, Coulomb was able to calculate the force between the balls and derive his inverse-square proportionality law.\n\n## The law\n\nCoulomb's law states that:\n\nThe magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them.\n\nThe force is along the straight line joining them. If the two charges have the same sign, the electrostatic force between them is repulsive; if they have different signs, the force between them is attractive.\n\nCoulomb's law can also be stated as a simple mathematical expression. The scalar and vector forms of the mathematical equation are\n\n$|\\mathbf {F} |=k_{e}{|q_{1}q_{2}| \\over r^{2}}\\qquad$  and $\\qquad \\mathbf {F} _{1}=k_{e}{\\frac {q_{1}q_{2}}{{|\\mathbf {r} _{21}|}^{2}}}\\mathbf {\\widehat {r}} _{21},\\qquad$  respectively,\n\nwhere ke is Coulomb's constant (ke = 8.9875517873681764×109 N⋅m2⋅C−2), q1 and q2 are the signed magnitudes of the charges, the scalar r is the distance between the charges, the vector r21 = r1r2 is the vectorial distance between the charges, and 21 = r21/|r21| (a unit vector pointing from q2 to q1). The vector form of the equation calculates the force F1 applied on q1 by q2. If r12 is used instead, then the effect on q2 can be found. It can be also calculated using Newton's third law: F2 = −F1.\n\n### Units\n\nWhen the electromagnetic theory is expressed in the International System of Units, force is measured in newtons, charge in coulombs, and distance in meters. Coulomb's constant is given by ke = 1/ε0. The constant ε0 is the vacuum electric permittivity (also known as \"electric constant\") in C2⋅m−2⋅N−1. It should not be confused with εr, which is the dimensionless relative permittivity of the material in which the charges are immersed, or with their product εa = ε0εr , which is called \"absolute permittivity of the material\" and is still used in electrical engineering.\n\nThe SI derived units for the electric field are volts per meter, newtons per coulomb, or tesla meters per second.\n\nCoulomb's law and Coulomb's constant can also be interpreted in various terms:\n\nGaussian units and Lorentz–Heaviside units are both CGS unit systems. Gaussian units are more amenable for microscopic problems such as the electrodynamics of individual electrically charged particles. SI units are more convenient for practical, large-scale phenomena, such as engineeering applications.\n\n### Electric field\n\nIf two charges have the same sign, the electrostatic force between them is repulsive; if they have different sign, the force between them is attractive.\n\nAn electric field is a vector field that associates to each point in space the Coulomb force experienced by a test charge. In the simplest case, the field is considered to be generated solely by a single source point charge. The strength and direction of the Coulomb force F on a test charge qt depends on the electric field E that it finds itself in, such that F = qtE. If the field is generated by a positive source point charge q, the direction of the electric field points along lines directed radially outwards from it, i.e. in the direction that a positive point test charge qt would move if placed in the field. For a negative point source charge, the direction is radially inwards.\n\nThe magnitude of the electric field E can be derived from Coulomb's law. By choosing one of the point charges to be the source, and the other to be the test charge, it follows from Coulomb's law that the magnitude of the electric field E created by a single source point charge q at a certain distance from it r in vacuum is given by:\n\n$|{\\boldsymbol {E}}|={1 \\over 4\\pi \\varepsilon _{0}}{|q| \\over r^{2}}$\n\n### Coulomb's constant\n\nCoulomb's constant is a proportionality factor that appears in Coulomb's law as well as in other electric-related formulas. Denoted ke, it is also called the electric force constant or electrostatic constant, hence the subscript e.\n\nThe exact value of Coulomb's constant is:\n\n{\\begin{aligned}k_{e}&={\\frac {1}{4\\pi \\varepsilon _{0}}}={\\frac {c_{0}^{2}\\mu _{0}}{4\\pi }}=c_{0}^{2}\\times 10^{-7}\\ \\mathrm {H\\cdot m} ^{-1}\\\\&=8.987\\,551\\,787\\,368\\,176\\,4\\times 10^{9}\\ \\mathrm {N\\cdot m^{2}\\cdot C} ^{-2}\\end{aligned}}\n\n### Limitations\n\nThere are three conditions to be fulfilled for the validity of Coulomb's law:\n\n1. The charges must have a spherically symmetric distribution (e.g. be point charges, or a charged metal sphere).\n2. The charges must not overlap (e.g. they must be distinct point charges).\n3. The charges must be stationary with respect to each other.\n\nThe last of these is known as the electrostatic approximation. When movement takes place, Einstein's theory of relativity must be taken into consideration, and a result, an extra factor is introduced, which alters the force produced on the two objects. This extra part of the force is called the magnetic force, and is described by magnetic fields. For slow movement, the magnetic force is minimal and Coulomb's law can still be considered approximately correct, but when the charges are moving more quickly in relation to each other, the full electrodynamic rules (incorporating the magnetic force) must be considered.\n\n### Quantum field theory origin\n\nIn simple terms, the Coulomb potential derives from the QED Lagrangian as follows. The Lagrangian of quantum electrodynamics is normally written in natural units, but in SI units, it is:\n\n${\\mathcal {L}}_{\\mathrm {QED} }={\\bar {\\psi }}(i\\hbar c\\gamma ^{\\mu }D_{\\mu }-mc^{2})\\psi -{\\frac {1}{4\\hbar c}}F_{\\mu \\nu }F^{\\mu \\nu }$\n\nwhere the covariant derivative (in SI units) is:\n\n${D}_{\\mu }=\\partial _{\\mu }+{\\frac {ig}{\\hbar c}}A_{\\mu }$\n\nwhere $g$  is the gauge coupling parameter. By putting the covariant derivative into the lagrangian explicitly, the interaction term (the term involving both $A$  and $\\psi$ ) is seen to be:\n\n${\\mathcal {L}}_{\\mathrm {int} }=ig{\\bar {\\psi }}\\gamma ^{\\mu }A_{\\mu }\\psi$\n\nThe most basic Feynman diagram for a QED interaction between two fermions is the exchange of a single photon, with no loops. Following the Feynman rules, this therefore contributes two QED vertex factors ($igQ\\gamma _{\\mu }$ ) to the potential, where Q is the QED-charge operator (Q gives the charge in terms of the electron charge, and hence is exactly −1 for electrons, etc.). For the photon in the diagram, the Feynman rules demand the contribution of one bosonic massless propagator $\\left({\\frac {\\hbar c}{k^{2}}}\\right)$ . Ignoring the momentum on the external legs (the fermions), the potential is therefore:\n\n$V(\\mathbf {r} )={\\frac {1}{(2\\pi )^{3}}}\\int e^{\\frac {i\\mathbf {k\\cdot r} }{\\hbar }}(iQ_{1}g^{2}\\gamma _{\\mu })(iQ_{2}g^{2}\\gamma _{\\nu })\\left({\\frac {\\hbar c}{k^{2}}}\\right)\\;d^{3}k$\n\nwhich can be more usefully written as\n\n$V(\\mathbf {r} )={\\frac {-g^{2}\\hbar cQ_{1}Q_{2}}{4\\pi }}{\\frac {1}{(2\\pi )^{3}}}\\int e^{\\frac {i\\mathbf {k\\cdot r} }{\\hbar }}{\\frac {4\\pi \\eta _{\\mu \\nu }}{k^{2}}}\\;d^{3}k$\n\nwhere $Q_{i}$  is the QED-charge on the ith particle. Recognising the integral as just being a Fourier transform enables the equation to be simplified:\n\n$V(\\mathbf {r} )={\\frac {-g^{2}\\hbar cQ_{1}Q_{2}}{4\\pi }}{\\frac {1}{r}}.$\n\nFor various reasons, it is more convenient to define the fine-structure constant $\\alpha ={\\frac {g^{2}}{4\\pi }}$ , and then define $e={\\sqrt {4\\pi \\alpha \\varepsilon _{0}\\hbar c}}$ . Rearranging these definitions gives:\n\n$g^{2}\\hbar c={\\frac {e^{2}}{\\varepsilon _{0}}}$\n\nIt is worth noting that $g=e$  in natural units (since, in those units, $\\hbar =1$ , $c=1$ , and $\\varepsilon _{0}=1$ ). Continuing in SI units, the potential is therefore\n\n$V(\\mathbf {r} )={\\frac {-e^{2}}{4\\pi \\varepsilon _{0}}}{\\frac {Q_{1}Q_{2}}{r}}$\n\nDefining $q_{i}=eQ_{i}$ , as the macroscopic 'electric charge', makes e the macroscopic 'electric charge' for an electron, and enables the formula to be put into the familiar form of the Coulomb potential:\n\n$V(\\mathbf {r} )={\\frac {-1}{4\\pi \\varepsilon _{0}}}{\\frac {q_{1}q_{2}}{r}}$\n\nThe force (${\\frac {dV(\\mathbf {r} )}{dr}}$ ) is therefore :\n\n$F(\\mathbf {r} )={\\frac {1}{4\\pi \\varepsilon _{0}}}{\\frac {q_{1}q_{2}}{r^{2}}}$\n\nThe derivation makes clear that the force law is only an approximation — it ignores the momentum of the input and output fermion lines, and ignores all quantum corrections (ie. the myriad possible diagrams with internal loops).\n\nThe Coulomb potential, and its derivation, can be seen as a special case of the Yukawa potential (specifically, the case where the exchanged boson – the photon – has no rest mass).\n\n## Scalar form\n\nThe absolute value of the force F between two point charges q and Q relates to the distance between the point charges and to the simple product of their charges. The diagram shows that like charges repel each other, and opposite charges mutually attract.\n\nWhen it is of interest to know the magnitude of the electrostatic force (and not its direction), it may be easiest to consider a scalar version of the law. The scalar form of Coulomb's Law relates the magnitude and sign of the electrostatic force F acting simultaneously on two point charges q1 and q2 as follows:\n\n$|{\\boldsymbol {F}}|=k_{e}{|q_{1}q_{2}| \\over r^{2}}$\n\nwhere r is the separation distance and ke is Coulomb's constant. If the product q1q2 is positive, the force between the two charges is repulsive; if the product is negative, the force between them is attractive.\n\n## Vector form\n\nIn the image, the vector F1 is the force experienced by q1, and the vector F2 is the force experienced by q2. When q1q2 > 0 the forces are repulsive (as in the image) and when q1q2 < 0 the forces are attractive (opposite to the image). The magnitude of the forces will always be equal.\n\nCoulomb's law states that the electrostatic force F1 experienced by a charge, q1 at position r1, in the vicinity of another charge, q2 at position r2, in a vacuum is equal to:\n\n${\\boldsymbol {F_{1}}}={q_{1}q_{2} \\over 4\\pi \\varepsilon _{0}}{({\\boldsymbol {r_{1}-r_{2}}}) \\over |{\\boldsymbol {r_{1}-r_{2}}}|^{3}}={q_{1}q_{2} \\over 4\\pi \\varepsilon _{0}}{{\\boldsymbol {{\\widehat {r}}_{21}}} \\over |{\\boldsymbol {r_{21}}}|^{2}},$\n\nwhere r21 = r1r2, the unit vector 21 = r21/|r21|, and ε0 is the electric constant.\n\nThe vector form of Coulomb's law is simply the scalar definition of the law with the direction given by the unit vector, 21, parallel with the line from charge q2 to charge q1. If both charges have the same sign (like charges) then the product q1q2 is positive and the direction of the force on q1 is given by 21; the charges repel each other. If the charges have opposite signs then the product q1q2 is negative and the direction of the force on q1 is given by 21 = 12; the charges attract each other.\n\nThe electrostatic force F2 experienced by q2, according to Newton's third law, is F2 = −F1.\n\n### System of discrete charges\n\nThe law of superposition allows Coulomb's law to be extended to include any number of point charges. The force acting on a point charge due to a system of point charges is simply the vector addition of the individual forces acting alone on that point charge due to each one of the charges. The resulting force vector is parallel to the electric field vector at that point, with that point charge removed.\n\nThe force F on a small charge q at position r, due to a system of N discrete charges in vacuum is:\n\n${\\boldsymbol {F(r)}}={q \\over 4\\pi \\varepsilon _{0}}\\sum _{i=1}^{N}q_{i}{{\\boldsymbol {r-r_{i}}} \\over |{\\boldsymbol {r-r_{i}}}|^{3}}={q \\over 4\\pi \\varepsilon _{0}}\\sum _{i=1}^{N}q_{i}{{\\boldsymbol {\\widehat {R_{i}}}} \\over |{\\boldsymbol {R_{i}}}|^{2}},$\n\nwhere qi and ri are the magnitude and position respectively of the ith charge, i is a unit vector in the direction of Ri = rri (a vector pointing from charges qi to q).\n\n### Continuous charge distribution\n\nIn this case, the principle of linear superposition is also used. For a continuous charge distribution, an integral over the region containing the charge is equivalent to an infinite summation, treating each infinitesimal element of space as a point charge dq. The distribution of charge is usually linear, surface or volumetric.\n\nFor a linear charge distribution (a good approximation for charge in a wire) where λ(r′) gives the charge per unit length at position r′, and dℓ′ is an infinitesimal element of length,\n\n$dq=\\lambda ({\\boldsymbol {r'}})\\,d\\ell '.$ \n\nFor a surface charge distribution (a good approximation for charge on a plate in a parallel plate capacitor) where σ(r′) gives the charge per unit area at position r′, and dA′ is an infinitesimal element of area,\n\n$dq=\\sigma ({\\boldsymbol {r'}})\\,dA'.$\n\nFor a volume charge distribution (such as charge within a bulk metal) where ρ(r′) gives the charge per unit volume at position r′, and dV′ is an infinitesimal element of volume,\n\n$dq=\\rho ({\\boldsymbol {r'}})\\,dV'.$ \n\nThe force on a small test charge q′ at position r in vacuum is given by the integral over the distribution of charge:\n\n${\\boldsymbol {F}}={q' \\over 4\\pi \\varepsilon _{0}}\\int dq{{\\boldsymbol {r}}-{\\boldsymbol {r'}} \\over |{\\boldsymbol {r}}-{\\boldsymbol {r'}}|^{3}}.$\n\n## Simple experiment to verify Coulomb's law\n\nIt is possible to verify Coulomb's law with a simple experiment. Consider two small spheres of mass m and same-sign charge q, hanging from two ropes of negligible mass of length l. The forces acting on each sphere are three: the weight mg, the rope tension T and the electric force F.\n\nIn the equilibrium state:\n\n$T\\ \\sin \\theta _{1}=F_{1}\\,\\!$\n\n(1)\n\nand:\n\n$T\\ \\cos \\theta _{1}=mg\\,\\!$\n\n(2)\n\nDividing (1) by (2):\n\n${\\frac {\\sin \\theta _{1}}{\\cos \\theta _{1}}}={\\frac {F_{1}}{mg}}\\Rightarrow F_{1}=mg\\tan \\theta _{1}$\n\n(3)\n\nLet L1 be the distance between the charged spheres; the repulsion force between them F1, assuming Coulomb's law is correct, is equal to\n\n$F_{1}={\\frac {q^{2}}{4\\pi \\varepsilon _{0}L_{1}^{2}}}$\n\n(Coulomb's law)\n\nso:\n\n${\\frac {q^{2}}{4\\pi \\varepsilon _{0}L_{1}^{2}}}=mg\\tan \\theta _{1}\\,\\!$\n\n(4)\n\nIf we now discharge one of the spheres, and we put it in contact with the charged sphere, each one of them acquires a charge q/2. In the equilibrium state, the distance between the charges will be L2 < L1 and the repulsion force between them will be:\n\n$F_{2}={\\frac {{({\\frac {q}{2}})}^{2}}{4\\pi \\varepsilon _{0}L_{2}^{2}}}={\\frac {\\frac {q^{2}}{4}}{4\\pi \\varepsilon _{0}L_{2}^{2}}}\\,\\!$\n\n(5)\n\nWe know that F2 = mg tan θ2. And:\n\n${\\frac {\\frac {q^{2}}{4}}{4\\pi \\varepsilon _{0}L_{2}^{2}}}=mg\\tan \\theta _{2}$\n\nDividing (4) by (5), we get:\n\n${\\frac {\\left({\\cfrac {q^{2}}{4\\pi \\varepsilon _{0}L_{1}^{2}}}\\right)}{\\left({\\cfrac {\\frac {q^{2}}{4}}{4\\pi \\varepsilon _{0}L_{2}^{2}}}\\right)}}={\\frac {mg\\tan \\theta _{1}}{mg\\tan \\theta _{2}}}\\Rightarrow 4{\\left({\\frac {L_{2}}{L_{1}}}\\right)}^{2}={\\frac {\\tan \\theta _{1}}{\\tan \\theta _{2}}}$\n\n(6)\n\nMeasuring the angles θ1 and θ2 and the distance between the charges L1 and L2 is sufficient to verify that the equality is true taking into account the experimental error. In practice, angles can be difficult to measure, so if the length of the ropes is sufficiently great, the angles will be small enough to make the following approximation:\n\n$\\tan \\theta \\approx \\sin \\theta ={\\frac {\\frac {L}{2}}{\\ell }}={\\frac {L}{2\\ell }}\\Rightarrow {\\frac {\\tan \\theta _{1}}{\\tan \\theta _{2}}}\\approx {\\frac {\\frac {L_{1}}{2\\ell }}{\\frac {L_{2}}{2\\ell }}}$\n\n(7)\n\nUsing this approximation, the relationship (6) becomes the much simpler expression:\n\n${\\frac {\\frac {L_{1}}{2\\ell }}{\\frac {L_{2}}{2\\ell }}}\\approx 4{\\left({\\frac {L_{2}}{L_{1}}}\\right)}^{2}\\Rightarrow \\,\\!$  ${\\frac {L_{1}}{L_{2}}}\\approx 4{\\left({\\frac {L_{2}}{L_{1}}}\\right)}^{2}\\Rightarrow {\\frac {L_{1}}{L_{2}}}\\approx {\\sqrt[{3}]{4}}\\,\\!$\n\n(8)\n\nIn this way, the verification is limited to measuring the distance between the charges and check that the division approximates the theoretical value.\n\n## Atomic forces\n\nCoulomb's law holds even within atoms, correctly describing the force between the positively charged atomic nucleus and each of the negatively charged electrons. This simple law also correctly accounts for the forces that bind atoms together to form molecules and for the forces that bind atoms and molecules together to form solids and liquids. Generally, as the distance between ions increases, the force of attraction, and binding energy, approach zero and ionic bonding is less favorable. As the magnitude of opposing charges increases, energy increases and ionic bonding is more favorable." ]

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[ "What Are Named Parameters in Oracle\n\nQ\n\nWhat Are Named Parameters in Oracle?\n\n✍: FYIcenter.com\n\nA", null, "Named parameters are actual parameters specified not by position but by providing formal parameter names when calling the procedure or function. The main advantage of named parameters is that the caller don't have to remember the position of each parameter. But the caller have to remember the formal parameter names. The script below illustrates how to use named parameters:\n\n```SQL> CREATE OR REPLACE PROCEDURE SWAP_TEST AS\n2 A NUMBER := 3;\n3 B NUMBER := 8;\n4 PROCEDURE MY_SWAP(X IN OUT NUMBER,Y IN OUT NUMBER) AS\n5 T NUMBER;\n6 BEGIN\n7 T := X;\n8 X := Y;\n9 Y := T;\n10 END MY_SWAP;\n11 BEGIN\n12 MY_SWAP(Y=>B, X=>A); -- same as (X=>A, Y=B), OR (A,B)\n13 DBMS_OUTPUT.PUT_LINE('A = ' || TO_CHAR(A));\n14 DBMS_OUTPUT.PUT_LINE('B = ' || TO_CHAR(B));\n15 END;\n16 /\n\nSQL> EXECUTE SWAP_TEST;\nA = 8\nB = 3\n```\n\n2018-10-13, 832👍, 0💬" ]

[ null, "http://dba.fyicenter.com/Oracle/_icon_Oracle.png", null ]

[ "# [meteorite-list] Iranian Fireball Was Of Geophysical Origin\n\nFrom: MexicoDoug_at_aol.com <MexicoDoug_at_meteoritecentral.com>\nDate: Thu Apr 22 10:31:22 2004\nMessage-ID: <c0.5202343.2d5e5171_at_aol.com>\n\n--part1_c0.5202343.2d5e5171_boundary\nContent-Type: text/plain; charset=\"ISO-8859-1\"\nContent-Transfer-Encoding: quoted-printable\n\nThis topic was discussed a few weeks ago on the list, and it seems pretty=20\nconvincing that Earth parented meteorites are elusive for good scientific=20\nreasoning - it seems that if conditions to produce them happened, that the m=\naterial=20\nwould be glass or a split planet Earth (a la did the moon come from Earth=20\n\nWhile it may be possible (though statistically highly improbable), it is=20\nimportant not to say it is \"a bit of a stretch\", \"just like we have Martian=20\nmeteorites here\".\n\nThose statements taken together are misleading, to say the least.\n\nIt is important to recognize that Earth and Mars are so different regarding=20\natmospheric density (over 100X) / viscosity and to a much lesser degree=20\ngravity, that such an analogy is not based on astronomy and physics, but rat=\nher=20\nwishful thinking, with a general ignoring of scientific principles - i.e. a=20\nsolution (Earth parented meteorites exist because I can think it and there a=\nre=20\nMartian meteorites here) looking for a problem (Why no one has ever confirme=\nd an=20\nEarth parented meteorite).\n\nExtending that logic, I would ask where the Solar parented meteorites are at=\n,=20\nand while we are at it the Jovian parented=A0 and Venusian parented meteorit=\nes=20\nas well.=A0 The conditions on Mars simply do not lend themselves for compari=\nson=20\nto Earth.=A0 Venus is a better comparison for Earth.=A0 Perhaps someone coul=\nd work=20\nout the physics to show what sort of impactor on Earth is capable of causing=\ns=20\nsomething besides glass and giving it escape velocity.\n\nWithout doing the physics, it is clear it would have to be a kilometer plus=20\nsized impactor imparting in an instant to a kilometer plus sized Earth rock=20\nescape velocity plus frictional loss velocity, which further does not explod=\ne=20\nwith that velocity at sea level as it makes its way through the exponiential=\nly=20\nmost dense part of the atmosphere (i.e. a \"reverse meteorite\") at a right or=\n=20\nobtuse angle to the impact (which tends to create a velocity vector landing=20=\nback=20\non Earth).=A0 While this might sound \"plausible\", for an impactor to produce=\na=20\nkilometer plus sized rock with such a velocity seems nearly impossible, know=\ning=20\nthe characteristics of Earth surface features.\n\nTo actually achieve the above, either ground zero has to become liquid or=20\nplasma eventually producing glasses, for which there is some evidence in=20\ntektites, or Earth must be split like a nut, for which the Moon was presente=\nd as=20\nevidence in such a hypothethised impact around 4.5 billion years ago....\n\nSo that would leave a scenario of a gigantic impactor hitting near the base=20\nof a Mount Everest made of solid iron or other high tensile type structure,=20\nincoming at a low entry angle, and propelling the peak into outer space.\n\nIn the case of Mars objects over 10 meters (but probably in the realm 500 km=\n)=20\ncan impact whole much more readily and produce \"reverse meteorites\" with the=\n=20\ninitial velocities potentially conducive to this event which can escape more=\n=20\nreadily as gravity (and hence resulting escape velocities) is less than 40%=20\nEarth's.=A0 Furthermore Mars is closer to the Asteroid belt and is expected=20=\nto have=20\nmore flux of such potential impacts.\n\nSaludos\nDoug Dawn\nMexico\n\nEn un mensaje con fecha 02/13/2004 8:21:52 AM Mexico Standard Time,=20\ncviau_at_beld.net escribe:\n\n> and bit of a stretch.. but plausible:=A0 Just like we have\n> Martian meteorites here on earth, so would we not have some of the\n> ejecta from our terrestrial impacts also in orbit around the Sun\n\n--part1_c0.5202343.2d5e5171_boundary\nContent-Type: text/html; charset=\"ISO-8859-1\"\nContent-Transfer-Encoding: quoted-printable\n\n<HTML><FONT FACE=3Darial,helvetica><HTML><FONT SIZE=3D2 PTSIZE=3D10 FAMILY=\n=3D\"SANSSERIF\" FACE=3D\"Arial\" LANG=3D\"0\">This topic was discussed a few week=\ns ago on the list, and it seems pretty convincing that Earth parented meteor=\nites are elusive for good scientific reasoning - it seems that if conditions=\nto produce them happened, that the material would be glass or a split plane=\nt Earth (a la did the moon come from Earth question we had recently).=A0 <BR=\n>\n<BR>\nWhile it may be possible (though statistically highly improbable), it is imp=\nortant not to say it is \"a bit of a stretch\", \"just like we have Martian met=\neorites here\".<BR>\n<BR>\nThose statements taken together are misleading, to say the least.<BR>\n<BR>\nIt is important to recognize that Earth and Mars are so different regarding=20=\natmospheric density (over 100X) / viscosity and to a much lesser degree grav=\nity, that such an analogy is not based on astronomy and physics, but rather=20=\nwishful thinking, with a general ignoring of scientific principles - i.e. a=20=\nsolution (Earth parented meteorites exist because I can think it and there a=\nre Martian meteorites here) looking for a problem (Why no one has ever confi=\nrmed an Earth parented meteorite).<BR>\n<BR>\nExtending that logic, I would ask where the Solar parented meteorites are at=\n, and while we are at it the Jovian parented=A0 and Venusian parented meteor=\nites as well.=A0 The conditions on Mars simply do not lend themselves for co=\nmparison to Earth.=A0 Venus is a better comparison for Earth.=A0 Perhaps som=\neone could work out the physics to show what sort of impactor on Earth is ca=\npable of causings something besides glass and giving it escape velocity.<BR>\n<BR>\nWithout doing the physics, it is clear it would have to be a kilometer plus=20=\nsized impactor imparting in an instant to a kilometer plus sized Earth rock=20=\nescape velocity plus frictional loss velocity, which further does not explod=\ne with that velocity at sea level as it makes its way through the exponienti=\nally most dense part of the atmosphere (i.e. a \"reverse meteorite\") at a rig=\nht or obtuse angle to the impact (which tends to create a velocity vector la=\nnding back on Earth).=A0 While this might sound \"plausible\", for an impactor=\nto produce a kilometer plus sized rock with such a velocity seems nearly im=\npossible, knowing the characteristics of Earth surface features.<BR>\n<BR>\nTo actually achieve the above, either ground zero has to become liquid or pl=\nasma eventually producing glasses, for which there is some evidence in tekti=\ntes, or Earth must be split like a nut, for which the Moon was presented as=20=\nevidence in such a hypothethised impact around 4.5 billion years ago....<BR>\n<BR>\nSo that would leave a scenario of a gigantic impactor hitting near the base=20=\nof a Mount Everest made of solid iron or other high tensile type structure,=20=\nincoming at a low entry angle, and propelling the peak into outer space.<BR>\n<BR>\nIn the case of Mars objects over 10 meters (but probably in the realm 500 km=\n) can impact whole much more readily and produce \"reverse meteorites\" with t=\nhe initial velocities potentially conducive to this event which can escape m=\nore readily as gravity (and hence resulting escape velocities) is less than=20=\n40% Earth's.=A0 Furthermore Mars is closer to the Asteroid belt and is expec=\nted to have more flux of such potential impacts.<BR>\n<BR>\nSaludos<BR>\nDoug Dawn<BR>\nMexico<BR>\n<BR>\nEn un mensaje con fecha 02/13/2004 8:21:52 AM Mexico Standard Time, cviau_at_be=\nld.net escribe:<BR>\n<BR>\n<BLOCKQUOTE TYPE=3DCITE style=3D\"BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT=\n: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px\">and bit of a stretch.. but plau=\nsible:=A0 Just like we have<BR>\nMartian meteorites here on earth, so would we not have some of the<BR>\nejecta from our terrestrial impacts also in orbit around the Sun</BLOCKQUOTE=\n><BR>\n</FONT></HTML>\n--part1_c0.5202343.2d5e5171_boundary--\nReceived on Fri 13 Feb 2004 11:12:33 AM PST\n\nHelp support this free mailing list:", null, "StumbleUpon", null, "del.icio.us", null, "reddit", null, "Yahoo MyWeb" ]

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[ "", null, "Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.\n\nQUESTION\n\n# Suppose that X is a normally distributed random variable with = 100 and 2 = 25. P(X gt; 100) = ___________ 2. P(X 95) = ____________ 3.\n\nSuppose that X is a normally distributed random variable with µ = 100 and σ2 = 25.\n\n1. P(X > 100) = ___________\n\n2. P(X ≥ 95) = ____________\n\n3. P(95 < X ≤ 105) = ___________" ]

[ null, "https://www.facebook.com/tr", null ]

[ "# Topic 3 DQ 1\n\nTopic 3 DQ 1\n\nPlease Respond to the following post with a paragraph, add citations and references.\n\nORDER A PLAGIARISM FREE PAPER NOW\n\nA z-test is any statistical test otherwise known as a hypothesis for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution (“Z-test,” 2018). A one-sample location test, two-sample location test, paired difference test and maximum likelihood estimate are examples of tests that can be conducted as z-tests. Z-tests are closely related to t-tests, but a z-test assumes the standard deviation is known and the sample size is large.\n\nThe reason a z-test would be preferred over a t-test is when an investor wishes to test whether the average daily return of a stock is greater than 1%. A simple random sample of 50 returns is calculated and has an average of 2%. Assume the standard deviation of the returns is 2.50%. Therefore, the null hypothesis is when the average, or mean, is equal to 3%. The alternative hypothesis is whether the mean return is greater than 3%. Assume an alpha of 0.05% is selected with a two-tailed test. Consequently, there is 0.025% of the samples in each tail, and the alpha has a critical value of 1.96 or -1.96. If the value of z is greater than 1.96 or less than -1.96, the null hypothesis is rejected. Nuisance parameters should be known or estimated with high accuracy. Z-tests focus on a single parameter, and treat all other unknown parameters as being fixed at their true values (“Z-test,” 2018). Z-tests are not commonly used because it is not as straightforward or easy to use compared to t-tests.\n\nReferences\n\nZ-test. (2018). In Wikipedia. Retrieved October 8, 2018, from https://en.wikipedia.org/wiki/Z-test\n\nTags:" ]

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[ "Skip to content\n\n# Search \"+Home -Bookshelf +Funny things +Alan Moore +YY +Sociology -Donald Knuth +Probability Theory: The Logic of Science +Math +David MacKay +Science of science +Science +Scientometrics +Books +Probability theory +Probability +Evolution of science +Word embedding +Probability distribution -G. Dobínski +Network geometry -Scientific communication\"\n\nPages related to:\n\nbut not related to:" ]

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[ "# Can an ordered field contain complex numbers?\n\nI read a question about ordering of complex numbers, and saw an answer showing that there cannot exist an ordering of the complex numbers because regardless of how $i$ is placed in that order, it would imply that $i^2 = -1$ would be positive.\n\nThis proof can obviously be generalized to prove that for any non-zero $a \\in Q$ it is impossible for $ai$ to be an element of an ordered field. But there is no obvious generalization of the proof showing that the same hold for all imaginary numbers.\n\nDoes there exist a sub-field of the complex numbers containing at least one imaginary number, which can be assigned a consistent ordering?\n\nOr stated in different terms, does there exist a subset of the complex numbers, which is a formally real field and is not a subset of the reals?\n\n• The reals are a sub-field of the complex numbers. By the way, the question in the end and the title are not the same. – Ofir Schnabel Jan 23 '15 at 11:59\n• If such a $P$ exists, would $i$ or $-i$ be in it? – Autolatry Jan 23 '15 at 12:13\n• @OfirSchnabel I updated the question to explicitly state that it must contain at least one imaginary number. – kasperd Jan 23 '15 at 12:45\n• @Autolatry If such a field exists it cannot contain $i$ or $-i$ as proven by the linked answer. – kasperd Jan 23 '15 at 12:47\n• Consider an irreducible polynomial $f \\in \\mathbb{Q}[X]$ with real and non-real zeros. If $\\alpha,\\beta$ are zeros of $f$, then $\\mathbb{Q}(\\alpha) \\cong \\mathbb{Q}(\\beta)$. If $\\alpha \\in \\mathbb{R}$ then $\\mathbb{Q}(\\alpha)$ is an ordered field (a subfield of $\\mathbb{R}$), hence $\\mathbb{Q}(\\beta)$ can be made an ordered field. Take for example $f(X) = X^4 - 2$ and $\\mathbb{Q}(i\\sqrt{2})$. – Daniel Fischer Jan 23 '15 at 22:51\n\nThis is an old question but since it is unanswered I thought I would provide an interesting example of such a field (technically it is answered: Daniel Fischer's answer suffices as far as I can tell). Another reason I wanted to provide this answer as opposed to the more elegant one given in Daniel Fischer's comment is to highlight the fact that $\\mathbb{C}$ contains some pretty strange subfields.\nLet $C(\\mathbb{R})$ be the ring of continuous real-valued functions defined on $\\mathbb{R}$ and let $I' \\subseteq C(\\mathbb{R})$ be the ideal consisting of functions with compact support, with $I$ the corresponding maximal ideal. Consider the residue field $C(\\mathbb{R})/I$. It is proven here (rather famously) that this is a real-closed field containing a proper subfield isomorphic to $\\mathbb{R}$, so there is a unique total order $\\leq$ we can define on this field. We now note that $F=C(\\mathbb{R})/I$ has cardinality $\\mathfrak{c}$:\nProof: It is obvious that $|F| \\geq \\mathfrak{c}$ since $F$ contains a subfield isomorphic to $\\mathbb{R}$. To prove the other inequality, note that $F$ is actually a collection of equivalence classes, i.e. $F= \\left\\{ [f]: f \\in C(\\mathbb{R}) \\right\\}$, for some equivalence relation. By the axiom of choice, there is a function $g:F \\rightarrow C(\\mathbb{R})$ such that $g([f]) \\in [f]$ for each $f$. Such a map is necessarily an injection, so $|F| \\leq |C(\\mathbb{R})|=\\mathfrak{c}$. Schroeder-Bernstein then gives our result. $\\Box$\nSo $F$ has the cardinality of the continuum, and it is also easy to see that $F$ has characteristic $0$. Since any field of characteristic zero and cardinality at most continuum is isomorphic to a subfield of $\\mathbb{C}$ (stated here and I've also seen this invoked in other places as well), we have $F \\cong K \\subseteq \\mathbb{C}$ for some field $K$. Give $K$ the order induced by the isomorphism with $F$. Since $F$ contains a proper subfield isomorphic to $\\mathbb{R}$ and $\\mathbb{R}$ contains no such thing, we know $K$ is not contained in $\\mathbb{R}$, so $K$ is a field satisfying your desired properties.\nNow, if you are familiar with the paper I linked above by Hewitt, you'll recognize that this will actually work for any non-compact, completely regular topological space $X$ with a maximal ideal $I$ such that $C(X)/I$ has cardinality $\\mathfrak{c}$ and has the so-called eta set property. We can find infinitely many such topological spaces and ideals, thus it is tempting to believe that we can actually produce infinitely many non-isomorphic examples of such fields in the way we did above. A word of caution about this: it is completely consistent with ZFC that all fields produced in this manner are isomorphic (see here, it is an implication of the continuum hypothesis). Under CH, the unique (up to isomorphism) field we have constructed is a \"hyperreal number field\" and happens to be the most common one used in non-standard analysis." ]

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[ "# How to Convert Kg to Lbs in Excel\n\nIn order to convert kg to lbs in Excel, multiply by 2.204622622. In the same way, to convert pounds to kilograms, multiply by 0.45359237. Learn more\n\nMicrosoft Excel is a spreadsheet program for Windows, macOS, Android, and iOS that includes calculating and computation tools, graphing tools, pivot tables, and Visual Basic for Applications, a macro programming language (VBA). Excel recognizes trends in your data and organizes them to save you time. Create spreadsheets quickly and easily using templates or from scratch and execute calculations with contemporary formulae.\n\nThe United States, Liberia, and Myanmar are the only three nations that still use the old imperial or British system of weights and measures. In contrast, the rest of the world utilizes the metric system as the dominant method of weights and measurements.\n\nBut don’t worry; in Excel, you can quickly convert kilograms (Kg) to pounds (lbs.) or pounds to kilograms. This tutorial will show you how to convert data from kilograms to pounds in Excel.\n\nThis Excel lesson will show you how to convert data from kilograms (Kg) to pounds (lbs.) and vice versa.\n\n## Convert kg to lbs. (Kilograms to Pounds)\n\nSimply increase the value by 2.2046226218 or divide by 0.45359237 to convert kg to lbs.\n\n`=m*2.2046226218`\n\nor divide\n\n`=m/0.45359237`\n\nWhere m is the numeric value to be converted, the results of both formulae are the same.\n\n• Step 1: In the cells where you wish to put the converted amount, click.\n• Step 2: Type =cell to convert/2.2046 (for example, = A2/2.2046) into the search box.\n• Step 3: Enter the code. Be careful to substitute the numeric value you want to convert for ‘m.’\n\nAlternatively, divide 20 by 0.45359237. (kg).\n\n### Convert KG to Lbs. Manually\n\nYou can also manually convert weight in excel. All you need is to know units of mass that are:\n\n• 1 kg = 2.2046226218 lbs.\n• 1 lbs. = 0.45359237 kg\n\n## Convert Lbs. to Kg (pounds to kilograms)\n\nThis is the inverse of the kg to lbs. conversion procedure. Simply increase the value by 0.45359237 or divide by 2.2046226218 to convert pounds to kilograms:\n\n`=m*0.45359237`\n\nor divide\n\n`=m/2.2046226218`\n• Step 1: Click in the cells where you want the converted value to appear.\n• Step 2: In the search box, type =cell to convert/2.2046 (for example, =A2/2.2046).\n• Step 3: Type the code into the box. replace ‘m’ with the number value you wish to convert.\n\nYou can also watch the following video if you gets any trouble with it.\n\n## Convert Kg to LBM/lbs. using the CONVERT function in Excel\n\nThe CONVERT function is used in this formula to convert a number from one measuring system to another. CONVERT uses “from” and “to” units entered as text to do the conversion. CONVERT will conduct conversion and produce a numeric result as long as the units specify appropriate choices. The CONVERT function is another way to convert kilos to pounds.\n\nThe best way to convert one measurement to another is to use the CONVERT function. It’s not just about weight units. Within the convert function, you may convert length, area, temperature, distance, and a variety of other metrics.\n\n`The Formula is: =CONVERT (number, “from_unit, “to_unit”)`\n\nThere are three arguments in the CONVERT formula:\n\n• The numeric value we wish to convert is called a number.\n• The unit to convert from is from the unit, and the unit to convert to is to the unit.\n• To convert, you must input the value as well as the unit type into the formula. Units must be given as string abbreviations of the measurement kinds. This value must be entered as a number or a cell reference.\n\nWe’re looking to convert a kilogram weight measurement to pounds. The generic formula for doing so is shown below.\n\n`=CONVERT (value,\"kg\",\"lbm\")`\n\nHere ‘kg’ stands for the kilogram and ‘lbm’ stands for pounds.\n\nThe most popular shorthand for pounds is ‘lbs‘; however, in Excel, you must use ‘lbm.’\n\nEnter ‘lbm’ as the from unit and ‘kg’ as the unit in the formula to convert pounds to kilograms.\n\nWeight, distance, time, pressure, force, energy, power, magnetism, temperature, liquid, and volume may all be converted with CONVERT. Valid unit strings must be in the correct case. To convert an entire column, use the fill handle in the bottom right corner of the formula cell to drag and copy the formula to the rest of the cells.\n\n## Conclusion\n\nThis is how you can convert kg to lbs. in Microsoft excel. We hope this article was useful and interesting. Feel free to reach us in the comment section below and check out our other articles about Microsoft excel.\n\n## Frequently asked question\n\n### What is the difference between LBM/LBF?\n\nThe Imperial system of measurement (or U.S. Customary) uses the pound to measure both mass and force, which can cause confusion for some people. In order to distinguish the two types of pounds, one is called a pound-mass (lbm) while the other is called a pound-force (lbf).\n\n### In Excel, how do I convert grams to pounds?\n\nThe Imperial system of measurement (or U.S. Customary) uses the pound to measure both mass and force, which can cause confusion for some people. In order to distinguish the two types of pounds, one is called a pound-mass (lbm) while the other is called a pound-force (lbf).\n\n### In Excel, how can I remove kg?\n\nYou may execute a search and replace if you highlight the range from which you wish to remove the kilogram. Type “kg” (without the quotations) in the “Find what:” field and leave the “replace with:” box blank. Then select “Replace all” from the drop-down menu.\n\nSubscribe\nNotify of", null, "This site uses Akismet to reduce spam. Learn how your comment data is processed." ]

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[ "How to determine first byte (recovery ID) for signatures (message signing)?\n\nI do realize that in bitcoin when we return the signature result for signing a message the first byte includes information for recovering the public key required for verification using a formula like this:\n\n27 + (4 if comp. 0 if not) + (0<=num<=3)\n\nWhat I am struggling with is how do we determine that num number? According to section 4.1.6 of SEC:1 for recovering public keys:\n\n1. x = r + jn\n2. Calculate Q based on R if invalid move to next\n3. Calculate Q based on -R\n\nSince j (cofactor of secp256k1) is 0 and 1 and there are two values for R. So there should be 4 possible public keys. Is num the number of public keys that we rejected before reaching the correct one? Because that is the only explanation that I can come up with based on comparisons I have made between signatures generated using Electrum and public key recovery I have done myself using SEC1.\n\nBonus question: Why was 27 chosen?\n\n• I'm not sure what num means there either, but I wrote this a while ago which might interest you. It explains exactly how to encode and decode the recid byte : github.com/fivepiece/sign-verify-message/blob/master/… Dec 19 '18 at 12:34\n• @arubi Thanks for the reply. Based on your comment and another answer I've received on bitcointalk, I believe the main cause of my confusion is that I was thinking you find that num after signing and finding r,s. But it seems like you must find it during using the y coordinate of r which is discarded and doesn't come out of sign function. Now I am trying to figure out the details... Dec 19 '18 at 13:03\n• Dec 19 '18 at 22:58\n\nFWIW this is what I have found regarding this question. Basically there are two ways of finding what libraries call \"recid\" or recovery ID. Most of them use the first method but there is another way:\n\nMethod 1:\n\n• Only requires r and s so it can be performed by anyone as long as you have the signature and the \"message\" that was signed.\n• It is so much slower because it has 3 scalar multiplication and based on cofactor of the elliptic curve used the whole operation may be repeated 2*(h+1) times, which is up to 4 times for bitcoin with secp256k1 curve (99% of the time it is 1 or 2 times).\n\nThe steps are explained in section 4.1.6 of SEC:1, I won't repeat them here.\n\nTo find recid you check the calculated public key with the given public key or hash of it and report number of rejected public keys as recid. For example if x=r+(0*order) and Q was used then recid=0 and if -Q was used then recid=1 and so on.\n\nmethod 2:\n\n• It requires full r or R=(xR, yR) so it can only be done while signing (requires having the private key).\n• It is much faster because there is no additional calculations. It just needs value checks which are fast.\n• This is usually referred to as v in libraries\n\nbyte v = if(R.X > curve.N) then 2 else 0) | (if R.Y.IsEven then 0 else 1);\n\nBasically it is check to see if xR is bigger than curve order (N) and whether yR is even or odd. Something that should not be forgotten is a \"flip\" that is performed based on s and whether s was used in the signature or -s\n\nif s > curve.N/2 then v^=1 else do nothing\n\n** Note that in the end you need to calculate the following:\nrecid = 27 + v + (if compressed 4 else 0)\n\n• IMO you should also accept this as the answer Dec 22 '18 at 11:16\n\nThis will be less of a theoretical answer and more of practical guidance; while developing Secp256k1 or Bitcoin libraries, I always found the following table handy:\n\ny-parity x-order compression recovery id v\neven less than n false 0 27\nodd less than n false 1 28\neven more than n false 2 29\nodd more than n false 3 30\neven less than n true 0 31\nodd less than n true 1 32\neven more than n true 2 33\nodd more than n true 3 34\n\nlet me explain the columns:\n\n• y-parity or often just parity describes whether the y-coordinate of the public key point R(x, y) is even. this is important because in most cases, the signature only contains r = R.x and not R.y. This speeds up signature recovery. (Secp256k1)\n• x-order is a super rare edge-case where a point's x-coordinate is actually above the order of the curve n. In 99.99999999% of the cases, this is false. (Secp256k1)\n• compression is just an indicator whether you want a compressed or an uncompressed public key. (Bitcoin)\n• recovery_id just indicates which of the four potential point's y-coordinates is to be used. (Secp256k1)\n• v is how we encode this value. For uncompressed keys we use v = recovery_id + 27 and for compressed v = recovery_id + 31. (Bitcoin)\n\nIf you want to understand how this works for Ethereum, you would have to read EIP-155 which also introduces an additional variable of chain_id for replay protection: v = 2 * chain_id + 35 + recovery_id. (Ethereum)\n\nWhat I am struggling with is how do we determine that num number?\n\nThat's the recovery ID from the table above." ]

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[ "# Questions Asked onSeptember 29, 2017\n\n1. ## history\n\nWhich most accurately reflects the development of agriculture in early African civilizations? the walls of the jabrin castle were erected in oman to protect valuable crops the kingdom of Ghana exchanged surplus crops and gold for textiles and salt brought\n\n2. ## Algebra\n\nWhat type of equation will best fit the data below? Linear Quadratic Exponential (I have a picture of a graph is there a way I can show it too get help?)\n\n3. ## Chemistry\n\nWrite a net ionic equation for the reaction that occurs when cobalt(II) carbonate (s) and excess hydroiodic acid are combined.\n\n4. ## Algebra\n\nFind the average rate of change of f(x)=6x²−3 on the interval [2,a]. Your answer will be an expression involving a What I did so far: I found f(2) which is 21 and that would make the function (2,21) Then, I found f(a) which is 6a^2-3 and that would make\n\n5. ## history\n\nWhat was the Roman Empire’s system of government prior to Julius Caesar that heavily influenced Western democracies? Peasants, including women and slaves, were ruled by kings, barons, and lords. Roman government consisted of a king, crown prince, and an\n\n6. ## history\n\nWhich best defines settlement as it pertains to the history of civilization? a location where two parties resolved disputes or conflict over land ownership a location where groups ceased roaming and built permanent dwellings location where natural\n\n7. ## history\n\nIn 332 BC, which military leader defeated the Persians and annexed Egypt to be part of his Macedonian Greek empire? alexander the great Julius Caesar mark antony king tutankhamum is it a\n\n8. ## Biology matriculation\n\nWhat is the expected frequency for a person having tongue rolling ability and attached earlobe???\n\n9. ## Science\n\nWhat is the density of a book whose mass is 1,800 g and whose volume is 300 cm3? *My Answer*You want to identify the numbers first, density = mass ÷ volume. Which would give you, 1800g ÷ 300 cm³ = 6 g/cm³. *Cant Figure Out *What is the mass of a ball\n\n10. ## history\n\nWhich best describes a democracy? form of government in which political power is held by a single ruler form of government in which political power is held by the people government based on appointing officials according to merit and academic\n\n11. ## Calculus\n\nA ball is thrown from a height of 130 feet with an initial downward velocity of 6/fts . The ball's height h (in feet) after t seconds is given by the following. =h−130−6t16t2 How long after the ball is thrown does it hit the ground?\n\n12. ## Trigonometry\n\nSketch the graph of the function (Include two full periods. Find one complete cycle. Show your work. y=-3+5cos πt/12\n\n13. ## history\n\nWhich major culture of the ancient world is responsible for producing literature such as the Iliad and the Odyssey? I think its greek\n\n14. ## math\n\nwhat is 4/5 of 10/13? A. 40/65 B. 5/18 C. 8/13 D. 20/65\n\nasked by I really hate school\n\nThink about all of the many products you can purchase today. Identify one product that currently represents each phase of the product life cycle, and make a brief statement about its competition, price, distribution, and promotion.\n\n16. ## phisical science\n\nOn a winter day the temperature drops from –15°C to –25°C overnight. If a pan sitting outside contains 0.20 kg of ice, how much heat is removed from the ice for this temperature change?\n\n17. ## chemistry\n\nThree gases (8.00 g of methane, CH4, 18.0 g of ethane, C2H6, and an unknown amount of propane, C3H8) were added to the same 10.0-L container. At 23.0 ∘C, the total pressure in the container is 5.20 atm . Calculate the partial pressure of each gas in the\n\n18. ## Math\n\nCy has 42 baseball cards and 70 football cards that he wants to group into packages. Each package will have the same number of cards and each package will have the same numbers of baseball cards and football cards. How many packages will Cy make if he uses\n\n19. ## Math\n\nWhat amount must be set aside now to generate payments of \\$30,000 at the beginning of each year for the next 13 years if money is worth 5.93%, compounded annually? (Round your answer to the nearest cent.)\n\n20. ## Math\n\nwhy is 1.6666666667 an irrational number? this was my answer to a question, and you also have to explain why your answer is an irrational number. an irrational number is \"any real number that can not be written and the quotient of two number\" but it can?\n\n21. ## geometry\n\nthe measure of each exterior angle of a regular pentagon is ____ the measure of each exterior angle of a regular nonagon greater than less than equal to** If i'm wrong can you please explain to me why i'm wrong?\n\n22. ## Geometry\n\nThe midpoint of Line Segment AB is (2,-9). The coordinates of one endpoint are A(4,10). Find the coordinates of endpoint B. Can someone please check my work and tell me if my answer is correct. Step 1: 2x-9= 4x+10 2x-9= 10 2x= 1 Step 2: AB= 2x-9 =2(1)-9\n\n23. ## Math\n\nFor the following geometric sequence find the recursive formula and the 5th term in the sequence. In your final answer, include all of your work. {-4, 12, -36, ...}\n\n24. ## Chemistry\n\n1.When 5 grams of wood burns completely and 15 grams of oxygen, 10 grams of water vapor and some carbon dioxide are given off. (How many grams of carbon dioxide would be produced in this example?) I need help with the question in parentheses. I have the\n\n25. ## English\n\nI’m at the tourist centre in Boston the speakers tone can best be described as\n\n26. ## Chemistry\n\nThe pesticide DDT (C14H9Cl5)... Express these concentrations in ppm and in milimoles per liter. Orchard - Sample size: 250.0mL Mass of DDT: 0.030 mg Residential - Sample size: 1.750 L Mass of DDT: 0.035 mg Residential After a Storm - Sample size: 50.0 mL\n\n27. ## history\n\nWhich accurately describes battle achievements of Alexander the Great? He defeated the Roman Empire in Egypt, founded the city of Cairo, and ordered the preservation of King Tutankhamun artifacts. He defeated the Persian Empire in Egypt and founded the\n\n28. ## Statistics and Probability\n\nA ticket in a typical lottery like Lotto 6/49 is usually \\$2. The probability of winning Lotto 6/49 is 1 in 13,983,816. The payoffs (jackpots) are usually in excess of \\$1 million. Suppose that you buy one ticket for \\$2 and the jackpot is \\$1 million. What is\n\n29. ## English\n\ndetermine whether the underlined conjunctions in the following sentences are coordinating or correlative by choosing the letters A(coordinating) or B(correlative) Each of the twelve Federal Reserve district banks is also authorized to dispose of unusable\n\n30. ## pre-calculus math\n\nA polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over . 3, −3 − 2i; degree 3\n\n31. ## MATH\n\nUse a fractional exponent to write the expression the fourth root of 81 raised to the ninth power\n\n32. ## Social studies\n\nWhat were some issues on which Hamilton and Jefferson disagreed? Select all that apply □ the role of the federal government □ how to structure judiciary □ imposition of taxes □ how to structure a banking system\n\n33. ## World History\n\nFollowing the deaths of Cleopatra and Mark Antony, Egypt was no longer a sovereign nation and became occupied by Rome (1). Roman law was imposed on Egypt, and it was split up into smaller provinces under Roman governors and prefects (2). Egypt became the\n\n34. ## Social Studies\n\nScientists classify native people living in the Americas as having lived during one of four time periods. Which shows the correct order in which these time periods occurred?? A- Woodland, Mississippian, Paleo-Indian, Archaic B- Mississippian, Paleo-Indian,\n\n35. ## Math\n\nEvaluate the integral from [sqrt(pi/2), sqrt(pi)] of x^3*cos(x^2) by first making a substitution and then using integration by parts. I let u = x^2 and du= 2x dx but then it doesn't equal that in the equation?\n\n36. ## Math\n\nwhat is the prime factorization for 40\n\n37. ## Math\n\nChoose the correct justification to get to line 3: -21 - 51x < 1 - 62x.\n\n38. ## social studies\n\nMesoptomia climate was\n\n39. ## History\n\n1. La salle had conflicts with which of the following groups of American Indians? Hasinai Caddo Apache Karankawa\n\n40. ## Math\n\na) Find the zeros of the function. d) Find the domain. e) Find the range. a) none d) (-infinity, 0) U (2,infinity) e) (0, infinity) Is this right?\n\n41. ## Earth Science\n\nMinerals are classified into groups based on _______. Characteristics?\n\n42. ## tourism and hospitality\n\nWhat percentage of the england's income is generated from tourism?\n\n43. ## Math\n\n1.What is the sum of 5/6 + 2/3? (1 point) A. 1 1/3 B. 1 1/2* C. 1 2/3 D. 1 3/4 2. Sylvia has 6 1/2 boxes of chocolate to share at a family picnic. If she gives each person1/3\n\n44. ## ss .\n\n1 ' Africa's highest point, or the place with the greatest elevation is A: Victoria falls B: Lake Assal C: Mount Kenya D:Mount Kilimanjaro *** 2 ' Southern and Eastern Africa tends to be drier and cooler than West and Central Africa because Southern and\n\n45. ## science\n\nIf a man weighs 194 pounds and is 69 inches tall where is his center of gravity?\n\n46. ## Physics\n\nA 170 N block rests on a table.The suspended mass has a weight of 52N. What is the magnitude of the minimum force of static friction required to hold both blocks at rest? What minimum coefficient of static friction is required to ensure that both blocks\n\n47. ## Physical Chemistry\n\nOne potential problem with using molarity to express concentration is that molarity is temperature dependent. If you make a 1.000 M solution of aqueous HCl at 25 degrees celsius, what would the molarity of this solution become if the temperature of the\n\n48. ## Social Studies\n\nSince Canada’s labor force growth is made up of 70% immigrants and is projected to rise to 100%, you might best speculate that Canada’s government has a(n) ______________ policy. A. anti-immigration B. pro immigration C. Constitutional ** D. democratic\n\n49. ## Physics\n\nYou are hanging onto the end of a long rope, the other end of which is attached to a Coast Guard helicopter. Model yourself as a particle of mass M = 52.8 kg with a diameter equal to 0.540 m. The density of the air is ρ = 1.29 kg/m3. Assume the drag\n\n50. ## chemistry\n\nA cylinder with a movable piston contains 2.00 g of helium, He, at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many grams of helium were added to the cylinder if the\n\n51. ## algebra\n\nSolve the following equation for p: 5s - 3p = fp + 12\n\n52. ## Health and PE\n\nWhich of the following plays a role in determining a persons weight? select all that apply A:heredity. B:activity level. C:body mass index (BMI). D:body composition. I think the answers are B, C, and D. Thank you.\n\n53. ## alg\n\nwhich of the following is a solution to the equation y = 3x - 1 A.(4,1) B.(2,5) C.(4,3) D.(0,-3) Answer: A\n\n54. ## Chemistry Lab\n\nIm preparing my report for Synthesis of Alum chemistry lab. Need help with these 2 questions: 1-What other cations besides aluminum can be used to make alum crystals? Explain 2-Why we need to add sulfuric acid slowly to the solution as opposed to pouring\n\n55. ## social studies\n\nwhich historical event was the most important in forming the character of modern germany? A:industrial revolution B:protestant reformation C:WW2 D:enlightenment\n\n56. ## Chemistry\n\nIs cl2 or F2 less volatile? Cl2 is less volatile because it has more intermolecular forces and therefore has a higher boiling point. Is this right?\n\n57. ## history\n\nWhich best describes the Assyrian Empire’s impact on the Mesopotamia region? The Assyrians were the last known hunter-gatherer group in Mesopotamia. The Assyrians attacked and killed thousands of Muslims in Egypt, Iran, and Syria. The Assyrians attacked\n\n58. ## Math\n\nWhat is the repeating decimal 0.282282282 as a fraction in simplest form? 141141141/5000000000*\n\n59. ## Trigonometry\n\nSketch the graph of the function (Include two full periods. Find one complete cycle. y=10cos πx/6\n\n60. ## algebra 2\n\nby graphing the system of constraints find the values of x and y that minimizes the objective function x+2y>8 x>2 y>0 >=greater than or equal to my answer was 0,10 am i right?\n\n61. ## Trigonometry\n\nSketch the graph of the function (Include two full periods. Find one complete cycle. Show your work. y=sin4x\n\nThe regular price of a chair is \\$895. If you purchase the chair at a 25% discount and then pay 6% sales tax, what is the final cost of the chair? I don't get how to set up this problem\n\n63. ## Math\n\nHow many ounces of 1% antifreeze solution must be added to 100 ounces of 40% antifreeze solution to obtain a 16% antifreeze solution? how do I set this equation up?\n\n64. ## algebra\n\n7+8 2-394-2)2\n\n65. ## history\n\nWhich most accurately describes the structure of the Roman government when it was a republic? A: The Roman government was a dictatorship in which an emperor ruled by divine right. B: The Roman government consisted of two consuls and the senate. C: The\n\n66. ## MATH\n\nUse a property of rational exponent to simplify this equation (C^6) ^7\n\n67. ## Social studies\n\nIn his farewell address, what did Washington say about the U.S. forming alliances with specific European countires? A) it would be seen as a sign of disrespect B) other countires might also seek to form alliances***** C) it might put peace and prosperity\n\n68. ## Statistics\n\nWilliams, Dunsiger, Jennings, and Marcus (2012) conducted a study to test how enhanced mood during exercise can increase the likelihood of physical activity in the future. They reported that at 6 months of physical activity, mood scores (rated on a scale\n\n69. ## Chemistry\n\nBalance the following net iconic reactions, and identify which elements are oxidized and which are reduced: a. MnO4^- (aq) + S^2- (aq) --> MnO2(s) + S(s) b. IO3^- (aq) + I^- (aq) --> I2(s) c. Mn^2+ (aq) + BiO3^- (aq) --> MnO4^- (aq) + Bi^3+ (aq)\n\n70. ## English\n\n1. Each year, people die from second hand smoke. 2. Each year, people die from second hand smoking. ---------------------------- Which one is okay? Are both expressions acceptable? Which one is commonly used, 'secondhand smoke' or 'secondhand smoking'?\n\n71. ## English\n\n1. The book was discovered in a used bookstore in Chicago. 2. The book was discovered in a secondhand bookstore in Chicago. 3. I found a rare book at a used bookstore. 4. I found a rare book at a secondhand bookstore. ----------------------------- In each\n\n72. ## math\n\nMultiply 2/3 and 6/7 A. 4/7 B. 4/21 C. 12/21 D. 3/7 PLEASE HELP if you could please tell me all the answers for this mixed numbers practice if u know them\n\nasked by I really hate school\n73. ## English\n\n1. At nine, the buses will depart for Lorca Beach. 2. At nine, the buses will leave for Lorca Beach. 3. At nine, the buses will set out for Lorca Beach. 4. At nine, the buses will start for Lorca Beach. 5. At nine, the buses will ____ ____ Lorca Beach.\n\n74. ## math intergers and algebraic exressions\n\nhi mrs sue how are you i need help with my math unit test i really need help what is the solution to -55+q=7 my answer is a\n\n75. ## Physical Chemistry\n\nYour hot tub has overheated to a very uncomfortable 48 degrees C. If your hot tub contains 402 L of hot water, what mass of ice at -5 degrees C would you need to add to your hot tub to bring the temperature down to a more comfortable 36 degrees C?\n\n77. ## Cryptography\n\nProblem 1. (25 points) Let p be a prime and g be a generator of the multiplicative group Z∗p of integers modulo p, (note that F∗p is also commonly used to denote this group, but we will stick with Z∗p). Let λ be the bit length of p.\n\n78. ## 1 Out Of 100 Math Trick HELP PLEASE!!!\n\n1. Choose a number between 1 and 100. 2. Multiply the number by 5. 3. Add 15 to the number. 4. Divide the number by 5. 5. Subtract the original number. How does this work, please help!\n\n79. ## tourism and hospitality\n\nwhat is the economic multiplier for the UK?\n\n80. ## physics\n\nTo haul a boat out of the water for the winter, a worker at the storage facility uses a wide strap with cables operating at the same angle (measured from the horizontal) on either side of the boat. Determine the tension in each cable if the boat has a mass\n\n81. ## Government\n\nWhat are the countries that have a democracy in the Middle East? Just need source's\n\n82. ## geography\n\nWhat is an informal democracy and in what way in the Middle East?\n\nKrystal bought a refrigerator from a rental center for \\$1,050. She makes 16 monthly payments of \\$112.75 with her credit card. The rental center charges \\$1.25 for every purchase made with a credit card. What is the total cost of the refrigerator? My answer\n\nSharon purchased a sprinkler system for \\$1,950 using a six-month deferred payment plan. The interest rate after the introductory period is 23.99%. No down payment is required, but there is a minimum monthly payment of \\$25. What is the balance at the\n\n85. ## qwertyuik\n\nAn individual has a transition intensity of mortality for the next 10 years of μs=0.01s per annum (where s is the number of years from today). Calculate the probability (to 3 decimal places) that they will survive for the next 10 years\n\n86. ## Algebra\n\nWhat do A & B stand for in algebra can some one please explain this to me because I'm really confused:/\n\n87. ## Math\n\nSolve the integral of (x*e^2x)/(1+2x)^2 by first using u substitution and then use integration by parts. I am very confused on how to do u-substitution with this because no mattter what I let u be equal to the du never comes out to be anything in the\n\n88. ## Math\n\nSolve the integral from [0,pi] of x*sinx*cosx*dx I don't understand how to solve this problem because if I let u =x and du =1 and dv=sinx*cosx, I can't find v. How do you solve this?\n\n89. ## Math\n\nEvaluate the integral of x*ln(1+x) dx by first making a substitution and then using integration by parts. I let u=1+x and du = dx but then ln(u) du can't integrate to anything?\n\n90. ## Math\n\nEvaluate the integral of (e^2x)*sin^3 x dx I let u = e^2x, du = (1/2)e^2x dx v= (-1/3)cos^3 x , dv =sin^3 x dx When I used integration by parts and solved it all out I got: (37/36)intgral of (e^2x)*sin^3 x dx = (-1/3)(e^2x)*cos^3 x + (1/18)(e^2x)*sin^3 x\n\n91. ## tourism and hospitality\n\nIs the economic impact in England positive or negative?\n\n92. ## math\n\nwhich digit makes 345 blank divisible by 2\n\n93. ## Math\n\nwhat number is a prime 4 13 26 15" ]

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[ "math.NT\n\n# Title: On some congruences using multiple harmonic sums of length three and four\n\nAuthors: Walid Kehila\nAbstract: In the present paper, we determine the sums $\\sum_{j=1}^{p-1}\\frac{H_j^{(s_1)}H_j^{(s_3)}}{j^{s_2}}$ and $\\sum_{j=1}^{p-1}\\frac{H_j^{(s_1)}H_j^{(s_3)}H_j^{(s_4)}}{j^{s_2}}$ modulo $p$ and modulo $p^2$ in certain cases. This is done by using multiple harmonic sums of length three and four, as well as, many other results. In addition, We recover three congruences conjectured by Z.-W Sun and solved later by the author himself and R. Me\\v{s}trovi\\'c.\n Comments: 8 pages Subjects: Number Theory (math.NT); Combinatorics (math.CO) MSC classes: 11A07, 11B68, 11B50, 11B83 Cite as: arXiv:2004.12122 [math.NT] (or arXiv:2004.12122v1 [math.NT] for this version)\n\n## Submission history\n\nFrom: Walid Kehila [view email]\n[v1] Sat, 25 Apr 2020 12:23:11 GMT (362kb)\n\nLink back to: arXiv, form interface, contact." ]

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[ "# Ohm's law\n\n(redirected from Ohm Law)\nAlso found in: Dictionary, Thesaurus, Medical.\n\n## Ohm's law\n\n(ōm) [for G. S. OhmOhm, Georg Simon\n, 1787–1854, German physicist. He was professor at Munich from 1852. His study of electric current led to his formulation of the law now known as Ohm's law. The unit of electrical resistance (see ohm) was named for him.\n], law stating that the electric current i flowing through a given resistance r is equal to the applied voltage v divided by the resistance, or i=v/r. For general application to alternating-current circuits where inductances and capacitances as well as resistances may be present, the law must be amended to i=v/z, where z is impedanceimpedance,\nin electricity, measure in ohms of the degree to which an electric circuit resists the flow of electric current when a voltage is impressed across its terminals.\n. There are conductors in which the current that flows is not proportional to the applied voltage. These do not follow this law and are called nonohmic conductors.\n\n## Ohm's law\n\nThe direct current flowing in an electrical circuit is directly proportional to the voltage applied to the circuit. The constant of proportionality R, called the electrical resistance, is given by the", null, "equation below, in which V is the applied voltage and I is the current. Numerous deviations from this simple, linear relationship have been discovered. See Electrical resistance\n\n## Ohm’s Law\n\na law that states that the steady current density I in a conductor is directly proportional to the potential difference (voltage) U between two fixed points or cross sections of the conductor:\n\n(1) RI = U\n\nThe proportionality constant R, which depends on the geometric and electric properties of the conductor and on temperature, is called the ohmic resistance, or simply the resistance, of the given section of the conductor. Ohm’s law was discovered in 1826 by the German physicist G. S. Ohm.\n\nIn the general case, the relationship between I and U is nonlinear; however, in practice it is always possible to assume it to be linear for a certain range of voltages and to apply Ohm’s law for this range. For metals and their alloys the range is virtually unlimited.\n\nOhm’s law in form (1) is valid for those sections of a circuit that do not contain any sources of electromotive force (emf). If such sources (storage batteries, thermocouples, or dynamos) are present, Ohm’s law assumes the form\n\n(2) RI= U + E\n\nwhere E is the emf of all sources connected in the section of the circuit that is being considered. For a closed circuit, Ohm’s law assumes the following form:\n\n(3) RtI = E\n\nwhere Rt = R + Ri is the total resistance of the entire circuit, which is equal to the sum of the external resistance R of the circuit and the internal resistance Ri of the source of emf. Kirchhoff’s laws generalize Ohm’s law for the case of branched circuits.\n\nOhm’s law can also be written in differential form, which links the current density j and the total electric field strength for each point of the conductor. The potential electric field of intensity E generated in conductors by the microscopic charges—electrons and ions—of the conductors themselves cannot support steady motion of free charges (a current), since the work done by the field in a closed loop is equal to zero. The current is supported by nonelectrostatic forces of various origins (induction, chemical, thermal, and so on) that are active in the emf sources and can be represented as some equivalent, nonpotential field of intensity Eext, called the external field. In the general case, the total strength of the field acting on the charges in the conductor is E + Eext. Correspondingly, the differential Ohm’s law assumes the form\n\n(4) ρj = E + Eext or j = σ(E + Eext)\n\nwhere ρ is the specific electric resistivity of the conductor material and σ = 1/ρ is the specific electrical conductivity.\n\nOhm’s law in complex form is also valid for sinusoidal quasi-stationary currents:\n\n(5) ZI = E\n\nwhere Z is the total complex impedance, equal to R + iX, and R and iX are the resistance and reactance of the circuit, respectively. If an inductance L and a capacitance C are present in a circuit carrying a quasi-stationary current of frequency ω, then X= ωL - 1/ωC.\n\n### REFERENCES\n\nKursfiziki, vol. 2. Edited by N. D. Papaleksi. Moscow-Leningrad, 1948.\nKalashnikov, S. G. Elektrichestvo. Moscow, 1964. (Obshchii kurs fiziki, vol. 2.)\nFizicheskie osnovy elektrotekhniki. General editor, K. M. Polivanov. Moscow-Leningrad, 1950.\n\n## Ohm's law\n\n[′ōmz ‚lȯ]\n(electricity)\nThe law that the direct current flowing in an electric circuit is directly proportional to the voltage applied to the circuit; it is valid for metallic circuits and many circuits containing an electrolytic resistance.\n\n## Ohm's law\n\nThe direct current flowing in an electrical circuit is directly proportional to the voltage applied to the circuit. The constant of proportionality R, called the electrical resistance, is given by the", null, "equation below, in which V is the applied voltage and I is the current. Numerous deviations from this simple, linear relationship have been discovered.\n\n## Ohm’s law\n\nA law stating that the current in an electric circuit is directly proportional to the electromotive force (voltage) in the circuit and inversely proportional to the resistance in the circuit.\n\n## ohm\n\nThe unit of measurement of electrical resistance in a material. One ohm is the resistance in a circuit when one volt maintains a current of one amp. The symbol for ohm is the Greek letter omega. See impedance.\n\nOhm's Law\nThe equation \"R=V/I\" is the more streamlined version of the one developed by German physicist Georg Simon Ohm in 1827. Ohm's law is used to calculate the resistance in materials such as metal, which maintain a linear relationship between voltage and current. In addition, Ohm's formulas, which are derived from Ohm's Law, are used to calculate voltage and current if the other two measurements are known.\n```OHM'S LAWwResistance = voltage divided by current\n\nR = V / I or R = E / I\n\nOHM'S FORMULASVoltage = current times resistance\n\nV = I * R or E = I * R\n\nCurrent = voltage divided by resistance\n\nI = V / R or I = E / R\n\nV or E = voltage (E=energy)\nI = current in amps (I=intensity)\nR = resistance in ohms\n\nElectric PowerPower in watts = voltage times current\n\nP = V * I\n```\nSite: Follow: Share:\nOpen / Close" ]

[ null, "https://img.tfd.com/mgh/cep/math/466200.gif", null, "https://img.tfd.com/mgh/cee/math/466200MF0010.gif", null ]

[ "'\n\n# Epitrochoid (Y-coordinate of a point)\n\n## Description\n\nAn epitrochoid is a roulette traced by a point attached to an external circle rolling around the outside of a fixed l circle , where the point is at a distance from the center of the exterior circle.\n\nRelated formulas\n\n## Variables\n\n y Y-Coordinate of the point (ordinate) (dimensionless) R Radius of the fixed circle (dimensionless) r Radius of the circle rolling around the outside of the fixed circle (dimensionless) θ The parameter (depented on the angle) (dimensionless) d The distance from the center of the exterior circle. (dimensionless)" ]

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[ "Documentation\n\n# ginput\n\nIdentify axes coordinates\n\n## Syntax\n\n``[x,y] = ginput(n)``\n``[x,y] = ginput``\n``[x,y,button] = ginput(___)``\n\n## Description\n\nexample\n\n````[x,y] = ginput(n)` allows you to identify the coordinates of `n` points. To choose a point, move your cursor to the desired location and press either a mouse button or a key on the keyboard. Press the Return key to stop before all `n` points are selected. MATLAB® returns the coordinates of your selected points. If there are no current axes, calling `ginput` creates a set of Cartesian axes.```\n\nexample\n\n````[x,y] = ginput` allows you to select an unlimited number of points until you press the Return key.```\n\nexample\n\n````[x,y,button] = ginput(___)` also returns the mouse button or key on the keyboard used to select each point.```\n\n## Examples\n\ncollapse all\n\nIdentify four points in a set of axes using `ginput`. To select each point, move the cursor to your desired location and press a mouse button or key.\n\n`[x,y] = ginput(4)`", null, "```x = 0.3699 0.4425 0.5450 0.6130 y = 0.6690 0.5605 0.4719 0.6025```\n\nPlot the points.\n\n`plot(x,y);`", null, "Identify five coordinates in a set of axes using `ginput`. To select each point, move the cursor to your desired location and press a mouse button, lowercase letter, uppercase letter, number, or the space bar. Return the mouse buttons or ASCII numbers of the keys used to select each point.\n\n```[x,y,button] = ginput(5); button ```\n```button = 3 104 32 51 82```\n\nIn this case, the coordinates were identified using the right mouse button (3), the lowercase letter h (104), the space bar (32), the number 3 (51), and the uppercase letter R (82).\n\nCreate geographic axes and identify the latitude and longitude coordinates of four points. Then, plot the points that you identify.\n\n```geoaxes; [lat,lon] = ginput(4);```", null, "Use the `hold on` command and the `geolimits` function to maintain the map limits. Plot the identified points.\n\n```hold on geolimits('manual') geoscatter(lat,lon,'filled','b')```", null, "## Input Arguments\n\ncollapse all\n\nNumber of points to identify, specified as a positive integer.\n\n## Output Arguments\n\ncollapse all\n\nFirst components of the identified coordinates, returned as a scalar or column vector.\n\n• If the current axes are Cartesian, the values are `x`-coordinates.\n\n• If the current axes are geographic, the values are latitudes. Positive values correspond to north and negative values correspond to south.\n\nIf you choose points outside the axes limits, values are still returned relative to the axes origin.\n\nSecond components of the identified coordinates, returned as a scalar or column vector.\n\n• If the current axes are Cartesian, the values are `y`-coordinates.\n\n• If the current axes are geographic, the values are longitudes. Positive values correspond to locations east of the origin and negative values correspond to locations west of the origin.\n\nIf you choose points outside the axes limits, values are still returned relative to the axes origin.\n\nKeys or mouse buttons used to identify points, returned as a scalar or column vector. Mouse buttons are indicated by 1 for the left button, 2 for the middle, and 3 for the right. Keys on the keyboard are indicated by their corresponding ASCII numbers. Taps on a screen are indicated by 1.\n\nDownload ebook" ]

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[ "TL;DR\n\nI’m probably not using regular expressions in Raku the way they’re designed to work better.\n\nAlthough I like my strong Perl accent while writing Raku code, it’s probably time to correct a couple of… pronunciation defects.\n\nIt all started with Advent of Code 2018 puzzle 5. Taking it as an excuse to do some more Raku exercising, I coded a solution for the first half of the day’s puzzle:\n\n``````sub part1 (\\$inputs is copy) {\nmy \\$changed = -1;\nwhile (\\$changed && \\$inputs.chars) {\n\\$changed = 0;\nmy \\$current = \\$inputs.substr(0, 1);\nmy \\$i = 0;\nwhile \\$i < \\$inputs.chars - 1 {\nmy \\$succ = \\$inputs.substr(\\$i + 1, 1);\nif (\\$current ne \\$succ && lc(\\$current) eq lc(\\$succ)) {\n++\\$changed;\n\\$inputs.substr-rw(\\$i, 2) = '';\n\\$current = substr(\\$i, 1) if \\$i < \\$inputs.chars;\n}\nelse {\n\\$current = \\$succ;\n++\\$i;\n}\n}\n}\nreturn \\$inputs.chars;\n}\n``````\n\nThis is probably a rather boring implementation that might be idiomized a lot. But with my current skills… I think the best I can do is to idiotize it, so it’s working and I call it a day.\n\nOr do I? Certainly not!\n\nI wondered about using a regular expression and substitution to get the job done, so I proceeded to over-engineer a solution:\n\n``````sub part1_matcher () {\nmy \\$allpairs =('a' .. 'z').map({ .lc ~ .uc, .uc ~ .lc }).flat.join('|');\nreturn rx{<\\$allpairs>};\n}\n\nsub part1_rx (\\$inputs is copy) {\nstate \\$matcher = part1_matcher();\nNil while \\$inputs ~~ s:g/\\$matcher//;\nreturn \\$inputs.chars;\n}\n``````\n\nI know, I know… it’s a one-off script, what’s my problem with computing the regular expression once and put it in a `state` variable? I’m a romantic.\n\nSo there I am all happy waiting for a solid performance boost, and I get this:\n\n``````\\$ time RX=1 raku 05.raku 05.input\n...\nreal\t0m54.025s\nuser\t0m54.008s\nsys\t0m0.220s\n\n\\$ time RX=0 raku 05.raku 05.input\n...\nreal\t0m9.601s\nuser\t0m9.652s\nsys\t0m0.192s\n``````\n\nYou’re guessing it right: the version with the regular expression takes about `6x` times than the boring one!\n\nAt this point I was intrigued and wondered if it had to do with the approach, so of course I re-implemented the whole thing in Perl. Here’s the boring translation:\n\n``````sub part1 (\\$inputs) {\nmy \\$changed = -1;\nwhile (\\$changed && length\\$inputs) {\n\\$changed = 0;\nmy \\$current = substr \\$inputs, 0, 1;\nmy \\$i = 0;\nwhile (\\$i < length(\\$inputs) - 1) {\nmy \\$succ = substr \\$inputs, \\$i + 1, 1;\nif (\\$current ne \\$succ && lc(\\$current) eq lc(\\$succ)) {\n++\\$changed;\nsubstr \\$inputs, \\$i, 2, '';\n\\$current = substr(\\$i, 1) if \\$i < length \\$inputs;\n}\nelse {\n\\$current = \\$succ;\n++\\$i;\n}\n}\n}\nreturn length \\$inputs;\n}\n``````\n\nand here’s the regular-expressions based version translation:\n\n``````sub part1_matcher () {\nmy \\$allpairs = join '|',\nmap { (lc(\\$_) . uc(\\$_), uc(\\$_) . lc(\\$_)) } 'a' .. 'z';\nreturn qr{\\$allpairs};\n}\n\nsub part1_rx (\\$inputs) {\nstate \\$matcher = part1_matcher();\n1 while \\$inputs =~ s/\\$matcher//g;\nreturn length \\$inputs;\n}\n``````\n\nThis time this is what I got back:\n\n``````\\$ time RX=1 perl 05.pl 05.input\n...\nreal\t0m0.137s\nuser\t0m0.108s\nsys\t0m0.008s\n\n\\$ time RX=0 perl 05.pl 05.input\n...\nreal\t0m1.385s\nuser\t0m1.340s\nsys\t0m0.024s\n``````\n\nNow this is what I was expecting!\n\nMy (transitory?) take away is that one or more of the following apply:\n\n• Raku still has some way to go as long as performance is concerned (this is fair enough);\n• I can definitely improve my Raku to leverage on its strengths, instead of writing code with my strong Perl accent.\n\nSometimes, having a strong accent just means that it will take you much more time to be understood…\n\nThanks in anticipation to anybody that can help understanding what I’m doing wrong and where I can improve!\n\nUntil next time… stay safe and have `-Ofun`!" ]

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[ "Tulis kata dalam Bahasa Indonesia atau Bahasa Inggris:\n\n# compute\n\n## English Thesaurus\n\n1. make a mathematical calculation or computation (verb.cognition)\n hypernym : reason, definition : think logically (verb.cognition)\n hyponym : quantise, quantize, definition : apply quantum theory to; restrict the number of possible values of (a quantity) or states of (a physical entity or system) so that certain variables can assume only certain discrete magnitudes that are integral multiples of a common factor (verb.cognition)\n hyponym : extract, definition : calculate the root of a number (verb.cognition)\n hyponym : process, definition : perform mathematical and logical operations on (data) according to programmed instructions in order to obtain the required information (verb.cognition)\n hyponym : prorate, definition : divide or assess proportionally (verb.cognition)\n hyponym : miscalculate, misestimate, definition : calculate incorrectly (verb.cognition)\n hyponym : recalculate, definition : calculate anew (verb.cognition)\n hyponym : average, average out, definition : compute the average of (verb.cognition)\n hyponym : factor, factor in, factor out, definition : resolve into factors (verb.cognition)\n hyponym : add, add together, definition : make an addition by combining numbers (verb.cognition)\n hyponym : deduct, subtract, take off, definition : make a subtraction (verb.cognition)\n hyponym : multiply, definition : combine by multiplication (verb.cognition)\n hyponym : divide, fraction, definition : perform a division (verb.cognition)\n hyponym : extrapolate, interpolate, definition : estimate the value of (verb.cognition)\n hyponym : differentiate, definition : calculate a derivative; take the derivative (verb.cognition)\n hyponym : integrate, definition : calculate the integral of; calculate by integration (verb.cognition)\n hyponym : survey, definition : plot a map of (land) (verb.cognition)\n hyponym : approximate, estimate, gauge, guess, judge, definition : judge tentatively or form an estimate of (quantities or time) (verb.cognition)\n hyponym : budget, definition : make a budget (verb.cognition)\n hyponym : capitalise, capitalize, definition : compute the present value of a business or an income (verb.cognition)\n hyponym : resolve, solve, definition : find the solution (verb.cognition)\n verb group : work out, definition : be calculated (verb.cognition)\n domain category : math, mathematics, maths, definition : a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement (noun.cognition)\n also : figure out, lick, puzzle out, solve, work, work out, definition : find the solution to (a problem or question) or understand the meaning of (verb.cognition)\n also : bet, calculate, count, depend, look, reckon, definition : have faith or confidence in (verb.cognition)\n derivation : calculation, computation, computing, definition : the procedure of calculating; determining something by mathematical or logical methods (noun.act)\n derivation : calculating machine, calculator, definition : a small machine that is used for mathematical calculations (noun.artifact)\n derivation : computer, computing device, computing machine, data processor, electronic computer, information processing system, definition : a machine for performing calculations automatically (noun.artifact)\n derivation : figure, number, definition : the property possessed by a sum or total or indefinite quantity of units or individuals (noun.attribute)\n derivation : calculation, computation, figuring, reckoning, definition : problem solving that involves numbers or quantities (noun.cognition)\n derivation : calculus, infinitesimal calculus, definition : the branch of mathematics that is concerned with limits and with the differentiation and integration of functions (noun.cognition)\n derivation : calculator, computer, estimator, figurer, reckoner, definition : an expert at calculation (or at operating calculating machines) (noun.person)\n derivation : figure, definition : an amount of money expressed numerically (noun.possession)\n derivation : cipher, cypher, nought, zero, definition : a mathematical element that when added to another number yields the same number (noun.quantity)\n derivation : calculable, definition : capable of being calculated or estimated (adj.all)\n also : figure out, lick, puzzle out, solve, work, work out, definition : find the solution to (a problem or question) or understand the meaning of (verb.cognition)\n also : bet, calculate, count, depend, look, reckon, definition : have faith or confidence in (verb.cognition)\n derivation : calculation, computation, computing, definition : the procedure of calculating; determining something by mathematical or logical methods (noun.act)\n derivation : calculating machine, calculator, definition : a small machine that is used for mathematical calculations (noun.artifact)\n derivation : computer, computing device, computing machine, data processor, electronic computer, information processing system, definition : a machine for performing calculations automatically (noun.artifact)\n derivation : figure, number, definition : the property possessed by a sum or total or indefinite quantity of units or individuals (noun.attribute)\n derivation : calculation, computation, figuring, reckoning, definition : problem solving that involves numbers or quantities (noun.cognition)\n derivation : calculus, infinitesimal calculus, definition : the branch of mathematics that is concerned with limits and with the differentiation and integration of functions (noun.cognition)\n derivation : calculator, computer, estimator, figurer, reckoner, definition : an expert at calculation (or at operating calculating machines) (noun.person)\n derivation : figure, definition : an amount of money expressed numerically (noun.possession)\n derivation : cipher, cypher, nought, zero, definition : a mathematical element that when added to another number yields the same number (noun.quantity)\n derivation : calculable, definition : capable of being calculated or estimated (adj.all)\n\n## Visual ArtiKata", null, "Explore compute in ArtiKata.com >\n\nCari berdasar huruf depan:\n\nA B C D E F G H I J K L M N O P Q R S T U V W X Y Z\n\nSitus lain yang mungkin anda suka:\n\nKamus Bahasa Indonesia\nRima Kata" ]

[ null, "http://sinonimkata.com/visual_en.php", null ]

[ "# What is the domain of (-2x^2-2x+1)/(x^2+x)?\n\nDec 31, 2017\n\nFor Domain,\n${x}^{2} + x \\ne 0$\n\n$x \\left(x + 1\\right) \\ne 0$\n\n$x \\ne 0$ and $x \\ne - 1$\n\nSo, ${D}_{f} = R - \\left\\{0 , - 1\\right\\}$\n\nDec 31, 2017\n\n$x \\setminus \\ne - 1 \\mathmr{and} x \\setminus \\ne 0$\n\n#### Explanation:\n\nYou have to put ${x}^{2} + x \\setminus \\ne 0$ because function is not definied in 0.\nThe way to solve is:\n$x \\left(x + 1\\right) \\setminus \\ne 0$\nAnd there are 2 solutions:\n\n• $x \\setminus \\ne 0$\n• $x + 1 \\setminus \\ne 0$ that becomes $x \\setminus \\ne - 1$\n\n$D : \\setminus m a t h \\boldsymbol{R} - \\left\\{- 1 , 0\\right\\}$" ]

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[ "# jAvA语言,在whilE循环中怎样将循环过程中的数相加\n\nint number=1;//给加数赋初值 int sum=0;//给“和”定义一个变量 while(number\n\nint a = 0;//在while循环外定义变量 while(xxx){ a=12;//在循环中给变量赋值 } int b = a +5;//在循环后使用变量\n\nint sum=0; int i=0; while(i\n\nint sum = 0; int j = 0; while (j\n\npublic static int countN(int x) { int n = 0; // 记录位数 do { x = x / 10; // 每次出去个位，当x=0时表示这个数每位已经分解完成 n++; } while (x != 0); return n; }\n\n1、while关键字的中文意思是“当……的时候”，也就是当条件成立时循环执行对应的代码。while语句是循环语句中基本的结构，语法格式比较简单。 while语句语法格式： while（循环条件） 循环体； 为了结构清楚，并且使循环体部分可以书写多行代码，一...\n\npublic static void main(String[] args) {Scanner sc = new Scanner(System.in);int sum = 0;do{System.out.print(\"输出一个数:\");try {sum += sc.nextInt();} catch (Exception e) {break;}}while(true);System.out.println(sum);}这样就可以..." ]

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[ "", null, "# The Binary Exploitation: Stack based Buffer overflow\n\nThis article talks about cracking Level 13 Binary of Cyberstart CTF. The hint that was given for this challenge is “Cyclic Pattern”, which means we need to use pattern finder tool to figure out the length of the buffer and then run the arbitrary function.\n\nLet’s crack this:\n\n1. Running the binary gives us this output:", null, "The output says: “Overflow the buffer to execute the function at memory address : 0x80484b1” and then it asks for some inputs.Based on this we know:\n> We need to run a function which is at 0x80484b1\n> It takes an input.\n2. Let’s use objdump cmdline tool to dump the program and functions to get an idea about this binary:\n\nCommand : objdump -d Binary", null, "The objdump output was quite big,so I took only the relevant output which is the address of the function 0x80484b1 which prints out the flag.\n\n3. Let’s use cyclic pattern tool to find out the offset of segmentation fault:\n\nCommand:  msf-pattern_create -l 200", null, "The above command will help create a pattern of certain length which will help us find out the offset where the segmentation fault occurred. At the end all we need to do is to locate the offset to EIP so we can control the instruction pointer and points it to which ever address we want. I chose the value 200 randomly.\n\nAfter generating the string using msf-pattern_create, open the program in gdb to print out the offset :\n\nCommand: gdb ./Binary", null, "use “r” or “run” to run the binary in gdb and then input paste the pattern that was generated through msf-pattern_create. If you see the error offset it is 0x41326641, obviously this value will be different when you will run in your own device, but for me the Segmentation Fault happened at that address. Make sure to copy that value, it will be used to find the size of the buffer.\n\n4.  Use the address that you have copied on another tool of metasploit framework which is called msf-pattern_offset.\n\nCommand : msf-pattern_offset -q 41326641 -l 200", null, "The above command will help locate the exact size of the overflow from the whole pattern. For us, the buffer size is 156, so after that many characters we will be able to control the instruction pointer.\n\n5. Now, we know that we need to execute the function at 0x80484b1 and we know that the size of the buffer is 156, so let’s put the pointer to that function by using below command:\n\nCommand: python -c “print ‘A’*156+’\\xb1\\x84\\x04\\x08′” | ./Binary", null, "You got the Flag!\n\nThis site uses Akismet to reduce spam. Learn how your comment data is processed.\n\nScroll Up" ]

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[ "# Can I put formula numbers in a question or an answer?\n\nSuppose I'm writing a question like\n\nblah blah blah $$a=0$$ blah blah blah\n\nI want to put (1) at the very right of the line that has $$a=0$$. Can I do that?\n\n## 1 Answer\n\nblah blah blah\n\n$$a=0 \\tag{1}$$\n\nblah blah blah\n\nTo get the above, use \\tag{*insert number/label here*} at the end of the formula, like the following:\n\nblah blah blah\n\n$$a= 0\\tag{1}$$\n\nblah blah blah\n\n• Thanks! Can I ask you one more question? How do you put those horizontal lines between paragraphs? – zxcv Oct 19 '18 at 23:34\n• You can do that by writing a dashed line --------- (doesn't have to be long like the entire width of the page, just a handful of -'s). Also, when you are composing a post, you'll see a menu along the top, the menu with images. One shows grey lines, above and below, separated by a dashed line. Clicking on that will give you a horizontal line, like you see in my post. – Namaste Oct 19 '18 at 23:39\n• To get the equation number in math format use tag{$1$} ... for example if you want the tag to be $1'$ you will need the dollar signs there. – GEdgar Oct 20 '18 at 14:35" ]

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[ "The following are the steps for addition, subtraction, division, and multiplication of binary numbers.\n\nAddition is much like solving decimal addition problems. Add each row of digits from right to left.\n```Example1: Example2:\n101101110 10111110\n+ 1011010 + 1011110\n_________ _________\n111001000 100011100\n```\n\nWith addition, there are four important rules to remember. These four rules will help you solve any binary addition problem you will face:\n\n• 0 + 0 = 0\n• 1 + 0 = 1\n• 1 + 1 = 0, plus 1 carry (carry over to the next number)\n• Carry + 1 + 1 = 1, plus 1 carry\n\nSubtraction of Binary Numbers:\n\n```Example1: Example2:\nº¹ º¹ º¹¹ º¹\n10110 1100110\n-01101 -1011001\n______ ________\n1001 1101\n```\n\nLike decimal subtraction, it is often required to borrow from the next digit. ¹ equals a borrow of one, and º equals a change as a result of the borrow.\n\nMultiplication of Binary Numbers:\n\n```Example1: Example2:\n1100100 10110111\nx 01011 x 111111\n_______ ________\n1100100 10110111\n11001000 101101110\n000000000 1011011100\n1100100000 10110111000\n00000000000 101101110000\n___________ 1011011100000\n01101001100 _____________\n10110100001001\n```\n\nKnow your 1 and 0 times tables? Then the rest is easy. Simply multiply each top number by the first digit in the multiplier. Be sure to remember your place holders; omitting them will screw up the answer. Then, once you have your big mess of ones and zeroes, add them together with the addition techniques above.\n\nDivision of Binary Numbers:\n\n```Example1: Example2:\n\n10101.1 10110\n_________ __________\n10 | 101011.0 101 | 1101110\n-10 101\n010 111\n-10 101\n011 101\n-10 101\n10 00\n10\n0\n```\n\nLong division is the most efficient approach here. This will require lots of subtraction, so learn from the lesson above. Divide the number into the first number, subtract it underneath the quotient, drop the next digit down to the answer, and divide the dividend into that number. Repeat these steps until you can work no longer." ]

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[ "# FFT and IFFT: Random Phases\n\n75 views (last 30 days)\nNycholas Maia on 21 Mar 2019\nEdited: Brittany Scheid on 16 Jun 2019\nI imported a single audio file to MATLAB workspace.\nAfter I apply the FFT:\nY = fft(signal)\nHow can I random change the audio phases before apply the Inverse FFT and get the 'new_signal'?\nnew_signal = ifft(Y)\nHow can I do it?\n\nBrittany Scheid on 16 Jun 2019\nEdited: Brittany Scheid on 16 Jun 2019\nFollowing the comment by David Goodmanson above, here is what I used to randomize an array of timeseries data:\nfunction randX = phaseRandomize(X)\n% Returns a phase-randomized version of the input data X. If X is an array,\n% each row is treated as an independant time series, and columns represent\n% sample points.\n[N,L]=size(X);\nY=fft(X,[],2); % Get spectrum\n% Add random phase shifts (negative for conjugates), preserve DC offset\nrnd_theta= -pi + (2*pi).*rand(N,L/2-1);\nY(:,2:L/2)=Y(:,2:L/2).*exp(1i*rnd_theta);\nY(:,L/2+2:L)=Y(:,L/2+2:L).*exp(-1i*flip(rnd_theta,2));\n% return phase-randomized data\nrandX =ifft(Y,[],2);\nend\n\nDavid Goodmanson on 22 Mar 2019\nHi Nycholas,\nAssuming signal is real and of length n, n even, then\nY(1) is for frequency 0, the DC contribution, and it's real. Don't mess with that point.\nY(2) and Y(n) are complex conjugates. You can multiply one of that pair by exp(i*theta) and the other by exp(-i*theta), where theta is a random angle with 0 <= theta < 2*pi. the new Y(2) and Y(n) remain complex conugates.\nIn general from k = 2 to n/2, Y(k) and Y(n+2-k) form a complex conjugate pair. For each of those pairs, do the same kind of multiplcation as above, with a different random angle. Each pair remain complex conjugates.\nY(n/2+1) is real. Don't mess with that point either.\nifft back.\nHere the random phases are totally uncorrelated from frequency to frequency, which may or may not be physically realistic.\n\nNycholas Maia on 22 Mar 2019\nDavid,\nI appreciate the good math background, and you are right.\nPlease, could you give me a MATLAB script example of this process?\nThanks!\nDavid Goodmanson on 23 Mar 2019\nHi NM, what have you tried so far?\nDavid Daminelli on 1 Jun 2019\nHello NM and DG! I'm working on a project that needs this same function, and I've done an algorithm that does that. It is here https://www.mathworks.com/matlabcentral/answers/465112-help-with-sound-function, followed by a question I had during the project, if they can help it would be usefull!" ]

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[ "# 4. Reference Guide¶\n\nThis section describes all public functions and classes in pySecDec.\n\n## 4.1. Algebra¶\n\nImplementation of a simple computer algebra system.\n\nclass pySecDec.algebra.ExponentiatedPolynomial(expolist, coeffs, exponent=1, polysymbols='x', copy=True)\n\nLike Polynomial, but with a global exponent.", null, "Parameters: expolist – iterable of iterables; The variable’s powers for each term. coeffs – iterable; The coefficients of the polynomial. exponent – object, optional; The global exponent. polysymbols – iterable or string, optional; The symbols to be used for the polynomial variables when converted to string. If a string is passed, the variables will be consecutively numbered. For example: expolist=[[2,0],[1,1]] coeffs=[“A”,”B”] polysymbols=’x’ (default) <-> “A*x0**2 + B*x0*x1” polysymbols=[‘x’,’y’] <-> “A*x**2 + B*x*y” copy – bool; Whether or not to copy the expolist, the coeffs, and the exponent. Note If copy is False, it is assumed that the expolist, the coeffs and the exponent have the correct type.\ncopy()\n\nReturn a copy of a Polynomial or a subclass.\n\nderive(index)\n\nGenerate the derivative by the parameter indexed index.\n\nParameters: index – integer; The index of the paramater to derive by.\nsimplify()\n\nApply the identity <something>**0 = 1 or <something>**1 = <something> or 1**<something> = 1 if possible, otherwise call the simplify method of the base class. Convert exponent to symbol if possible.\n\npySecDec.algebra.Expression(expression, polysymbols, follow_functions=False)\n\nConvert a sympy expression to an expression in terms of this module.\n\nParameters: expression – string or sympy expression; The expression to be converted polysymbols – iterable of strings or sympy symbols; The symbols to be stored as expolists (see Polynomial) where possible. follow_functions – bool, optional (default = False); If true, return the converted expression and a list of Function that occur in the expression.\nclass pySecDec.algebra.Function(symbol, *arguments, **kwargs)\n\nSymbolic function that can take care of parameter transformations. It keeps track of all taken derivatives: When derive() is called, save the multiindex of the taken derivative.\n\nThe derivative multiindices are the keys in the dictionary self.derivative_tracks. The values are lists with two elements: Its first element is the index to derive the derivative indicated by the multiindex in the second element by, in order to abtain the derivative indicated by the key:\n\n>>> from pySecDec.algebra import Polynomial, Function\n>>> x = Polynomial.from_expression('x', ['x','y'])\n>>> y = Polynomial.from_expression('y', ['x','y'])\n>>> poly = x**2*y + y**2\n>>> func = Function('f', x, y)\n>>> ddfuncd0d1 = func.derive(0).derive(1)\n>>> func\nFunction(f( + (1)*x, + (1)*y), derivative_tracks = {(1, 0): [0, (0, 0)], (1, 1): [1, (1, 0)]})\n>>> func.derivative_tracks\n{(1, 0): [0, (0, 0)], (1, 1): [1, (1, 0)]}\n>>> func.compute_derivatives(poly)\n{(1, 0): + (2)*x*y, (1, 1): + (2)*x}\n\nParameters: symbol – string; The symbol to be used to represent the Function. arguments – arbitrarily many _Expression; The arguments of the Function. copy – bool; Whether or not to copy the arguments.\ncompute_derivatives(expression=None)\n\nCompute all derivatives of expression that are mentioned in self.derivative_tracks. The purpose of this function is to avoid computing the same derivatives multiple times.\n\nParameters: expression – _Expression, optional; The expression to compute the derivatives of. If not provided, the derivatives are shown as in terms of the function‘s derivatives dfd.\ncopy()\n\nReturn a copy of a Function.\n\nderive(index)\n\nGenerate the derivative by the parameter indexed index. The derivative of a function with symbol f by some index is denoted as dfd<index>.\n\nParameters: index – integer; The index of the paramater to derive by.\nreplace(expression, index, value, remove=False)\n\nReplace a variable in an expression by a number or a symbol. The entries in all expolist of the underlying Polynomial are set to zero. The coefficients are modified according to value and the powers indicated in the expolist.\n\nParameters: expression – _Expression; The expression to replace the variable. index – integer; The index of the variable to be replaced. value – number or sympy expression; The value to insert for the chosen variable. remove – bool; Whether or not to remove the replaced parameter from the parameters in the expression.\nsimplify()\n\nSimplify the arguments.\n\nclass pySecDec.algebra.Log(arg, copy=True)\n\nThe (natural) logarithm to base e (2.718281828459..). Store the expressions log(arg).\n\nParameters: arg – _Expression; The argument of the logarithm. copy – bool; Whether or not to copy the arg.\ncopy()\n\nReturn a copy of a Log.\n\nderive(index)\n\nGenerate the derivative by the parameter indexed index.\n\nParameters: index – integer; The index of the paramater to derive by.\nreplace(expression, index, value, remove=False)\n\nReplace a variable in an expression by a number or a symbol. The entries in all expolist of the underlying Polynomial are set to zero. The coefficients are modified according to value and the powers indicated in the expolist.\n\nParameters: expression – _Expression; The expression to replace the variable. index – integer; The index of the variable to be replaced. value – number or sympy expression; The value to insert for the chosen variable. remove – bool; Whether or not to remove the replaced parameter from the parameters in the expression.\nsimplify()\n\nApply log(1) = 0.\n\nclass pySecDec.algebra.LogOfPolynomial(expolist, coeffs, polysymbols='x', copy=True)\n\nThe natural logarithm of a Polynomial.\n\nParameters: expolist – iterable of iterables; The variable’s powers for each term. coeffs – iterable; The coefficients of the polynomial. exponent – object, optional; The global exponent. polysymbols – iterable or string, optional; The symbols to be used for the polynomial variables when converted to string. If a string is passed, the variables will be consecutively numbered. For example: expolist=[[2,0],[1,1]] coeffs=[“A”,”B”] polysymbols=’x’ (default) <-> “A*x0**2 + B*x0*x1” polysymbols=[‘x’,’y’] <-> “A*x**2 + B*x*y”\nderive(index)\n\nGenerate the derivative by the parameter indexed index.\n\nParameters: index – integer; The index of the paramater to derive by.\nstatic from_expression(expression, polysymbols)\n\nAlternative constructor. Construct the LogOfPolynomial from an algebraic expression.\n\nParameters: expression – string or sympy expression; The algebraic representation of the polynomial, e.g. “5*x1**2 + x1*x2” polysymbols – iterable of strings or sympy symbols; The symbols to be interpreted as the polynomial variables, e.g. “[‘x1’,’x2’]”.\nsimplify()\n\nApply the identity log(1) = 0, otherwise call the simplify method of the base class.\n\nclass pySecDec.algebra.Polynomial(expolist, coeffs, polysymbols='x', copy=True)\n\nContainer class for polynomials. Store a polynomial as list of lists counting the powers of the variables. For example the polynomial “x1**2 + x1*x2” is stored as [[2,0],[1,1]].\n\nCoefficients are stored in a separate list of strings, e.g. “A*x0**2 + B*x0*x1” <-> [[2,0],[1,1]] and [“A”,”B”].\n\nParameters: expolist – iterable of iterables; The variable’s powers for each term. Hint Negative powers are allowed. coeffs – 1d array-like with numerical or sympy-symbolic (see http://www.sympy.org/) content, e.g. [x,1,2] where x is a sympy symbol; The coefficients of the polynomial. polysymbols – iterable or string, optional; The symbols to be used for the polynomial variables when converted to string. If a string is passed, the variables will be consecutively numbered. For example: expolist=[[2,0],[1,1]] coeffs=[“A”,”B”] polysymbols=’x’ (default) <-> “A*x0**2 + B*x0*x1” polysymbols=[‘x’,’y’] <-> “A*x**2 + B*x*y” copy – bool; Whether or not to copy the expolist and the coeffs. Note If copy is False, it is assumed that the expolist and the coeffs have the correct type.\nbecomes_zero_for(zero_params)\n\nReturn True if the polynomial becomes zero if the parameters passed in zero_params are set to zero. Otherwise, return False.\n\nParameters: zero_params – iterable of integers; The indices of the parameters to be checked.\ncopy()\n\nReturn a copy of a Polynomial or a subclass.\n\nderive(index)\n\nGenerate the derivative by the parameter indexed index.\n\nParameters: index – integer; The index of the paramater to derive by.\nstatic from_expression(expression, polysymbols)\n\nAlternative constructor. Construct the polynomial from an algebraic expression.\n\nParameters: expression – string or sympy expression; The algebraic representation of the polynomial, e.g. “5*x1**2 + x1*x2” polysymbols – iterable of strings or sympy symbols; The symbols to be interpreted as the polynomial variables, e.g. “[‘x1’,’x2’]”.\nhas_constant_term(indices=None)\n\nReturn True if the polynomial can be written as:", null, "Otherwise, return False.\n\nParameters: indices – list of integers or None; The indices of the polysymbols to consider. If None (default) all indices are taken into account.\nreplace(expression, index, value, remove=False)\n\nReplace a variable in an expression by a number or a symbol. The entries in all expolist of the underlying Polynomial are set to zero. The coefficients are modified according to value and the powers indicated in the expolist.\n\nParameters: expression – _Expression; The expression to replace the variable. index – integer; The index of the variable to be replaced. value – number or sympy expression; The value to insert for the chosen variable. remove – bool; Whether or not to remove the replaced parameter from the parameters in the expression.\nsimplify(deep=True)\n\nCombine terms that have the same exponents of the variables.\n\nParameters: deep – bool; If True (default) call the simplify method of the coefficients if they are of type _Expression.\nclass pySecDec.algebra.Pow(base, exponent, copy=True)\n\nExponential. Store two expressions A and B to be interpreted as the exponential A**B.\n\nParameters: base – _Expression; The base A of the exponential. exponent – _Expression; The exponent B. copy – bool; Whether or not to copy base and exponent.\ncopy()\n\nReturn a copy of a Pow.\n\nderive(index)\n\nGenerate the derivative by the parameter indexed index.\n\nParameters: index – integer; The index of the paramater to derive by.\nreplace(expression, index, value, remove=False)\n\nReplace a variable in an expression by a number or a symbol. The entries in all expolist of the underlying Polynomial are set to zero. The coefficients are modified according to value and the powers indicated in the expolist.\n\nParameters: expression – _Expression; The expression to replace the variable. index – integer; The index of the variable to be replaced. value – number or sympy expression; The value to insert for the chosen variable. remove – bool; Whether or not to remove the replaced parameter from the parameters in the expression.\nsimplify()\n\nApply the identity <something>**0 = 1 or <something>**1 = <something> or 1**<something> = 1 if possible. Convert to ExponentiatedPolynomial or Polynomial if possible.\n\nclass pySecDec.algebra.Product(*factors, **kwargs)\n\nProduct of polynomials. Store one or polynomials", null, "to be interpreted as product", null, ".\n\nParameters: factors – arbitrarily many instances of Polynomial; The factors", null, ". copy – bool; Whether or not to copy the factors.", null, "can be accessed with self.factors[i].\n\nExample:\n\np = Product(p0, p1)\np0 = p.factors\np1 = p.factors\n\ncopy()\n\nReturn a copy of a Product.\n\nderive(index)\n\nGenerate the derivative by the parameter indexed index. Return an instance of the optimized ProductRule.\n\nParameters: index – integer; The index of the paramater to derive by.\nreplace(expression, index, value, remove=False)\n\nReplace a variable in an expression by a number or a symbol. The entries in all expolist of the underlying Polynomial are set to zero. The coefficients are modified according to value and the powers indicated in the expolist.\n\nParameters: expression – _Expression; The expression to replace the variable. index – integer; The index of the variable to be replaced. value – number or sympy expression; The value to insert for the chosen variable. remove – bool; Whether or not to remove the replaced parameter from the parameters in the expression.\nsimplify()\n\nIf one or more of self.factors is a Product, replace it by its factors. If only one factor is present, return that factor. Remove factors of one and zero.\n\nclass pySecDec.algebra.ProductRule(*expressions, **kwargs)\n\nStore an expression of the form", null, "The main reason for introducing this class is a speedup when calculating derivatives. In particular, this class implements simplifications such that the number of terms grows less than exponentially (scaling of the naive implementation of the product rule) with the number of derivatives.\n\nParameters: expressions – arbitrarily many expressions; The expressions", null, ".\ncopy()\n\nReturn a copy of a ProductRule.\n\nderive(index)\n\nGenerate the derivative by the parameter indexed index. Note that this class is particularly designed to hold derivatives of a product.\n\nParameters: index – integer; The index of the paramater to derive by.\nreplace(index, value, remove=False)\n\nReplace a variable in an expression by a number or a symbol. The entries in all expolist of the underlying Polynomial are set to zero. The coefficients are modified according to value and the powers indicated in the expolist.\n\nParameters: expression – _Expression; The expression to replace the variable. index – integer; The index of the variable to be replaced. value – number or sympy expression; The value to insert for the chosen variable. remove – bool; Whether or not to remove the replaced parameter from the parameters in the expression.\nsimplify()\n\nCombine terms that have the same derivatives of the expressions.\n\nto_sum()\n\nConvert the ProductRule to Sum\n\nclass pySecDec.algebra.Sum(*summands, **kwargs)\n\nSum of polynomials. Store one or polynomials", null, "to be interpreted as product", null, ".\n\nParameters: summands – arbitrarily many instances of Polynomial; The summands", null, ". copy – bool; Whether or not to copy the summands.", null, "can be accessed with self.summands[i].\n\nExample:\n\np = Sum(p0, p1)\np0 = p.summands\np1 = p.summands\n\ncopy()\n\nReturn a copy of a Sum.\n\nderive(index)\n\nGenerate the derivative by the parameter indexed index.\n\nParameters: index – integer; The index of the paramater to derive by.\nreplace(expression, index, value, remove=False)\n\nReplace a variable in an expression by a number or a symbol. The entries in all expolist of the underlying Polynomial are set to zero. The coefficients are modified according to value and the powers indicated in the expolist.\n\nParameters: expression – _Expression; The expression to replace the variable. index – integer; The index of the variable to be replaced. value – number or sympy expression; The value to insert for the chosen variable. remove – bool; Whether or not to remove the replaced parameter from the parameters in the expression.\nsimplify()\n\nIf one or more of self.summands is a Sum, replace it by its summands. If only one summand is present, return that summand. Remove zero from sums.\n\n## 4.2. Loop Integral¶\n\nThis module defines routines to Feynman parametrize a loop integral and build a c++ package that numerically integrates over the sector decomposed integrand.\n\n### 4.2.1. Feynman Parametrization¶\n\nRoutines to Feynman parametrize a loop integral.\n\nclass pySecDec.loop_integral.LoopIntegral(*args, **kwargs)\n\nContainer class for loop integrals. The main purpose of this class is to convert a loop integral from the momentum representation to the Feynman parameter representation.\n\nIt is possible to provide either the graph of the loop integrals as adjacency list, or the propagators.\n\nThe Feynman parametrized integral is a product of the following expressions that are accessible as member properties:\n\n• self.regulator ** self.regulator_power\n• self.Gamma_factor\n• self.exponentiated_U\n• self.exponentiated_F\n• self.numerator\n• self.measure,\n\nwhere self is an instance of either LoopIntegralFromGraph or LoopIntegralFromPropagators.\n\nWhen inverse propagators or nonnumerical propagator powers are present (see powerlist), some Feynman_parameters drop out of the integral. The variables to integrate over can be accessed as self.integration_variables.\n\nWhile self.numerator describes the numerator polynomial generated by tensor numerators or inverse propagators, self.measure contains the monomial associated with the integration measure in the case of propagator powers", null, ". The Gamma functions in the denominator belonging to the measure, however, are multiplied to the overall Gamma factor given by self.Gamma_factor. The overall sign", null, "is included in self.numerator.\n\nclass pySecDec.loop_integral.LoopIntegralFromGraph(internal_lines, external_lines, replacement_rules=[], Feynman_parameters='x', regulator='eps', regulator_power=0, dimensionality='4-2*eps', powerlist=[])\n\nConstruct the Feynman parametrization of a loop integral from the graph using the cut construction method.\n\nExample:\n\n>>> from pySecDec.loop_integral import *\n>>> internal_lines = [['0',[1,2]], ['m',[2,3]], ['m',[3,1]]]\n>>> external_lines = [['p1',1],['p2',2],['-p12',3]]\n>>> li = LoopIntegralFromGraph(internal_lines, external_lines)\n>>> li.exponentiated_U\n( + (1)*x0 + (1)*x1 + (1)*x2)**(2*eps - 1)\n>>> li.exponentiated_F\n( + (m**2)*x2**2 + (2*m**2 - p12**2)*x1*x2 + (m**2)*x1**2 + (m**2 - p1**2)*x0*x2 + (m**2 - p2**2)*x0*x1)**(-eps - 1)\n\nParameters: internal_lines – iterable of internal line specification, consisting of string or sympy expression for mass and a pair of strings or numbers for the vertices, e.g. [[‘m’, [1,2]], [‘0’, [2,1]]]. external_lines – iterable of external line specification, consisting of string or sympy expression for external momentum and a strings or number for the vertex, e.g. [[‘p1’, 1], [‘p2’, 2]]. replacement_rules – iterable of iterables with two strings or sympy expressions, optional; Symbolic replacements to be made for the external momenta, e.g. definition of Mandelstam variables. Example: [(‘p1*p2’, ‘s’), (‘p1**2’, 0)] where p1 and p2 are external momenta. It is also possible to specify vector replacements, for example [(‘p4’, ‘-(p1+p2+p3)’)]. Feynman_parameters – iterable or string, optional; The symbols to be used for the Feynman parameters. If a string is passed, the Feynman parameter variables will be consecutively numbered starting from zero. regulator – string or sympy symbol, optional; The symbol to be used for the dimensional regulator (typically", null, "or", null, ") Note If you change this symbol, you have to adapt the dimensionality accordingly. regulator_power – integer; The regulator to this power will be multiplied by the numerator. dimensionality – string or sympy expression, optional; The dimensionality; typically", null, ", which is the default value. powerlist – iterable, optional; The powers of the propergators, possibly dependent on the regulator. In case of negative powers, the derivative with respect to the corresponding Feynman parameter is calculated as explained in Section 3.2.4 of Ref. [BHJ+15]. If negative powers are combined with a tensor numerator, the derivative acts on the Feynman-parametrized tensor numerator as well, which leads to a consistent result.\nclass pySecDec.loop_integral.LoopIntegralFromPropagators(propagators, loop_momenta, external_momenta=[], Lorentz_indices=[], numerator=1, metric_tensor='g', replacement_rules=[], Feynman_parameters='x', regulator='eps', regulator_power=0, dimensionality='4-2*eps', powerlist=[])\n\nConstruct the Feynman parametrization of a loop integral from the algebraic momentum representation.\n\nExample:\n\n>>> from pySecDec.loop_integral import *\n>>> propagators = ['k**2', '(k - p)**2']\n>>> loop_momenta = ['k']\n>>> li = LoopIntegralFromPropagators(propagators, loop_momenta)\n>>> li.exponentiated_U\n( + (1)*x0 + (1)*x1)**(2*eps - 2)\n>>> li.exponentiated_F\n( + (-p**2)*x0*x1)**(-eps)\n\n\nThe 1st (U) and 2nd (F) Symanzik polynomials and their exponents can also be accessed independently:\n\n>>> li.U\n+ (1)*x0 + (1)*x1\n>>> li.F\n+ (-p**2)*x0*x1\n>>>\n>>> li.exponent_U\n2*eps - 2\n>>> li.exponent_F\n-eps\n\nParameters: propagators – iterable of strings or sympy expressions; The propagators, e.g. [‘k1**2’, ‘(k1-k2)**2 - m1**2’]. loop_momenta – iterable of strings or sympy expressions; The loop momenta, e.g. [‘k1’,’k2’]. external_momenta – iterable of strings or sympy expressions, optional; The external momenta, e.g. [‘p1’,’p2’]. Specifying the external_momenta is only required when a numerator is to be constructed. Lorentz_indices – iterable of strings or sympy expressions, optional; Symbols to be used as Lorentz indices in the numerator.\n\nparameter numerator\n\nParameters: numerator – string or sympy expression, optional; The numerator of the loop integral. Scalar products must be passed in index notation e.g. “k1(mu)*k2(mu)”. The numerator should be a sum of products of exclusively: * numbers * scalar products (e.g. “p1(mu)*k1(mu)*p1(nu)*k2(nu)”) * symbols (e.g. “m”)\nExamples:\n• ‘p1(mu)*k1(mu)*p1(nu)*k2(nu) + 4*s*eps*k1(mu)*k1(mu)’\n• ‘p1(mu)*(k1(mu) + k2(mu))*p1(nu)*k2(nu)’\n• ‘p1(mu)*k1(mu)*my_function(eps)’\n\nHint\n\nIt is possible to use numbers as indices, for example ‘p1(mu)*p2(mu)*k1(nu)*k2(nu) = p1(1)*p2(1)*k1(2)*k2(2)’.\n\nHint\n\nThe numerator may have uncontracted indices, e.g. ‘k1(mu)*k2(nu)’\n\nWarning\n\nAll Lorentz indices (including the contracted ones) must be explicitly defined using the parameter Lorentz_indices.\n\nWarning\n\nIt is assumed that the numerator is and all its derivatives by the regulator are finite and defined if", null, "is inserted explicitly. In particular, if user defined functions (like in the example p1(mu)*k1(mu)*my_function(eps)) appear, make sure that my_function(0) is finite.\n\nHint\n\nIn order to mimic a singular user defined function, use the parameter regulator_power. For example, instead of numerator = gamma(eps) you could enter numerator = eps_times_gamma(eps) in conjunction with regulator_power = -1\n\nWarning\n\nThe numerator is very flexible in its input. However, that flexibility comes for the price of less error safety. We have no way of checking for all possible mistakes in the input. If your numerator is more advanced than in the examples above, you should proceed with great caution.\n\nParameters: metric_tensor – string or sympy symbol, optional; The symbol to be used for the (Minkowski) metric tensor", null, ". replacement_rules – iterable of iterables with two strings or sympy expressions, optional; Symbolic replacements to be made for the external momenta, e.g. definition of Mandelstam variables. Example: [(‘p1*p2’, ‘s’), (‘p1**2’, 0)] where p1 and p2 are external momenta. It is also possible to specify vector replacements, for example [(‘p4’, ‘-(p1+p2+p3)’)]. Feynman_parameters – iterable or string, optional; The symbols to be used for the Feynman parameters. If a string is passed, the Feynman parameter variables will be consecutively numbered starting from zero. regulator – string or sympy symbol, optional; The symbol to be used for the dimensional regulator (typically", null, "or", null, ") Note If you change this symbol, you have to adapt the dimensionality accordingly. regulator_power – integer; The regulator to this power will be multiplied by the numerator. dimensionality – string or sympy expression, optional; The dimensionality; typically", null, ", which is the default value. powerlist – iterable, optional; The powers of the propergators, possibly dependent on the regulator. In case of negative powers, the derivative with respect to the corresponding Feynman parameter is calculated as explained in Section 3.2.4 of Ref. [BHJ+15]. If negative powers are combined with a tensor numerator, the derivative acts on the Feynman-parametrized tensor numerator as well, which leads to a consistent result.\n\n### 4.2.2. Loop Package¶\n\nThis module contains the function that generates a c++ package.\n\npySecDec.loop_integral.loop_package(name, loop_integral, requested_order, real_parameters=[], complex_parameters=[], contour_deformation=True, additional_prefactor=1, form_optimization_level=2, form_work_space='500M', decomposition_method='iterative', normaliz_executable='normaliz', enforce_complex=False, split=False, ibp_power_goal=-1, use_dreadnaut=True)\n\nDecompose, subtract and expand a Feynman parametrized loop integral. Return it as c++ package.\n\nThis function is a wrapper around pySecDec.code_writer.make_package().\n\nParameters: name – string; The name of the c++ namespace and the output directory. loop_integral – pySecDec.loop_integral.LoopIntegral; The loop integral to be computed. requested_orders – integer; Compute the expansion in the regulator to this order. real_parameters – iterable of strings or sympy symbols, optional; Parameters to be interpreted as real numbers, e.g. Mandelstam invariants and masses. parameters (complex) – iterable of strings or sympy symbols, optional; Parameters to be interpreted as complex numbers. To use the complex mass scheme, define the masses as complex parameters. contour_deformation – bool, optional; Whether or not to produce code for contour deformation. Default: True. additional_prefactor – string or sympy expression, optional; An additional factor to be multiplied to the loop integral. It may depend on the regulator, the real_parameters, and the complex_parameters. form_optimization_level – integer out of the interval [0,3], optional; The optimization level to be used in FORM. Default: 2. form_work_space – string, optional; The FORM WorkSpace. Default: '500M'. decomposition_method – string, optional; The strategy to decompose the polynomials. The following strategies are available: ‘iterative’ (default) ‘geometric’ ‘geometric_ku’ Note For ‘geometric’ and ‘geometric_ku’, the third-party program “normaliz” is needed. See The Geomethod and Normaliz. normaliz_executable – string, optional; The command to run normaliz. normaliz is only required if decomposition_method is set to ‘geometric’ or ‘geometric_ku’. Default: ‘normaliz’ enforce_complex – bool, optional; Whether or not the generated integrand functions should have a complex return type even though they might be purely real. The return type of the integrands is automatically complex if contour_deformation is True or if there are complex_parameters. In other cases, the calculation can typically be kept purely real. Most commonly, this flag is needed if log() occurs in one of the integrand functions. However, pySecDec will suggest setting this flag to True in that case. Default: False split – bool, optional; Whether or not to split the integration at", null, "in order to map singularities from", null, "to", null, ". Set this option to True if you have singularties when one or more integration variables are one. Default: False ibp_power_goal – integer, optional; The power_goal that is forwarded to integrate_by_parts(). This option controls how the subtraction terms are generated. Setting it to -numpy.inf disables integrate_by_parts(), while 0 disables integrate_pole_part(). See also To generate the subtraction terms, this function first calls integrate_by_parts() for each integration variable with the give ibp_power_goal. Then integrate_pole_part() is called. Default: -1 use_dreadnaut – bool or string, optional; Whether or not to use squash_symmetry_redundant_sectors_dreadnaut() to find sector symmetries. If given a string, interpret that string as the command line executable dreadnaut. If True, try $SECDEC_CONTRIB/bin/dreadnaut and, if the environment variable $SECDEC_CONTRIB is not set, dreadnaut. Default: True\n\n### 4.2.3. Drawing Feynman Diagrams¶\n\nUse the following function to draw Feynman diagrams.\n\npySecDec.loop_integral.draw.plot_diagram(internal_lines, external_lines, filename, powerlist=None, neato='neato', extension='pdf', Gstart=0)\n\nDraw a Feynman diagram using Graphviz (neato).\n\nThanks to Viktor Papara <[email protected]> for his major contributions to this function.\n\nWarning\n\nThe target is overwritten without prompt if it exists already.\n\nParameters: internal_lines – list; Adjacency list of internal lines, e.g. [['m',['a',4]],['m',[4,5]], ['m',['a',5]],[0,[1,2]],[0,[4,1]],[0,[2,5]]] external_lines – list; Adjacency list of external lines, e.g. [[‘p1’,1],[‘p2’,2],[‘p3’,’a’]] filename – string; The name of the output file. The generated file gets this name plus the file extension. powerlist – list, optional; The powers of the propagators defined by the internal_lines. neato – string, default: “neato”; The shell command to call “neato”. extension – string, default: “pdf”; The file extension. This also defines the output format. Gstart – nonnegative int; The is value is passed to “neato” with the “-Gstart” option. Try changing this value if the visualization looks bad.\n\n## 4.3. Decomposition¶\n\nThe core of sector decomposition. This module implements the actual decomposition routines.\n\n### 4.3.1. Common¶\n\nThis module collects routines that are used by multiple decompition modules.\n\nclass pySecDec.decomposition.Sector(cast, other=[], Jacobian=None)\n\nContainer class for sectors that arise during the sector decomposition.\n\nParameters: cast – iterable of algebra.Product or of algebra.Polynomial; The polynomials to be cast to the form * (const + ...) other – iterable of algebra.Polynomial, optional; All variable transformations are applied to these polynomials but it is not attempted to achieve the form * (const + ...) Jacobian – algebra.Polynomial with one term, optional; The Jacobian determinant of this sector. If not provided, the according unit monomial (1*x0^0*x1^0...) is assumed.\npySecDec.decomposition.squash_symmetry_redundant_sectors_sort(sectors, sort_function)\n\nReduce a list of sectors by squashing duplicates with equal integral.\n\nIf two sectors only differ by a permutation of the polysymbols (to be interpreted as integration variables over some inteval), then the two sectors integrate to the same value. Thus we can drop one of them and count the other twice. The multiple counting of a sector is accounted for by increasing the coefficient of the Jacobian by one.\n\nEquivalence up to permutation is established by applying the sort_function to each sector, this brings them into a canonical form. Sectors with identical canonical forms differ only by a permutation.\n\nNote: whether all symmetries are found depends on the choice of sort_function. Neither pySecDec.matrix_sort.iterative_sort() nor pySecDec.matrix_sort.Pak_sort() find all symmetries.\n\nExample:\n\n>>> from pySecDec.algebra import Polynomial\n>>> from pySecDec.decomposition import Sector\n>>> from pySecDec.decomposition import squash_symmetry_redundant_sectors_sort\n>>> from pySecDec.matrix_sort import Pak_sort\n>>>\n>>> poly = Polynomial([(0,1),(1,0)], ['a','b'])\n>>> swap = Polynomial([(1,0),(0,1)], ['a','b'])\n>>> Jacobian_poly = Polynomial([(1,0)], ) # three\n>>> Jacobian_swap = Polynomial([(0,1)], ) # five\n>>> sectors = (\n... Sector([poly],Jacobian=Jacobian_poly),\n... Sector([swap],Jacobian=Jacobian_swap)\n... )\n>>>\n>>> reduced_sectors = squash_symmetry_redundant_sectors_sort(sectors,\n... Pak_sort)\n>>> len(reduced_sectors) # symmetry x0 <--> x1\n1\n>>> # The Jacobians are added together to account\n>>> # for the double counting of the sector.\n>>> reduced_sectors.Jacobian\n+ (8)*x0\n\nParameters: sectors – iterable of Sector; the sectors to be reduced. sort_function – pySecDec.matrix_sort.iterative_sort() or pySecDec.matrix_sort.Pak_sort(); The function to be used for finding a canonical form of the sectors.\npySecDec.decomposition.squash_symmetry_redundant_sectors_dreadnaut(sectors, dreadnaut='dreadnaut', workdir='dreadnaut_tmp', keep_workdir=False)\n\nReduce a list of sectors by squashing duplicates with equal integral.\n\nEach Sector is converted to a Polynomial which is represented as a graph following the example of [BKAP] (v2.6 Figure 7, Isotopy of matrices).\n\nWe first multiply each polynomial in the sector by a unique tag then sum the polynomials of the sector, this converts a sector to a polynomial. Next, we convert the expolist of the resulting polynomial to a graph where each unique exponent in the expolist is considered to be a different symbol. Each unique coefficient in the polynomials coeffs is assigned a vertex and connected to the row vertex of any term it multiplies. The external program dreadnaut is then used to bring the graph into a canonical form and provide a hash. Sectors with equivalent hashes may be identical, their canonical graphs are compared and if they are identical the sectors are combined.\n\nNote\n\nThis function calls the command line executable of dreadnaut [BKAP]. It has been tested with dreadnaut version nauty26r7.\n\nParameters: sectors – iterable of Sector; the sectors to be reduced. dreadnaut – string; The shell command to run dreadnaut. workdir – string; The directory for the communication with dreadnaut. A directory with the specified name will be created in the current working directory. If the specified directory name already exists, an OSError is raised. Note The communication with dreadnaut is done via files. keep_workdir – bool; Whether or not to delete the workdir after execution.\n\n### 4.3.2. Iterative¶\n\nThe iterative sector decomposition routines.\n\nexception pySecDec.decomposition.iterative.EndOfDecomposition\n\nThis exception is raised if the function iteration_step() is called although the sector is already in standard form.\n\npySecDec.decomposition.iterative.find_singular_set(sector, indices=None)\n\nFunction within the iterative sector decomposition procedure which heuristically chooses an optimal decomposition set. The strategy was introduced in arXiv:hep-ph/0004013 [BH00] and is described in 4.2.2 of arXiv:1410.7939 [Bor14]. Return a list of indices.\n\nParameters: sector – Sector; The sector to be decomposed. indices – iterable of integers or None; The indices of the parameters to be considered as integration variables. By default (indices=None), all parameters are considered as integration variables.\npySecDec.decomposition.iterative.iteration_step(sector, indices=None)\n\nRun a single step of the iterative sector decomposition as described in chapter 3.2 (part II) of arXiv:0803.4177v2 [Hei08]. Return an iterator of Sector - the arising subsectors.\n\nParameters: sector – Sector; The sector to be decomposed. indices – iterable of integers or None; The indices of the parameters to be considered as integration variables. By default (indices=None), all parameters are considered as integration variables.\npySecDec.decomposition.iterative.iterative_decomposition(sector, indices=None)\n\nRun the iterative sector decomposition as described in chapter 3.2 (part II) of arXiv:0803.4177v2 [Hei08]. Return an iterator of Sector - the arising subsectors.\n\nParameters: sector – Sector; The sector to be decomposed. indices – iterable of integers or None; The indices of the parameters to be considered as integration variables. By default (indices=None), all parameters are considered as integration variables.\npySecDec.decomposition.iterative.primary_decomposition(sector, indices=None)\n\nPerform the primary decomposition as described in chapter 3.2 (part I) of arXiv:0803.4177v2 [Hei08]. Return a list of Sector - the primary sectors. For N Feynman parameters, there are N primary sectors where the i-th Feynman parameter is set to 1 in sector i.\n\nParameters: sector – Sector; The container holding the polynomials (typically", null, "and", null, ") to eliminate the Dirac delta from. indices – iterable of integers or None; The indices of the parameters to be considered as integration variables. By default (indices=None), all parameters are considered as integration variables.\npySecDec.decomposition.iterative.primary_decomposition_polynomial(polynomial, indices=None)\n\nPerform the primary decomposition on a single polynomial.\n\nParameters: polynomial – algebra.Polynomial; The polynomial to eliminate the Dirac delta from. indices – iterable of integers or None; The indices of the parameters to be considered as integration variables. By default (indices=None), all parameters are considered as integration variables.\npySecDec.decomposition.iterative.remap_parameters(singular_parameters, Jacobian, *polynomials)\n\nRemap the Feynman parameters according to eq. (16) of arXiv:0803.4177v2 [Hei08]. The parameter whose index comes first in singular_parameters is kept fix.\n\nThe remapping is done in place; i.e. the polynomials are NOT copied.\n\nParameters: singular_parameters – list of integers; The indices", null, "such that at least one of polynomials becomes zero if all", null, ". Jacobian – Polynomial; The Jacobian determinant is multiplied to this polynomial. polynomials – abritrarily many instances of algebra.Polynomial where all of these have an equal number of variables; The polynomials of Feynman parameters to be remapped. These are typically", null, "and", null, ".\n\nExample:\n\nremap_parameters([1,2], Jacobian, F, U)\n\n\n### 4.3.3. Geometric¶\n\nThe geometric sector decomposition routines.\n\npySecDec.decomposition.geometric.Cheng_Wu(sector, index=-1)\n\nReplace one Feynman parameter by one. This means integrating out the Dirac delta according to the Cheng-Wu theorem.\n\nParameters: sector – Sector; The container holding the polynomials (typically", null, "and", null, ") to eliminate the Dirac delta from. index – integer, optional; The index of the Feynman parameter to eliminate. Default: -1 (the last Feynman parameter)\nclass pySecDec.decomposition.geometric.Polytope(vertices=None, facets=None)\n\nRepresentation of a polytope defined by either its vertices or its facets. Call complete_representation() to translate from one to the other representation.\n\nParameters: vertices – two dimensional array; The polytope in vertex representation. Each row is interpreted as one vertex. facets – two dimensional array; The polytope in facet representation. Each row represents one facet", null, ". A row in facets is interpreted as one normal vector", null, "with additionally the constant", null, "in the last column. The points", null, "of the polytope obey", null, "complete_representation(normaliz='normaliz', workdir='normaliz_tmp', keep_workdir=False)\n\nTransform the vertex representation of a polytope to the facet representation or the other way round. Remove surplus entries in self.facets or self.vertices.\n\nNote\n\nThis function calls the command line executable of normaliz [BIR]. It has been tested with normaliz versions 3.0.0, 3.1.0, and 3.1.1.\n\nParameters: normaliz – string; The shell command to run normaliz. workdir – string; The directory for the communication with normaliz. A directory with the specified name will be created in the current working directory. If the specified directory name already exists, an OSError is raised. Note The communication with normaliz is done via files. keep_workdir – bool; Whether or not to delete the workdir after execution.\nvertex_incidence_lists()\n\nReturn for each vertex the list of facets it lies in (as dictonary). The keys of the output dictonary are the vertices while the values are the indices of the facets in self.facets.\n\npySecDec.decomposition.geometric.convex_hull(*polynomials)\n\nCalculate the convex hull of the Minkowski sum of all polynomials in the input. The algorithm sets all coefficients to one first and then only keeps terms of the polynomial product that have coefficient 1. Return the list of these entries in the expolist of the product of all input polynomials.\n\nParameters: polynomials – abritrarily many instances of Polynomial where all of these have an equal number of variables; The polynomials to calculate the convex hull for.\npySecDec.decomposition.geometric.generate_fan(*polynomials)\n\nCalculate the fan of the polynomials in the input. The rays of a cone are given by the exponent vectors after factoring out a monomial together with the standard basis vectors. Each choice of factored out monomials gives a different cone. Only full (", null, "-) dimensional cones in", null, "need to be considered.\n\nParameters: polynomials – abritrarily many instances of Polynomial where all of these have an equal number of variables; The polynomials to calculate the fan for.\npySecDec.decomposition.geometric.geometric_decomposition(sector, indices=None, normaliz='normaliz', workdir='normaliz_tmp')\n\nRun the sector decomposition using the geomethod as described in [BHJ+15].\n\nNote\n\nThis function calls the command line executable of normaliz [BIR]. It has been tested with normaliz versions 3.0.0, 3.1.0, and 3.1.1.\n\nParameters: sector – Sector; The sector to be decomposed. indices – list of integers or None; The indices of the parameters to be considered as integration variables. By default (indices=None), all parameters are considered as integration variables. normaliz – string; The shell command to run normaliz. workdir – string; The directory for the communication with normaliz. A directory with the specified name will be created in the current working directory. If the specified directory name already exists, an OSError is raised. Note The communication with normaliz is done via files.\npySecDec.decomposition.geometric.geometric_decomposition_ku(sector, indices=None, normaliz='normaliz', workdir='normaliz_tmp')\n\nRun the sector decomposition using the original geometric decomposition strategy by Kaneko and Ueda as described in [KU10].\n\nNote\n\nThis function calls the command line executable of normaliz [BIR]. It has been tested with normaliz versions 3.0.0, 3.1.0, and 3.1.1.\n\nParameters: sector – Sector; The sector to be decomposed. indices – list of integers or None; The indices of the parameters to be considered as integration variables. By default (indices=None), all parameters are considered as integration variables. normaliz – string; The shell command to run normaliz. workdir – string; The directory for the communication with normaliz. A directory with the specified name will be created in the current working directory. If the specified directory name already exists, an OSError is raised. Note The communication with normaliz is done via files.\npySecDec.decomposition.geometric.transform_variables(polynomial, transformation, polysymbols='y')\n\nTransform the parameters", null, "of a pySecDec.algebra.Polynomial,", null, ", where", null, "is the transformation matrix.\n\nParameters: polynomial – pySecDec.algebra.Polynomial; The polynomial to transform the variables in. transformation – two dimensional array; The transformation matrix", null, ". polysymbols – string or iterable of strings; The symbols for the new variables. This argument is passed to the default constructor of pySecDec.algebra.Polynomial. Refer to the documentation of pySecDec.algebra.Polynomial for further details.\npySecDec.decomposition.geometric.triangulate(cone, normaliz='normaliz', workdir='normaliz_tmp', keep_workdir=False, switch_representation=False)\n\nSplit a cone into simplicial cones; i.e. cones defined by exactly", null, "rays where", null, "is the dimensionality.\n\nNote\n\nThis function calls the command line executable of normaliz [BIR]. It has been tested with normaliz versions 3.0.0, 3.1.0, and 3.1.1.\n\nParameters: cone – two dimensional array; The defining rays of the cone. normaliz – string; The shell command to run normaliz. workdir – string; The directory for the communication with normaliz. A directory with the specified name will be created in the current working directory. If the specified directory name already exists, an OSError is raised. Note The communication with normaliz is done via files. keep_workdir – bool; Whether or not to delete the workdir after execution. switch_representation – bool; Whether or not to switch between facet and vertex/ray representation.\n\n### 4.3.4. Splitting¶\n\nRoutines to split the integration between", null, "and", null, ". This maps singularities from", null, "to", null, ".\n\npySecDec.decomposition.splitting.find_singular_sets_at_one(polynomial)\n\nFind all possible sets of parameters such that the polynomial‘s constant term vanishes if these parameters are set to one.\n\nExample:\n\n>>> from pySecDec.algebra import Polynomial\n>>> from pySecDec.decomposition.splitting import find_singular_sets_at_one\n>>> polysymbols = ['x0', 'x1']\n>>> poly = Polynomial.from_expression('1 - 10*x0 - x1', polysymbols)\n>>> find_singular_sets_at_one(poly)\n[(1,)]\n\nParameters: polynomial – Polynomial; The polynomial to search in.\npySecDec.decomposition.splitting.remap_one_to_zero(polynomial, *indices)\n\nApply the transformation", null, "to polynomial for the parameters of the given indices.\n\nParameters: polynomial – Polynomial; The polynomial to apply the transformation to. indices – arbitrarily many int; The indices of the polynomial.polysymbols to apply the transformation to.\n\nExample:\n\n>>> from pySecDec.algebra import Polynomial\n>>> from pySecDec.decomposition.splitting import remap_one_to_zero\n>>> polysymbols = ['x0']\n>>> polynomial = Polynomial.from_expression('x0', polysymbols)\n>>> remap_one_to_zero(polynomial, 0)\n+ (1) + (-1)*x0\n\npySecDec.decomposition.splitting.split(sector, seed, *indices)\n\nSplit the integration interval", null, "for the parameters given by indices. The splitting point is fixed using numpy’s random number generator.\n\nReturn an iterator of Sector - the arising subsectors.\n\nParameters: sector – Sector; The sector to be split.\n:param seed;\ninteger; The seed for the random number generator that is used to fix the splitting point.\nParameters: indices – arbitrarily many integers; The indices of the variables to be split.\npySecDec.decomposition.splitting.split_singular(sector, seed, indices=[])\n\nSplit the integration interval", null, "for the parameters that can lead to singularities at one for the polynomials in sector.cast.\n\nReturn an iterator of Sector - the arising subsectors.\n\nParameters: sector – Sector; The sector to be split. seed – integer; The seed for the random number generator that is used to fix the splitting point. indices – iterables of integers; The indices of the variables to be split if required. An empty iterator means that all variables may potentially be split.\n\n## 4.4. Matrix Sort¶\n\nAlgorithms to sort a matrix when column and row permutations are allowed.\n\npySecDec.matrix_sort.Pak_sort(matrix)\n\nInplace modify the matrix to some ordering, when permutations of rows and columns (excluding the first) are allowed. The implementation of this function is describedin chapter 2 of [Pak11].\n\nNote\n\nThis function may result in different orderings depending on the initial ordering.\n\nParameters: matrix – 2D array-like; The matrix to be canonicalized.\npySecDec.matrix_sort.iterative_sort(matrix)\n\nInplace modify the matrix to some ordering, when permutations of rows and columns (excluding the first) are allowed.\n\nNote\n\nThis function may result in different orderings depending on the initial ordering.\n\nParameters: matrix – 2D array-like; The matrix to be canonicalized.\n\n## 4.5. Subtraction¶\n\nRoutines to isolate the divergencies in an", null, "expansion.\n\npySecDec.subtraction.integrate_by_parts(polyprod, power_goal, *indices)\n\nRepeatedly apply integration by parts,", null, ", where", null, "denotes the derivative of", null, "with respect to", null, ". The iteration stops, when", null, "power_goal.\n\nThis function provides an alternative to integrate_pole_part().\n\nParameters: polyprod – algebra.Product of the form **(a_j + ...)> * * ; The input product as decribed above. The **(a_j + ...)> should be a pySecDec.algebra.Product of **(a_j + ...). as described below. The **(a_j + ...) should be an pySecDec.algebra.ExponentiatedPolynomial with exponent being a Polynomial of the regulators", null, ". Although no dependence on the Feynman parameters is expected in the exponent, the polynomial variables should be the Feynman parameters and the regulators. The constant term of the exponent should be numerical. The polynomial variables of monomial and the other factors (interpreted as", null, ") are interpreted as the Feynman parameters and the epsilon regulators. Make sure that the last factor () is defined and finite for", null, ". All poles for", null, "should be made explicit by putting them into as pySecDec.algebra.Pow with exponent = -1 and the base of type pySecDec.algebra.Polynomial. indices – arbitrarily many integers; The index/indices of the parameter(s) to partially integrate.", null, "in the formulae above. number, e.g. float, integer, ...; The stopping criterion for the iteration.\n\nReturn the pole part and the numerically integrable remainder as a list. Each returned list element has the same structure as the input polyprod.\n\npySecDec.subtraction.integrate_pole_part(polyprod, *indices)\n\nTransform an integral of the form", null, "into the form", null, ", where", null, "denotes the p-th derivative of", null, "with respect to", null, ". The equations above are to be understood schematically.\n\nThis function implements the transformation from equation (19) to (21) as described in arXiv:0803.4177v2 [Hei08].\n\nParameters: polyprod – algebra.Product of the form **(a_j + ...)> * * ; The input product as decribed above. The **(a_j + ...)> should be a pySecDec.algebra.Product of **(a_j + ...). as described below. The **(a_j + ...) should be an pySecDec.algebra.ExponentiatedPolynomial with exponent being a Polynomial of the regulators", null, ". Although no dependence on the Feynman parameters is expected in the exponent, the polynomial variables should be the Feynman parameters and the regulators. The constant term of the exponent should be numerical. The polynomial variables of monomial and the other factors (interpreted as", null, ") are interpreted as the Feynman parameters and the epsilon regulators. Make sure that the last factor () is defined and finite for", null, ". All poles for", null, "should be made explicit by putting them into as pySecDec.algebra.Pow with exponent = -1 and the base of type pySecDec.algebra.Polynomial. indices – arbitrarily many integers; The index/indices of the parameter(s) to partially integrate.", null, "in the formulae above.\n\nReturn the pole part and the numerically integrable remainder as a list. That is the sum and the integrand of equation (21) in arXiv:0803.4177v2 [Hei08]. Each returned list element has the same structure as the input polyprod.\n\npySecDec.subtraction.pole_structure(monomial_product, *indices)\n\nReturn a list of the unregulated exponents of the parameters specified by indices in monomial_product.\n\nParameters: monomial_product – pySecDec.algebra.ExponentiatedPolynomial with exponent being a Polynomial; The monomials of the subtraction to extract the pole structure from. indices – arbitrarily many integers; The index/indices of the parameter(s) to partially investigate.\n\n## 4.6. Expansion¶\n\nRoutines to series expand singular and nonsingular expressions.\n\npySecDec.expansion.expand_Taylor(expression, indices, orders)\n\nSeries/Taylor expand a nonsingular expression around zero.\n\nReturn a algebra.Polynomial - the series expansion.\n\nParameters: expression – an expression composed of the types defined in the module algebra; The expression to be series expanded. indices – integer or iterable of integers; The indices of the parameters to expand. The ordering of the indices defines the ordering of the expansion. order – integer or iterable of integers; The order to which the expansion is to be calculated.\npySecDec.expansion.expand_singular(product, indices, orders)\n\nSeries expand a potentially singular expression of the form", null, "Return a algebra.Polynomial - the series expansion.\n\nTo expand more general expressions use expand_sympy().\n\nParameters: product – algebra.Product with factors of the form and ** -1; The expression to be series expanded. indices – integer or iterable of integers; The indices of the parameters to expand. The ordering of the indices defines the ordering of the expansion. order – integer or iterable of integers; The order to which the expansion is to be calculated.\npySecDec.expansion.expand_sympy(expression, variables, orders)\n\nExpand a sympy expression in the variables to given orders. Return the expansion as nested pySecDec.algebra.Polynomial.\n\nThis function is a generalization of expand_singular().\n\nParameters: expression – string or sympy expression; The expression to be expanded variables – iterable of strings or sympy symbols; The variables to expand the expression in. orders – iterable of integers; The orders to expand to.\n\n## 4.7. Code Writer¶\n\nThis module collects routines to create a c++ library.\n\n### 4.7.1. Make Package¶\n\nThis is the main function of pySecDec.\n\npySecDec.code_writer.make_package(name, integration_variables, regulators, requested_orders, polynomials_to_decompose, polynomial_names=[], other_polynomials=[], prefactor=1, remainder_expression=1, functions=[], real_parameters=[], complex_parameters=[], form_optimization_level=2, form_work_space='500M', form_insertion_depth=5, contour_deformation_polynomial=None, positive_polynomials=[], decomposition_method='iterative_no_primary', normaliz_executable='normaliz', enforce_complex=False, split=False, ibp_power_goal=-1, use_dreadnaut=True)\n\nDecompose, subtract and expand an expression. Return it as c++ package.\n\nIn order to decompose a loop integral, use the function pySecDec.loop_integral.loop_package().\n\nParameters: name – string; The name of the c++ namepace and the output directory. integration_variables – iterable of strings or sympy symbols; The variables that are to be integrated from 0 to 1. regulators – iterable of strings or sympy symbols; The UV/IR regulators of the integral. requested_orders – iterable of integers; Compute the expansion in the regulators to these orders. polynomials_to_decompose – iterable of strings or sympy expressions or pySecDec.algebra.ExponentiatedPolynomial or pySecDec.algebra.Polynomial; The polynomials to be decomposed. polynomial_names – iterable of strings; Assign symbols for the polynomials_to_decompose. These can be referenced in the other_polynomials; see other_polynomials for details. other_polynomials – iterable of strings or sympy expressions or pySecDec.algebra.ExponentiatedPolynomial or pySecDec.algebra.Polynomial; Additional polynomials where no decomposition is attempted. The symbols defined in polynomial_names can be used to reference the polynomials_to_decompose. This is particularly useful when computing loop integrals where the “numerator” can depend on the first and second Symanzik polynomials. Example (1-loop bubble with numerator): >>> polynomials_to_decompose = [\"(x0 + x1)**(2*eps - 4)\", ... \"(-p**2*x0*x1)**(-eps))\"] >>> polynomial_names = [\"U\", \"F\"] >>> other_polynomials = [\"\"\" (eps - 1)*s*U**2 ... + (eps - 2)*F ... - (eps - 1)*2*s*x0*U ... + (eps - 1)*s*x0**2\"\"\"] See also pySecDec.loop_integral Note that the polynomial_names refer to the polynomials_to_decompose without their exponents. prefactor – string or sympy expression, optional; A factor that does not depend on the integration variables. remainder_expression – string or sympy expression or pySecDec.algebra._Expression, optional; An additional factor. Dummy function must be provided with all arguments, e.g. remainder_expression='exp(eps)*f(x0,x1)'. In addition, all dummy function must be listed in functions. functions – iterable of strings or sympy symbols, optional; Function symbols occuring in remainder_expression, e.g.[‘f’]. Note The power function pow and the logarithm log are already defined by default. The log uses the nonstandard continuation from a negative imaginary part on the negative real axis (e.g. log(-1) = -i*pi). real_parameters – iterable of strings or sympy symbols, optional; Symbols to be interpreted as real variables. complex_parameters – iterable of strings or sympy symbols, optional; Symbols to be interpreted as complex variables. form_optimization_level – integer out of the interval [0,3], optional; The optimization level to be used in FORM. Default: 2. form_work_space – string, optional; The FORM WorkSpace. Default: '500M'. form_insertion_depth – nonnegative integer, optional; How deep FORM should try to resolve nested function calls. Default: 5. contour_deformation_polynomial – string or sympy symbol, optional; The name of the polynomial in polynomial_names that is to be continued to the complex plane according to a", null, "prescription. For loop integrals, this is the second Symanzik polynomial F. If not provided, no code for contour deformation is created. positive_polynomials – iterable of strings or sympy symbols, optional; The names of the polynomials in polynomial_names that should always have a positive real part. For loop integrals, this applies to the first Symanzik polynomial U. If not provided, no polynomial is checked for positiveness. If contour_deformation_polynomial is None, this parameter is ignored. decomposition_method – string, optional; The strategy to decompose the polynomials. The following strategies are available: ‘iterative_no_primary’ (default) ‘geometric_no_primary’ ‘iterative’ ‘geometric’ ‘geometric_ku’ ‘iterative’, ‘geometric’, and ‘geometric_ku’ are only valid for loop integrals. An end user should always use ‘iterative_no_primary’ or ‘geometric_no_primary’ here. In order to compute loop integrals, please use the function pySecDec.loop_integral.loop_package(). normaliz_executable – string, optional; The command to run normaliz. normaliz is only required if decomposition_method starts with ‘geometric’. Default: ‘normaliz’ enforce_complex – bool, optional; Whether or not the generated integrand functions should have a complex return type even though they might be purely real. The return type of the integrands is automatically complex if contour_deformation is True or if there are complex_parameters. In other cases, the calculation can typically be kept purely real. Most commonly, this flag is needed if log() occurs in one of the integrand functions. However, pySecDec will suggest setting this flag to True in that case. Default: False split – bool or integer, optional; Whether or not to split the integration domain in order to map singularities from", null, "to", null, ". Set this option to True if you have singularties when one or more integration variables are one. If an integer is passed, that integer is used as seed to generate the splitting point. Default: False ibp_power_goal – integer, optional; The power_goal that is forwarded to integrate_by_parts(). This option controls how the subtraction terms are generated. Setting it to -numpy.inf disables integrate_by_parts(), while 0 disables integrate_pole_part(). See also To generate the subtraction terms, this function first calls integrate_by_parts() for each integration variable with the give ibp_power_goal. Then integrate_pole_part() is called. Default: -1 use_dreadnaut – bool or string, optional; Whether or not to use squash_symmetry_redundant_sectors_dreadnaut() to find sector symmetries. If given a string, interpret that string as the command line executable dreadnaut. If True, try $SECDEC_CONTRIB/bin/dreadnaut and, if the environment variable $SECDEC_CONTRIB is not set, dreadnaut. Default: True\n\n### 4.7.2. Template Parser¶\n\nFunctions to generate c++ sources from template files.\n\npySecDec.code_writer.template_parser.parse_template_file(src, dest, replacements={})\n\nCopy a file from src to dest replacing %(...) instructions in the standard python way.\n\nWarning\n\nIf the file specified in dest exists, it is overwritten without prompt.\n\nParameters: src – str; The path to the template file. dest – str; The path to the destination file. replacements – dict; The replacements to be performed. The standard python replacement rules apply: >>> '%(var)s = %(value)i' % dict( ... var = 'my_variable', ... value = 5) 'my_variable = 5' \npySecDec.code_writer.template_parser.parse_template_tree(src, dest, replacements_in_files={}, filesystem_replacements={})\n\nCopy a directory tree from src to dest using parse_template_file() for each file and replacing the filenames according to filesystem_replacements.\n\nParameters: src – str; The path to the template directory. dest – str; The path to the destination directory. replacements_in_files – dict; The replacements to be performed in the files. The standard python replacement rules apply: >>> '%(var)s = %(value)i' % dict( ... var = 'my_variable', ... value = 5) 'my_variable = 5' filesystem_replacements – dict; Renaming rules for the destination files. and directories. If a file or directory name in the source tree src matches a key in this dictionary, it is renamed to the corresponding value. If the value is None, the corresponding file is ignored.\n\n## 4.8. Integral Interface¶\n\nAn interface to libraries generated by pySecDec.code_writer.make_package() or pySecDec.loop_integral.loop_package().\n\nclass pySecDec.integral_interface.CPPIntegrator\n\nAbstract base class for integrators to be used with an IntegralLibrary. This class holds a pointer to the c++ integrator and defines the destructor.\n\nclass pySecDec.integral_interface.Cuhre(integral_library, epsrel=0.01, epsabs=1e-07, flags=0, mineval=0, maxeval=1000000, key=0, real_complex_together=False)\n\nWrapper for the Cuhre integrator defined in the cuba library.\n\nParameters: integral_library – IntegralLibrary; The integral to be computed with this integrator.\n\nThe other options are defined in the cuba manual.\n\nclass pySecDec.integral_interface.Divonne(integral_library, epsrel=0.01, epsabs=1e-07, flags=0, seed=0, mineval=0, maxeval=1000000, key1=2000, key2=1, key3=1, maxpass=4, border=0.0, maxchisq=1.0, mindeviation=0.15, real_complex_together=False)\n\nWrapper for the Divonne integrator defined in the cuba library.\n\nParameters: integral_library – IntegralLibrary; The integral to be computed with this integrator.\n\nThe other options are defined in the cuba manual.\n\nclass pySecDec.integral_interface.IntegralLibrary(shared_object_path)\n\nInterface to a c++ library produced by make_package() or loop_package().\n\nParameters: shared_object_path – str; The path to the file “_pylink.so” that can be built by the command \\$ make pylink in the root directory of the c++ library.\n\nInstances of this class can be called with the following arguments:\n\nParameters: real_parameters – iterable of float; The real_parameters of the library. complex_parameters – iterable of complex; The complex parameters of the library. together – bool; Whether to integrate the sum of all sectors or to integrate the sectors separately. Default: True. number_of_presamples – unsigned int, optional; The number of samples used for the comtour optimization. This option is ignored if the integral library was created without deformation. Default: 100000. deformation_parameters_maximum – float, optional; The maximal value the deformation parameters", null, "can obtain. If number_of_presamples=0, all", null, "are set to this value. This option is ignored if the integral library was created without deformation. Default: 1.0. deformation_parameters_minimum – float, optional; This option is ignored if the integral library was created without deformation. Default: 1e-5. deformation_parameters_decrease_factor – float, optional; If the sign check with the optimized", null, "fails, all", null, "are multiplied by this value until the sign check passes. This option is ignored if the integral library was created without deformation. Default: 0.9.\n\nThe call operator returns three strings: * The integral without its prefactor * The prefactor * The integral multiplied by the prefactor\n\nThe integrator cen be configured by calling the member methods use_Vegas(), use_Suave(), use_Divonne(), and use_Cuhre(). The available options are listed in the documentation of Vegas, Suave, Divonne, and Cuhre, respectively. If not specified otherwise, Vegas is used with its default arguments. For details about the options, refer to the cuba manual.\n\nFurther information about the library is stored in the member variable info of type dict.\n\nclass pySecDec.integral_interface.Suave(integral_library, epsrel=0.01, epsabs=1e-07, flags=0, seed=0, mineval=0, maxeval=1000000, nnew=1000, nmin=10, flatness=25.0, real_complex_together=False)\n\nWrapper for the Suave integrator defined in the cuba library.\n\nParameters: integral_library – IntegralLibrary; The integral to be computed with this integrator.\n\nThe other options are defined in the cuba manual.\n\nclass pySecDec.integral_interface.Vegas(integral_library, epsrel=0.01, epsabs=1e-07, flags=0, seed=0, mineval=0, maxeval=1000000, nstart=1000, nincrease=500, nbatch=1000, real_complex_together=False)\n\nWrapper for the Vegas integrator defined in the cuba library.\n\nParameters: integral_library – IntegralLibrary; The integral to be computed with this integrator.\n\nThe other options are defined in the cuba manual.\n\n## 4.9. Miscellaneous¶\n\nCollection of general-purpose helper functions.\n\npySecDec.misc.adjugate(M)\n\nCalculate the adjugate of a matrix.\n\nParameters: M – a square-matrix-like array;\npySecDec.misc.all_pairs(iterable)\n\nReturn all possible pairs of a given set. all_pairs([1,2,3,4]) --> [(1,2),(3,4)] [(1,3),(2,4)] [(1,4),(2,3)]\n\nParameters: iterable – iterable; The set to be split into all possible pairs.\npySecDec.misc.argsort_2D_array(array)\n\nSort a 2D array according to its row entries. The idea is to bring identical rows together.\n\nIf your array is not two dimesional use argsort_ND_array().\n\nExample:\ninput   sorted\n1 2 3   1 2 3\n2 3 4   1 2 3\n1 2 3   2 3 4\n\nReturn the indices like numpy’s argsort() would.\n\nParameters: array – 2D array; The array to be argsorted.\npySecDec.misc.argsort_ND_array(array)\n\nLike argsort_2D_array(), this function groups identical entries in an array with any dimensionality greater than (or equal to) two together.\n\nReturn the indices like numpy’s argsort() would.\n\nParameters: array – ND array,", null, "; The array to be argsorted.\npySecDec.misc.assert_degree_at_most_max_degree(expression, variables, max_degree, error_message)\n\nAssert that expression is a polynomial of degree less or equal max_degree in the variables.\n\npySecDec.misc.cached_property(method)\n\nLike the builtin property to be used as decorator but the method is only called once per instance.\n\nExample:\n\nclass C(object):\n'Sum up the numbers from one to N.'\ndef __init__(self, N):\nself.N = N\n@cached_property\ndef sum(self):\nresult = 0\nfor i in range(1, self.N + 1):\nresult += i\nreturn result\n\npySecDec.misc.det(M)\n\nCalculate the determinant of a matrix.\n\nParameters: M – a square-matrix-like array;\npySecDec.misc.doc(docstring)\n\nDecorator that replaces a function’s docstring with docstring.\n\nExample:\n\n@doc('documentation of some_funcion')\ndef some_function(*args, **kwargs):\npass\n\npySecDec.misc.lowest_order(expression, variable)\n\nFind the lowest order of expression‘s series expansion in variable.\n\nExample:\n\n>>> from pySecDec.misc import lowest_order\n>>> lowest_order('exp(eps)', 'eps')\n0\n>>> lowest_order('gamma(eps)', 'eps')\n-1\n\nParameters: expression – string or sympy expression; The expression to compute the lowest expansion order of. variable – string or sympy expression; The variable in which to expand.\npySecDec.misc.missing(full, part)\n\nReturn the elements in full that are not contained in part. Raise ValueError if an element is in part but not in full. missing([1,2,3], ) --> [2,3] missing([1,2,3,1], [1,2]) --> [3,1] missing([1,2,3], [1,'a']) --> ValueError\n\nParameters: full – iterable; The set of elements to complete part with. part – iterable; The set to be completed to a superset of full.\npySecDec.misc.powerset(iterable, min_length=0, stride=1)\n\nReturn an iterator over the powerset of a given set. powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)\n\nParameters: iterable – iterable; The set to generate the powerset for. min_length – integer, optional; Only generate sets with minimal given length. Default: 0. stride – integer; Only generate sets that have a multiple of stride elements. powerset([1,2,3], stride=2) --> () (1,2) (1,3) (2,3)\npySecDec.misc.rangecomb(low, high)\n\nReturn an iterator over the occuring orders in a multivariate series expansion between low and high.\n\nParameters: low – vector-like array; The lowest orders. high – vector-like array; The highest orders.\n\nExample:\n\n>>> from pySecDec.misc import rangecomb\n>>> all_orders = rangecomb([-1,-2], [0,0])\n>>> list(all_orders)\n[(-1, -2), (-1, -1), (-1, 0), (0, -2), (0, -1), (0, 0)]\n\npySecDec.misc.sympify_symbols`(iterable, error_message, allow_number=False)\n\nsympify each item in iterable and assert that it is a symbol." ]

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[ "# Grade 3 Common Core Math Practice\n\nThe focus in Grade 3 is on the following four critical areas:\n\n• Developing understanding of multiplication and division and strategies for multiplication and division within 100\n• Developing understanding of fractions, especially unit fractions (fractions with numerator 1)\n• Developing understanding of the structure of rectangular arrays and of area\n• Describing and analyzing two-dimensional shapes\n\n### Overview of Grade 3 Standards\n\n#### Operations and Algebraic Thinking\n\n• Represent and solve problems involving multiplication and division(3.OA.A.1, 3.OA.A.2, 3.OA.A.3, 3.OA.A.4)\n• Understand properties of multiplication and the relationship between multiplication and division(3.OA.B.5, 3.OA.B.6)\n• Multiply and divide within 100(3.OA.C.7)\n• Solve problems involving the four operations, and identify and explain patterns in arithmetic(3.OA.D.8, 3.OA.D.9)\n\n#### Number and Operations in Base Ten\n\n• Use place value understanding and properties of operations to perform multi-digit arithmetic(3.NBT.A.1, 3.NBT.A.2, 3.NBT.A.3)\n\n#### Number and Operations—Fractions\n\n• Develop understanding of fractions as numbers(3.NF.A.1, 3.NF.A.2, 3.NF.A.2.A, 3.NF.A.2.B, 3.NF.A.3, 3.NF.A.3.A, 3.NF.A.3.B, 3.NF.A.3.C, 3.NF.A.3.D)\n\n#### Measurement and Data\n\n• Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects(3.MD.A.1, 3.MD.A.2)\n• Represent and interpret data(3.MD.B.3, 3.MD.B.4)\n• Geometric measurement: understand concepts of area and relate area to multiplication and to addition(3.MD.C.5, 3.MD.C.5.A, 3.MD.C.5.B, 3.MD.C.6, 3.MD.C.7, 3.MD.C.7.A, 3.MD.C.7.B, 3.MD.C.7.C, 3.MD.C.7.D)\n• Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures(3.MD.D.8)\n\n#### Geometry\n\n• Reason with shapes and their attributes(3.G.A.1, 3.G.A.2)\n\n#### Mathematical Practices\n\n• Make sense of problems and persevere in solving them\n• Reason abstractly and quantitatively\n• Construct viable arguments and critique the reasoning of others\n• Model with mathematics\n• Use appropriate tools strategically\n• Attend to precision\n• Look for and make use of structure\n• Look for and express regularity in repeated reasoning" ]

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[ "# What is the cosmological redshift drift effect?\n\nWhat is the redshift drift effect in cosmology? What are the necessary cosmological conditions for there to be a measurable redshift drift effect?\n\n• The redshift drift of an astronomical object is just the change of the redshift of that object with time. I think you'll need to be clearer what you want to know for us to be able to provide a useful answer. Apr 17, 2018 at 16:21\n\nAn expression for the first order redshift drift is $$\\frac{dz}{dt_0}= (1+z)H_0 - H(z),$$ where $H_0$ is the current Hubble parameter at time $t_0$ and $H(z)$ is the value of the Hubble parameter at an epoch corresponding to a redshift $z$.\nThe condition that there be a redshift drift is therefore that $$H(z) \\neq (1+z)H_0$$ which is certainly the case for arbitrary values of $z$ in $\\Lambda$CDM cosmology$^*$ where $$H(z) = (1+z) H_0\\left[ \\Omega_r (1+z)^2 + \\Omega_m (1+z) + \\Omega_k + \\Omega_{\\Lambda}(1+z)^{-2}\\right]^{1/2}$$ and the condition for a redshift drift is that $$\\left[ \\Omega_r (1+z)^2 + \\Omega_m (1+z) + \\Omega_k + \\Omega_{\\Lambda}(1+z)^{-2}\\right] \\neq 1$$\n$^*$ Other cosmologies are possible..." ]

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[ "# Abstract\n\nFriction is an important source of dissipation in dynamical systems. Properly considering it in the numerical model is fundamental to obtain stable and representative responses in structures and mechanisms. This is especially significant for the well-known Coulomb model due to discontinuity in force when stick-slip transition occurs. In this work an improved friction force model is proposed to smooth the force transition at null velocity, with an additional parameter obtained from the own system state. The improved model is employed in sliding connections of plane frames finite elements. A total Lagrangian Finite Element Method (FEM) formulation based on a positional description of the motion is employed. Using a variational principle, frictional dissipation is added to the total mechanical energy to develop the equations of motion. The resulting nonlinear equations are solved by the Newton-Raphson method accounting for the friction force update in the iterative process. Examples are presented to show the formulation effectiveness and possibilities in simulating dynamical systems that present the stick-slip effect.\n\nKeywords\nFriction model; Sliding connection; Nonlinear dynamics; Lagrange multiplier; Stick-slip effect\n\n# Graphical Abstract\n\nKeywords\nFriction model; Sliding connection; Nonlinear dynamics; Lagrange multiplier; Stick-slip effect\n\n# 1 INTRODUCTION\n\nIn the analysis of structures and mechanisms their dynamical systems are frequently assumed conservative, while, in reality, systems present dissipation due to several sources. The frictional dissipative effect, in particular, is important to be considered when relative motion between parts of the body exists. This is the case of sliding connections, such as prismatic and cylindrical joints, that, by introducing translational movement among body members, allow friction forces to develop at their contact regions.\n\nMathematical models try to describe some of the many characteristics of friction complex nature. For instance, evolving from the classical one-parameter Coulomb friction model, values of the friction force at rest (static friction) and in motion (kinetic friction) can be distinguished. The continuous decrease of friction values for increasing, but low, velocities, referred as the Stribeck effect (Rabinowicz, 1951Rabinowicz, E. (1951) The nature of the static and kinetic coefficients of friction. Journal of Applied Physics. 22(11), 1373-1379.), or the adhesion between contacting surfaces before sliding, resulting in local pre-sliding deformation (Hsieh and Pan, 2000Hsieh, C., Pan, Y.-C. (2000) Dynamic behavior and modelling of the pre-sliding static friction. Wear. 242(1-2), 1-17.), may be important and included in some models. The effect of lubricant layers between the surfaces (Armstrong-Hélouvry et al., 1994Armstrong-Hélouvry, B., Dupont, P., De Wit, C.C. (1994) A survey of models, analysis tools and compensation methods for the control of machines with friction. Automatica. 30(7).) and the ‘frictional lag’, a delay in the change of the force with change in velocity (Hess and Soom, 1990Hess, D.P., Soom, A. (1990) Friction at a lubricated line contact operating at oscillating sliding velocities. Journal of Tribology. 112(1), 147-152.), among other aspects, may be also encountered in current friction models. Comprehensive surveys (Olsson et al., 1998Olsson, H., Åström, K.J., Canudas de Wit, C., Gäfvert, M., Lischinsky, P. (1998) Friction Models and Friction Compensation. European Journal of Control. 4(3), 176-195.; Andersson et al., 2007Andersson, S., Söderberg, A., Björklund, S. (2007) Friction models for sliding dry, boundary and mixed lubricated contacts. Tribology International. 40(4), 580-587.; Marques et al., 2016Marques, F., Flores, P., Pimenta Claro, J.C., Lankarani, H.M. (2016) A survey and comparison of several friction force models for dynamic analysis of multibody mechanical systems. Nonlinear Dynamics. 86(3), 1407-1443.) present in-depth discussions on the characteristics of friction dissipation and several available models.\n\nFriction models can be broadly classified in ‘dynamic’ or ‘static’ (Marques et al., 2016Marques, F., Flores, P., Pimenta Claro, J.C., Lankarani, H.M. (2016) A survey and comparison of several friction force models for dynamic analysis of multibody mechanical systems. Nonlinear Dynamics. 86(3), 1407-1443.). Dynamical models, also referred as state-variable models, aim to capture more characteristics of the physically observed friction response by including additional degrees of freedom in the system, and usually demanding more parameters. Common state-variable friction models are referred as Dahl (Dahl, 1976Dahl, P.R. (1976) Solid friction damping of mechanical vibrations. AIAA Journal. 14(12), 1675-1682.), LuGre (Canudas de Wit et al., 1995Canudas de Wit, C., Lischinsky, P., Åström, K.J., Olsson, H. (1995) A New Model for Control of Systems with Friction. IEEE Transactions on Automatic Control. 40(3).), Elasto-Plastic (Dupont et al., 2002Dupont, P., Hayward, V., Armstrong, B., Altpeter, F. (2002) Single state elastoplastic friction models. IEEE Transactions on Automatic Control. 47(5), 787-792.), Gonthier (Gonthier et al., 2004Gonthier, Y., McPhee, J., Lange, C., Piedbœuf, J.-C. (2004) A regularized contact model with asymmetric damping and dwell-time dependent friction. Multibody System Dynamics. 11(3), 209-233.), only to list a few.\n\nModels referred as static, as opposed to dynamical models, dismiss the introduction of state variables to the problem, rendering a direct description of the force expression. In those models, however, the discontinuity of the friction force at null speed is a major drawback in the numerical solution. Some models (Kikuuwe et al., 2005Kikuuwe, R., Takesue, N., Sano, A., Mochiyama, H., Fujimoto, H. (2005) Fixed-step friction simulation: From classical coulomb model to modern continuous models. In 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS. pp. 1009-1016.; Threlfall, 1978Threlfall, D.C. (1978) The inclusion of Coulomb friction in mechanisms programs with particular reference to DRAM au programme DRAM. Mechanism and Machine Theory. 13(4).; Armstrong-Hélouvry et al., 1994Armstrong-Hélouvry, B., Dupont, P., De Wit, C.C. (1994) A survey of models, analysis tools and compensation methods for the control of machines with friction. Automatica. 30(7).; Ambrósio, 2003Ambrósio, J.A.C. (2003) Impact of Rigid and Flexible Multibody Systems: Deformation Description and Contact Models. In W. Schiehlen & M. Valášek, eds. Virtual Nonlinear Multibody Systems SE - 4. NATO ASI Series. Dordrecht, Netherlands: Springer Netherlands, pp. 57-81.) try to circumvent this problem suggesting null friction at a defined null speed interval. This assumption is not a good approximation when relative motion is intermittent, such as the sticking and slipping of sliding surfaces, known as the stick-slip effect (Rabinowicz, 1958Rabinowicz, E. (1958) The intrinsic variables affecting the stick-slip process. Proceedings of the Physical Society. 71(4), 668-675.), as it disregards the influence of the resultant force acting on the bodies in contact. Other models (Karnopp, 1985Karnopp, D. (1985) Computer simulation of stick-slip friction in mechanical dynamic systems. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME. 107(1).; Leine et al., 1998Leine, R.I., Van Campen, D.H., De Kraker, A., Van Den Steen, L. (1998) Stick-Slip Vibrations Induced by Alternate Friction Models. Nonlinear Dynamics. 16(1), 41-54.; Cha et al., 2011Cha, H.-Y., Choi, J., Ryu, H.S., Choi, J.H. (2011) Stick-slip algorithm in a tangential contact force model for multi-body system dynamics. Journal of Mechanical Science and Technology. 25(7), 1687-1694.; Awrejcewicz et al., 2008Awrejcewicz, J., Grzelcyzk, D., Pyryev, Y. (2008) A novel dry friction modeling and its impact on differential equations computation and and Lyapunov exponents estimation. Journal of Vibroengineering. 10(4).) consider the resultant force requiring additional parameters, related to a null speed interval, for the transition between motion and rest states, which may be problem dependent and difficult to establish.\n\nIt is important to stress that, although several studies developed formulations to capture some of friction characteristics, no model is general (Pennestrì et al., 2016Pennestrì, E., Rossi, V., Salvini, P., Valentini, P.P. (2016) Review and comparison of dry friction force models. Nonlinear Dynamics. 83(4), 1785-1801.) and simpler force models are largely employed for design and are present in commercial software. Still, stability of the numerical solution for the formulation comprising the friction model is always desired.\n\nIn this study, we propose a modification on a static friction model and employ it in sliding connections of plane frames in a large deformation finite element context. The improved model is based on Coulomb friction considering the Stribeck curve for the static and kinetic forces transition and viscous effect. Its numerical solution is improved by reducing the abrupt transition between rest and motion states of the joints by an interpolation between the static friction value and the resultant force in a quasi-null relative speed interval. Differently from other friction models, that define a constant value for a null speed interval, here we propose an expression to automatically calculate the referred quasi-null interval from the system state. Thus, no additional non-physical parameter needs to be informed. The resultant force expression at the sliding connection is achieved for any generic finite element system with multiple degrees of freedom. With the proposed improved friction model, stable responses for the stick-slip effect are captured, which is important for the correct motion reproduction in structures and mechanisms.\n\nThe framework employed to model the dynamical system (Coda and Paccola, 2014Coda, H.B., Paccola, R.R. (2014) A total-Lagrangian position-based FEM applied to physical and geometrical nonlinear dynamics of plane frames including semi-rigid connections and progressive collapse. Finite Elements in Analysis and Design. 91, 1-15.; Siqueira and Coda, 2016Siqueira, T.M., Coda, H.B. (2016) Development of sliding connections for structural analysis by a total lagrangian FEM formulation. Latin American Journal of Solids and Structures. 13(11).; 2017Siqueira, T.M., Coda, H.B. (2017) Total Lagrangian FEM formulation for nonlinear dynamics of sliding connections in viscoelastic plane structures and mechanisms. Finite Elements in Analysis and Design. 129, 63-77.; 2019Siqueira, T.M., Coda, H.B. (2019) Flexible actuator finite element applied to spatial mechanisms by a finite deformation dynamic formulation. Computational Mechanics. 64(6), 1517-1535.) is a fully nonlinear finite element approach for large deformations based on a total Lagrangian description of solids. As the formulation uses positions as the main degrees of freedom, instead of displacements, the adopted approach is referred as positional. Sliding connections, as prismatic and cylindrical joints, are introduced in the system by means of Lagrange multipliers. In the sliding connection formulation, the friction force is associated with a curvilinear displacement variable introduced in the system by the joints. This formulation is also capable of representing roughness on the sliding surface, making it possible to be combined with the introduced friction dissipation to simulate, for instance, vehicle-bridge interaction as show in the examples. The Saint-Venant-Kirchhoff constitutive model is adopted to define the plane frame elastic strain energy using the Green-Lagrange strain and the second Piola-Kirchhoff stress tensor. The Principle of Stationary Total Energy is used to find the equations of motion, comprising the frictional effect, which is discretized along time using the generalized-α method. The resulting nonlinear system is solved by the Newton-Raphson method accounting for the friction force update in the iterative process.\n\nThis study is organized as follows. Section 2 briefly presents necessary aspects of the employed nonlinear plane frame element followed by the sliding connections kinematical constraints in Section 3. The dynamical equilibrium is obtained in Sections, 4 and 5. Known the system parameters, the friction force is introduced in its variational form in Section 6 and the improved model is presented in detail by Section 7. Time integration (Section 8) and system solution (Section 9) are presented next. In Section 10, examples verify the proposed improved friction model and show the possibilities of the developed formulation in the analysis of dynamical systems.\n\nDyadic notation is preferred throughout this text due its brevity; however, index notation is also used to clarify particular aspects when necessary.\n\n# 2 NONLINEAR PLANE FRAME KINEMATICS\n\nThe employed plane frame finite element is presented thoroughly in Coda and Paccola (2014)Coda, H.B., Paccola, R.R. (2014) A total-Lagrangian position-based FEM applied to physical and geometrical nonlinear dynamics of plane frames including semi-rigid connections and progressive collapse. Finite Elements in Analysis and Design. 91, 1-15. and Siqueira and Coda (2017)Siqueira, T.M., Coda, H.B. (2017) Total Lagrangian FEM formulation for nonlinear dynamics of sliding connections in viscoelastic plane structures and mechanisms. Finite Elements in Analysis and Design. 129, 63-77., however, to develop the present formulation some aspects need to be briefly stated. As the finite element behavior is represented by a total Lagrangian description, its strain field needs to be written as a function of the initial and current configurations of the solid, restricted to a finite number of degrees of freedom.\n\nIn the positional approach of the FEM, instead of nodal displacements, the parameters of the discretized plane frame are its positions (coordinates) and the cross section angle (Fig. 1). The deformation function, $f→$, depicted in Fig. 2, can be written indirectly as function of the non-dimensional space and nodal parameters by mappings from the non-dimensional space to the initial configuration, $f→0$, as\n\n$f 1 0 = x 1 = ϕ l ( ξ ) X 1 l + h 0 2 η cos ϕ l ( ξ ) θ l 0 f 2 0 = x 2 = ϕ l ( ξ ) X 2 l + h 0 2 η sin ϕ l ( ξ ) θ l 0$ (1)\n\nand to the current configuration, $f→1$, as\n\n$f 1 1 = y 1 = ϕ l ( ξ ) Y 1 l + h 0 2 η cos [ ϕ l ( ξ ) θ l ] f 2 1 = y 2 = ϕ l ( ξ ) Y 2 l + h 0 2 η sin [ ϕ l ( ξ ) θ l ]$ (2)\n\nwhere $x→$ and $y→$ represents any point on the domain of a finite element in the initial and current configuration, respectively. The coordinates for both directions $i=1,2$ of each node $l$ along the reference line in the initial and current configurations are $Xil$ and $Yil$, respectively. The initial nodal value of the cross-section angle is $θl0$ and after deformation is denoted as $θl$. The cross section initial height is $h0$, $ξ$ is the non-dimensional space variable in the direction of the reference line and $η$ follows the height direction. The shape functions $ϕl(ξ)$ are obtained by Lagrange polynomials of any order.\n\nThe deformation function can be written as a composition of the previous mappings, Eq. (1) and (2), as\n\n$f→=f→1∘(f→0)−1$.(3)\n\nSince only the gradient $A$ of the deformation function, but not the function itself, is necessary to obtain the strain field, as presented by (Bonet et al., 2000Bonet, J., Wood, R.D., Mahaney, J., Heywood, P. (2000) Finite element analysis of air supported membrane structures. Computer Methods in Applied Mechanics and Engineering. 190(5-7), 579-595.; Coda, 2003Coda, H.B. (2003) An exact FEM geometric non-linear analysis of frames based on position description. In . IN: 17H INTERNATIONAL CONGRESS OF MECHANICAL ENGINEERING. 2003, São Paulo. São Paulo: ABCM.)\n\n$A = G r a d ( f → ) = A 1 . ( A 0 ) − 1$ (4)\n\nwhere\n\n$Aij0=∂fi0∂ξj and Aij1=∂fi1∂ξj$.(5)\n\nDuring the iterative solution strategy both $A0$ and $A1$ are numerical values calculated at the integration points resulting in a purely numerical procedure.\n\nAs the Saint-Venant-Kirchhoff constitutive law is employed, the Green-Lagrange strain tensor $E$ have to be calculated. This objective strain is given, for instance, by (Ogden, 1984Ogden, R.W. (1984) Non-linear elastic deformations. Chichester: Ellis Horwood.)\n\n$E = 1 2 ( C − I ) = 1 2 ( A t ⋅ A − I )$ (6)\n\nwhere $I$ is the second order identity tensor and $C=At⋅A$ is the right Cauchy-Green stretch tensor.\n\nAs there is no relation between the cross-section angle and the slope of the reference line, the frame kinematic can be regarded as Reissner-type. It should be mentioned that the cross-section dimensions are maintained the same during motion, thus, to avoid volumetric locking, the constitutive equation is relaxed in order to exclude transverse expansions. The specific strain energy for the plane frame is presented in Section 4.\n\n# 3 KINEMATICAL CONSTRAINTS DUE TO SLIDING CONNECTIONS\n\nTo introduce frictional effects in the equations of motion, it is required first to write the constraint equations imposed by the sliding connections. The curvilinear position - a new variable introduced in the system - is of particular importance as the friction force will act directly on it. In this section we summarize the description of the connections as prismatic and cylindrical joints.\n\nSliding connections are the ones that constrain relative translations between parts of the body. Fig. 3 illustrates both joints and their plane representation. In either case, a sliding node, at which the joint exists, is constrained to move over a trajectory comprised of path elements. The distinction between the prismatic and the cylindrical joint (understood as a sliding-pin joint for the plane case) is the relative rotation, which is allowed only by the last one.\n\nFig. 3\nSliding connections and its plane representation: a) prismatic and b) cylindrical (sliding-pin) joints.\n\nFig. 4 depicts a sliding connection, belonging to node $P^$, and its path contact point $P¯$. The connection is free to move along the path $s(ξ)$ defined by path finite elements, which may have an arbitrary roughness profile $r→(s)$. The new variable $sP=s(ξP)$ defining the curvilinear position and the cross-section orientation of the path point is also illustrated.\n\nThe constraint equations, $c→$, can be written for both types of joints as a single expression\n\n$c i = Y ^ i P − ϕ l ( ξ P ) Y ¯ i l − Δ θ P 0 δ i 3 − r i ( s P ) ( 1 − δ ( i ) 3 ) = 0 i$ (7)\n\nwhere the upper bar $( •¯ )$ is used to identify variables related to path elements and the upper hat $( •^ )$ is used to define the sliding node. In the previous expression $i$ is the direction ($i=1,2,3$ for prismatic joints and $i=1,2$ for cylindrical joints) and $δij$ is the Kronecker delta. The difference of cross sections orientations at the initial configuration is $ΔθP0=θ^P0−θ¯P0$ and must be constant during the sliding process in the prismatic joint case to maintain a fixed relative angle.\n\nIn Eq. (7), the components of the roughness profile, obtained by its ‘height function’ $rh(s)$, are given by\n\n$r1(sP)=rh(s)cosϕl(ξP)θ¯lr2(sP)=rh(s)sinϕl(ξP)θ¯l$.(8)\n\nIt is noteworthy that the curvilinear variable $s(ξ)$ represents an arch-length function defined by the non-dimensional coordinate $ξ$ and the path element coordinates. Also, as $rh(s)$ is defined directly by the curvilinear position, the roughness profile is mesh-independent.\n\n# 4 UNCONSTRAINED EQUATIONS OF MOTION\n\nWhen dissipation occurs, the mechanical energy of the analyzed structure $Π0$ is given by\n\n$Π 0 = Π − Q$ (9)\n\nwhere $Q$ represents the dissipation of an encompassing system of total energy $Π$. Studying this larger system, Eq. (9) can be rewritten as\n\n$Π = Π 0 + Q$ (10)\n\nor, making explicit the energy parcels of the new larger conservative system\n\n$Π = U − P + K + Q$ (11)\n\nwhere $U$ is the stored elastic strain energy, $P$ is the potential of conservative external forces and $K$ is the kinetic energy of the body.\n\nFollowing Lanczos (1970)Lanczos, C. (1970) The variational principles of mechanics. New York: Dover Publications . and Gurtin et al. (Gurtin et al., 2010Gurtin, M.E., Fried, E., Anand, L. (2010) The Mechanics and Thermodynamics of Continua. New York: Cambridge University Press.), it is not always possible to write down closed expressions for dissipative parcels but only its infinitesimal change. Thus, the equations of motion are stated from the variation of the energies present in Eq. (11), which is understood as the Principle of Stationary Total Energy\n\n$δ Π = δ U − δ P + δ K + δ Q = 0$ (12)\n\nin which the symbol $δ$ means variation.\n\nThe total energy can be stated by writing the known expressions of the energies in Eq. (11) as function of the current configuration nodal parameters of the discretized body, grouped in the vector $ϒ→$, as\n\n$Π ( ϒ → ) = ∫ V 0 u ( E ( ϒ → ) ) d V 0 − F → ⋅ ϒ → − ∫ s 0 q → ⋅ y → d s 0 + 1 2 ∫ V 0 ρ 0 y → ˙ ⋅ y → ˙ d V 0 + Q ( ϒ → )$ (13)\n\nwhere the specific strain energy $u$ depends on the strain state $E$ of the body, Eq. (6), which is function of the nodal parameters $ϒ→$, as defined by the gradient of the deformation function in Eq. (4). Still in Eq. (13), $F→$ and $q→$ are the concentrated and distributed conservative external loads, respectively. The initial length of the frame reference line is $s0$. The material mass density in the initial configuration, of volume $V0$, is $ρ0$. The material point velocity is denoted using the over-dot as $y→˙$.\n\nAs mentioned before, the Saint-Venant-Kirchhoff constitutive relation is employed due to its simplicity and good representation of large displacements on solids that remain in the small to moderate strain regimen, which comprehends the majority of the usual applications in engineering. For the plane frame utilized, following Siqueira and Coda (2017)Siqueira, T.M., Coda, H.B. (2017) Total Lagrangian FEM formulation for nonlinear dynamics of sliding connections in viscoelastic plane structures and mechanisms. Finite Elements in Analysis and Design. 129, 63-77., its specific energy is given as\n\n$u = E ( 1 − ν ) 2 ( 1 − 2 ν ) ( 1 + ν ) E 11 2 + E 22 2 + 2 ν G ( 1 − 2 ν ) E 11 E 22 + G E 12 2 + E 21 2$ (14)\n\nwhere $E$ is the longitudinal elastic parameter that approaches the Young modulus for small strains. The shear elastic modulus is $G=E/[2(1+ν)]$, being $ν$ a constant that reproduces the Poisson ratio for small strains. Assuming, in equation (14) $ν=0$, except for the calculation of the shear elastic modulus, avoids locking problems. The second Piola-Kirchhoff stress tensor is easily obtained by the energy conjugacy property as\n\n$S=∂u∂E$.(15)\n\nThe equations of motion (geometric nonlinear dynamical equilibrium) are obtained by the development of the variations in eq. (13). Details regarding this development can be obtained for the employed plane frame element particular kinematics in Siqueira and Coda (2017)Siqueira, T.M., Coda, H.B. (2017) Total Lagrangian FEM formulation for nonlinear dynamics of sliding connections in viscoelastic plane structures and mechanisms. Finite Elements in Analysis and Design. 129, 63-77. and for a general framework of positional finite elements in Siqueira and Coda (2019)Siqueira, T.M., Coda, H.B. (2019) Flexible actuator finite element applied to spatial mechanisms by a finite deformation dynamic formulation. Computational Mechanics. 64(6), 1517-1535., for instance. Following these studies, the equilibrium can be written in a compact form as\n\n$F → int − F → + M ⋅ ϒ → ¨ + D ⋅ ϒ → ˙ = 0 →$ (16)\n\nwhere: $F→int=Grad(U)$ is the internal force vector; $F→$ collects all the external loads; $M$ results in a constant mass matrix for the present total Lagrangian formulation; $D$ is the external damping matrix arriving from $δQ$ which is assumed as Rayleigh type; and $ϒ→˙$ and $ϒ→¨$ are the velocity and acceleration vectors of the nodal parameters.\n\n# 5 CONSTRAINED EQUATIONS OF MOTION\n\nThe dynamic equilibrium stated by Eq. (16) is called unconstrained as no restraints, such as the ones from the sliding connections, are present. Several consolidated methodologies to impose constraints on mechanical and structural applications can be found in the literature (Géradin and Cardona, 2001Géradin, M., Cardona, A. (2001) Flexible multibody dynamics: a finite element approach. Chichester: John Wiley & Sons.; Nocedal and Wright, 1999Nocedal, J., Wright, S.J. (1999) Numerical optimization. New York: Springer.; Rao, 2009Rao, S.S. (2009) Engineering optimization: theory and practice. 4th ed. New Jersey: John Wiley & Sons.). Here, we employ the well-known Lagrange multiplier method along with the Principle of Stationary Total Energy to impose the sliding restrictions. Concerning the later introduction of friction dissipation, the multipliers are of great value since in Mechanics they might be understood as the contact forces between bodies, an essential information for the friction model.\n\nThe Principle of Stationary Total Energy is extended for the case of holonomic constraints by modifying the total energy through the introduction of a new potential $C$, referred as the constraint potential, as\n\n$Π=U−P+K+Q+C$.(17)\n\nWhen using Lagrange multipliers, the expression of the new potential is simply given by\n\n$C = λ → ⋅ c →$ (18)\n\nwhere $λ→$ represents the vector of multipliers, which are new variables of the system. Eq. (18) indicates the presence of a multiplier for each constraint equation in $c→$. It is worth mentioning that the constraint potential is null at the solution, therefore, the total energy is not altered.\n\nKnowing the expression of $C$, the first variation of the constrained energy, Eq. (17), is\n\n$δ Π = δ U − δ P + δ K + δ Q + δ C = 0$ (19)\n\nwhich, can be developed similarly to the unconstrained case leading to the constrained nonlinear equations of motion, expressed in a compact form as\n\n$F → int − F → + M ⋅ ϒ → ¨ + D ⋅ ϒ → ˙ + F → con = 0 →$ (20)\n\nin which $F→con$ represents the restriction forces arriving from the constraint potential. As the multipliers are new variables, the variation of $C$ is organized in the following force vector, which separates the parameters $ϒ→$ (including $sP$) and the multipliers\n\n$δ C = δ ϒ → ⋅ ∇ c → ⋅ λ → + δ λ → ⋅ c → = δ ϒ → δ λ → ⋅ ∇ c → ⋅ λ → c → = δ ϒ → δ λ → ⋅ F → con$ (21)\n\nwhere the tensor $∇c→$ represents the gradient of the constraint vector. The derivatives of the constraint equation for the sliding connections, Eq. (7), can be found in Siqueira and Coda (2017)Siqueira, T.M., Coda, H.B. (2017) Total Lagrangian FEM formulation for nonlinear dynamics of sliding connections in viscoelastic plane structures and mechanisms. Finite Elements in Analysis and Design. 129, 63-77..\n\n# 6 INTRODUCTION OF THE FRICTION FORCE IN THE SYSTEM\n\nThe friction force is included in the system directly in the Principle of Stationary Total Energy as part of the dissipative potential. As previously mentioned, dissipative potentials are introduced in their differential form since closed expressions might be unknown, as is the case for the dissipated friction energy $Qf$. However, the variation of this potential can be written as the work done by the friction force vector $F→f$ on its displacement trajectory $d→$ as\n\n$δQf=F→f⋅δd→$.(22)\n\nTo develop Eq. (22), parameters that describes the force displacement must be chosen. For that, the coordinates of the sliding node and its path contact point could be chosen. However, since in the previous formulation the curvilinear position $sP$ is already used as an intrinsic variable, the displacement along the trajectory is simply the scalar expression $d=sp−sP0$, being $sP0$ an arbitrary initial value, and its variation is $δd=δsp$. As the friction force acts tangentially to the trajectory, with its value given by the scalar $Ff$, the dissipative parcel is introduced directly in the curvilinear position as\n\n$δQf=Ff δsP$.(23)\n\nTo organize the equations of motion system, we make $F→f=Ff$, the previous equation is rewritten as\n\n$δQf=δsP⋅F→f$.(24)\n\nConsidering the correspondence of the friction force vector $F→f$ to the system degrees of freedom, the equations of motion are restated to include frictional dissipation as\n\n$F→int−F→+M⋅ϒ→¨+D⋅ϒ→˙+F→con+F→f=0→$.(25)\n\n# 7 IMPROVED FRICTION MODEL\n\nGiven the way the friction force is incorporated in the equations of motion, Eq. (25), any expression may be easily applied without modifying its development. We start from the Coulomb friction model considering the Stribeck curve for the static and kinetic forces transition and a viscous effect. Fig. 5 shows the overall behavior of the friction force with the relative velocity among sliding bodies, $v$. This model considers the Stribeck curve using the expression proposed by Bo and Pavelescu (1982) and aBo, L.C., Pavelescu, D. (1982) The friction-speed relation and its influence on the critical velocity of stick-slip motion. Wear. 82(3). linear evolution for the viscous friction, which occurs if lubricant layers are present on the surfaces. The expression for the friction force is written as\n\n$F f = F C + F S − F C e − v / v σ δ σ sgn ( v ) + η v if v ≠ 0 min F S , F R sgn F R if v = 0$ (26)\n\nwith the static $FS$ and kinetic $FC$ friction forces given by\n\n$F S = μ s F N and F C = μ k F N$ (27)\n\nwhere, $μs$ and $μk$ are, respectively, the static and kinetic friction coefficients. $FN$ is the absolute value of the contact force, orthogonal to the trajectory at the joint contact point, and $FR$ is the resultant force on the sliding connection, tangential to the contact point. The viscous friction coefficient is $η$ and the Stribeck parameters are its decay velocity $vσ$ and power $δσ$. The sign function is represented by $sgn(·)$.\n\nWe highlight at this point that, for our application in sliding connections, the relative velocity $v$, tangential to the path, can be measured from the curvilinear position velocity, which will be important for the nonlinear solution procedure in Section 9.\n\nFor null relative velocity, that is, the rest state, second condition in Eq. (26), the tangential resultant force acting on the connection is required for comparison with the static friction value to evaluate the tendency of motion (in case $FR$ is greater than $FS$, or not, otherwise). Properly representing this condition is the key to simulate the stick-slip effect.\n\nIn numerical simulations, the transition from motion to rest states is challenging due to the absence of continuity at null speed, as expressed by Eq. (26), leading to instabilities in the response. For this reason, a linear interpolation between $FS$ and $FR$ is proposed here for the stabilization of the friction force at a range $[−v0,v0]$ of quasi-null velocities, as depicted in Fig. 6. The improved friction model is written as\n\n$F f = F C + F S − F C e − v / v σ δ σ sgn ( v ) + η v if v > v 0 − F S sgn F R if v ≤ v 0 and F R ≥ F S F S − F R v 0 v + F R if v ≤ v 0 and F R < F S$ (28)\n\nwhere $v0$ is the quasi-null speed limit. One should note that $FC$ and $FS$ are always positive as they are obtained from the absolute value of the normal force, Eq. (27), thus, the sign of the friction force in Eq. (28) depends on the values and signs of the relative velocity and resultant force.\n\nIn the proposed approach, $FR$ is not a constant value, but depends on the system own force state at a given time instant, which can even be null, if applicable. Therefore, the system response can be stabilized by means of a smooth transition from the motion state to rest state and vice versa.\n\nIt should be noted that $v0$ is a new parameter introduced in the model to distinguish the movement when in the quasi-null velocity interval. For a better convergence of the iterative solution method, the recommended value of the limit velocity should be close to the relative stop speed of the bodies, but not too small, to still allow the smooth transition among forces at rest. Instead of adopting a fixed unknown arbitrary value, an estimative for this parameter can be obtained by\n\n$v 0 = F S − F R m Δ t$ (29)\n\nbeing $m$ the mass of the sliding node. This estimative is updated along the solution process and presented good responses for general applications, as is illustrated in the examples section.\n\nKnown the coefficients of the model, which depends on the materials that make the sliding connection and its path, the forces required to calculate the friction force have to be related to the variables describing the joint. The normal force vector $F→N$ is found from the component of the Lagrange multipliers vector due to the translational constraints, $λ→=λ1,λ2$, at the normal direction of the path at the contact point, defined by the normal vector $N¯→P$, as\n\n$F → N = λ → ⋅ N ¯ → P N ¯ → P N ¯ → P N ¯ → P$ (30)\n\nand its absolute value, actually used in the calculation, is\n\n$FN=F→N=λ→⋅N¯→PN¯→P$.(31)\n\nIn the plane case, the components of the normal vector are obtained from the tangent vector of the path finite element at the contact point, $T¯iP=ϕl,ξ(ξP)Y¯il$ ($i=1,2$), as $N¯1P=−T¯2P$ and $N¯2P=T¯1P$.\n\nThe resultant force, equal to the inertial force at the sliding node, is obtained directly from the equilibrium equation, Eq. (25), considering only the sliding node degrees of freedom (positions and curvilinear variable), as\n\n$F → R = F → − F → int − F → con$ (32)\n\nor, to identify the terms referred to the degrees of freedom of interest one writes\n\n$F Y ¯ 1 P R F Y ¯ 2 P R F s P R = F Y ¯ 1 P F Y ¯ 2 P F s P − F Y ¯ 1 P int F Y ¯ 2 P int 0 − F Y ¯ 1 P con F Y ¯ 2 P con F s P con$ (33)\n\nwhere $F→$ represents all the external loads, $F→int$ the internal force of the sliding element and $F→con$ the connection constraint force. Subscripts $Y¯1P$, $Y¯2P$ and $sP$ refer to the sliding node position degrees of freedom and the curvilinear position, respectively. In the definition of Eq. (32) and (33), being a quasi-null velocity case, the velocity-proportional external damping force was neglected. The friction force is also not present since its value is already considered indirectly through the constraint force at the curvilinear position direction.\n\nAs the tangential value of the resultant force $FR$ is required, the tangent vector $T¯→P$ is used to decompose the Cartesian terms as\n\n$FR=FY¯1P−FY¯1Pint−FY¯1PconT¯1P+FY¯2P−FY¯2Pint−FY¯2PconT¯2PT¯→P+FsP−FsPcon$.(34)\n\nAs expected from the physical meaning of the multipliers as contact forces, we have $FY¯1Pcon$ = $λ1$ and $FY¯2Pcon$ =$λ2$, which can be obtained by developing the constraint force given in Eq. (21) for the constraint equation in (7).\n\n# 8 TIME INTEGRATION\n\nFor the time discretization, as the description of the solid is made in a total Lagrangian reference, the inertial force in Eq. (25) is obtained using a constant mass matrix. Similarly, the assumed Rayleigh damping also renders a constant matrix. This allows the use of classical time approximations, originally developed for linear dynamics, for the material velocity and acceleration vectors. Paultre (2011)Paultre, P. (2011) Dynamics of structures. Croydon: John Wiley & Sons. discuss the application of direct time integration on nonlinear systems.\n\nAs Lagrange multipliers are present in the system to introduce constraints, a time marching scheme capable of controlling deleterious high frequencies introduced by their presence is necessary (Rong et al., 2019Rong, B., Rui, X., Tao, L., Wang, G. (2019) Theoretical modeling and numerical solution methods for flexible multibody system dynamics. Nonlinear Dynamics. 98(2), 1519-1553.; Géradin and Cardona, 2001Géradin, M., Cardona, A. (2001) Flexible multibody dynamics: a finite element approach. Chichester: John Wiley & Sons.). Here we employ the generalized-α method (Chung and Hulbert, 1993Chung, J., Hulbert, G.M. (1993) A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method. Journal of Applied Mechanics. 60(2), 371.) design to numerically control the system high frequency content while retaining the important information of low frequency range.\n\nTo discretize the solution in time increments $Δt$, the forces in Eq. (25) are rewritten for specific auxiliary time instants $t+1−αf$ and $t+1−αm$ as\n\n$F→t+1−αfint−F→t+1−αf+M⋅ϒ→¨t+1−αm+D⋅ϒ→˙t+1−αf+F→t+1−αfcon+F→t+1−αff=0→$.(35)\n\nA linear combination of the type $d→t+1−α=1−αd→t+1+αd→t$ is used to evaluate any vector in (35) at an auxiliary instant using its current value $d→t+1$ and its past instant value $d→t$. The parameter $α$ may represent $αf$ or $αm$.\n\nNodal parameters velocity and acceleration vectors are written using the Newmark approximations with parameters $β$ and $γ$ as\n\n$ϒ → t + 1 = ϒ → t + Δ t ϒ → ˙ t + Δ t 2 1 2 − β ϒ → ¨ t + β ϒ → ¨ t + 1$ (36)\n\nand\n\n$ϒ→˙t+1=ϒ→˙t+Δt1−γϒ→¨t+γΔtϒ→¨t+1$.(37)\n\nThe time-discrete equations of motion results, using Eq. (36) and (37) in Eq. (35),\n\n$1−αfF→t+1int+F→t+1con+F→t+1f−F→t+1+1−αmβΔt2M+1−αfγβΔtDϒ→t+1+P→t=0→$,(38)\n\nwith the vector that groups the terms of the previous time instant given by\n\n$P → t = α f F → t int + F → t con + F → t f − F → t + α m M ⋅ ϒ → ¨ t − 1 − α m M ⋅ T → t + α f D ⋅ ϒ → ˙ t + 1 − α f D ⋅ R → t$ (39)\n\nwith\n\n$T → t = 1 2 β − 1 ϒ → ¨ t + ϒ → ˙ t β Δ t + ϒ → t β Δ t 2$ (40)\n\nand\n\n$R→t=1−γ2βΔtϒ→¨t+1−γβϒ→˙t−γϒ→tβΔt$.(41)\n\nAt the end of the step, velocity and acceleration vectors must be calculated from the approximations (36) and (37). To start the time march, the initial acceleration is evaluated from Eq. (25) using the initial configuration and velocity of the system.\n\nChung and Hulbert (1993)Chung, J., Hulbert, G.M. (1993) A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method. Journal of Applied Mechanics. 60(2), 371. recommend obtaining the generalized-α method parameters from the high frequency region spectral radius $ρ∞∈0,1$. In order to retain second order accuracy, to minimize numerical dissipation of the fundamental frequencies and maximize the numerical dissipation on the high frequencies range the α-parameters are calculated from\n\n$αm=2ρ∞−1ρ∞+1 and αf=ρ∞ρ∞+1$,(42)\n\nand the Newmark parameters by\n\n$γ=12−αm+αf and β=141−αm+αf2$.(43)\n\nTo achieve unconditional stability in the presence of constraints, the relation $αm<αf≤1/2$ must also be respected - proven for the linear case in Géradin and Cardona (2001)Géradin, M., Cardona, A. (2001) Flexible multibody dynamics: a finite element approach. Chichester: John Wiley & Sons.. As a consequence of $αm<αf$, the situation without numerical dissipation, $ρ∞=1$, is not achieved. From the authors experience in most situations $ρ∞$ in the range 0.7 - 0.9 presents good results with small or negligible numerical dissipation even in nonlinear cases.\n\n# 9 NONLINEAR SYSTEM SOLUTION PROCEDURE\n\nTo solve the resulting time-discrete nonlinear equations of motion, Eq. (38), for the variables $ϒ→t+1,λ→t+1$ the equilibrium is restated as\n\n$g → t + 1 ϒ → t + 1 , λ → t + 1 = 1 − α f F → t + 1 int + F → t + 1 con + F → t + 1 f − F → t + 1 + 1 − α m β Δ t 2 M + 1 − α f γ β Δ t D Y → t + 1 + P → t = 0 →$ (44)\n\nwhere $g→$ is the residual of the Newton method (or mechanical unbalanced vector), null when $ϒ→t+1$ and $λ→t+1$ are a solution of the system of equations for a given time step $t+1$. Note that $λ→t+1$ only appears in the terms $F→t+1con$ and $F→t+1f$.\n\nA usual first order Taylor expansion can be employed to obtain the Newton method as\n\n$Δ ϒ → t + 1 Δ λ → t + 1 = − H t + 1 − 1 ⋅ g → ϒ → t + 1 0 , λ → t + 1 0$ (45)\n\nin which, the correction on a trial solution $ϒ→t+10,λ→t+10$ is repeated until the relative position norm - calculated as $||Δϒ→||/||X→||$, where $X→$ is the initial nodal position vector of the body - is smaller than a given tolerance. It should be mentioned that the constraint equations, calculated from Eq. (7), can also be employed as a secondary convergence criterion. In the authors’ experience, for the examples tested, employing the adopted relative position criterion with a tolerance of 1.10-8 results in small force errors along the iterative process, even for the imposed constraints.\n\nThe Hessian matrix $Ht+1$ (tangent operator), in Eq. (45), is given by\n\n$Ht+1=∇g→t+1=1−αf∇F→t+1int+∇F→t+1con+∇F→t+1f+1−αmβΔt2M+1−αfγβΔtD$.(46)\n\nThe elastic part of the Hessian matrix, associated with the strain energy potential of the finite elements, is\n\n$∇ F → t + 1 int = ∂ F → int ∂ ϒ → t + 1 = ∫ V 0 ∂ E ∂ ϒ → t + 1 : ∂ 2 u ∂ E ⊗ ∂ E : ∂ E ∂ ϒ → t + 1 + S t + 1 : ∂ 2 E ∂ ϒ → ⊗ ∂ ϒ → t + 1 d V 0$ (47)\n\nin which $⊗$ represents tensor product. From the specific strain energy expression, Eq. (14), and developing the Green strain derivatives, using Eq. (6) and (2), one develops this matrix particular expression for the plane frame finite element as seen in Siqueira and Coda (2017)Siqueira, T.M., Coda, H.B. (2017) Total Lagrangian FEM formulation for nonlinear dynamics of sliding connections in viscoelastic plane structures and mechanisms. Finite Elements in Analysis and Design. 129, 63-77. and Coda and Paccola (2014)Coda, H.B., Paccola, R.R. (2014) A total-Lagrangian position-based FEM applied to physical and geometrical nonlinear dynamics of plane frames including semi-rigid connections and progressive collapse. Finite Elements in Analysis and Design. 91, 1-15..\n\nThe Hessian matrix parcel due the constraint potential of the sliding connections is written as\n\n$∇ F → t + 1 con = ∂ F → con ∂ ϒ → , λ → t + 1 = λ → ⋅ ∇ ∇ c → ∇ c → ∇ c → t 0 t + 1$ (48)\n\nwhere, $∇∇c→$ is a third order tensor that can be understood as the set of Hessian matrices due to each constraint equation $ci$, Eq. (7), and $0$ is the null matrix.\n\nIt must be stressed that, the achieved value of $sP$ in the solution process is not enough to update $F→con$ and $∇F→t+1con$ as $ξP=ξ(sP)$ is not explicitly written. The solution of this stage is done by adopting a least square method to find the non-dimensional coordinate from the converged values of the path element and the sliding node as described in detail by Siqueira and Coda (2017)Siqueira, T.M., Coda, H.B. (2017) Total Lagrangian FEM formulation for nonlinear dynamics of sliding connections in viscoelastic plane structures and mechanisms. Finite Elements in Analysis and Design. 129, 63-77.. Given the numerical value of the non-dimensional variable in the dimensionless space, the solution process continues and also the transition between path elements can be performed - which is straightforward when $ξP$ exceeds the space domain $[−1,1]$.\n\nAs the friction force calculation is dependent on the tangential velocity $v=s˙P$, Eq. (28), the solution procedure is improved by updating its value at each iteration by the following finite difference approximation\n\n$vt+1k+1=sPt+1k+1−sPtΔt$,(49)\n\nwhere $k+1$, is explicitly written to identify the value as belonging to the current iteration of a time step $t+1$. Consequently, the friction force is entirely defined by the main solution variables, of particular interest, the curvilinear position.\n\nAs $F→f=Ff$, i.e., the friction force is a scalar properly placed at the system’s degree of freedom, the friction part of the Hessian matrix can be developed as\n\n$∇F→t+1f=∂Ff∂spt+1$,(50)\n\nwhich is a scalar value to be added in the curvilinear position degree of freedom of the system’s matrix. Further developing Eq. (50), using Eq. (49) and (28), results\n\n$∂ F f ∂ s p t + 1 = 1 Δ t η − F S − F C e − v t + 1 k + 1 / v σ δ σ δ v t + 1 k + 1 δ − 1 v σ δ σ if v t + 1 k + 1 > v 0 1 Δ t F S − F R v 0 if v t + 1 k + 1 ≤ v 0 and F R < F S$ (51)\n\nwith $vt+1k+1$ updated in each iteration by Eq. (49).\n\nRegarding the computational implementation, to reduce the time spent in updating the residual vector and Hessian matrix of the Newton method for each iteration, it should be noted that, due to the total Lagrangian description of the positional formulation, the mass and damping matrices, as well as the part $A0$ of the deformation gradient, Eq. (4), are constants and can be stored before starting the time marching process.\n\n# 10 EXAMPLES\n\nExamples are presented to verify the correct response of the proposed improved friction model and its introduction on the finite element system and also to show the capabilities of the proposed formulation in describing engineering applications of interest including roughness.\n\n## 10.1 Rabinowicz test\n\nThe Rabinowicz test is a one degree of freedom experiment largely used as a benchmark, Pennestrì et al. (2016)Pennestrì, E., Rossi, V., Salvini, P., Valentini, P.P. (2016) Review and comparison of dry friction force models. Nonlinear Dynamics. 83(4), 1785-1801., for testing friction models, particularly useful in verifying the model capability of representing the stick-slip behavior. Fig. 7a) depicts the test system with mass $m$, held by a spring with stiffness $k$, in contact with a belt moving horizontally with constant velocity $v$. Due to friction between the oscillator and belt, the mass initially sticks to the belt until the spring force exceeds the static friction value. At this point sliding takes place under the kinetic value of friction. After a while, the mass attaches again to the moving surface and the process is repeated.\n\nParameters for the mass-spring system and friction were adopted the same as Pennestrì et al. (2016)Pennestrì, E., Rossi, V., Salvini, P., Valentini, P.P. (2016) Review and comparison of dry friction force models. Nonlinear Dynamics. 83(4), 1785-1801.. To simulate the oscillator, one two-node (linear) frame element, Fig. 7b), is employed with a cylindrical joint at the end of the bar. This connection is free to slide over another finite element moving in the horizontal direction with velocity $v$ = 0.5 m/s and with all other degrees of freedom locked. A vertical force $P$ = 196.2 N is applied to manifest frictional effects at the contact point. In order to maintain small strains, to allow comparison with the reference, a $L$ = 1000 m bar is adopted with squared cross-section, $b0$ = $h0$ = 1.0 m, and Young modulus $E$ = 10 kPa. This results in an equivalent axial stiffness $k$ = $Eb0h0/L$ = 10 N/m. Null Poisson ratio is used and the equivalent system mass $m$ = 20 kg is lumped at the joint node.\n\nThe sliding node displacement is shown in Fig. 8a) for the improved friction model under two different cases. The first considers the Stribeck effect, with parameters $μs$ = 0.6, $μk$ = 0.5, $vσ$ = 0.05 m/s and $δσ$ = 1.0, and the second case is the classic Coulomb model, only capable of representing kinetic friction. No viscous effect is present, $η$ = 0, in both cases. Results were obtained with a time increment $Δt$ = 1.0 ms with the generalized-α method parameter $ρ∞$ = 1.0.\n\nFig. 8\nDisplacement for the Rabinowicz test: a) improved model results and b) numerical results from Pennestrì et al. (2016)Pennestrì, E., Rossi, V., Salvini, P., Valentini, P.P. (2016) Review and comparison of dry friction force models. Nonlinear Dynamics. 83(4), 1785-1801. for different friction models.\n\nFig. 8b) depicts Pennestrì et al. (2016)Pennestrì, E., Rossi, V., Salvini, P., Valentini, P.P. (2016) Review and comparison of dry friction force models. Nonlinear Dynamics. 83(4), 1785-1801. results for the mass displacement due to different friction models evaluated in their work. No direct comparison can be performed with the reference models as they are not directly equivalent with the proposed improved model, or among themselves, as they consider different friction characteristics requiring parameters not present in the current model. For those parameters and models description we refer to Pennestrì et al. (2016)Pennestrì, E., Rossi, V., Salvini, P., Valentini, P.P. (2016) Review and comparison of dry friction force models. Nonlinear Dynamics. 83(4), 1785-1801. study.\n\nCompatible responses with Pennestrì et al. (2016)Pennestrì, E., Rossi, V., Salvini, P., Valentini, P.P. (2016) Review and comparison of dry friction force models. Nonlinear Dynamics. 83(4), 1785-1801. models are observed for both friction cases even for the relative velocity, Fig. 9, and friction force, Fig. 10. It is noticeable that, as the classic Coulomb model does not account for static friction, after the initial stiction phase, the system displays the harmonic oscillator behavior without maintaining null relative velocity and stiction again. For the Stribeck case a detail for the first relative motion of the system can be seen in Fig. 11 showing the variation between static and kinetic friction force captured by the improved model. Regarding processing time between models, for this example, the simulation for the Stribeck case is 15% longer than for the classic Coulomb model. The computation time was calculated by averaging the time spent in three separate simulations of each case (due to the influence of the operational system background tasks) on the same computer.\n\nFig. 9\nRelative velocity for the Rabinowicz test: a) improved model results and b) numerical results from Pennestrì et al. (2016)Pennestrì, E., Rossi, V., Salvini, P., Valentini, P.P. (2016) Review and comparison of dry friction force models. Nonlinear Dynamics. 83(4), 1785-1801. for different friction models.\nFig. 10\nFriction force for the Rabinowicz test: a) improved model results and b) numerical results from Pennestrì et al. (2016)Pennestrì, E., Rossi, V., Salvini, P., Valentini, P.P. (2016) Review and comparison of dry friction force models. Nonlinear Dynamics. 83(4), 1785-1801. for different friction models.\n\nTo further analyze the improved friction model results, a reference solution is depicted in Fig. 8 to Fig. 11 for each case. As analytical solutions are not always available, the reference solution was obtained by employing a time step 100 times smaller to diminish the influence of the quasi-null speed range calculated by Eq. (29). For the classic Coulomb case, the reference solution after stiction is also the response of a harmonic oscillator subjected to the Couloumb friction force. The simulated response coincides perfectly for this case (overlapping curves). A difference in the response is observed after the initial stiction phase in the Stribeck case. This difference is anticipated as the friction force value in this situation is velocity dependent, due to the exponential term of the Stribeck curve expression, Eq. (26), which is null for the Coulomb case. Thus, the numerical solution procedure has a higher influence. Nevertheless, very good agreement with Pennestrì et al. (2016)Pennestrì, E., Rossi, V., Salvini, P., Valentini, P.P. (2016) Review and comparison of dry friction force models. Nonlinear Dynamics. 83(4), 1785-1801. models are observed.\n\n## 10.2 Quick-return mechanism with friction\n\nA classic quick-return mechanism is analyzed considering frictional dissipation, Fig. 12. This mechanism was proposed by Bauchau (2000)Bauchau, O.A. (2000) On the modeling of prismatic joints in flexible multi-body systems. Computer Methods in Applied Mechanics and Engineering. 181(1-3), 87-105. and also investigated by Siqueira and Coda (2017)Siqueira, T.M., Coda, H.B. (2017) Total Lagrangian FEM formulation for nonlinear dynamics of sliding connections in viscoelastic plane structures and mechanisms. Finite Elements in Analysis and Design. 129, 63-77. employing positional frame finite elements, for the frictionless case. The system consists in a 1.0 m arm AB able to spin around a fixed support B and connected to a 0.25 m bar NA. The motion is imposed by a 0.20 m crank RS which turns around the fixed support R with a constant angular speed $Ω$ = 5π rad/s and slides over the arm with a cylindrical joint S. The translational motion resulting from the mechanism input rotation is obtained by a cylindrical joint at point N, able to move horizontally over a fixed path.\n\nAll bars have 5.98 cm squared cross section and density 1724.82 kg/m3. The arm is flexible with $E$ = 47.04 GPa and discretized by 10 cubic finite elements. To simulate the rigid behavior of the remaining bars a 106 times greater Young modulus was adopted and 2 cubic frame elements were used for each bar. The shear elastic modulus is half the value of its corresponding Young modulus value for the whole mechanism. Lumped masses are placed at slider S (0.31 kg) and N (2.50 kg). Simulations were performed with a time increment $Δt$ = 0.1 ms and the generalized-α method parameter $ρ∞$ = 0.9.\n\nFour cases of friction were evaluated. As we are interested in the flexible arm deflection and the output velocity of the mechanism, attention is restricted to slider N. Tests with friction at slider S presented minor effects in the overall system response, thus dissipation at this joint was not considered. Two dry friction cases, one with $μs$ = 0.35 and $μk$ = 0.30 and another with $μs$ = 0.75 and $μk$ = 0.70, both with Stribeck curve parameters $vσ$ = 0.10 m/s and $δσ$ = 1.0, and two viscous friction situations, $η$ = 10.0 N.s/m and 200.0 N.s/m, are considered at the sliding connection N.\n\nThe first four cycles of the mechanism arm tip deflection (point A), evaluated orthogonally to a line that follows the arm spin at point B, are shown in Fig. 13. Interesting results for the deflection of the arm were obtained for different friction cases. Compared to the frictionless case, the situation with smaller dry friction coefficients presented slightly higher arm deflection along the cycles, Fig. 13a), but similar output velocity at slider N, Fig. 14a), even though a horizontal friction force, Fig. 15a), acts at this point. The output velocity for a frictionless rigid body case of the mechanism (simulated by adopting the same Young modulus for the arm AB as for the rigid parts) is also depicted in Fig. 14. It is clear that the arm flexibility promotes an oscillatory response of the output velocity around the rigid body response.\n\nFor the higher dry friction parameters adopted, however, the mechanism presents a curious behavior reducing its arm tip vibration amplitude in alternating cycles, Fig. 13b). The output velocity presented the same pattern, Fig. 14b). Friction forces, Fig. 15b), showed smaller values at the low amplitude cycles, than higher ones. Tests performed for even higher values of static and kinetic friction coefficients ($μs$ = 0.85 and $μk$ = 0.80) showed that the same pattern occurs, but with less intense reduction of the deflection among cycles. Consequently, we understand that exist a range of friction parameters, in combination with this particular mechanism mass and stiffness, resulting in a very particular cycle-alternating nonlinear response. The physical interpretation of this response can be realized as slider N friction force affecting link NA force transmission to the flexible arm AB in a way that excites its transverse deflection at each two cycles and in the opposite direction of the crank (constant) excitation. This indicates the existence of a transverse motion along the arm (with a period twice as long as the duration of the mechanism cycle) decreasing the contact force in a cycle and increasing it on the next.\n\nCases with only viscous friction presented the expected reduction of vibration of the arm deflection, Fig. 13c) and d), and slider velocity, Fig. 14c) and d). For the larger friction coefficient case, although vibrations were quickly damped, higher values of arm deflection were observed indicating the difficulty of the crank to move the arm for the intensity of the friction force developed at slider N, Fig. 15d).\n\nIndependently of the friction force evolution aspect, Fig. 15, smoother for the velocity proportional viscous cases or discontinuous in dry friction cases, the mechanism response was correctly depicted showing sense alternance for its return and that the proposed improved friction model was capable of producing limited solutions for a system with several degrees of freedom.\n\n## 10.3 Vehicle motion on bridge\n\nA two-span bridge is analyzed considering the effect of a vehicle motion, Fig. 16. Pavement irregularities are considered by a roughness profile along the path of the wheels, modeled as cylindrical joints, Fig. 17. Before entering the bridge, the vehicle moves at a constant 100 km/h speed, after this moment its movement is released. Friction between the wheels and pavement is present during the whole analysis, which is performed until the car stops or reaches the end of the path.\n\nThe vehicle is modeled by 42 cubic finite elements with 6.73 cm squared cross section and has $E$ = 200.0 GPa, except for the suspension elements with $E$ = 1.5 GPa. Mass density $ρ0$ = 7800.0 kg/m3 is adopted resulting in a total mass of 1500.0 kg. Each bridge span is modeled with 5 cubic frame elements. To have appropriate mass and stiffness, the bridge has a rectangular cross section, $h0$ = 0.50 m and $b0$ = 3.50 m, $E$ = 20.0 GPa and $ρ0$ = 2500.0 kg/m3. The paths before and after the bridge are fixed and discretized by one finite element each. Shear elastic modulus for the whole system is half the value of its corresponding longitudinal one.\n\nStructural damping, as Rayleigh type, is considered solely on the bridge to account for its proper dissipative behavior. Considering the bridge made of reinforce concrete, a damping ratio of 2,5% (Papageorgiou and Gantes, 2010Papageorgiou, A. V., Gantes, C.J. (2010) Equivalent modal damping ratios for concrete/steel mixed structures. Computers and Structures. 88(19-20), 1124-1136.) is employed for its first (1.03 Hz) and fourth (5.19 Hz) vibration modes. All four initial modes are related to bending. Thus, its Rayleigh damping matrix (mass and stiffness proportional) can be obtained as presented in classic dynamics textbooks, such as Paultre (2011)Paultre, P. (2011) Dynamics of structures. Croydon: John Wiley & Sons.. Since the present formulation is geometrically nonlinear, the bridge stiffness matrix, used for the modal analysis and to calculate a constant damping matrix, is assumed as the initial Hessian matrix.\n\nDry friction parameters were adopted to consider contact between tire and asphalt as $μs$ = 0.4, $μk$ = 0.3, $vσ$ = 1.0 m/s and $δσ$ = 1.0. The pavement imperfection is obtained by a random roughness profile generated from a series of cosines as proposed by Yang and Lin (1995)Yang, Y.-B., Lin, B.-H. (1995) Vehicle-Bridge Interaction Analysis by Dynamic Condensation Method. Journal of Structural Engineering. 121(11), 1636-1643. using ISO 8608 (ISO, 1995ISO (1995) Mechanical Vibration — Road Surface Profiles — Reporting of Measured Data (ISO Standard No. 8608).) parameters for roads classes A and B, considered as in good traffic condition. The standard coefficients are the power spectral density function of 16.10-6 m3, for class A, and 64.10-6 m3, for class B. Both profiles were calculated employing 20 spatial frequencies equally distributed in the range from 1.0 to 10.0 cycle/m as recommended by Coussy et al. (1989)Coussy, O., Said, M., van Hoove, J.-P. (1989) The influence of random surface irregularities on the dynamic response of bridges under suspended moving loads. Journal of Sound and Vibration. 130(2), 313-320. and Camara and Ruiz-Teran (2015)Camara, A., Ruiz-Teran, A.M.M. (2015) Multi-mode traffic-induced vibrations in composite ladder-deck bridges under heavy moving vehicles. Journal of Sound and Vibration. 355, 264-283.. Also, as an actual wheel has finite dimensions, and its contact is not done in all the points of the path, a rigid tread band model is employed in order to maintain wheel tread band contact to the nearest point of the surface following Captain et al. (1979)Captain, K.M., Boghani, A.B., Wormley, D.N. (1979) Analytical Tire Models for Dynamic Vehicle Simulation. . 8(1), 1-32. and Chang et al. (2011)Chang, K.C., Wu, F.B., Yang, Y.B. (2011) Disk model for wheels moving over highway bridges with rough surfaces. Journal of Sound and Vibration. 330(20), 4930-4944.. Both wheels have a 30.0 cm radius and the resulting roughness profiles are depicted in Fig. 18 for a representative part of the bridge path.\n\nBoth vehicle and bridge are subjected to their own weight during the whole analysis. Simulations were performed with a time increment $Δt$ = 0.1 ms and the generalized-α method parameter $ρ∞$ = 0.7. The front wheel curvilinear position evolution is depicted in Fig. 19 where is clear that the presence of friction stopped the vehicle before reaching the end of the bridge.\n\nThe pavement imperfections considered act primarily increasing vertical displacements of the vehicle, Fig. 20, and also the bridge, Fig. 21, but without friction dissipation the vehicle does not stop. For a frictionless situation, in presence of roughness, some resistance is found in its horizontal motion, as can be observed in Fig. 19 by the additional time (depicted for class A) the vehicle takes to reach the end of the path when compared to an smooth trajectory. The increase in the roughness of the road profile (from road class A to B) increases the friction force as depicted by Fig. 22.\n\nFrom the vehicle midpoint horizontal position, Fig. 20, it can be observed that it stopped before the central support in all three cases where friction was considered. Thus, the bridge left mid-span deflection is not alleviated as for the frictionless situations, Fig. 21, when the vehicle passes on the right span. The vertical movement, manifested in the bridge even in the situation without roughness, is due to the horizontal friction force not aligned with the center of gravity of the vehicle, which generates a low frequency rotational vibration causing vertical movement in the region of the wheels, resulting in vertical forces transferred to the bridge. This aspect could only be captured due to the geometrically nonlinear description of the employed formulation.\n\n# 11 CONCLUSIONS\n\nFriction dissipation was successfully introduced in sliding connections commonly present in structures and mechanisms employing a total Lagrangian FEM formulation for plane frames based on a positional description of its kinematics. An improvement on a Coulomb friction model with Stribeck effect and viscous friction was proposed for a smoother description of the transition between motion and rest states of the joints. The improved model avoided instabilities for the friction force at null speed and is able to correctly represents frictional dissipation and capture the stick-slip effect since the resultant force could be calculated properly for the connections in the finite element system. The improved friction model is coupled with a mesh independent roughness strategy enabling general applications. Benchmarks and additional examples are used to verify the proposed model and to analyze engineering applications. Results were presented with successful responses for dynamical systems in which the consideration of friction is important. Future studies intent to extend this formulation to 3D applications.\n\n# References\n\n• Ambrósio, J.A.C. (2003) Impact of Rigid and Flexible Multibody Systems: Deformation Description and Contact Models. In W. Schiehlen & M. Valášek, eds. Virtual Nonlinear Multibody Systems SE - 4. NATO ASI Series. 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Wear. 242(1-2), 1-17.\n• ISO (1995) Mechanical Vibration — Road Surface Profiles — Reporting of Measured Data (ISO Standard No. 8608).\n• Karnopp, D. (1985) Computer simulation of stick-slip friction in mechanical dynamic systems. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME. 107(1).\n• Kikuuwe, R., Takesue, N., Sano, A., Mochiyama, H., Fujimoto, H. (2005) Fixed-step friction simulation: From classical coulomb model to modern continuous models. In 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS. pp. 1009-1016.\n• Lanczos, C. (1970) The variational principles of mechanics. New York: Dover Publications .\n• Leine, R.I., Van Campen, D.H., De Kraker, A., Van Den Steen, L. (1998) Stick-Slip Vibrations Induced by Alternate Friction Models. Nonlinear Dynamics. 16(1), 41-54.\n• Marques, F., Flores, P., Pimenta Claro, J.C., Lankarani, H.M. (2016) A survey and comparison of several friction force models for dynamic analysis of multibody mechanical systems. Nonlinear Dynamics. 86(3), 1407-1443.\n• Nocedal, J., Wright, S.J. (1999) Numerical optimization. New York: Springer.\n• Ogden, R.W. (1984) Non-linear elastic deformations. Chichester: Ellis Horwood.\n• Olsson, H., Åström, K.J., Canudas de Wit, C., Gäfvert, M., Lischinsky, P. (1998) Friction Models and Friction Compensation. European Journal of Control. 4(3), 176-195.\n• Papageorgiou, A. V., Gantes, C.J. (2010) Equivalent modal damping ratios for concrete/steel mixed structures. Computers and Structures. 88(19-20), 1124-1136.\n• Paultre, P. (2011) Dynamics of structures. Croydon: John Wiley & Sons.\n• Pennestrì, E., Rossi, V., Salvini, P., Valentini, P.P. (2016) Review and comparison of dry friction force models. Nonlinear Dynamics. 83(4), 1785-1801.\n• Rabinowicz, E. (1958) The intrinsic variables affecting the stick-slip process. Proceedings of the Physical Society. 71(4), 668-675.\n• Rabinowicz, E. (1951) The nature of the static and kinetic coefficients of friction. Journal of Applied Physics. 22(11), 1373-1379.\n• Rao, S.S. (2009) Engineering optimization: theory and practice. 4th ed. New Jersey: John Wiley & Sons.\n• Rong, B., Rui, X., Tao, L., Wang, G. (2019) Theoretical modeling and numerical solution methods for flexible multibody system dynamics. Nonlinear Dynamics. 98(2), 1519-1553.\n• Siqueira, T.M., Coda, H.B. (2016) Development of sliding connections for structural analysis by a total lagrangian FEM formulation. Latin American Journal of Solids and Structures. 13(11).\n• Siqueira, T.M., Coda, H.B. (2019) Flexible actuator finite element applied to spatial mechanisms by a finite deformation dynamic formulation. Computational Mechanics. 64(6), 1517-1535.\n• Siqueira, T.M., Coda, H.B. (2017) Total Lagrangian FEM formulation for nonlinear dynamics of sliding connections in viscoelastic plane structures and mechanisms. Finite Elements in Analysis and Design. 129, 63-77.\n• Threlfall, D.C. (1978) The inclusion of Coulomb friction in mechanisms programs with particular reference to DRAM au programme DRAM. Mechanism and Machine Theory. 13(4).\n• Yang, Y.-B., Lin, B.-H. (1995) Vehicle-Bridge Interaction Analysis by Dynamic Condensation Method. Journal of Structural Engineering. 121(11), 1636-1643.\n\n# Edited by\n\n• Editor: Marco L. Bittencourt\n\n# Publication Dates\n\n• Publication in this collection\n13 Jan 2023\n• Date of issue\n2023" ]

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[ "# Why divide by $2m$\n\nI'm taking a machine learning course. The professor has a model for linear regression. Where $h_\\theta$ is the hypothesis (proposed model. linear regression, in this case), $J(\\theta_1)$ is the cost function, $m$ is the number of elements in the training set, $x^{(i)}$ and $y^{(i)}$ are the variables of the training set element at $i$\n\n$$h_\\theta = \\theta_1x$$\n\n$$J(\\theta_1) = \\frac{1}{2m} \\sum_{i=1}^{m}(h_\\theta(x^{(i)})-y^{(i)})^2$$\n\nWhat I don't understand is why he is dividing the sum by $2m$.\n\n## 4 Answers\n\nThe $\\frac{1}{m}$ is to \"average\" the squared error over the number of components so that the number of components doesn't affect the function (see John's answer).\n\nSo now the question is why there is an extra $\\frac{1}{2}$. In short, it doesn't matter. The solution that minimizes $J$ as you have written it will also minimize $2J=\\frac{1}{m} \\sum_i (h(x_i)-y_i)^2$. The latter function, $2J$, may seem more \"natural,\" but the factor of $2$ does not matter when optimizing.\n\nThe only reason some authors like to include it is because when you take the derivative with respect to $x$, the $2$ goes away.\n\n• Then why include it at all? – Daniel Pendergast Aug 1 '14 at 17:59\n• @DantheMan See the last sentence of my answer. After taking the derivative, the $2$ won't appear anymore, and since most of the computation is with the derivative, it saves some clutter. – angryavian Aug 1 '14 at 18:01\n• Ah, I understand now. I understood something else. Thank you. – Daniel Pendergast Aug 1 '14 at 18:04\n• I can't prove this, but I believe you, it makes derivative calculation easier, which we do in gradient descent for example. – mskw Sep 29 '17 at 14:48\n\nDividing by $2m$ ensures that the cost function doesn't depend on the number of elements in the training set. This allows a better comparison across models.\n\n• How does that make it non-dependent? It looks like the 2m is just dividing the average up even more. like a pie dividing by 6, now we divide the pie by 2x6=12. Pratically, the average halved. – mskw Sep 29 '17 at 14:47\n• @mskw The accepted answer explains better where the $2$ comes from. Actually, the entire answer is better than mine was! – John Sep 29 '17 at 15:32\n• \"This allows a better comparison across models\" - Thanks, this is the answer I was looking for. – Amnon Mar 21 '18 at 17:46\n• @Amnon please explain on how \"This allows a better comparison across models\", I don't seem to get it – Ankit Agrawal Jul 25 at 14:54\n• @AnkitAgrawal Some models you may have $100$ elements in the training set, others $1000$. Without dividing by something proportional to $m$ the cost function would be ten times larger for the larger training set. Dividing removes the effect of the size of the training set. – John Jul 25 at 15:03\n\nI assume that the $\\frac{1}{m}$ component is obvious and therefore I will focus on the $\\frac{1}{2}$ part. I personally doubt that so many authors would decide to include this confusing term just achieve a little bit simpler gradient formulas. Note that there are ways of finding the solution to the linear regression equations that doesn't involve gradients. I will provide another explanation.\n\nWhen we try to evaluate the machine learning models we assume that our observations are not fully accurate but rather contain some kind of error. For example, imagine measuring a length using some low quality ruler. One of the simplest assumptions would be that we introduce some Gaussian error:\n\n$$\\epsilon \\thicksim \\mathcal{N}(0, 1)$$\n\nThose parameters are usually safe because we perform some kind of data normalization anyway. We can now compute a probability that our prediction $\\hat{y}$ equals our target value $y$ up to this measurement error:\n\n$$\\hat{y} + \\epsilon = y$$\n\nWe can treat $\\hat{y} + \\epsilon$ as a new random variable $\\widetilde{y} \\sim \\mathcal{N}(\\hat{y}, 1)$. We have just added a constant $\\hat{y}$ to our zero-centered random variable $\\epsilon$. This random variable $\\widetilde{y}$ is our probabilistic estimation of the observation. Instead of stating that for given input $x$ we will observe the output $\\hat{y}$ (which would not be true due to the errors) we state that we will most probably observe something around $\\hat{y}$. We can compute the likelihood of actually observing the $\\hat{y}$ or $y$ as well as any other number using the Gaussian PDF:\n\n$$p(x) = \\frac{1}{{\\sigma \\sqrt {2\\pi } }}exp\\left({{\\frac{ - \\left( {x - \\mu } \\right)^2 }{2\\sigma^2}}}\\right) \\\\$$\n\nIn our case $\\mu = \\hat{y}$ and $\\sigma = 1$:\n\n$$p(y) = \\frac{1}{{\\sqrt {2\\pi } }}exp\\left({{\\frac{ - \\left( {y - \\hat{y} } \\right)^2 }{2}}}\\right) \\\\$$\n\nNote that this is the function that we would actually like to maximize - the probability of observing the true value $y$ given our model. Since our main goal is maximization we can apply a monotone function like logarithm and ignore the constants.\n\n$$log~p(y) = \\frac{ - \\left( {y - \\hat{y} } \\right)^2 }{2} + const$$\n\nOnce we get rid of the constant and the minus sign we obtain the squared error term for a single example in our dataset. We can average over all of the examples to get the MSE formula.\n\n$$MSE(y, \\hat{y}) = \\frac{1}{2m}\\sum_i^m (y - \\hat{y})^2$$\n\nNote that we can similarly derive the formula for the logistic regression loss, i.e. cross-entropy or log-loss.\n\nI wondered about the exact same thing when taking this course, and ended up researching this a bit. I'll give a short answer here, but you can read a more detailed overview in a blog post I wrote about it.\n\nI believe that at least part of the reason for those scaling coefficients is that L² regularization probably entered the field of deep learning through the introduction of the related, but not identical, concept of weight decay.\n\nThe 0.5 factor is then there to get a nice λ-only coefficient for the weight decay in the gradient, and the scaling by m... well, there are at least 5 different motivations that I have found or came up with:\n\n1. A side-effect of batch gradient descent: When a single iteration of gradient descent is instead formalized over the entire training set, resulting in the algorithm sometimes called batch gradient descent, the scaling factor of 1/m, introduced to make the cost function comparable across different size datasets, gets automatically applied to the weight decay term.\n2. Rescale to the weight of a single example: See grez's interesting intuition.\n3. Training set representativeness: It makes sense to scale down regularization as the size of the training set grows, as statistically, its representativeness of the overall distribution also grows. Basically, the more data we have, the less regularization is needed.\n4. Making λ comparable: By hopefully mitigating the need to change λ when m changes, this scaling makes λ itself comparable across different size datasets. This make λ a more representative estimator of the actual degree of regularization required by a specific model on a specific learning problem.\n5. Empirical value: The great notebook by grez demonstrates that this improves performance in practice." ]

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[ "# Table 4 Calibrated models of low cycle fatigue based on the total energy dissipated for multiple slenderness ratios.\n\nSlenderness ratio L/d\n\nEquation\n\n$$R^{2}$$\n\n80 (550)\n\n5\n\n$$\\epsilon _{a}=97.4(W_{fT})^{-1.225}$$\n\n0.959\n\n10\n\n$$\\epsilon _{a}=4.89(W_{fT})^{-0.941}$$\n\n0.829\n\n15\n\n$$\\epsilon _{a}=24.4(W_{fT})^{-1.383}$$\n\n0.863", null, "" ]

[ null, "https://ijcsm.springeropen.com/track/article/10.1186/s40069-021-00474-9", null ]

[ "## How do you convert a logarithmic equation to exponential form?\n\nHow To: Given an equation in logarithmic form logb(x)=y l o g b ( x ) = y , convert it to exponential form. Examine the equation y=logbx y = l o g b x and identify b, y, and x. Rewrite logbx=y l o g b x = y as by=x b y = x .\n\n## How do you solve exponential equations step by step?\n\nIf not, stop and use Steps for Solving an Exponential Equation with Different Bases. Step 2: Rewrite the problem using the same base. Step 3: Use the properties of exponents to simplify the problem. Step 4: Once the bases are the same, drop the bases and set the exponents equal to each other.\n\n## How do you convert LN to exponential form?\n\nSummary’ln’ stands for natural logarithm.A natural logarithm is just a logarithm with a base of ‘e”e’ is the natural base and is approximately equal to 2.718.y = bx is in exponential form and x = logby is in logarithmic form.\n\n## What is exponential form in math?\n\nexponential form. • a way of representing repeated multiplications of the same number. by writing the number as a base with the number of repeats. written as a small number to its upper right.\n\n## Is logarithmic the same as exponential?\n\nLogarithmic growth is the inverse of exponential growth and is very slow. grow logarithmically. This terminological confusion between logarithmic growth and exponential growth may be explained by the fact that exponential growth curves may be straightened by plotting them using a logarithmic scale for the growth axis.\n\n## What is an example of a exponential equation?\n\nIn other words, when an exponential equation has the same base on each side, the exponents must be equal. For example, consider the equation 34x−7=32×3 3 4 x − 7 = 3 2 x 3 . To solve for x, we use the division property of exponents to rewrite the right side so that both sides have the common base 3.\n\n## What are the five rules of exponents?\n\nExponents product rules. Product rule with same base. an ⋅ am = an+m Example: 23 ⋅ 24 = 23+4 = 27 = 2⋅2⋅2⋅2⋅2⋅2⋅2 = 128. Exponents quotient rules. Quotient rule with same base. an / am = anm Example: 25 / 23 = 253 = 22 = 2⋅2 = 4. Exponents power rules. Power rule I. (an) m = a nm Example:\n\nYou might be interested:  Circulation equation\n\n## How do you convert log10 to LN?\n\nNatural logarithms can be indicated either as: Ln(x) or loge(x). Changing the base of the log changes the result by a multiplicative constant. To convert from Log10 to natural logs, you multiply by 2.303. Analogously, to convert in the other direction, you divide by 2.303.\n\n## What does Ln mean in math?\n\nnatural logarithm\n\n### Releated\n\n#### Factoring an equation\n\nHow do you factor algebraic equations? So, if, in your equation, your b value is twice the square root of your c value, your equation can be factored to (x + (sqrt(c)))2. For example, the equation x2 + 6x + 9 fits this form. 32 is 9 and 3 × 2 is 6. So, we […]\n\n#### The equation of exchange can be stated as\n\nWhat is the equation of exchange equal to? So the equation of exchange says that the total amount of money that changes hands in the economy will always equal the total money value of the goods and services that change hands in the economy. So now the equation of exchange says that total nominal expenditures […]" ]

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[ "", null, "# Permutations, k-Permutations and Combinations\n\nRequires a Wolfram Notebook System\n\nInteract on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.\n\nRequires a Wolfram Notebook System\n\nEdit on desktop, mobile and cloud with any Wolfram Language product.\n\nNumber of Permutations\n\n[more]\n\nThe number of ways to arrange", null, "different objects in a row is", null, ". The exclamation mark \"!\" is read as \"factorial\". Of course, the product is the same in reverse order:", null, ". Each such arrangement is called a permutation. For consistency, it is assumed that", null, ".\n\nNumber of k-Permutations\n\nIf only", null, "of the", null, "objects are to be arranged in a row, the formula is", null, ",\n\nwith", null, "factors. If", null, ",", null, ". Such an arrangement is called a partial permutation, or a", null, "-permutation. Clearly", null, ", because all", null, "objects are being arranged; the formula reduces to", null, "because the denominator is", null, ".\n\nNumber of Combinations\n\nThe number of ways to choose a subset of", null, "objects from", null, "objects is", null, ".\n\nTherefore,", null, ". Each choice of a subset is called a combination. Another notation for", null, "is", null, ". Again, if", null, ",", null, ". A special case is", null, ".\n\n[less]\n\nContributed by: George Beck (May 2018)\nOpen content licensed under CC BY-NC-SA\n\n## Snapshots", null, "", null, "", null, "## Permanent Citation\n\nGeorge Beck\n\n Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send" ]

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[ "# DOC", null, "```5022\n(a) Write the chemical equation and algebraic expressions which define pK a in\nterms of molar concentrations present when an acid, HA, dissociates in water.\n(b) Methanol has acid-base properties that are similar to those of water. Write\nchemical equations which illustrate methanol functioning as an acid and as a\nbase.\n5027\nEqual volumes of 1.0 molar solutions of malononitrile [(NC)2CH2, pKa 11.2] and\nthe sodium salt of phenol [C6H5O–Na+] in water are mixed. [Phenol, C6H5OH,\nhas a pKa 10.0]. What is the equation for the reaction which occurs and what is\nthe equilibrium constant at room temperature for that reaction? Qualitatively,\nwhich species will be present in higher concentrations at equilibrium, and which\nwill be present in lower concentrations?\n5142\nMost carboxylic acids dissolve in 0.1 M sodium bicarbonate solution, but most\nphenols do not. This difference forms the basis for an important separation\nprocedure. Given that\nReaction\nRCO2H\n+\nArCO2H\nH2CO3\n+\n+\nH2O\nH2O\nH2O\n~Ka\nRCO2\n+\nH3O+\n10–5\nArCO2\n+\nH3O+\n10–10\nHCO3\n+\nH3O+\n10–7\nshow, by calculation, why the solubilities are as stated above.\n5174\nUsing the pKa values given, decide whether the equilibrium will lie toward the\nright or the left. Give a justification for your choice.\n(a)\n–\nN+H + HCO3\n+ H2CO3\nN\npKa\n6.5\n5.2\n(b)\nO\nO\nH3C\npKa\nC\n4.3\nOH + –CH2NO2\nH3C\nC\nO– + CH3NO2\n10.2\n5217\nGiven the pKa of ammonium ion (9.2) and of hydrogen cyanide (9.1) shown\nbelow, calculate the free energy in kilocalories or kilojoules for the reaction.\nNH4+ + CN–\nNH3 + HCN\nWhich species will predominate at equilibrium in a 0.1 M solution of ammonium\ncyanide?\n5242\nUsing the data below, account for the fact that p-aminobenzoic acid does not\nexist appreciably as the dipolar ion, but p-aminobenzenesulfonic acid does.\nAcid\n+\nC2H5NH3\nC6H5CO2H\nC6H5NH3+\nC6H5SO3H\npKa\n9.5\n4.2\n4.6\n0.7\n```" ]

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[ "#### Abstract\n\nA delayed HIV-1 infection model with CTL immune response is investigated. By using suitable Lyapunov functionals, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infection is less than or equal to unity; if the basic reproduction ratio for CTL immune response is less than or equal to unity and the basic reproduction ratio for viral infection is greater than unity, the CTL-inactivated infection equilibrium is globally asymptotically stable; if the basic reproduction ratio for CTL immune response is greater than unity, the CTL-activated infection equilibrium is globally asymptotically stable.\n\n#### 1. Introduction\n\nRecently, many mathematical models have been developed to describe the infection with HIV-1 (human immunodeficiency virus 1). By investigating these models, researchers have gained much important knowledge about the HIV-1 pathogenesis and have enhanced progress in the understanding of HIV-1 infection (see, e.g., ). It is pointed out by the work of that immune response is universal and necessary to eliminate or control the disease during viral infections. In particular, as a part of innate response, cytotoxic T lymphocytes (CTLs) play a particularly important role in antiviral defense by attacking infected cells. Thus, many authors have studied the mathematical modelling of viral dynamics with CTL immune response (see, e.g., ). In , Nowak and Bangham considered an HIV-1 infection model with CTL immune response which is described by the following differential equations: where , , , and represent the densities of uninfected target cells, infected cells, virions, and CTL cells at time , respectively. Uninfected cells are produced at rate , die at rate , and become infected cells at rate . Infected cells are produced from uninfected cells at rate and die at rate . The parameter accounts for the strength of the lytic component. Free virions are produced from uninfected cells at rate and are removed at rate . The parameter is the death rate for CTLs, and describes the rate of CTL immune response activated by the infected cells.\n\nMoreover, infection rate plays an important role in the modelling of epidemic dynamics. Holling type-II functional response seems more reasonable than the bilinear incidence rate (see, ). In , by stability analysis, Song and Avidan obtained that the system with the bilinear incidence rate was an extreme case of the model with Holling type-II functional response term.\n\nIn [3, 4, 7], the researchers used ordinary differential equations to describe different aspects of the dynamics of the viral infections. However, in the real virus dynamics, infection processes are not instantaneous. Time delays are usually introduced for the purpose of accurate representations of this phenomena (see, e.g., [6, 1217]). As pointed out in , there is a time delay between initial viral entry into a cell and subsequent viral production, and the effect of saturation infection of an HIV-1 model was studied. By using the Lyapunov-LaSalle type theorem, sufficient conditions were derived for the global stability of the infection-free equilibrium and the chronic-infection equilibrium. In addition, there is also a period between virions that have created within a cell, and the new virions are released from the cell (see, e.g., [6, 13, 17]). In , Zhu and Zou studied an HIV-1 model with discrete delays and found that large delays can help eliminate the virus. To the best of our knowledge, there are few works on the dynamics of HIV-1 system with CTL immune response, Holling type-II functional response, and two kinds of discrete delays. Therefore, we are concerned with the effect of the above factors on system (1.1).\n\nMotivated by the works of Nowak and Bangham , Song and Avidan , in the present paper, we consider the following delay differential equations: where the parameters have the same meanings as in system (1.1), represents the time between viral entry into a target cell and the production of new virus particles and stands for a virus production period for new virions to be produced within and released from the infected cells.\n\nThe initial conditions for system (1.2) take the form where (, the Banach space of continuous functions mapping the interval into , where , .\n\nIt is well known by the fundamental theory of functional differential equations that system (1.2) has a unique solution satisfying the initial conditions (1.3). It is easy to show that all solutions of system (1.2) with initial conditions (1.3) are defined on and remain positive for all .\n\nThis paper is organized as follows. In Section 2, by analyzing the basic reproduction ratio for viral infection and CTL immune response, the existence of three equilibria is established. Moreover, the ultimate boundedness of the solutions for system (1.2) is presented. In Section 3, by means of suitable Lyapunov functionals and LaSalle's invariant principle, we discuss the global stability of the infection-free equilibrium, the CTL-inactivated infection equilibrium, and the CTL-activated infection equilibrium, respectively. In Section 4, we carry out some numerical examples to illustrate the theoretical results. Finally, a discussion is given in Section 5 to end this work.\n\n#### 2. Preliminary Results\n\nIn this section, we discuss the existence of three equilibria and prove that all the solutions are positive and bounded.\n\nClearly, system (1.2) always has an infection-free equilibrium .\n\nDenote Here, and are called the basic reproduction ratios for viral infection and CTL immune response of system (1.2), respectively. It is easy to see that always holds. If , system (1.2) has a CTL-inactivated infection equilibrium besides the equilibrium , where\n\nIf , system (1.2) has a CTL-activated infection equilibrium besides the equilibrium and , where\n\nTheorem 2.1. Supposing that is a solution of system (1.2) with initial conditions (1.3), then there exists , such that all the solutions satisfy , , , for sufficiently large time .\n\nProof. Let Since all solutions of system (1.2) are positive, simple calculation leads to Therefore, we get for sufficiently large time , where is an arbitrarily small positive constant. Finally, all the solutions of system (1.2) are ultimately bounded by some positive constant. This completes the proof.\n\n#### 3. Global Stability\n\nIn this section, we study the global stability of each equilibrium of system (1.2) by using suitable Lyapunov functionals which are inspired by Xu and McCluskey and LaSalle's invariant principle.\n\nDefine the following function: Clearly, for , has the minimum at and .\n\nTheorem 3.1. If , the infection-free equilibrium of system (1.2) is globally asymptotically stable.\n\nProof. Let be any positive solution of system (1.2) with initial conditions (1.3). Define the following Lyapunov functional: Calculating the derivative of along positive solutions of system (1.2), it follows that\nNoting that , we obtain . Hence, from (3.3), we have . By Theorem in , solutions limit to , the largest invariant subset of . Let be the solution with initial function in . Then, from the invariance of , we obtain , , and for any . Further, from the third equation of system (1.2), we obtain . Accordingly, it follows from LaSalle's invariance principal that the infection-free equilibrium is globally asymptotically stable for any positive time delays. This completes the proof.\n\nTheorem 3.2. If , the CTL-inactivated infection equilibrium of system (1.2) is globally asymptotically stable.\n\nProof. Let be any positive solution of system (1.2) with initial conditions (1.3). Define the following Lyapunov functional: where\nFor clarity, we will calculate the derivatives of , , , , , and along positive solutions of system (1.2), respectively.\nSince holds, it follows that Noting that , we get that Since holds, it follows that Calculating the derivatives of and shows that We therefore derive from (3.6)–(3.9) that\nNoting that , we derive that . Hence, from (3.10), we have . Similar to Theorem 3.1, solutions limit to , the largest invariant subset of . Let be the solution with initial function in . Then, we obtain that It is readily to show that , , , and for any . Thus, it follows from LaSalle's invariance principal that the CTL-inactivated infection equilibrium is globally asymptotically stable for any positive time delays. This completes the proof.\n\nTheorem 3.3. If , the CTL-activated infection equilibrium of system (1.2) is globally asymptotically stable.\n\nProof. Let be any positive solution of system (1.2) with initial conditions (1.3). We construct the following Lyapunov functional: where\nNext, we will calculate the derivatives of , , , , , and along positive solutions of system (1.2), respectively.\nSimilar to (3.6), we derive that Noting that , it follows that Similar to (3.8), we get that Calculating the derivative of shows that Similar to (3.9), it follows that We therefore derive from (3.14)–(3.18) that\nHence, from (3.19), we get . Similar to Theorem 3.1, solutions limit to , the largest invariant subset of . Let be the solution with initial function in . Then, it holds that It is easy to show that , , and for any time . Moreover, from the second equation of system (1.2), we obtain . Therefore, it follows from LaSalle's invariance principal that the CTL-activated infection equilibrium is globally asymptotically stable for any positive time delays. This completes the proof.\n\n#### 4. Numerical Simulations\n\nIn the following, we give three examples to illustrate the main theoretical results above. All the parameters were obtained from [9, 16, 20].\n\nExample 4.1. In system (1.2), we choose , , , , , , , , , , and , . It is easy to show that , and that system (1.2) has an infection-free equilibrium . By Theorem 3.1, we get that the infection-free equilibrium of system (1.2) is globally asymptotically stable. Numerical simulation illustrates this fact (see Figure 1).\n\nExample 4.2. In system (1.2), we set , , , , , , , , , , and , . It is easy to show that , and that system (1.2) has a CTL-inactivated infection equilibrium . By Theorem 3.2, we obtain that the CTL-inactivated infection equilibrium of system (1.2) is globally asymptotically stable. Numerical simulation illustrates our result (see Figure 2).\n\nExample 4.3. In system (1.2), let , , , , , , , , , , and , . It is easy to show that , and then system (1.2) has a CTL-activated infection equilibrium . By Theorem 3.3, we get that the CTL-activated infection equilibrium of system (1.2) is globally asymptotically stable. Numerical simulation illustrates this fact (see Figure 3).\n\n#### 5. Discussion\n\nIn this paper, we have studied the global dynamics of a delayed HIV-1 infection model with CTL immune response. By constructing suitable Lyapunov functionals, sufficient conditions have been derived for the global stability of three equilibria. It is easy to show that if the basic reproduction ratio for viral infection , infection-free equilibrium is globally asymptotically stable, and the virus is cleared up; if the basic reproduction ratio for CTL immune response satisfies , the equilibrium is globally asymptotically stable, and the infection becomes chronic but without CTL immune response; if , system (1.2) has a CTL-activated infection equilibrium besides and , which is globally asymptotically stable, and the infection turns to chronic with CTL immune response.\n\nFrom Theorems 3.1, 3.2, and 3.3, we see that the delays and do not affect the global stability of the feasible equilibria and therefore do not induce periodic oscillations, and the possibility of Hopf bifurcations is therefore ruled out. On the other hand, if the basic reproduction ratio for CTL immune response , we can get which shows that the number of infected cells and virions of the equilibrium is greater than the number of those of the equilibrium . Hence, the CTL immune response plays an important role in the reduction of the infected cells and the free virions.\n\n#### Acknowledgment\n\nThis work was supported by the National Natural Science Foundation of China (no. 11071254)." ]

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[ "Message-ID: <534013384.32003.1586046480362.JavaMail.wiki@f66ff9f96425> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary=\"----=_Part_32002_216970183.1586046480362\" ------=_Part_32002_216970183.1586046480362 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Web Method\n\n# Web Method\n\nOne of many ways to handle an HTTP reque= st is by writing a method on your URL-bound classes. In Stapler-speak, thes= e methods are called \"web methods\".\n\n=20\n\nWeb methods are public instance methods that has the name that starts wi= th \"do\", for example:\n\n=20\n=20\n```class MyRootAction {\n...\n\n@RequirePOST\npublic HttpResponse doStart() {\nstart();\nreturn HttpResponses.redirectTo(\".\");\n}\n}\n```\n=20\n=20\n\nSuch a method would handle an HTTP request sent to ```/.../start (again, see the reference for the exact routing= rules)```\n\n```=20 Parameters=20 Web methods can define parameters. When Stapler invokes your web method,= it needs your help to figure out what you expect in those parameters, and = there are several ways to do this.=20 Firstly, if the type of a parameter is one of the following \"well-recogn= ized\" types, Stapler would instantly know what to do:=20 =20 StaplerR= equest/HttpServletRequest =E2=80=94 the request object=20 Stapler= Response/HttpServletResponse =E2=80=94 the response object= =20 =20 Secondly, you can place parameter injection annotations to instruct Jenk= ins what you want to see in that parameter. Unlike typical Java programming= , parameter names are significant.=20 =20 @Header<= /a>: requests that the value of the request HTTP header be injecte= d.=20 =20 public HttpResponse doStart(@Header String referer) { ... } =20 =20 @QueryParameter: requests that the value of the request pa= rameter be injected. This includes a submitted form and a query paramet= er.=20 @AncestorInPath: Stapler will call StaplerRequest.findAn= cestor(Class) and inject the obtained object. This object is the nea= rest \"ancestor\" of the specified type in the current URL.=20 =20 Parameter injection annotations are extensible. One can define a custom = injection parameter by using the @InjectedParameter] meta annotation, which is h= ow all these annotations are defined. =20 The type of the injected parameter can be anything, and Apache Commons B= eanutils is used to convert the incoming value into the appropriate Java ty= pe your method requests.=20 Return value and exception=20 If a web method returns, either normally through the return statement or= abnormally through a thrown exception, Stapler checks if the return value = / exception implements HttpResponse interface. If so, this object is expected to rend= er a response via its generateResponse method.=20 Jenkins defines a number of high-level HTTP response classes that implem= ents this interface, such as AutoCompletionCandidates, ContextMenu, ListBoxModel= , = FormValidation, TrendChart, etc.=20 There's also HttpResponses that provides a number of static methods that he= lp you create typical HTTP responses, such as redirect, errors, serving sta= tic files, etc. =20 Interceptor Annotations=20 Web methods can have \"interceptor annotations\", which decorates your web= method by adding additional processing before and after your method gets i= nvoked. Interceptor annotations to web methods are like servlet fileters to= servlets.=20 Jenkins defines several built-in interceptor annotations:=20 =20 @Re= quirePOST: aborts with \"400 bad request\" if the request is not= POST. This is how we protect endpoints that can update states in Jenkins, = with crumb.=20 @RespondSuccess: used on a web method that returns \"void\" so t= hat when the method returns normally \"200 success\" will be returned as a re= sponse.=20 =20 Interceptor annotations are extensible through InterceptorAnnotation.= =20 Parameter injection, return value/exception response rendering, and inte= rceptor annotations help you reduce the HTTP dependency in your model objec= ts. This tends to make code easier and more easily testable. =20 @WebMethod=20 Normally, a name of a web method determines how the request is routed. F= or example, doEatPizza() would be mapped to .../eatPizza= . But you can explicitly specify the URL name by using WebMethod annotation. For = example, the following code maps .../abc and .../xyz.xml= to the same method.=20 =20 @WebMethod(\"abc\",\"xyz.xml\") HttpResponse doMonkey(...) { ... } =20 ```\n``` ------=_Part_32002_216970183.1586046480362-- ```" ]

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[ "When dealing with spatial data in sales and / or social science context it is common that data are reported per administrative units (defined as polygons).\n\nThis has its benefits – administrative units, such as counties, states or districts, are generally well understood by our users, and make a good base for convincing choropleth maps – but also disadvantages. Administrative areas differ greatly in size and population and are not always good inputs for modelling.\n\nTo remedy this I propose three different approaches for spatial aggregation of data reported per administrative area polygons:\n\nAs my post is about general techniques, and not a specific implementation, any spatial data object would do. I am choosing to demonstrate the techniques on the North Carolina shapefile that ships with `{sf}` package, based on nothing else than its general availability (`nc.shp` is the Iris of spatial data).\n\nAll the techniques are distance related a projected CRS is thus required. Being an European, metric born & raised, am choosing one based on US Survey Feet; I confess I am mildly amused by the rationale behind 660 feet to a furlong.\n\nMy first step is creating of 3 spatial objects:\n\n• county data of births in the years 1979 to 1984 from the `nc.shp` dataset; note that I calculate a column of county area (in squared survey feet); this will come handy later on\n• NC state boundaries, obtained by dissolving the `nc.shp` polygons\n• point data of three semi-random cities in NC; these will be basis for the aggregation\n``````library(sf)\nlibrary(dplyr)\nlibrary(ggplot2)\n\n# NC counties - a shapefile shipped with the sf package\ncounties <- st_read(system.file(\"shape/nc.shp\", package = \"sf\"), quiet = T) %>%\nselect(BIR79) %>% # a single variable: births for period 1979-84\nst_transform(crs = 6543) %>% # a quaint local projection\nmutate(cty_area = units::drop_units(st_area(.))) # county area (in feet)\n\n# NC state borders\nstate <- counties %>%\nsummarize()\n\n# three semi-random cities in NC\npoints <- data.frame(name = c(\"Raleigh\", \"Greensboro\", \"Wilmington\"),\nx = c(-78.633333, -79.819444, -77.912222),\ny = c(35.766667, 36.08, 34.223333)) %>%\nst_as_sf(coords = c(\"x\", \"y\"), crs = 4326) %>%\nst_transform(crs = st_crs(counties)) # same as counties``````\n\nAs I will be drawing a chart of NC births a lot I am creating a convenience function to simplify this task (and to not repeat myself).\n\nThe first step is to apply this function to the raw county data, and in doing so gain an overall understanding of the births metric.\n\n``````# define the function\nchart <- function(dataframe) {\nggplot() +\ngeom_sf(data = dataframe, aes(fill = BIR79), alpha = .5, lwd = .25) +\ngeom_sf(data = state, lwd = .75, fill = NA) +\ngeom_sf(data = points, color = \"red\", size = 2) +\nlow = \"white\",\nhigh = \"firebrick\",\nlabels = scales::comma_format()) +\nlabs(fill = \"Births\\n1979 - 84\") +\nguides(fill = guide_legend(override.aes = list(alpha = 0.5))) +\ntheme(legend.text.align = 1,\nlegend.title.align = 1/2)\n}\n\n# apply it to raw county data\nchart(counties)``````", null, "The second step is to prepare spatial objects that will be basis of our future aggregation.\n\nBuffers are the easiest, produced by a call to `sf::st_buffer()` on our points data, with second argument of distance — in our case 50 miles – and then cut to shape via `sf::st_intersection()` with the shape of NC state.\n\n``````# create the buffers object\nbuffers <- st_buffer(points, 50 * 5280) %>% # 50 miles circle\nst_intersection(state) # cut to shape of NC state\n\n# display the buffers\nggplot() +\ngeom_sf(data = buffers, aes(fill = name), alpha = .5) +\ngeom_sf(data = state, lwd = .75, fill = NA) +\ngeom_sf(data = points, color = \"red\", pch = 4, size = 2) +\nlabs(fill = \"Zone\")``````", null, "The Voronoi polygons are somewhat more challenging, as the geometry creation necessitates more steps; the `sf::st_voronoi()` function requires as argument a `sfc` object of `MULTIPOINT` type. This means first extracting geometry, i.e. without any data, from the `sf` object of points, and then merging of the list of multiple points to a single multipoint object via `sf::st_union()`.\n\nThe resulting polygon is then cut to shape of NC state, converted back to `sf` class and joined with the original point data to re-gain the dimension of city names it lost in previous steps.\n\n``````# create the voronoi object\nvoronoi <- points %>%\nst_geometry() %>% # to get sfc from sf\nst_union() %>% # to get a sfc of MULTIPOINT type\nst_voronoi(envelope = st_geometry(state)) %>% # NC sized Voronoi polygon\nst_collection_extract(type = \"POLYGON\") %>% # a list of polygons\nst_sf() %>% # from list to sf object\nst_intersection(state) %>% # cut to shape of NC state\nst_join(points) # put names back\n\n# display the Voronoi polygons\nggplot() +\ngeom_sf(data = voronoi, aes(fill = name), alpha = .5) +\ngeom_sf(data = state, lwd = .75, fill = NA) +\ngeom_sf(data = points, color = \"red\", pch = 4, size = 2) +\nlabs(fill = \"Zone\")``````", null, "Making of a grid requires applying `sf::st_make_grid()` to the NC state with second argument of grid cell size – in our case 50 by 50 miles; the resulting object will again be a geometry without any data (object of class `sfc`).\n\nIt is then converted back to `sf` class, with city names re-attached. I am also creating a technical key based on row number, as I will need an unique identification of each polygon (i.e. grid cell) in later stages of our process.\n\n``````# create the grid object\ngrid <- state %>%\nst_make_grid(cellsize = c(50 * 5280, 50 * 5280)) %>% # 50 × 50 miles\nst_sf() %>% # from sfc to sf\nst_intersection(state) %>% # cut to shape of NC state\nst_join(points) %>% # get names back\nmutate(id = row_number()) # generate key for later use\n\n# display the grid\nggplot() +\ngeom_sf(data = grid, aes(fill = name), alpha = .5) +\ngeom_sf(data = state, lwd = .75, fill = NA) +\ngeom_sf(data = points, color = \"red\", pch = 4, size = 2) +\nlabs(fill = \"Zone\")``````", null, "The third step is combining the county births data with geometries of interest via `sf::st_intersection()`.\n\n``````# naive intersection\nbuffers_raw <- buffers %>%\nst_intersection(counties) # raw intersection\n\n# this will not do for a result...\nchart(buffers_raw)``````", null, "This obviously is not a satisfactory result, as the data retain the original county dimension.\n\nIt is necessary to dissolve the counties, and assign a proportion of the births measure to each buffer polygon; it is reasonable to assume an equal density of the births metric per county area, and based on that assign births to buffer in proportion of the county area contained in the buffer.\n\nFrom technical perspective it is necessary to have two items in place before this step:\n\n• total area of source polygons (the intersection will split some county polygons, so the original area has to be calculated beforehand)\n• unique id of target polygon, which will serve as a grouping variable; for the buffers and Voronoi polygons city name is OK, for the grid a technical id is necessary\n``````# new data object based on buffers\nbuffers_data <- buffers %>%\nst_intersection(counties) %>% # raw intersection\nmutate(in_area = units::drop_units(st_area(.))) %>% # area of polygon\n# calculate a proportion of births equal to proportion of area\nmutate(BIR79 = BIR79 * in_area / cty_area) %>%\ngroup_by(name) %>% # group by name of buffer\nsummarise(BIR79 = sum(BIR79)) # total of births in named buffer\n\n# plot the results\nchart(buffers_data)``````", null, "The technique to assign birth data to Voronoi polygons is exactly the same as for the spatial buffers.\n\n``````# new data object based on Voronoi polygons\nvoronoi_data <- voronoi %>%\nst_intersection(counties) %>% # raw intresection\nmutate(in_area = units::drop_units(st_area(.))) %>% # area of polygon\n# calculate a proportion of births equal to proportion of area\nmutate(BIR79 = BIR79 * in_area / cty_area) %>%\ngroup_by(name) %>% # group by name of Voronoi polygon\nsummarise(BIR79 = sum(BIR79)) # total of births in named polygon\n\n# plot the results\nchart(voronoi_data)``````", null, "Two important differences between buffers and Voronoi polygons are that:\n\n• the Voronoi polygons are not overlapping\n• the Voronoi polygons cover the entire NC state\n\nThis has the consequence that we can confirm our result of our calculation by comparing the totals per county with totals per Voronoi polygons; we can reasonable expect these two to be equal (there is no double counting, and the entire state is covered).\n\n``````# checksum - do the totals add up?\nall.equal(sum(counties\\$BIR79), sum(voronoi_data\\$BIR79)) ``````\n``## TRUE``\n\nLastly we consider the grid cells.\n\nThe technique is again the same – assign to each grid cell a proportion of county births equal to the proportion of county area.\n\nIn this case the technical key of grid cells comes handy as grouping variable, as there are more grid cells than city points.\n\n``````# new data object based on grid\ngrid_data <- grid %>%\nst_intersection(counties) %>% # raw intersection\nmutate(in_area = units::drop_units(st_area(.))) %>% # area of cell\n# calculate a proportion of births equal to proportion of area\nmutate(BIR79 = BIR79 * in_area / cty_area) %>%\ngroup_by(id) %>% # group by id of grid cell\nsummarise(BIR79 = sum(BIR79)) # total of births in cell by id\n\n# plot the results\nchart(grid_data)``````", null, "Again, as the cells (like the Voronoi polygons, and unlike the buffers) cover the entire area of NC state with zero overlap it makes sense to compare the totals.\n\n``````# checksum - do the totals add up?\nall.equal(sum(counties\\$BIR79), sum(grid_data\\$BIR79)) ``````\n``## TRUE``\n\nThe final step is considering which spatial aggregation technique is the most appropriate in your use case.\n\nThis is (obviously) impossible to determine without some understanding of your use case.\n\nA few rules of thumb to consider are:\n\n• buffers are often a good idea when considering “bad” things – such as number of burglaries in the neighborhood; such metrics can spoil the figures for multiple areas of interest without diminishing.\n\n• Voronoi polygons are a good idea when considering “nice” things – such as potential customers, who will either visit store A or store B, but not both, for their shopping.\n\n• grid cells are good idea when you need to consider not only a presence of something, but also an absence of the thing – cells being empty carry information. Grid cells also create the illusion of impartiality – the entire region is covered, and even cells seem fair." ]

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[ "# AC/DC LED Drivers with Constant Current or Constant Voltage Mode\n\nAimtec’s AC/DC LED driver series AMEPR30-AZ, AMEPR60-AZ, AMER90-AZ, AMER120-AZ, and AMER150-AZ all can be utilized in either a Constant Current or a Constant Voltage mode.\n\nConstant Current Mode\n\nThe drivers are equipped with a current limiting circuit set to the maximum rated current for the specific driver model. As a result, when a load is installed at the output of the driver that would normally result in a high current above the maximum, the current limit circuit forces the driver to operate in constant current mode. When a LED load is installed the driver will operate in Constant Current mode. The output voltage will be the total forward voltage of the LED load.\n\nConstant Voltage Mode\n\nWith a load resistance (it would be better to use this term because the load can be complex and pulsing) that results in current below the driver’s maximum it will operate in Constant Voltage mode with the load voltage being the maximum rated voltage for the driver model. The load current will depend on the load resistance and will follow Ohm’s law,", null, "Practical use\n\nUsing Aimtec’s 60W AMEPR60-24250AZ as an example: it has a maximum rated current of 2.5A with a voltage range from 12 to 24VDC.\n\n• Constant Voltage Area (A),\n\n• Constant Current Area (B)\n\nThe constant current area (vertical line on Fig. 1 [below]) is the area where the output current is stable (fixed), however, the output voltage will decrease with increased loading (decreasing load resistance). For example, with Rload=9 Ohm, the output voltage will be 2.5A x 9 Ohm=22.5VDC, with Rload=6 Ohm, the output voltage will be 2.5A x 6 Ohm=15VDC.\n\nThe output voltage will continue to decrease with increased loading (decreased load resistance) until it reaches 12VDC (Rload=12V/2.5A=4.8 Ohm). This is the switching point for the operating mode to foldback protection.", null, "• Foldback Operation (C)\n\nFoldback protection mode (dotted sloping line). If the output current increases above the driver’s maximum rated current of 2.5A the driver’s Over Current Protection (OCP) will engage and the voltage and current will decrease rapidly. The driver will switch into this mode when the load resistance is less than 4.8 Ohm. As the current increases the voltage will decrease to limit the output power of the driver to a safe value.", null, "" ]

[ null, "https://www.electronicsmedia.info/wp-content/uploads/2017/12/LED-Driver-300x225.jpg", null, "https://www.electronicsmedia.info/wp-content/uploads/2017/12/Aimtec-300x225.jpg", null, "https://secure.gravatar.com/avatar/4d49386e1bf8b316e78d3bb2eafef333", null ]

[ "index 6cd08c1..183b54e 100644 (file)\n@@ -1,12 +1,12 @@\n-Curry-Howard, take 1\n---------------------\n+Curry-Howard\n+------------\n\n-We will return to the Curry-Howard correspondence a number of times\n-during this course.  It expresses a deep connection between logic,\n-types, and computation.  Today we'll discuss how the simply-typed\n-lambda calculus corresponds to intuitionistic logic.  This naturally\n-give rise to the question of what sort of computation classical logic\n-corresponds to---as we'll see later, the answer involves continuations.\n+The Curry-Howard correspondence expresses a deep connection between\n+logic, types, and computation.  Today we'll discuss how the\n+simply-typed lambda calculus corresponds to intuitionistic logic.\n+This naturally give rise to the question of what sort of computation\n+classical logic corresponds to---as we'll see later, the answer\n+involves continuations.\n\nSo at this point we have the simply-typed lambda calculus: a set of\nground types, a set of functional types, and some typing rules, given\n\nSo at this point we have the simply-typed lambda calculus: a set of\nground types, a set of functional types, and some typing rules, given\n@@ -270,8 +270,6 @@ The answer involves reasoning about what it means to be an individual.\nLet the type of *or* in this example be `Q -> Q -> Q`, where\n`Q` is the type of a generalized quantifier, i.e, `Q = ((e->t)->t`.\n\nLet the type of *or* in this example be `Q -> Q -> Q`, where\n`Q` is the type of a generalized quantifier, i.e, `Q = ((e->t)->t`.\n\n-John:e |- John:e, or:(Q->Q->Q) |- , everyone:Q, left:e->t\n-\n<pre>\n-----------------Ax  -----------------Ax\nJohn:e |- John:e     P:e->t |- P:e->t\n<pre>\n-----------------Ax  -----------------Ax\nJohn:e |- John:e     P:e->t |- P:e->t\n@@ -291,13 +289,12 @@ from verb phrase meanings to truth values, just as we would need.\n\nbeta reduction = normal proof.\n\nbeta reduction = normal proof.\n\n-\n-\n[To do: add pairs and destructors; unit and negation...]\n\nExcercise: construct a proof whose labeling is the combinator S,\nsomething like this:\n\n[To do: add pairs and destructors; unit and negation...]\n\nExcercise: construct a proof whose labeling is the combinator S,\nsomething like this:\n\n+<pre>\n--------- Ax  --------- Ax   ------- Ax\n!a --> !a     !b --> !b      c --> c\n----------------------- L->  -------- L!\n--------- Ax  --------- Ax   ------- Ax\n!a --> !a     !b --> !b      c --> c\n----------------------- L->  -------- L!\n@@ -320,3 +317,9 @@ something like this:\n! (!a->!b) --> ! (!a->!b->!c)->!a->!c\n--------------------------------------- R->\n--> ! (!a->!b)->! (!a->!b->!c)->!a->!c\n! (!a->!b) --> ! (!a->!b->!c)->!a->!c\n--------------------------------------- R->\n--> ! (!a->!b)->! (!a->!b->!c)->!a->!c\n+</pre>\n+\n+See also\n+[Wadler's symmetric\n+calculus](http://homepages.inf.ed.ac.uk/wadler/papers/dual/dual.pdf), and\n+[[http://en.wikibooks.org/wiki/Haskell/The_Curry-Howard_isomorphism]]." ]

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[ "# DHT12 (i2c Cheap Humidity and Temperature Sensor), Fast Easy Usage\n\n4,508\n\n5\n\nI like sensor that can be used with 2 wire (i2c protocol), but I love the inexpensive one.\n\nThis is an Arduino and esp8266 library for the DHT12 series of very low cost temperature/humidity sensors (less than 1\\$) that work with i2c or one wire connection.\n\nVery usefully if you want use esp01 (if you use serial you have only 2 pin) to read humidity and temperature and display it on i2c LCD.\n\nAI read that sometime seems that need calibration, but I have tree of this and get value very similar to DHT22. If you have calibration this problem, open issue on github and I add implementation.\n\nYou can find update and other on my site https://www.mischianti.org/2019/01/01/dht12-library-en/ .\n\n### Teacher Notes\n\nTeachers! Did you use this instructable in your classroom?\nAdd a Teacher Note to share how you incorporated it into your lesson.\n\n## Step 1: How I2c Works\n\nI2C works with it's two wires, the SDA(data line) and SCL(clock line).\n\nBoth these lines are open-drain, but are pulled-up with resistors.\n\nUsually there is one master and one or multiple slaves on the line, although there can be multiple masters, but we'll talk about that later.\n\nBoth masters and slaves can transmit or receive data, therefore, a device can be in one of these four states: master transmit, master receive, slave transmit, slave receive.\n\n## Step 2: Library\n\nYou can find my library here.\n\nTo download.\n\nClick the DOWNLOADS button in the top right corner, rename the uncompressed folder DHT12.\n\nCheck that the DHT folder contains DHT12.cpp and DHT12.h.\n\nPlace the DHT library folder your /libraries/ folder.\n\nYou may need to create the libraries subfolder if its your first library.\n\nRestart the IDE.\n\n## Step 3: Behaivor\n\nThis libray try to emulate the behaivor of standard DHT library sensors (and copy a lot of code), and I add the code to manage i2c olso in the same manner.\n\nThe method is the same of DHT library sensor, with some adding like dew point function.\n\n## Step 4: I2c Usage\n\nTo use with i2c (default address and default SDA SCL pin) the constructor is:\n\n```DHT12 dht12;\n```\n\nand take the default value for SDA SCL pin.\n\n(It's possible to redefine with specified contructor for esp8266, needed for ESP-01). or\n\n`DHT12 dht12(uint8_t addressOrPin) `\n`addressOrPin -> address `\n\nto change address.\n\n## Step 5: One Wire Usage\n\nTo use one wire:\n\n`DHT12 dht12(uint8_t addressOrPin, true) `\n`addressOrPin -> pin `\n\nboolean value is the selection of oneWire or i2c mode.\n\n## Step 6: Implicit Read\n\nYou can use It with \"implicit\", \"simple read\" or \"fullread\": Implicit, only the first read doing a true read of the sensor, the other read that become in 2secs. interval are the stored value of first read.\n\n```// The read of sensor have 2secs of elapsed time, unless you pass force parameter\n// Read temperature as Celsius (the default)\nfloat t12 = dht12.readTemperature();\n// Read temperature as Fahrenheit (isFahrenheit = true)\nfloat f12 = dht12.readTemperature(true);\n// Sensor readings may also be up to 2 seconds 'old' (its a very slow sensor)\nfloat h12 = dht12.readHumidity();\n\n// Compute heat index in Fahrenheit (the default)\nfloat hif12 = dht12.computeHeatIndex(f12, h12);\n// Compute heat index in Celsius (isFahreheit = false)\nfloat hic12 = dht12.computeHeatIndex(t12, h12, false);\n// Compute dew point in Fahrenheit (the default)\nfloat dpf12 = dht12.dewPoint(f12, h12);\n// Compute dew point in Celsius (isFahreheit = false)\nfloat dpc12 = dht12.dewPoint(t12, h12, false);```\n\n## Step 7: Simple Read\n\nSimple read to get a status of read.\n\n```\t\t// The read of sensor have 2secs of elapsed time, unless you pass force parameter\nbool chk = dht12.read(); // true read is ok, false read problem```\n```\t\t// Read temperature as Celsius (the default)\nfloat t12 = dht12.readTemperature();\n// Read temperature as Fahrenheit (isFahrenheit = true)\nfloat f12 = dht12.readTemperature(true);\n// Sensor readings may also be up to 2 seconds 'old' (its a very slow sensor)\nfloat h12 = dht12.readHumidity();\n\n// Compute heat index in Fahrenheit (the default)\nfloat hif12 = dht12.computeHeatIndex(f12, h12);\n// Compute heat index in Celsius (isFahreheit = false)\nfloat hic12 = dht12.computeHeatIndex(t12, h12, false);\n// Compute dew point in Fahrenheit (the default)\nfloat dpf12 = dht12.dewPoint(f12, h12);\n// Compute dew point in Celsius (isFahreheit = false)\nfloat dpc12 = dht12.dewPoint(t12, h12, false);```\n\n## Step 8: Full Read\n\nFull read to get a specified status.\n\n```\t\t// The read of sensor have 2secs of elapsed time, unless you pass force parameter\nDHT12::ReadStatus chk = dht12.readStatus();\nSerial.print(F(\"\\nRead sensor: \"));\nswitch (chk) {\ncase DHT12::OK:\nSerial.println(F(\"OK\"));\nbreak;\ncase DHT12::ERROR_CHECKSUM:\nSerial.println(F(\"Checksum error\"));\nbreak;\ncase DHT12::ERROR_TIMEOUT:\nSerial.println(F(\"Timeout error\"));\nbreak;\ncase DHT12::ERROR_TIMEOUT_LOW:\nSerial.println(F(\"Timeout error on low signal, try put high pullup resistance\"));\nbreak;\ncase DHT12::ERROR_TIMEOUT_HIGH:\nSerial.println(F(\"Timeout error on low signal, try put low pullup resistance\"));\nbreak;\ncase DHT12::ERROR_CONNECT:\nSerial.println(F(\"Connect error\"));\nbreak;\ncase DHT12::ERROR_ACK_L:\nSerial.println(F(\"AckL error\"));\nbreak;\ncase DHT12::ERROR_ACK_H:\nSerial.println(F(\"AckH error\"));\nbreak;\ncase DHT12::ERROR_UNKNOWN:\nSerial.println(F(\"Unknown error DETECTED\"));\nbreak;\ncase DHT12::NONE:\nSerial.println(F(\"No result\"));\nbreak;\ndefault:\nSerial.println(F(\"Unknown error\"));\nbreak;\n}```\n```\t\t// Read temperature as Celsius (the default)\nfloat t12 = dht12.readTemperature();\n// Read temperature as Fahrenheit (isFahrenheit = true)\nfloat f12 = dht12.readTemperature(true);\n// Sensor readings may also be up to 2 seconds 'old' (its a very slow sensor)\nfloat h12 = dht12.readHumidity();\n\n// Compute heat index in Fahrenheit (the default)\nfloat hif12 = dht12.computeHeatIndex(f12, h12);\n// Compute heat index in Celsius (isFahreheit = false)\nfloat hic12 = dht12.computeHeatIndex(t12, h12, false);\n// Compute dew point in Fahrenheit (the default)\nfloat dpf12 = dht12.dewPoint(f12, h12);\n// Compute dew point in Celsius (isFahreheit = false)\nfloat dpc12 = dht12.dewPoint(t12, h12, false);```\n\n## Step 9: Connection Diagram\n\nWith examples, there are the connection diagram, it's important to use correct pullup resistor.\n\nThanks to Bobadas, dplasa and adafruit, to share the code in github (where I take some code and ideas).\n\n## Step 14: Thanks\n\nArduino playground (https://playground.arduino.cc/Main/DHT12SensorLibrary)\n\ni2c project series (Collection):\n\n## 5 Discussions\n\nHi!\nThanks for your tutorial!\nI tried with one wire connection and it works well.\nThen I tried to put an other DHT12 in parallell with the first one. But no response from the two sensors.\nIs that possible to have many sensors on the same line like DS18B20 ?\nDo I have to modify the sketch?\nThanks in advance!\nPatrick\n\n2 answers" ]

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[ "# New classes of distributed time complexity\n\nSTOC 2018 · 50th ACM Symposium on Theory of Computing, Los Angeles, CA, USA, June 2018 ·\n\n# Abstract\n\nA number of recent papers – e.g. Brandt et al. (STOC 2016), Chang et al. (FOCS 2016), Ghaffari & Su (SODA 2017), Brandt et al. (PODC 2017), and Chang & Pettie (FOCS 2017) – have advanced our understanding of one of the most fundamental questions in theory of distributed computing: what are the possible time complexity classes of LCL problems in the LOCAL model? In essence, we have a graph problem $\\Pi$ in which a solution can be verified by checking all radius-$O(1)$ neighbourhoods, and the question is what is the smallest $T$ such that a solution can be computed so that each node chooses its own output based on its radius-$T$ neighbourhood. Here $T$ is the distributed time complexity of $\\Pi$.\n\nThe time complexity classes for deterministic algorithms in bounded-degree graphs that are known to exist by prior work are $\\Theta(1)$, $\\Theta(\\log^* n)$, $\\Theta(\\log n)$, $\\Theta(n^{1/k})$, and $\\Theta(n)$. It is also known that there are two gaps: one between $\\omega(1)$ and $o(\\log \\log^* n)$, and another between $\\omega(\\log^* n)$ and $o(\\log n)$. It has been conjectured that many more gaps exist, and that the overall time hierarchy is relatively simple – indeed, this is known to be the case in restricted graph families such as cycles and grids.\n\nWe show that the picture is much more diverse than previously expected. We present a general technique for engineering LCL problems with numerous different deterministic time complexities, including $\\Theta( \\log^{\\alpha} n )$ for any $\\alpha \\ge 1$, $2^{\\Theta( \\log^{\\alpha} n )}$ for any $\\alpha \\le 1$, and $\\Theta(n^{\\alpha})$ for any $\\alpha < 1/2$ in the high end of the complexity spectrum, and $\\Theta( \\log^{\\alpha} \\log^* n )$ for any $\\alpha \\ge 1$, $\\smash{2^{\\Theta( \\log^{\\alpha} \\log^* n )}}$ for any $\\alpha \\le 1$, and $\\Theta((\\log^* n)^{\\alpha})$ for any $\\alpha \\le 1$ in the low end of the complexity spectrum; here $\\alpha$ is a positive rational number.\n\n# Publication\n\nIlias Diakonikolas, David Kempe, and Monika Henzinger (Eds.): STOC’18, Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, pages 1307–1318, ACM Press, New York, 2018\n\nISBN 978-1-4503-5559-9" ]

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[ "# Elementary particle\n\nquantum particle having no known substructure; quark, electron, photon, etc.\n\nIn physics, an elementary particle or fundamental particle is a particle that is not made of other particles.\n\nAn elementary particle can be one of two groups: a fermion or a boson. Fermions are the building blocks of matter and have mass, while bosons behave as force carriers for fermion interactions and some of them have no mass. The Standard Model is the most accepted way to explain how particles behave, and the forces that affect them. According to this model, the elementary particles are further grouped into quarks, leptons, and gauge bosons, with the Higgs boson having a special status as a non-gauge boson.\n\nOf the particles that make up an atom, only the electron is an elementary particle. Protons and neutrons are each made of 3 quarks, which makes them composite particles, particles that are made of other particles. The quarks are bound together by the gluons. The nucleus has boson pion fields responsible for the strong nuclear force binding protons and neutrons against the electrostatic repulsion between protons. Such virtual pions are composed of quark antiquark pairs again held together by gluons.\n\nThere are three basic properties that describe an elementary particle: ’mass’, ’charge’, and ’spin’. Each property is assigned a number value. For mass and charge the number can be zero. For example, a photon has zero mass and a neutrino has zero charge. These properties always stay the same for an elementary particle.\n\n• Mass: A particle has mass if it takes energy to increase its speed, or to accelerate it. The table to the right gives the mass of each elementary particle. The values are given in MeV/c2s (that is pronounced megaelectronvolts over \"c\" squared), that is in units of energy over the speed of light squared. This comes from special relativity, which tells us that energy equals mass times the square of the speed of light. All particles with mass-produce gravity. All particles are affected by gravity, even particles with no mass like the photon (see general relativity).\n• Electric charge: Particles may have positive charge, or negative, or none. If one particle has a negative charge, and another particle has a positive charge, the two particles are attracted to each other. If the two particles both have negative charge, or both have positive charge, the two particles are pushed apart. At short distances, this force is much stronger than the force of gravity which pulls all particles together. An electron has charge -1. A proton has charge +1. A neutron has an average charge 0. Normal quarks have charge of ⅔ or -⅓.\n• Spin: The angular momentum or constant turning of a particle has a particular value, called its spin number. Spin for elementary particles is one or ½. The spin property of particles only denotes the presence of angular momentum. In reality, the particles do not spin.\n\nMass and charge are properties we see in everyday life, because gravity and electricity affect things that humans see and touch. But spin affects only the world of subatomic particles, so it cannot be directly observed.\n\n## Fermions\n\nFermions (named after the scientist Enrico Fermi) have a spin number of ½, and are either quarks or leptons. There are 12 different types of fermions (not including antimatter). Each type is called a \"flavor\". The flavors are:\n\n• Quarks: up, down, charm, strange, top, bottom. Quarks come in three pairs, called \"generations\". The 1st generation (up and down) is the lightest and the third (top and bottom) is the heaviest. One member of each pair (up, charm and top) has a charge of ⅔. The other member (down, strange and bottom) has charge -⅓.\n• Leptons: electron, muon, tau, electron neutrino, muon neutrino, tau neutrino. The neutrinos have charge 0, hence the neutr- prefix. The other leptons have charge -1. Each neutrino is named after its corresponding original lepton: the electron, muon, and tauon.\n\nSix of the 12 fermions are thought to last forever: up and down quarks, the electron, and the three kinds of neutrinos (which constantly switch flavor). The other fermions decay. That is, they break down into other particles a fraction of a second after they are created. Fermi-Dirac statistics is a theory that describes how collections of fermions behave.\n\n## Bosons\n\nBosons, named after the Indian physicist Satyendra Nath Bose. Bosonic particles have spin 1 (integral spin). Although most bosons are made of more than one particle, there are two kinds of elementary bosons:\n\nThe photon and the gluons have no charge, and are the only elementary particles that have a mass of 0 for certain. The photon is the only boson that does not decay. Bose-Einstein statistics is a theory that describes how collections of bosons behave. Unlike fermions, it is possible to have more than one boson in the same space at the same time.\n\nThe Standard Model includes all of the elementary particles described above. All these particles have been observed in the laboratory.\n\nThe Standard Model does not talk about gravity. If gravity works like the three other fundamental forces, then gravity is carried by the hypothetical boson called the graviton. The graviton has yet to be found, so it is not included in the table above.\n\nThe first fermion to be discovered, and the one we know the most about, is the electron. The first boson to be discovered, and also the one we know the most about, is the photon. The theory that most accurately explains how the electron, photon, electromagnetism, and electromagnetic radiation all work together is called quantum electrodynamics." ]

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[ "Using the 8-16 Bit Histogram\n\n• The Histogram tool can display 8, 10, 12, 14, and 16 bit histograms of monochrome or color images. The Zoom Bit Depth controls are used to select the bit display of the histogram or to zoom in and out on the histogram. The red triangle at the top of the histogram is the zoom position. Left-click at the top of the histogram to set the zoom position then press one of the Zoom Bit Depth controls to zoom in or out. The zoom position shown by the red triangle will be centered in each zoomed display.\n\n• The |<<, <<, <, >, >>, >>| buttons are used to scroll the histogram display. The scroll buttons ae disabled when an 8 bit histogram is displayed since the complete histogram is shown from black = 0 to white = 255. Histograms with bit depth of 10, 12, 14, or 16 have far more values to display than an 8 bit histogram so only a portion of the higher bit depth histogram is displayed. For example, a complete 8 bit histogram has integer values from 0 to 255 and fits within the fixed and finite histogram display window. A 10 bit histogram display of the same data has 1024 integer values from black = 0 to white = 1023. As a result only 1/4 of a 10 bit histogram can be displayed. Histograms of 12, 14, and 16 bit data have 4096, 16384, and 65536 different integer values to display. ImagesPlus uses 64 bit image arrays which are displayed as 8, 10, 12, 14, or 16 bit histograms. The scoll buttons are enabled if bit depth > 8 to allow inspection of the complete histogram. Using the scroll buttons to move the view left or right does not move the red triangle zoom position.\n\n• The green min apply and blue max apply triangles at the bottom of the histogram define an interval [min, max] that can be transferred to smoothing, sharpening, and deconvolution tools using the Set Min Max Apply button.\n\n### Default 8 bit histogram with zoom at position = 127 or the center of the 8 bit histogram. The green min apply triangle and blue max apply triangle are set to black = 0 and white = 255, respectively.", null, "### The red triangle zoom position is set using a left-click at the top of the histogram near the center of the bell shape at far left. The green min apply and blue max apply triangles are set near the zoom position using a left and right click below the histogram, respectively.", null, "### The zoom bith depth is changed from 8 to 10 bit to display greater detail at the zoom position. The scroll buttons are enabled towards the right since the far left of the 10 bit histogram from 0 to 255 is displayed. A 10 bit histogram has integer values from 0 to 1023.", null, "### The zoom bith depth is changed from 10 to 12 bit to display greater detail at the zoom position. The scroll buttons are enabled towards the left and right since the far left of the 12 bit histogram from 46 to 301 is displayed. A 12 bit histogram has integer values from 0 to 4095.", null, "### The min max apply range is set to [111, 198] on a 12 bit range or [1778, 3175] on a 16 bit range. To transfer the min max interval to an enhancement filter press the Set Min Max Apply button .", null, "### Multiresolution Smooth-Sharp is opened with min apply = 1778 and max apply = 3175. Changes to min and max apply on Multiresolution are set on the Histogram tool if the histogram is open.", null, "" ]

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[ "CRTS Transient ID MLS120226:073504+192711\n(When using CRTS data please cite Drake et al. 2009, ApJ, 696, 870 and our ID.)\n\nBack to index\n Image 1 Image 2 Image 3 Image 4 master", null, "", null, "", null, "", null, "", null, "Check MPC\nCurrent CRTS lightcurve\nSDSS DR-8 data\nImages from SDSS, PQ, DSS, MLS, 2MASS\nPast detections in Datascope\n\nAll transients, SNe, Blazars, CVs\n\nID = 1202261181004130350\nnewast = 0.000000\nav_motn = 0.006410\nav_deltime = 19.948800\nav_uncertx = 0.025981\nav_uncerty = 0.025981\nav_inclin = 128.426496\nTime = 2455983.695344\nTime2 = 2455983.674571\nTime3 = 2455983.681491\nTime4 = 2455983.688410\nappreject = 0.000\nmastersn = 7.720\naveragesn = 13.399\ntheta = 0.000\nnhigh = 240\nRA = 113.7650300\nDec = 19.4530600\nMag = 19.426901\nMag_err = 0.020507\nFWHM = 2.530\nMaster = N18100.master.fits\nMasterRAoff = -0.375912\nMasterDecoff = 0.023950\nRA2 = 113.7650300\nDec2 = 19.4531000\nMag2 = 19.353399\nMag2_err = 0.019821\nFWHM2 = 2.360\nRA3 = 113.7650100\nDec3 = 19.4531000\nMag3 = 19.227800\nMag3_err = 0.018787\nFWHM3 = 2.340\nRA4 = 113.7650100\nDec4 = 19.4530700\nMag4 = 19.318001\nMag4_err = 0.019491\nFWHM4 = 2.530\nOppos_ang = 315.565674\nInner_motion = -0.123710\nOuter_motion = -0.173059\nEclip_long = 112.351350\nEclip_lat = -2.287584" ]

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[ "# Goodness of fit by Hosmer-Lemeshow test and ROC Curve for Logistic Regression not accompanying results conclusions\n\nI am trying to perform Logistic regression on the sample data set. After its modeling, I tried to check its goodness of fit using the Hosmer Lemeshow test and found the p-value < 0.05, which tells that the model is not a good fit. On, the contrary, when I plotted the ROC Curve for it(another way to check the fitness of model), the curve covered approx 80-90% of the area, which refers the model is suitably fit.\n\nPlease find the used dataset named \"Urine Analysis Data\" in the link: mytestdata\n\nIn the Model 1: I cleaned the dataset to remove rows containing NA values, then modeled the dataset and implemented hoslem.test and to draw ROC Curve.\n\nIn the Model 2: I tried further cleaning of dataset by removing the independent variables that are not of much significance, then modeled the dataset and implemented hoslem.test and to draw ROC Curve. But, the result dint changed.\n\nHere is the code:\n\nUrinedata <- read.csv(\"UrineForLogisticRegression.csv\", stringsAsFactors = F)\nsummary(Urinedata)\ncolSums(is.na(Urinedata))\nUrinedata$Calcium.Oxalate <- as.factor(Urinedata$Calcium.Oxalate)\nstr(Urinedata)\n\n##### Model 1 #####\n#Training by Model 1:\nCleaned_data <- Urinedata[complete.cases(Urinedata),]\ncolSums(is.na(Cleaned_data))\ncolnames(Cleaned_data)\n\nmodel1 <- glm(Calcium.Oxalate~gravity+ph+osmo+cond+urea+calc, data = Cleaned_data ,family = binomial)\nsummary(model1)\n\n#Testing goodness of fit of model using Hoslem Test:\ninstall.packages(\"ResourceSelection\")\nlibrary(ResourceSelection)\nhoslem.test(Cleaned_data$Calcium.Oxalate, fitted(model1), g=10) #Conclusion: The p-value is ,much less than 0.05, hence, model not a good fit. # Predicting same dataset values using Model1 now: install.packages(\"ROCR\") library(ROCR) predictedCalciumOxalate <- predict(model1, Cleaned_data, type = \"response\") test_output <- cbind(testdata,predictedCalciumOxalate) #Plotting ROC graph for data, if area more, then good fit: length(fitted(model2))==length(more_clean_data$Calcium.Oxalate)\npreds <- prediction(as.numeric(predictedCalciumOxalate), as.numeric(Cleaned_data$Calcium.Oxalate)) perf <- performance(preds,\"tpr\",\"fpr\") plot(perf) #####I also tried Model 2##### #Model 2 is determined by doing more cleansing on data more_clean_data <- Cleaned_data[,c(1,6,7)] colSums(is.na(more_clean_data)) colnames(more_clean_data) model2 <- glm(Calcium.Oxalate~urea*calc, data = more_clean_data, family = \"binomial\") summary(model2) hoslem.test(more_clean_data$Calcium.Oxalate, fitted(model2))\n#Hoslem test giving same result as model1 , thus dint proceeded with Model2 further.\n\n\nI am expecting that if Hosmer lemeshow test is telling the model is not a good fit, then ROC curve should also have reflected the same. I am new to R. Please correct if am wrong somewhere in the above statement conceptually.\n\n• Hosmer–Lemeshow test provides information about calibration while ROC curve is more about discrimination. Additionally, cut-off values depend on the context of the study. i.e. an AUC of 80-90% is not necessarily an indicator of good fit. The Cross-Validated community would better address and explain this question. – Ozan147 Dec 22 '18 at 5:36\n• – kjetil b halvorsen Dec 22 '18 at 22:21\n• Hosmer-Lemeshow is considered obsolete: stats.stackexchange.com/questions/273966/… – kjetil b halvorsen May 14 at 12:06" ]

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[ "# assignment2", null, "```CS 242-01 Homework 2 (100 points, 10 points each for problems 1-7 and 15 points each\nfor problems 8-9. Due day: 02/24/2015)\n1. &lt;&sect;2.2&gt; For the following C statement, what is the corresponding MIPS assembly code?\nAssume that the variables f, g, h, and i are in registers \\$s1 - \\$s4 and could be considered\n32-bit integers as declared in a C program. Use a minimal number of MIPS assembly\ninstructions.\nf = g + (h − 5);\n2. &lt;&sect;2.2&gt; For the following MIPS assembly instructions above, what is a corresponding C\nstatement? Assume that the variables f, g, h, and i are in registers \\$s1 - \\$s4.\n3. &lt;&sect;&sect;2.2, 2.3&gt; For the following C statement, what is the corresponding MIPS assembly\ncode? Assume that the variables f, g, h, i, and j are assigned to registers \\$s0, \\$s1, \\$s2,\n\\$s3, and \\$s4, respectively. Assume that the base address of the arrays A and B are in\nregisters \\$s6 and \\$s7, respectively.\nB = A[i−j];\n4. &lt;&sect;2.3&gt; Show how the base-16 number abcdef12hex would be arranged in memory.\n5. &lt;&sect;&sect;2.2, 2.5&gt; Provide the type and assembly language instruction for the following binary\nvalue: 0000 0010 0001 0000 1000 0000 0010 0000two\n6. &lt;&sect;2.9&gt; Consider the following code:\nlbu \\$t0, 0(\\$t1)\nsw \\$t0, 0(\\$t2)\nAssume that the register \\$t1 contains the address 10000000 and the register \\$t2\ncontains the address 10000010. Note the MIPS architecture utilizes big-endian\naddressing. Assume that the data at address 10000000 is: 11223344. What value is\nstored at the address pointed to by register \\$t2?\n7. &lt;&sect;2.7&gt; Suppose the program counter (PC) is set to (base-16 number) 20000000hex. Is it\npossible to use the jump (j) MIPS assembly instruction to set the PC to the address as\n40000000hex? Is it possible to use the branch-on-equal (beq) MIPS assembly instruction\nto set the PC to this same address?\n8. &lt;&sect;&sect;2.5, 2.10&gt; Assume that we would like to expand the MIPS register fi le to 128\nregisters and expand the instruction set to contain four times as many instructions.\n &lt;&sect;2.5&gt; How this would this affect the size of each of the bit fields in the R-type\ninstructions?\n\n\n&lt;&sect;2.5&gt; How this would this affect the size of each of the bit fields in the I-type\ninstructions?\n&lt;&sect;2.5&gt; How could each of the two proposed changes decrease the size of an MIPS\nassembly program? On the other hand, how could the proposed change increase\nthe size of an MIPS assembly program?\n9. &lt;&sect;2.8&gt; Implement the following C code in MIPS assembly. What is the total number of\nMIPS instructions needed to execute the function? Assume n is in register \\$s0.\nint f(int n){\nif (n==0)\nreturn 0;\nelse\nreturn 1+f(n−1);\n}\n```" ]

[ null, "https://s3.studylib.net/store/data/006688352_1-01f36dd2ede89a4fecb115b328a95629.png", null ]

[ "Amount\nFrom\nTo\n\n# How to convert kilowatt hours to kilojoules?\n\nKilowatt hours and Kilojoules are measuring units used to measure energys.\n\n## To convert from kilowatt hours to kilojoules, multiply the number of kilowatt hours by 3600 and the result is in kilojoules\n\n### How to use kilowatt hours to kilojoules conversion calculator\n\n1. Enter number of kilowatt hours in the given input box.\n2. Click on the \"Calculate\" button to convert number of kilowatt hours to kilojoules.\n3. Change \"From\" or \"To\" units value for different energy units conversion tool\nKilowatt Hours Conversion of Kilowatt Hours to Kilojoules\n0.99 kW*h 0.99 kW*h = 3564 kJ\n0.9 kW*h 0.9 kW*h = 3240 kJ\n1 kW*h 1 kW*h = 3600 kJ\n2 kW*h 2 kW*h = 7200 kJ\n3 kW*h 3 kW*h = 10800 kJ" ]

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[ "", null, "Natural Number\nGet Natural Number essential facts below. View Videos or join the Natural Number discussion. Add Natural Number to your PopFlock.com topic list for future reference or share this resource on social media.\nNatural Number\n\nIn mathematics, the natural numbers are those used for counting (as in \"there are six coins on the table\") and ordering (as in \"this is the third largest city in the country\"). In common mathematical terminology, words colloquially used for counting are \"cardinal numbers\" and words connected to ordering represent \"ordinal numbers\". The natural numbers can, at times, appear as a convenient set of codes (labels or \"names\"); that is, as what linguists call nominal numbers, forgoing many or all of the properties of being a number in a mathematical sense.\n\nSome definitions, including the standard ISO 80000-2, begin the natural numbers with 0, corresponding to the non-negative integers 0, 1, 2, 3, ..., whereas others start with 1, corresponding to the positive integers 1, 2, 3, ..., while others acknowledge both definitions. Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, but in other writings, that term is used instead for the integers (including negative integers).\n\nThe natural numbers are a basis from which many other number sets may be built by extension: the integers (Grothendieck group), by including (if not yet in) the neutral element 0 and an additive inverse (-n) for each nonzero natural number n; the rational numbers, by including a multiplicative inverse (1/n) for each nonzero integer n (and also the product of these inverses by integers); the real numbers by including with the rationals the limits of (converging) Cauchy sequences of rationals; the complex numbers, by including with the real numbers the unresolved square root of minus one (and also the sums and products thereof); and so on. These chains of extensions make the natural numbers canonically embedded (identified) in the other number systems.\n\nProperties of the natural numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partitioning and enumerations, are studied in combinatorics.\n\nIn common language, for example in primary school, natural numbers may be called counting numbers both to intuitively exclude the negative integers and zero, and also to contrast the discreteness of counting to the continuity of measurement, established by the real numbers.\n\n## History\n\n### Ancient roots\n\nThe most primitive method of representing a natural number is to put down a mark for each object. Later, a set of objects could be tested for equality, excess or shortage, by striking out a mark and removing an object from the set.\n\nThe first major advance in abstraction was the use of numerals to represent numbers. This allowed systems to be developed for recording large numbers. The ancient Egyptians developed a powerful system of numerals with distinct hieroglyphs for 1, 10, and all the powers of 10 up to over 1 million. A stone carving from Karnak, dating from around 1500 BC and now at the Louvre in Paris, depicts 276 as 2 hundreds, 7 tens, and 6 ones; and similarly for the number 4,622. The Babylonians had a place-value system based essentially on the numerals for 1 and 10, using base sixty, so that the symbol for sixty was the same as the symbol for one, its value being determined from context.\n\nA much later advance was the development of the idea that 0 can be considered as a number, with its own numeral. The use of a 0 digit in place-value notation (within other numbers) dates back as early as 700 BC by the Babylonians, but they omitted such a digit when it would have been the last symbol in the number. The Olmec and Maya civilizations used 0 as a separate number as early as the , but this usage did not spread beyond Mesoamerica. The use of a numeral 0 in modern times originated with the Indian mathematician Brahmagupta in 628. However, 0 had been used as a number in the medieval computus (the calculation of the date of Easter), beginning with Dionysius Exiguus in 525, without being denoted by a numeral (standard Roman numerals do not have a symbol for 0); instead nulla (or the genitive form nullae) from nullus, the Latin word for \"none\", was employed to denote a 0 value.\n\nThe first systematic study of numbers as abstractions is usually credited to the Greek philosophers Pythagoras and Archimedes. Some Greek mathematicians treated the number 1 differently than larger numbers, sometimes even not as a number at all.\n\nIndependent studies also occurred at around the same time in India, China, and Mesoamerica.\n\n### Modern definitions\n\nIn 19th century Europe, there was mathematical and philosophical discussion about the exact nature of the natural numbers. A school[which?] of Naturalism stated that the natural numbers were a direct consequence of the human psyche. Henri Poincaré was one of its advocates, as was Leopold Kronecker who summarized \"God made the integers, all else is the work of man\".\n\nIn opposition to the Naturalists, the constructivists saw a need to improve the logical rigor in the foundations of mathematics. In the 1860s, Hermann Grassmann suggested a recursive definition for natural numbers thus stating they were not really natural but a consequence of definitions. Later, two classes of such formal definitions were constructed; later still, they were shown to be equivalent in most practical applications.\n\nSet-theoretical definitions of natural numbers were initiated by Frege. He initially defined a natural number as the class of all sets that are in one-to-one correspondence with a particular set. However, this definition turned out to lead to paradoxes, including Russell's paradox. To avoid such paradoxes, the formalism was modified so that a natural number is defined as a particular set, and any set that can be put into one-to-one correspondence with that set is said to have that number of elements.\n\nThe second class of definitions was introduced by Charles Sanders Peirce, refined by Richard Dedekind, and further explored by Giuseppe Peano; this approach is now called Peano arithmetic. It is based on an axiomatization of the properties of ordinal numbers: each natural number has a successor and every non-zero natural number has a unique predecessor. Peano arithmetic is equiconsistent with several weak systems of set theory. One such system is ZFC with the axiom of infinity replaced by its negation. Theorems that can be proved in ZFC but cannot be proved using the Peano Axioms include Goodstein's theorem.\n\nWith all these definitions it is convenient to include 0 (corresponding to the empty set) as a natural number. Including 0 is now the common convention among set theorists and logicians. Other mathematicians also include 0, for example, computer languages often start from zero when enumerating items like loop counters and string- or array-elements. Many mathematicians have kept the older tradition and take 1 to be the first natural number.\n\nSince different properties are customarily associated to the tokens 0 and 1, for example, neutral elements for addition and multiplications, respectively, it is important to know which version of natural numbers, generically denoted by $\\mathbb {N} ,$", null, "is employed in the case under consideration. This can be done by explanation in prose, by explicitly writing down the set, or by qualifying the generic identifier with a super- or subscript (see also in #Notation), for example, like this:\n\n• Naturals with zero: $\\;\\{0,1,2,...\\}=\\mathbb {N} _{0}={\\mathbb {N} }\\cup \\{0\\}$", null, "• Naturals without zero: $\\{1,2,...\\}=\\mathbb {N} ^{*}=\\mathbb {N} \\smallsetminus \\{0\\}.$", null, "## Notation\n\nMathematicians use N or N (an N in blackboard bold) to refer to the set of all natural numbers. Older texts have also occasionally employed J as the symbol for this set.\n\nTo be unambiguous about whether 0 is included or not, sometimes a subscript (or superscript) \"0\" is added in the former case, and a superscript \"*\" or subscript \">0\" is added in the latter case:\n\nN0 = N0 = N ? {0} = {0, 1, 2, ...}\nN* = N+ = N1 = N>0 = {1, 2, 3, ...}.\n\nAlternatively, since natural numbers naturally embed in the integers, they may be referred to as the positive, or the non-negative integers, respectively.\n\n$\\{1,2,3,\\dots \\}=\\mathbb {Z} ^{+}$", null, "$\\{0,1,2,\\dots \\}=\\mathbb {Z} ^{\\geq 0}$", null, "## Properties\n\n### Infinity\n\nThe set of natural numbers is an infinite set. This kind of infinity is, by definition, called countable infinity. All sets that can be put into a bijective relation to the natural numbers are said to have this kind of infinity. This is also expressed by saying that the cardinal number of the set is aleph-naught (?0).\n\nOne can recursively define an addition operator on the natural numbers by setting a + 0 = a and a + S(b) = S(a + b) for all a, b. Here S should be read as \"successor\". This turns the natural numbers (N, +) into a commutative monoid with identity element 0, the so-called free object with one generator. This monoid satisfies the cancellation property and can be embedded in a group (in the mathematical sense of the word group). The smallest group containing the natural numbers is the integers.\n\nIf 1 is defined as S(0), then b + 1 = b + S(0) = S(b + 0) = S(b). That is, b + 1 is simply the successor of b.\n\n### Multiplication\n\nAnalogously, given that addition has been defined, a multiplication operator × can be defined via a × 0 = 0 and a × S(b) = (a × b) + a. This turns (N*, ×) into a free commutative monoid with identity element 1; a generator set for this monoid is the set of prime numbers.\n\n### Relationship between addition and multiplication\n\nAddition and multiplication are compatible, which is expressed in the distribution law: a × (b + c) = (a × b) + (a × c). These properties of addition and multiplication make the natural numbers an instance of a commutative semiring. Semirings are an algebraic generalization of the natural numbers where multiplication is not necessarily commutative. The lack of additive inverses, which is equivalent to the fact that N is not closed under subtraction (that is, subtracting one natural from another does not always result in another natural), means that N is not a ring; instead it is a semiring (also known as a rig).\n\nIf the natural numbers are taken as \"excluding 0\", and \"starting at 1\", the definitions of + and × are as above, except that they begin with a + 1 = S(a) and a × 1 = a.\n\n### Order\n\nIn this section, juxtaposed variables such as ab indicate the product a × b, and the standard order of operations is assumed.\n\nA total order on the natural numbers is defined by letting a b if and only if there exists another natural number c where a + c = b. This order is compatible with the arithmetical operations in the following sense: if a, b and c are natural numbers and a b, then a + c b + c and ac bc.\n\nAn important property of the natural numbers is that they are well-ordered: every non-empty set of natural numbers has a least element. The rank among well-ordered sets is expressed by an ordinal number; for the natural numbers, this is denoted as ? (omega).\n\n### Division\n\nIn this section, juxtaposed variables such as ab indicate the product a × b, and the standard order of operations is assumed.\n\nWhile it is in general not possible to divide one natural number by another and get a natural number as result, the procedure of division with remainder is available as a substitute: for any two natural numbers a and b with b ? 0 there are natural numbers q and r such that\n\na = bq + r      and      r < b.\n\nThe number q is called the quotient and r is called the remainder of the division of a by b. The numbers q and r are uniquely determined by a and b. This Euclidean division is key to several other properties (divisibility), algorithms (such as the Euclidean algorithm), and ideas in number theory.\n\n### Algebraic properties satisfied by the natural numbers\n\nThe addition (+) and multiplication (×) operations on natural numbers as defined above have several algebraic properties:\n\n• Closure under addition and multiplication: for all natural numbers a and b, both a + b and a × b are natural numbers.\n• Associativity: for all natural numbers a, b, and c, a + (b + c) = (a + b) + c and a × (b × c) = (a × b) × c.\n• Commutativity: for all natural numbers a and b, a + b = b + a and a × b = b × a.\n• Existence of identity elements: for every natural number a, a + 0 = a and a × 1 = a.\n• Distributivity of multiplication over addition for all natural numbers a, b, and c, a × (b + c) = (a × b) + (a × c).\n• No nonzero zero divisors: if a and b are natural numbers such that a × b = 0, then a = 0 or b = 0 (or both).\n\n## Generalizations\n\nTwo important generalizations of natural numbers arise from the two uses of counting and ordering: cardinal numbers and ordinal numbers.\n\n• A natural number can be used to express the size of a finite set; more precisely, a cardinal number is a measure for the size of a set, which is even suitable for infinite sets. This concept of \"size\" relies on maps between sets, such that two sets have the same size, exactly if there exists a bijection between them. The set of natural numbers itself, and any bijective image of it, is said to be countably infinite and to have cardinality aleph-null (?0).\n• Natural numbers are also used as linguistic ordinal numbers: \"first\", \"second\", \"third\", and so forth. This way they can be assigned to the elements of a totally ordered finite set, and also to the elements of any well-ordered countably infinite set. This assignment can be generalized to general well-orderings with a cardinality beyond countability, to yield the ordinal numbers. An ordinal number may also be used to describe the notion of \"size\" for a well-ordered set, in a sense different from cardinality: if there is an order isomorphism (more than a bijection!) between two well-ordered sets, they have the same ordinal number. The first ordinal number that is not a natural number is expressed as ?; this is also the ordinal number of the set of natural numbers itself.\n\nThe least ordinal of cardinality ?0 (that is, the initial ordinal of ?0) is ? but many well-ordered sets with cardinal number ?0 have an ordinal number greater than ?.\n\nFor finite well-ordered sets, there is a one-to-one correspondence between ordinal and cardinal numbers; therefore they can both be expressed by the same natural number, the number of elements of the set. This number can also be used to describe the position of an element in a larger finite, or an infinite, sequence.\n\nA countable non-standard model of arithmetic satisfying the Peano Arithmetic (that is, the first-order Peano axioms) was developed by Skolem in 1933. The hypernatural numbers are an uncountable model that can be constructed from the ordinary natural numbers via the ultrapower construction.\n\nGeorges Reeb used to claim provocatively that The naïve integers don't fill up N. Other generalizations are discussed in the article on numbers.\n\n## Formal definitions\n\n### Peano axioms\n\nMany properties of the natural numbers can be derived from the five Peano axioms:\n\n1. 0 is a natural number.\n2. Every natural number has a successor which is also a natural number.\n3. 0 is not the successor of any natural number.\n4. If the successor of $x$", null, "equals the successor of $y$", null, ", then $x$", null, "equals $y$", null, ".\n5. The axiom of induction: If a statement is true of 0, and if the truth of that statement for a number implies its truth for the successor of that number, then the statement is true for every natural number.\n\nThese are not the original axioms published by Peano, but are named in his honor. Some forms of the Peano axioms have 1 in place of 0. In ordinary arithmetic, the successor of $x$", null, "is $x+1$", null, ". Replacing axiom 5 by an axiom schema, one obtains a (weaker) first-order theory called Peano arithmetic.\n\n### Constructions based on set theory\n\n#### Von Neumann ordinals\n\nIn the area of mathematics called set theory, a specific construction due to John von Neumann defines the natural numbers as follows:\n\n• Set 0 = { }, the empty set,\n• Define S(a) = a ? {a} for every set a. S(a) is the successor of a, and S is called the successor function.\n• By the axiom of infinity, there exists a set which contains 0 and is closed under the successor function. Such sets are said to be inductive. The intersection of all such inductive sets is defined to be the set of natural numbers. It can be checked that the set of natural numbers satisfies the Peano axioms.\n• It follows that each natural number is equal to the set of all natural numbers less than it:\n• 0 = { },\n• 1 = 0 ? {0} = {0} = {{ }},\n• 2 = 1 ? {1} = {0, 1} = {{ }, {{ }}},\n• 3 = 2 ? {2} = {0, 1, 2} = {{ }, {{ }}, {{ }, {{ }}}},\n• n = n-1 ? {n-1} = {0, 1, ..., n-1} = {{ }, {{ }}, ..., {{ }, {{ }}, ...}}, etc.\n\nWith this definition, a natural number n is a particular set with n elements, and n m if and only if n is a subset of m. The standard definition, now called definition of von Neumann ordinals, is: \"each ordinal is the well-ordered set of all smaller ordinals.\"\n\nAlso, with this definition, different possible interpretations of notations like Rn (n-tuples versus mappings of n into R) coincide.\n\nEven if one does not accept the axiom of infinity and therefore cannot accept that the set of all natural numbers exists, it is still possible to define any one of these sets.\n\n#### Zermelo ordinals\n\nAlthough the standard construction is useful, it is not the only possible construction. Ernst Zermelo's construction goes as follows:\n\n• Set 0 = { }\n• Define S(a) = {a},\n• It then follows that\n• 0 = { },\n• 1 = {0} = {{ }},\n• 2 = {1} = {{{ }}},\n• n = {n-1} = {{{...}}}, etc.\nEach natural number is then equal to the set containing just the natural number preceding it. This is the definition of Zermelo ordinals. Unlike von Neumann's construction, the Zermelo ordinals do not account for infinite ordinals." ]

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[ "## 以当地货币和语言购买\n\n• 澳大利亚 / 澳元 \\$\n• 加拿大 / 加元 \\$\n• 中国 / 人民币 ¥\n• 法国 / 欧元 €\n• 德国 / 欧元 €\n• 香港 / 港元 \\$\n• 爱尔兰 / 欧元 €\n• 意大利 / 欧元 €\n• 日本 / 日元 ¥\n• 科威特 / 美元 \\$\n• 澳门 / 港元 \\$\n• 荷兰 / 欧元 €\n• 卡塔尔 / 美元 \\$\n• 沙特阿拉伯 / 美元 \\$\n• 新加坡 / 新加坡元 \\$\n• 韩国 / 韩元 ₩\n• 西班牙 / 欧元 €\n• 台湾 / 新台币 \\$\n• 阿拉伯联合酋长国 / 美元 \\$\n• 英国 / 英镑 £\n• 美国 / 美元 \\$\n• 不符合您的要求？阅读更多\n• 简体中文\n• 英语\n• 英语\n• 简体中文\n• 英语\n• 英语\n• 英语\n• 简体中文\n• 英语\n• 英语\n• 英语\n• 英语\n• 英语\n• 简体中文\n• 英语\n• 英语\n• 英语\n• 英语\n• 简体中文\n• 英语\n• 英语\n• 英语\n• 简体中文\n• 英语\n• 英语\n• 简体中文\n• 英语\n• 英语\n• 简体中文\n\n## 国际送货\n\nselfridges.com 上几乎所有的商品均可提供国际配送服务，您的订单可发往全世界 130 个国家/地区，包括北美、澳洲、中东及中国。\n\n• 阿尔及利亚\n• 安道尔\n• 安提瓜和巴布达\n• 阿鲁巴\n• 澳大利亚\n• 奥地利\n• 阿塞拜疆\n• 巴林\n• 孟加拉国\n• 巴巴多斯\n• 白俄罗斯\n• 比利时\n• 伯利兹\n• 百慕大\n• 玻利维亚\n• 博兹瓦纳\n• 文莱\n• 保加利亚\n• 柬埔寨\n• 加拿大\n• 开曼群岛\n• 智利\n• 中国大陆\n• 哥伦比亚\n• 哥斯达黎加\n• 克罗地亚\n• 塞浦路斯\n• 捷克共和国\n• 丹麦\n• 多米尼克\n• 多米尼加共和国\n• 厄瓜多尔\n• 埃及\n• 萨尔瓦多\n• 爱沙尼亚\n• 芬兰\n• 法国\n• 法属圭亚那\n• 德国\n• 直布罗陀\n• 希腊\n• 格林纳达\n• 瓜德罗普岛\n• 危地马拉\n• 根西岛\n• 圭亚那\n• 洪都拉斯\n• 香港\n• 匈牙利\n• 冰岛\n• 印度\n• 印度尼西亚\n• 爱尔兰\n• 以色列\n• 意大利\n• 牙买加\n• 日本\n• 泽西岛\n• 约旦\n• 哈萨克斯坦\n• 肯尼亚\n• 科威特\n• 老挝\n• 拉脱维亚\n• 黎巴嫩\n• 莱索托\n• 列支敦士登\n• 立陶宛\n• 卢森堡\n• 澳门\n• 马来西亚\n• 马尔代夫\n• 马耳他\n• 马提尼克岛\n• 马约特岛\n• 墨西哥\n• 摩纳哥\n• 蒙特塞拉特\n• 摩洛哥\n• 缅甸\n• 纳米比亚\n• 荷兰\n• 新西兰\n• 尼加拉瓜\n• 尼日利亚\n• 挪威\n• 阿曼\n• 巴基斯坦\n• 巴拿马\n• 巴拉圭\n• 秘鲁\n• 菲律宾\n• 波兰\n• 葡萄牙\n• 波多黎各\n• 卡塔尔\n• 留尼汪岛\n• 罗马尼亚\n• 卢旺达\n• 圣基茨与尼维斯\n• 圣卢西亚\n• 圣马丁岛（法属）\n• 圣马力诺\n• 沙特阿拉伯\n• 塞尔维亚\n• 新加坡\n• 斯洛伐克\n• 斯洛文尼亚\n• 南非\n• 韩国\n• 西班牙\n• 斯里兰卡\n• 苏里南\n• 斯威士兰\n• 瑞典\n• 瑞士\n• 台湾\n• 坦桑尼亚\n• 泰国\n• 特立尼达和多巴哥\n• 土耳其\n• 乌干达\n• 乌克兰\n• 阿拉伯联合酋长国\n• 英国\n• 美国\n• 乌拉圭\n• 委内瑞拉\n• 越南\n\n# OFF-WHITE C/O VIRGIL ABLOH 图案印花针织棉连帽衫\n\n#### 很抱歉！本款产品目前缺货\n\nOFF-WHITE C/O VIRGIL ABLOH 平纹针织棉帽衫\n100% 棉; 94% 棉, 6% 弹性纤维\n\n## 英国和欧洲\n\n\\$400.00\n• 无限英国定时、指定日和标准配送\n• 英国境内次日配送（英国时间下午 6 点前下单）\n• 无限欧盟地区标准配送\n• 免费退货\n• 无人购买的产品\n\n## 全球\n\n\\$1,545.00\n• 订单金额超过\\$ 1,545.00英国时间，指定日期和标准交货时间不受限制\n• 订单金额超过\\$ 1,545.00全球不限次数的送货" ]

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[ "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Can this ODE be solved?\n\n• To: mathgroup at smc.vnet.net\n• Subject: [mg15386] Can this ODE be solved?\n• From: Harry Kiesel <ghkiesel at mcs.drexel.edu>\n• Date: Tue, 12 Jan 1999 03:14:49 -0500\n• Sender: owner-wri-mathgroup at wolfram.com\n\n```mathgroup at smc.vnet.net\n\nHi Folks:\n\nMathematica 3.0 returned the following ODE unsolved. I beleive the\nsolution involves special functions.\n\nIs there a way of sloving this type of equation with Mathematica.\n\nThe equation is\n\n(t-t^3/4)*D[G[t],t,t]+(t^2/4+2*x*t)*D[G[t],t]+(x+t/4)*G[t]==0.\n\nThanks for any help.\n\nHarry Kiesel\n\n```\n\n• Prev by Date: save 3d-graphics as tiff\n• Next by Date: Strange results\n• Previous by thread: Re: save 3d-graphics as tiff\n• Next by thread: Re: Can this ODE be solved?" ]

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[ "Question about permutations and subsets\n\nConsider $n$ people who are attending a party. We assume that every person has an equal probability of being born on any day during the year, independently of everyone else, and ignore the additional complication presented by leap years (i.e., nobody is born on February $29$). What is the probability that each person has a distinct birthday?\n\nThe solution to this problem is $\\frac{365 \\cdot 364 \\cdot \\ldots \\cdot (365 - n + 1)}{365^n}$.\n\nI was wondering why the sample space contains birthday lists like $b_1b_2\\ldots b_n$. Why don't we choose $n$ places out of $365$ instead? I am not sure but to me it seems like the order shouldn't matter here.\n\n• I am not sure, but maybe this seems like one of those problems where saying order does matter gets you the same answer as saying order doesn't matter. – Noble Mushtak Dec 22 '16 at 20:44\n• Actually, after doing it where order doesn't matter, I got $\\frac{{365 \\choose n}}{{365+n-1 \\choose n}}$ which is not the same as the solution to the problem. The numerator is from choosing $n$ distinct birthdays from $365$ days without order and the denominator is by saying each day has $d_i$ people with that birthday, putting all of those numbers together to make a $365$-tuple, and then finding the number of tuples that sum to $n$ to represent $n$ peoples' birthdays. – Noble Mushtak Dec 22 '16 at 20:55\n• @NobleMushtak. Not only did you get rid of order, but you also got rid of sampling with replacement. So you can't possibly have birthday matches. Also, what year has $365 + n - 1$ distinguishable days? $(n > 1).$ – BruceET Dec 23 '16 at 2:19\n• @BruceET The numerator of my solution is the number of combinations for distinct birthdays. The denominator of my solution is found by saying each day has non-negative people with that day as their birthday and that the sum of the number of people for each day is $n$ since there are $n$ people total. Since there are $365$ days, this is like finding the number of $365$-tuples that sum to $n$, so I used stars-and-bars to get $365+n-1 \\choose n$. – Noble Mushtak Dec 23 '16 at 17:39\n\nBirthday Problem. This is the famous 'birthday problem' or, because some people find the answer surprising 'birthday paradox'. There are lots of links to it on this site and elsewhere on the Internet, so I will get right to the point, and just try to answer your specific question.\n\nOften when sampling is 'with replacement' it is more convenient to look at ordered outcomes. The birthday problem clearly involves sampling with replacement because it is possible for a birthday to be selected more than once.\n\nThere are many problems that can be answered with either ordered or unordered samples. The important thing is that if you are using ordered samples in the denominator (to count outcomes in the whole sample space), you must also use ordered samples in the the numerator (to count 'favorable' outcomes). In the birthday problem it is especially easy to use a sample space with $365^n$ ordered samples in the denominator, so it is natural to start with that and, accordingly, to use ordered samples in the numerator.\n\nUrn Problem. Here is a problem in which you can use either ordered or unordered outcomes: I have an urn containing 5 balls, 3 red and 2 green. I withdraw two balls without replacement. What is the probability I get two balls of the same color:\n\nOrdered (permutations).\n\nCount all ordered outcomes in denominator: $5(4) = 20.$\n\nNumerator. Ways with two red: $3(2) = 6.$ Ways with two green: 2(1) = 2.\n\nAnswer. $(6+2)/20 = 2/5$\n\nUnordered (combinations).\n\nDenominator: ${5 \\choose 2} = 10.$\n\nNumerator: Both red: ${3 \\choose 2}{2 \\choose 0} = 3.$ Both green: ${2 \\choose 2}{3 \\choose 0} = 1.$\n\nAnswer: $(3 + 1)/10 = 2/5.$\n\nHowever, suppose my task to find the probability that I choose a red ball and then a green ball. This new problem involves order, and I have no choice but to use ordered outcomes throughout: $6/20 = 3/10.$\n\nProblem with solution based on combination, is that it cannot \"see\" orderings. Consider very simple example: two coin flips. What is probability of event $A_1$, that two flips will be different? One reasoning is with orderings: first and second flip. There are $\\#\\Omega_1=2^2$ possibilities.First flip can be arbitrary - hence 2 options, but the second has to be opposed. Thus $\\#A_1=2*1$, and the probability $P(A_1) = \\frac{\\#A_1}{\\#\\Omega_1}=\\frac{2*1}{2^2}$. Now second approach: we don't worry about orderings, there are only three possibilities: two heads, two tails, or head and tail - $\\#\\Omega_2=3$ and $\\#A_2=1$ ($A$ is elementary event). You could rather guess probability, but lets apply equations: $P(A_2)=\\frac{\\binom{2}{2}}{\\binom{2+2-1}{1}}=\\frac{1}{3}$. Why there are different results? Because in first approach event \"different flips\" has probability $\\frac{1}{2}$ - bigger than for example \"two heads\", $\\frac{1}{4}$. In second approach all three events have the same probability, because they are elementary events.\n\nNow all to be done is to see that above example and your problem are in principle the same. To help you understand similarity: consider $n=3$ in birth problem. Take \"ordering approach\", $\\#\\Omega=365^3$. Let event $A$ means \"every person has distinct birthday: 1st, 2nd and 3rd Jan\", and $B$ - \"two persons have 1st Feb as birthday, and one person has birthday at 2nd Feb\". We can distinct (permute) those persons in our approach, so $P(A)=\\frac{3!}{365^3}=\\frac{6}{365^3}$ and in $B$ it is sufficient to decite which person has birthday at 2nd Feb $P(B)=\\frac{\\binom{3}{1}}{365^3}=\\frac{3}{365^3}$. Ok, so in this approach event (set) $A$ has six elementary events (elements) and $B$ has three. Now final part: in second approach where no person is distinguished, there is only one possibility to have three persons' birthdays at three different, fixed days; $\\#A'=1$, but $\\#B'=1$ as well! That is why $P(A')=\\frac{1}{\\binom{365+3-1}{3}}\\neq P(A)=\\frac{3!}{365^3}$.\n\nIn practice you have to use intuition and experience from similar exercises to decide about wheter to use ordering, but thumb rule is: if you have regular combinations, both approaches should give correct result, but using combination with repetition $\\binom{n+k-1}{k}$ is subtle and can give different results.\n\nNote: By $elementary\\ events$ I mean elements, or singletons of probability space, $event$ is always a subset. I assume, that all elementary events have the same probability (the same mass).\n\n... it seems like the order shouldn't matter here\n\nQuite right. The birthdays are really assigned independently at random to each of the people. Because the order doesn't matter, and all are equivalent, we can choose to regard the birthdays as being assigned in a sequence, any sequence. This enables us to work out the chances easily." ]

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[ "# Introduction\n\nA recurrent neural network (RNN) is a class of artificial neural networks where connections between nodes form a directed graph along a temporal sequence. This allows it to exhibit temporal dynamic behavior. Derived from feedforward neural networks.\n\nLong short-term memory (LSTM) is an artificial recurrent neural network architecture used in the field of deep learning. Unlike standard feedforward neural networks, LSTM has feedback connections. It can not only process single data points, but also entire sequences of data.\n\nplease refer to the below links for an in-depth explanation of LSTMs\n\nhttps://colah.github.io/posts/2015-08-Understanding-LSTMs/\n\nhttp://karpathy.github.io/2015/05/21/rnn-effectiveness/\n\n# Dataset\n\nThe dataset used here is the Apple stock price which you can get on yahoo finance here you can change the time period of the dataset according to your purpose and download it. The model is trained on the stock data from 3rd January 2017 to 31st December 2020. Our plan of attack is to take the stock price of 3rddays and try to predict the stock price for every 4rth day.\n\n`df=pd.read_csv('AAPL.csv')df.head()`\n\nThere are 1006 rows in our dataset, we have divided it into 65% containing training sample and the rest 35% as the testing sample. The plot given below contains Training sample in blue color and testing in green color.\n\n`plt.figure(figsize=(20,8))plt.plot(df.Close[:654],color='blue',label='Training data')plt.plot(df.Close[654:1006],color='g',label='Testing data')plt.xlabel('time')plt.ylabel('Stock Price')plt.title('Training and Testing Stock price')plt.legend()plt.show()`\n\n# Data Preprocessing\n\n1. Feature Scaling\n\nFeature Scaling is an important step of data preprocessing, If feature scaling is not performed, a machine learning algorithm would consider larger values to be higher and smaller values to be lower, regardless of the unit of measurement. The scaler used here is the Traditional MinMax Scaler. Minmax scaler Transform features by scaling each feature to a given range[0,1].\n\n`from sklearn.preprocessing import MinMaxScalersc=MinMaxScaler(feature_range=(0,1))df=sc.fit_transform(np.array(df).reshape(-1,1))df`\n\n2. Splitting the Data\n\nSplitting our dataset into 65% of train data and the remaining 35% of test sample\n\nSince our dataset contains 1006 rows therefore 654 rows for the training sample and the rest 352 rows for the testing sample\n\n`##splitting dataset into train and test splittraining_size=int(len(df1)*0.65)test_size=len(df1)-training_sizetrain_data,test_data=df1[0:training_size,:],df1[training_size:len(df1),:1]`\n\n3. Preparing the Data for our model\n\nSince we want to predict the stock price at a future time. We’ll predict the stock price at time t+1 relative to the stock price at time t. LSTM Architecture's memory is maintained by setting the time step, basically how many steps in the past we want the LSTM model to use\n\nThis time step could be any number say 3..4 or 50 or 60.\n\n`## We are going to take previous 3 days stock price and predict ##the price on the 4rth day hence time_step=3def create_dataset(dataset, time_step=3): dataX, dataY = [], []for i in range(len(dataset)-time_step-1): a = dataset[i:(i+time_step), 0] dataX.append(a) dataY.append(dataset[i + time_step, 0])return np.array(dataX), np.array(dataY)time_step =100X_train, y_train = create_dataset(train_data, time_step)X_test, y_test = create_dataset(test_data, time_step)print(X_train)`\n\nIn an LSTM network the input for each layer needs to contain the following information:\n\n1. The number of observation\n\n2. The time steps\n\n3. The numerical features\n\nTherefore we need to add a temporal dimension compared to a classical network\n\n`##reshape input to be [samples, time steps, features] which is required for LSTMX_train =X_train.reshape(X_train.shape,X_train.shape , 1)X_test = X_test.reshape(X_test.shape,X_test.shape , 1)`\n\nTherefore our Model would contain 650 training samples and the rest 349 testing sample\n\n# Building the Model\n\nA Stacked LSTM architecture can be defined as an LSTM model comprised of multiple LSTM layers. An LSTM layer above provides a sequence output rather than a single value output to the LSTM layer below. Specifically, one output per input time step, rather than one output time step for all input time steps.\n\n`from keras.models import Sequentialfrom keras.layers import LSTM, Dense`\n\nAfter Hyperparameter tuning we can build our model with 4 LSTM layers each containing the units 50,100,150,200 and a return function of true to pass the updated weight from one neuron to another also our model would contain dropout to reduce the overfitting, we would use adam optimizer and a loss function of mean_squared_error.\n\n`## First layermodel=Sequential()model.add(LSTM(units=50,input_shape=(X_train.shape,X_train.shape),return_sequences=True))model.add(Dropout(0.2))## Second Layermodel.add(LSTM(units= 100,return_sequences=True))model.add(Dropout(0.4))## Third layermodel.add(LSTM(units= 150,return_sequences=True))model.add(Dropout(0.5))## Fourth layermodel.add(LSTM(units= 200,return_sequences=False))model.add(Dropout(0.6))## Output Layermodel.add(Dense(units=1))model.compile(optimizer='adam',loss='mean_squared_error')model.summary()`\n`model.fit(X_train,y_train,epochs=100,batch_size=64,validation_data=(X_test,y_test),verbose=1)`\n\n# Model Evaluation\n\nWe can evaluate our model accuracy by plotting the predicted price of our model and the actual price\n\n`plt.figure(figsize=(20,6))plt.plot(y_test, color='r',label='Real Price')plt.plot(test_predict,color='g',label='Predicted Price')plt.title('Stock Price Prediction')plt.xlabel('Time')plt.ylabel('Stock Price')plt.legend()plt.show()`\n\nThe red color plot is the actual price for those 349 rows and the green color plot is the predicted price for those 349 rows. We can see that our predicted price has performed better and has predicted exact values at some places. Our model can also detect sharp increases or decreases in the price correctly. We can further tune our model by changing the hyperparameter but that’s another story for another time.\n\n# Resources\n\n1. https://colah.github.io/posts/2015-08-Understanding-LSTMs/" ]

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[ "Počet záznamů: 1\n\n# Peeling Potatoes Near-optimally in Near-linear Time\n\n1. 1.\n0478998 - UIVT-O 2018 RIV US eng J - Článek v odborném periodiku\nCabello, S. - Cibulka, J. - Kynčl, J. - Saumell, Maria - Valtr, P.\nPeeling Potatoes Near-optimally in Near-linear Time.\nSiam Journal on Computing. Roč. 46, č. 5 (2017), s. 1574-1602. ISSN 0097-5397\nGrant CEP: GA ČR GBP202/12/G061\nGrant ostatní:GA MŠk(CZ) LO1506; GA MŠk(CZ) EE2.3.30.0038\nInstitucionální podpora: RVO:67985807\nKlíčová slova: geometric optimization * potato peeling * visibility graph * geometric probability * approximation algorithm\nKód oboru RIV: BA - Obecná matematika\nObor OECD: Pure mathematics\nImpakt faktor: 0.902, rok: 2017\n\nWe consider the following geometric optimization problem: find a convex polygon of maximum area contained in a given simple polygon $P$ with $n$ vertices. We give a randomized near-linear-time $(1-\\varepsilon)$-approximation algorithm for this problem: in $O(n( \\log^2 n + (1/\\varepsilon^3) \\log n + 1/\\varepsilon^4))$ time we find a convex polygon contained in $P$ that, with probability at least $2/3$, has area at least $(1-\\varepsilon)$ times the area of an optimal solution. We also obtain similar results for the variant of computing a convex polygon inside $P$ with maximum perimeter. To achieve these results we provide new results in geometric probability. The first result is a bound relating the area of the largest convex body inside $P$ to the probability that two points chosen uniformly at random inside $P$ are mutually visible. The second result is a bound on the expected value of the difference between the perimeter of any planar convex body $K$ and the perimeter of the convex hull of a uniform random sample inside $K$.\nTrvalý link: http://hdl.handle.net/11104/0275024" ]

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[ "Combine files generated by redist.flip.anneal()\n\nredist.combine.anneal(file_name)\n\n## Arguments\n\nfile_name\n\nThe file name to search for in current working directory.\n\n## Value\n\nredist.combine.anneal returns an object of class \"redist\". The object redist is a list that contains the following components (the inclusion of some components is dependent on whether tempering techniques are used):\n\nplans\n\nMatrix of congressional district assignments generated by the algorithm. Each row corresponds to a geographic unit, and each column corresponds to a simulation.\n\ndistance_parity\n\nVector containing the maximum distance from parity for a particular simulated redistricting plan.\n\nmhdecisions\n\nA vector specifying whether a proposed redistricting plan was accepted (1) or rejected (0) in a given iteration.\n\nmhprob\n\nA vector containing the Metropolis-Hastings acceptance probability for each iteration of the algorithm.\n\npparam\n\nA vector containing the draw of the p parameter for each simulation, which dictates the number of swaps attempted.\n\nconstraint_pop\n\nA vector containing the value of the population constraint for each accepted redistricting plan.\n\nconstraint_compact\n\nA vector containing the value of the compactness constraint for each accepted redistricting plan.\n\nconstraint_segregation\n\nA vector containing the value of the segregation constraint for each accepted redistricting plan.\n\nconstraint_vra\n\nA vector containing the value of the vra constraint for each accepted redistricting plan.\n\nconstraint_similar\n\nA vector containing the value of the similarity constraint for each accepted redistricting plan.\n\nconstraint_partisan\n\nA vector containing the value of the partisan constraint for each accepted redistricting plan.\n\nconstraint_minority\n\nA vector containing the value of the minority constraint for each accepted redistricting plan.\n\nconstraint_hinge\n\nA vector containing the value of the hinge constraint for each accepted redistricting plan.\n\nconstraint_qps\n\nA vector containing the value of the QPS constraint for each accepted redistricting plan.\n\nbeta_sequence\n\nA vector containing the value of beta for each iteration of the algorithm. Returned when tempering is being used.\n\nmhdecisions_beta\n\nA vector specifying whether a proposed beta value was accepted (1) or rejected (0) in a given iteration of the algorithm. Returned when tempering is being used.\n\nmhprob_beta\n\nA vector containing the Metropolis-Hastings acceptance probability for each iteration of the algorithm. Returned when tempering is being used." ]

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[ "## 46060\n\n46,060 (forty-six thousand sixty) is an even five-digits composite number following 46059 and preceding 46061. In scientific notation, it is written as 4.606 × 104. The sum of its digits is 16. It has a total of 6 prime factors and 36 positive divisors. There are 15,456 positive integers (up to 46060) that are relatively prime to 46060.\n\n## Basic properties\n\n• Is Prime? No\n• Number parity Even\n• Number length 5\n• Sum of Digits 16\n• Digital Root 7\n\n## Name\n\nShort name 46 thousand 60 forty-six thousand sixty\n\n## Notation\n\nScientific notation 4.606 × 104 46.06 × 103\n\n## Prime Factorization of 46060\n\nPrime Factorization 22 × 5 × 72 × 47\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 4 Total number of distinct prime factors Ω(n) 6 Total number of prime factors rad(n) 3290 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0\n\nThe prime factorization of 46,060 is 22 × 5 × 72 × 47. Since it has a total of 6 prime factors, 46,060 is a composite number.\n\n## Divisors of 46060\n\n1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 47, 49, 70, 94, 98, 140, 188, 196, 235, 245, 329, 470, 490, 658, 940, 980, 1316, 1645, 2303, 3290, 4606, 6580, 9212, 11515, 23030, 46060\n\n36 divisors\n\n Even divisors 24 12 6 6\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 36 Total number of the positive divisors of n σ(n) 114912 Sum of all the positive divisors of n s(n) 68852 Sum of the proper positive divisors of n A(n) 3192 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 214.616 Returns the nth root of the product of n divisors H(n) 14.4298 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 46,060 can be divided by 36 positive divisors (out of which 24 are even, and 12 are odd). The sum of these divisors (counting 46,060) is 114,912, the average is 3,192.\n\n## Other Arithmetic Functions (n = 46060)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 15456 Total number of positive integers not greater than n that are coprime to n λ(n) 1932 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 4766 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares\n\nThere are 15,456 positive integers (less than 46,060) that are coprime with 46,060. And there are approximately 4,766 prime numbers less than or equal to 46,060.\n\n## Divisibility of 46060\n\n m n mod m 2 3 4 5 6 7 8 9 0 1 0 0 4 0 4 7\n\nThe number 46,060 is divisible by 2, 4, 5 and 7.\n\n• Arithmetic\n• Abundant\n\n• Polite\n• Practical\n\n## Base conversion (46060)\n\nBase System Value\n2 Binary 1011001111101100\n3 Ternary 2100011221\n4 Quaternary 23033230\n5 Quinary 2433220\n6 Senary 553124\n8 Octal 131754\n10 Decimal 46060\n12 Duodecimal 227a4\n20 Vigesimal 5f30\n36 Base36 zjg\n\n## Basic calculations (n = 46060)\n\n### Multiplication\n\nn×i\n n×2 92120 138180 184240 230300\n\n### Division\n\nni\n n⁄2 23030 15353.3 11515 9212\n\n### Exponentiation\n\nni\n n2 2121523600 97717377016000 4500862385356960000 207309721469541577600000\n\n### Nth Root\n\ni√n\n 2√n 214.616 35.8461 14.6498 8.56377\n\n## 46060 as geometric shapes\n\n### Circle\n\n Diameter 92120 289404 6.66496e+09\n\n### Sphere\n\n Volume 4.09318e+14 2.66599e+10 289404\n\n### Square\n\nLength = n\n Perimeter 184240 2.12152e+09 65138.7\n\n### Cube\n\nLength = n\n Surface area 1.27291e+10 9.77174e+13 79778.3\n\n### Equilateral Triangle\n\nLength = n\n Perimeter 138180 9.18647e+08 39889.1\n\n### Triangular Pyramid\n\nLength = n\n Surface area 3.67459e+09 1.15161e+13 37607.8\n\n## Cryptographic Hash Functions\n\nmd5 2a384b15e8016b260de6ef70a54dbd22 2ca789c1e56b18980fc2347492d1ae05282c0328 29f72c6fdb10ece738ace47897c93d1421c93b1b816282da855d6a4b3bec1835 b6be11f61a58c51da97df343459d49eb9a5d8d260232b2c8b5d41f6ab0bf72a6b10d1bdb4e2e073c9cc68b0bfc840a0d62c5d1c9a640a79d11f09560e7573a75 0fc53ff93e5c3b6cfe039690c3ab5646c4f35f4b" ]

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[ "# When will acid-base reactions occur before substitution reaction\n\nFor example, given the reaction below:", null, "The substrate is secondary, the solvent is aprotic and it is to react with a strong bulky base. From this, I assumed that the reaction would be $$\\ce{E2}$$. However, it instead begins with an acid-base reaction where the tert-butoxide removes the proton of hydroxide and then proceeds with a $$\\ce{Sn1}$$ reaction where the oxygen attacks the carbon of the leaving group to form an epoxide.\n\nHow can you determine if an acid-base reaction will take place before proceeding with a substitution reaction?" ]

[ null, "https://i.stack.imgur.com/s9ZnT.png", null ]

[ "", null, "Geometry\n\n# Length and Area Warmup\n\nIf each of the side lengths of a triangle triples, then the perimeter will:\n\nIs this statement true or false?\n\nIf the length and width of a rectangle double, then the area will double.", null, "If all circular pieces shown are semicircles and quarter circles, what is the area of the yellow region?", null, "Bo draws a 1-by-1 square (green). He begins a spiral by adding on a 2-by-1 rectangle (blue), then a 3-by-1 rectangle (pink), etc. Each rectangle is one unit longer than the previous rectangle added. What will be the perimeter of the spiral after the 8th rectangle is added?", null, "If the perimeter of Figure #1 is 12, what is the perimeter of the Figure #10?\n\n×" ]

[ null, "https://ds055uzetaobb.cloudfront.net/brioche/chapter/stolen%20calc%20area-GvaE8I.png", null, "https://ds055uzetaobb.cloudfront.net/brioche/uploads/8QRbqhbdmL-5e65e3cac6bdd82772d229ac2722af5346f8b610.png", null, "https://ds055uzetaobb.cloudfront.net/brioche/solvable/2a9b37250c.1d89a2ffef.pfptWr.png", null, "https://ds055uzetaobb.cloudfront.net/brioche/solvable/2a9b37250c.fb98339d96.yMtOWC.png", null ]

[ "# Testi I Matures-matematike\n\nApproved & Edited by ProProfs Editorial Team\nThe editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.\n| By Faton1\nF\nFaton1\nCommunity Contributor\nQuizzes Created: 1 | Total Attempts: 3,146\nPyetjet: 50 | Attempts: 3,149", null, "", null, "Settings", null, "", null, "TESTI I MATURËS-MATEMATIKË( ONLINE )50 detyraKoha 60 minutaPërgatiti: Faton HyseniMaj 2016\n\n• 1.\n\n### Janë dhënë bashkësitë  Prerja e tyre është bashkësia :\n\n• A.\n\n(-5,6]\n\n• B.\n\n(1,2]\n\n• C.\n\n[1,2]\n\n• D.\n\n(2,6]\n\nB. (1,2]\nExplanation\nThe correct answer is (1,2]. The given options represent different intervals. The interval (1,2] includes all real numbers greater than 1 and less than or equal to 2. It does not include the endpoints 1 and 2. Therefore, the set of numbers that satisfy the condition \"Janë dhënë bashkësia\" is the interval (1,2].\n\nRate this question:\n\n• 2.\n\n### Janë dhënë bashkësitë   dhe  . Numri i elementeve të   është :\n\n• A.\n\n4\n\n• B.\n\n5\n\n• C.\n\n6\n\n• D.\n\n7\n\nB. 5\nExplanation\nThe given question is incomplete and not readable, so it is not possible to generate an explanation for the correct answer.\n\nRate this question:\n\n• 3.\n\n### Nga barazimi  rrjedh që vlera e x-it është :\n\n• A.\n\n3\n\n• B.\n\n4\n\n• C.\n\n5\n\n• D.\n\n6\n\nD. 6\nExplanation\nThe given options suggest that the value of x is equal to 6.\n\nRate this question:\n\n• 4.\n\n### Nëse x-2=5, atëherë x2-4 është :\n\n• A.\n\n15\n\n• B.\n\n25\n\n• C.\n\n35\n\n• D.\n\n45\n\nD. 45\nExplanation\nIf x-2=5, then x=7. Substituting this value of x into x^2-4, we get 7^2-4=49-4=45. Therefore, the value of x^2-4 is 45.\n\nRate this question:\n\n• 5.\n\n### 20% e numrit 250 është :\n\n• A.\n\n5000\n\n• B.\n\n500\n\n• C.\n\n50\n\n• D.\n\n5\n\nC. 50\nExplanation\n20% of a number can be found by multiplying the number by 0.2. In this case, 20% of 250 is 250 * 0.2 = 50. Therefore, the correct answer is 50.\n\nRate this question:\n\n• 6.\n\n### Vlera e shprehjes  është :\n\n• A.\n\n8\n\n• B.\n\n6\n\n• C.\n\n4\n\n• D.\n\n2\n\nD. 2\nExplanation\nThe given expression evaluates to 2.\n\nRate this question:\n\n• 7.\n\n### Numri  është i barabartë me:\n\n• A.\n\n2\n\n• B.\n\n4\n\n• C.\n\n8\n\n• D.\n\n16\n\nC. 8\nExplanation\nThe given sequence is a geometric progression where each term is obtained by multiplying the previous term by 2. Starting from 2, the next term is 2 * 2 = 4, then 4 * 2 = 8, and so on. Therefore, the number that is equal to 8 in the sequence is the correct answer.\n\nRate this question:\n\n• 8.\n\n### Vlera e shprehjes  është :\n\n• A.\n\n5\n\n• B.\n\n1\n\n• C.\n\n0\n\n• D.\n\n-1\n\nD. -1\nExplanation\nThe given expression has only one value, which is -1.\n\nRate this question:\n\n• 9.\n\nB.\n• 10.\n\n### Nëse . Atëherë  është :\n\n• A.\n\n0\n\n• B.\n\n4\n\n• C.\n\n8\n\n• D.\n\n-16\n\nD. -16\nExplanation\nThe given sequence is a pattern of subtracting 4 from each number. Starting from 0, when we subtract 4, we get -4. Continuing this pattern, we subtract 4 from -4 to get -8, and then subtract 4 from -8 to get -12. Finally, subtracting 4 from -12 gives us -16, which is the next number in the sequence.\n\nRate this question:\n\n• 11.\n\n### Inekuacioni  është i njëvlershëm me :\n\n• A.\n\nX\n\n• B.\n\nX>3\n\n• C.\n\nX\n\n• D.\n\nX>-3\n\nB. X>3\nExplanation\nThe given inequality states that \"x is greater than 3\". This means that any value of x that is greater than 3 will satisfy the inequality. Therefore, the correct answer is x>3.\n\nRate this question:\n\n• 12.\n\n• A.\n\n-4\n\n• B.\n\n-3\n\n• C.\n\n2\n\n• D.\n\n3\n\nD. 3\n• 13.\n\nC.\n• 14.\n\n### Vlera e palejueshme e x-it në shprehjen  është :\n\n• A.\n\n1\n\n• B.\n\n3\n\n• C.\n\n6\n\n• D.\n\n9\n\nB. 3\nExplanation\nThe given options are numbers, and the question asks for the \"infinite value of x\" in the expression. Among the given options, only 3 is a number that can be considered as an \"infinite value\" in certain contexts. Therefore, the correct answer is 3.\n\nRate this question:\n\n• 15.\n\n### Prodhimi i rrënjëve reale të ekuacionit  është i barabartë me :\n\n• A.\n\n-5\n\n• B.\n\n5\n\n• C.\n\n6\n\n• D.\n\n30\n\nC. 6\nExplanation\nThe production of real roots of an equation is equal to 6.\n\nRate this question:\n\n• 16.\n\n### Ekuacioni  ka dy rrënjë reale të barabarta. Vlera e m është :\n\n• A.\n\n1\n\n• B.\n\n2\n\n• C.\n\n3\n\n• D.\n\n4\n\nD. 4\nExplanation\nThe equation has two equal real roots, and the value of m is 4.\n\nRate this question:\n\n• 17.\n\n### Vlera e shprehjes  është :\n\n• A.\n\n-1\n\n• B.\n\n0\n\n• C.\n\n1\n\n• D.\n\n2\n\nB. 0\nExplanation\nThe given expression evaluates to 0.\n\nRate this question:\n\n• 18.\n\n### Vlera  është :\n\n• A.\n\n2\n\n• B.\n\n4\n\n• C.\n\n6\n\n• D.\n\n8\n\nA. 2\nExplanation\nThe given sequence is an arithmetic progression with a common difference of 2. Each term is obtained by adding 2 to the previous term. Therefore, the next term in the sequence would be 10. However, since the answer options are limited to 2, 4, 6, and 8, the correct answer is 2, which is the next term in the sequence.\n\nRate this question:\n\n• 19.\n\n### Është dhënë . Vlera e -së është :\n\n• A.\n\n1\n\n• B.\n\n0\n\n• C.\n\n-1\n\n• D.\n\n-2\n\nA. 1\nExplanation\nThe given correct answer is 1.\n\nRate this question:\n\n• 20.\n\nA.\n• 21.\n\n### Është dhënë progresioni aritmetik me kufizën e parë 2 dhe me diferencë të progresionit 3. Kufiza e dhjetë e tij është :\n\n• A.\n\n10\n\n• B.\n\n29\n\n• C.\n\n30\n\n• D.\n\n45\n\nB. 29\nExplanation\nThe given arithmetic progression has a common difference of 3 and a first term of 2. To find the limit of the progression, we can use the formula for the nth term of an arithmetic progression: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.\n\nPlugging in the values, we have a limit of a1 + (n-1)d = 2 + (n-1)3 = 3n - 1. Since we are looking for the limit, we set n to infinity. Therefore, the limit of the progression is 3(infinity) - 1, which is infinity.\n\nTherefore, the correct answer is 29, as it is the only option that represents infinity.\n\nRate this question:\n\n• 22.\n\n### Tri kufizat e para të një progresioni aritmetik janë 8, 13, x-2 . Vlera e x-it është :\n\n• A.\n\n5\n\n• B.\n\n10\n\n• C.\n\n15\n\n• D.\n\n20\n\nD. 20\nExplanation\nThe given sequence is an arithmetic progression with a common difference of 5. The first term is 8, the second term is 13, and the third term is x-2. To find the value of x, we can use the formula for the nth term of an arithmetic progression: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference. Plugging in the values, we have x-2 = 8 + (3-1)5. Simplifying the equation, we get x-2 = 8 + 10, which gives x = 20.\n\nRate this question:\n\n• 23.\n\n### Mesatarja aritmetike e numrave 2, 4, 7, 9, 13 është :\n\n• A.\n\n7\n\n• B.\n\n8\n\n• C.\n\n9\n\n• D.\n\n10\n\nA. 7\nExplanation\nThe arithmetic mean of a set of numbers is found by adding up all the numbers in the set and then dividing the sum by the total number of numbers. In this case, the set of numbers is 2, 4, 7, 9, 13. Adding up these numbers gives us a sum of 35. Since there are 5 numbers in the set, we divide the sum by 5 to find the arithmetic mean. Therefore, the arithmetic mean of the given set of numbers is 7.\n\nRate this question:\n\n• 24.\n\n### Moda në vargun e numrave 2,2,3,3,3,3,4,4,5,5,5 është\n\n• A.\n\n2\n\n• B.\n\n3\n\n• C.\n\n4\n\n• D.\n\n5\n\nB. 3\nExplanation\nThe correct answer is 3 because it is the number that appears most frequently in the given list of numbers.\n\nRate this question:\n\n• 25.\n\n### Koeficienti këndor i drejtëzës 2x-y+5=0 është :\n\n• A.\n\n1\n\n• B.\n\n2\n\n• C.\n\n3\n\n• D.\n\n5\n\nB. 2\nExplanation\nThe given equation is in the form of a linear equation, which can be written as 2x - y + 5 = 0. The coefficient of x in this equation is 2, which is the slope of the line represented by this equation. Therefore, the correct answer is 2.\n\nRate this question:\n\n• 26.\n\n### Drejtëza 2x-3y+6=0 e pret boshtin Ox në pikën e abshisës :\n\n• A.\n\n-3\n\n• B.\n\n0\n\n• C.\n\n2\n\n• D.\n\n3\n\nA. -3\nExplanation\nThe given equation of the line represents a straight line in the form of Ax + By + C = 0. Here, A = 2, B = -3, and C = 6. To find the x-coordinate of the point where the line intersects the x-axis, we set y = 0 in the equation and solve for x. Plugging in y = 0, we get 2x + 6 = 0, which simplifies to x = -3. Therefore, the line intersects the x-axis at the point (-3, 0), and the x-coordinate of this point is -3.\n\nRate this question:\n\n• 27.\n\n### Pikat A(1,0), B(2,0) dhe C(3, 0) janë pikat e një :\n\n• A.\n\nParabole\n\n• B.\n\nRrethi\n\n• C.\n\nDrejtëze\n\n• D.\n\nHiperbole\n\nB. Rrethi\nExplanation\nThe given points A(1,0), B(2,0), and C(3,0) form a straight line on the x-axis. Since a circle is defined as a set of points equidistant from a center point, and these points do not meet that criteria, the correct answer is not a circle. Therefore, the correct answer is not a parabola, hyperbola, or circle. The only remaining option is a straight line, so the correct answer is a straight line.\n\nRate this question:\n\n• 28.\n\n### Janë dhënë pikat A(-1,2) dhe B(1,4). Pika C është mesi i segmentit AB.Ordinata e pikës C është :\n\n• A.\n\n1\n\n• B.\n\n2\n\n• C.\n\n3\n\n• D.\n\n4\n\nC. 3\nExplanation\nThe point C is the midpoint of the line segment AB. To find the coordinates of the midpoint, we take the average of the x-coordinates and the average of the y-coordinates of points A and B. The x-coordinate of point C is (-1+1)/2 = 0. The y-coordinate of point C is (2+4)/2 = 3. Therefore, the ordinate of point C is 3.\n\nRate this question:\n\n• 29.\n\n### Syprina e rrethit me perimetër  është :\n\nD.\nExplanation\nThe explanation for the correct answer is not available.\n\nRate this question:\n\n• 30.\n\n### Perimetri i një katrori është 16cm. Diametri i rrethit të brendashkruar të tij është :\n\n• A.\n\n4cm\n\n• B.\n\n6cm\n\n• C.\n\n8cm\n\n• D.\n\n10cm\n\nA. 4cm\nExplanation\nPër lehtësim vizatoni figurën.\n\nRate this question:\n\n• 31.\n\n### Vektorët  dhe  gëzojnë vetinë që :\n\n• A.\n\nKanë gjatësi të barabartë\n\n• B.\n\nJanë paralel\n\n• C.\n\nJanë pingul\n\n• D.\n\nJanë të barabartë\n\nB. Janë paralel\nExplanation\nThe correct answer is \"Janë paralel\" which means \"They are parallel\" in English. This suggests that the vectors in question have the same direction and will never intersect or meet.\n\nRate this question:\n\n• 32.\n\n• A.\n\n4\n\n• B.\n\n3\n\n• C.\n\n2\n\n• D.\n\n1\n\nC. 2\n• 33.\n\n• A.\n\n2\n\n• B.\n\n4\n\n• C.\n\n8\n\n• D.\n\n64\n\nB. 4\n• 34.\n\n### Është dhënë koni i drejtë rrethor me lartësi 6cm dhe përftuese 10cm. Rrezja e bazës së konit është :\n\n• A.\n\n2cm\n\n• B.\n\n4cm\n\n• C.\n\n6cm\n\n• D.\n\n8cm\n\nD. 8cm\nExplanation\nThe height of the cone is given as 6cm and the slant height is given as 10cm. To find the radius of the base, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle, with the height as one side and the radius as the other side. So, we can set up the equation as follows: (radius)^2 + (height)^2 = (slant height)^2. Plugging in the given values, we get (radius)^2 + 6^2 = 10^2. Simplifying the equation, we get (radius)^2 + 36 = 100. Subtracting 36 from both sides, we get (radius)^2 = 64. Taking the square root of both sides, we get radius = 8. Therefore, the radius of the cone is 8cm.\n\nRate this question:\n\n• 35.\n\n• A.\n\n81\n\n• B.\n\n90\n\n• C.\n\n100\n\n• D.\n\n110\n\nA. 81\n• 36.\n\n### Numri i grupeve treshe që mund të formohen me pesë libra të ndryshëm është:\n\n• A.\n\n3\n\n• B.\n\n5\n\n• C.\n\n10\n\n• D.\n\n20\n\nC. 10\nExplanation\nThere are a total of 10 different groups of three that can be formed from five different books. This can be calculated using the combination formula, which is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be selected. In this case, n = 5 and r = 3, so the calculation is 5! / (3!(5-3)!) = 5! / (3!2!) = (5x4x3x2x1) / (3x2x1x2x1) = 10. Therefore, there are 10 different groups of three that can be formed.\n\nRate this question:\n\n• 37.\n\n• A.\n\n0\n\n• B.\n\n0.5\n\n• C.\n\n0.9\n\n• D.\n\n1.1\n\nD. 1.1\n• 38.\n\n### Dy zare hedhen njëkohësisht. Sa është probabiliteti i ngjarjes që shuma e numrave të rënë të  jetë jo më shumë se 4 ?\n\n• A.\n\n1/2\n\n• B.\n\n1/3\n\n• C.\n\n1/6\n\n• D.\n\n1/9\n\nC. 1/6\nExplanation\nThe probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the event is the sum of the two numbers being less than or equal to 4. There are 6 possible outcomes when two dice are rolled (1,1), (1,2), (1,3), (2,1), (2,2), (3,1). Out of these 6 outcomes, only one outcome has a sum greater than 4, which is (3,1). Therefore, the probability of the sum being less than or equal to 4 is 5/6 or 1/6.\n\nRate this question:\n\n• 39.\n\n### Vlera e  është :\n\n• A.\n\n4\n\n• B.\n\n3\n\n• C.\n\n2\n\n• D.\n\n1\n\nC. 2\nExplanation\nThe correct answer is 2 because it is the only value that is listed in the given options.\n\nRate this question:\n\n• 40.\n\n### Vlera e  është :\n\n• A.\n\n1/3\n\n• B.\n\n1/4\n\n• C.\n\n1/6\n\n• D.\n\n1/9\n\nC. 1/6\nExplanation\nThe correct answer is 1/6 because it is the fraction that represents the value being asked for. The question does not provide any additional information or context to determine why 1/6 is the correct answer, but based solely on the options given, 1/6 is the fraction that matches the value being referred to.\n\nRate this question:\n\n• 41.\n\n### Derivati i funksionit  në pikën x=1 është :\n\n• A.\n\n1\n\n• B.\n\n10\n\n• C.\n\n12\n\n• D.\n\n16\n\nC. 12\nExplanation\nThe derivative of a function at a specific point represents the slope of the tangent line to the graph of the function at that point. In this case, the derivative of the function at x=1 is equal to 12. This means that the slope of the tangent line to the graph of the function at x=1 is 12.\n\nRate this question:\n\n• 42.\n\n### Vlera e x-it për tëcilën ka maksimum funksioni  është :\n\n• A.\n\n1\n\n• B.\n\n2\n\n• C.\n\n3\n\n• D.\n\n4\n\nB. 2\nExplanation\nThe maximum value of the function for any given value of x is 2.\n\nRate this question:\n\n• 43.\n\n### Derivati i funksionit y=sin2x  në pikën x është :\n\n• A.\n\n2sinx\n\n• B.\n\n2cosx\n\n• C.\n\n2cos2x\n\n• D.\n\n2sinxcosx\n\nD. 2sinxcosx\nExplanation\nThe derivative of the function y = sin2x can be found using the chain rule. First, we differentiate the outer function sin2x with respect to the inner function 2x, which gives us cos(2x). Then, we multiply this by the derivative of the inner function 2x with respect to x, which is 2. Therefore, the derivative of y = sin2x is 2cos(2x). The correct answer is 2cos(2x).\n\nRate this question:\n\n• 44.\n\n### Rrethi x2+y2 =9 kalon nëpër pikën me koordinata :\n\n• A.\n\n(3,3)\n\n• B.\n\n(9,0)\n\n• C.\n\n(0,3)\n\n• D.\n\n(1,1)\n\nC. (0,3)\nExplanation\nThe equation x^2 + y^2 = 9 represents a circle with a radius of 3 units centered at the origin. The point (0,3) lies on this circle because when we substitute x=0 and y=3 into the equation, we get 0^2 + 3^2 = 9, which is true. Therefore, (0,3) is a valid solution to the equation and represents a point on the circle.\n\nRate this question:\n\n• 45.\n\n### Qendra e rrethit  është pika me koordinata :\n\n• A.\n\n(0,0)\n\n• B.\n\n(5,0)\n\n• C.\n\n(0,5)\n\n• D.\n\n(5,4)\n\nB. (5,0)\nExplanation\nThe given answer (5,0) represents the coordinates of a point on the x-axis, where the x-coordinate is 5 and the y-coordinate is 0. In the given set of coordinates, this is the only point that lies on the x-axis. The other points have either a non-zero y-coordinate or both non-zero x and y coordinates.\n\nRate this question:\n\n• 46.\n\n### Ekuacioni 9x2+4y2=36 në planin koordinativ paraqet :\n\n• A.\n\nParabolë\n\n• B.\n\nElipsë\n\n• C.\n\nRreth\n\n• D.\n\nHiperbolë\n\nB. Elipsë\nExplanation\nThe equation 9x2+4y2=36 represents an ellipse in the coordinate plane. This can be determined by the fact that the coefficients of x2 and y2 are both positive, indicating that the ellipse is elongated in both the x and y directions. Additionally, the sum of the coefficients (9+4) is less than the constant term (36), indicating that the ellipse is not a circle.\n\nRate this question:\n\n• 47.\n\n### është i barabartë me :\n\n• A.\n\n1/2\n\n• B.\n\n-1/2\n\n• C.\n\n1\n\n• D.\n\n2\n\nA. 1/2\nExplanation\nThe given expression is a list of fractions: 1/2, -1/2, 1, and 2. The correct answer is 1/2, which is the first fraction in the list.\n\nRate this question:\n\n• 48.\n\n### Integrali i caktuar  është :\n\n• A.\n\n0\n\n• B.\n\n1\n\n• C.\n\n2\n\n• D.\n\nE\n\nB. 1\nExplanation\nThe given options are numerical values, and the correct answer is \"1\". It is unclear what the question is asking for, as there is no context or explanation provided. Without further information, it is impossible to determine the specific meaning or purpose of the integral being referred to.\n\nRate this question:\n\n• 49.\n\n### Numri i2009 është :\n\n• A.\n\n1\n\n• B.\n\n-1\n\n• C.\n\nI\n\n• D.\n\n-i\n\nC. I\nExplanation\nThe correct answer is \"i\". In mathematics, \"i\" represents the imaginary unit, which is defined as the square root of -1. It is used to work with complex numbers, which are numbers that have both a real and imaginary part. In this case, the question is asking for the value of \"i\" in the year 2009, so the answer is simply \"i\".\n\nRate this question:\n\n• 50.\n\n### Pjesa reale Re(z) e numrit kompleks  është:\n\n• A.\n\n1\n\n• B.\n\n-1\n\n• C.\n\nI\n\n• D.\n\n-i", null, "Back to top" ]

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[ "# Connection between log predictive density and Kullback-Leibler information measure\n\nI have read in Bayesian Data Analysis by Andrew Gelman that log predictive density can be used to compare Bayesian models due to its connection to the Kullback-Leibler information.\n\nThe log predictive density has an important role in statistical model comparison because of its connection to the Kullback-Leibler information measure. In the limit of large sample sizes, the model with the lowest Kullback-Leibler information—and thus, the highest expected log predictive density—will have the highest posterior probability. Thus, it seems reasonable to use expected log predictive density as a measure of overall model fit. Due to its generality, we use the log predictive density to measure predictive accuracy in this chapter.\n\nThe Kullback-Leibler divergence between $Q(\\theta)$ and $P(\\theta|y)$ is,\n\n$D_{KL}(Q||P) = \\sum_{\\theta}Q(\\theta)ln\\frac{Q(\\theta)}{P(\\theta|y)}$\n\n$D_{KL}(Q||P) = E_\\theta[lnQ(\\theta)] -E_\\theta[lnP(\\theta,y)]+lnP(y)$\n\n$D_{KL}(Q||P) = E_\\theta[lnQ(\\theta)] -E_\\theta[lnP(y|\\theta)P(\\theta)] +lnP(y)$\n\n1. Is this the connection between KL information and the expected log predictive density?\n2. If this is the connection, how do we assume that maximum expected log predictive density implies the minimum KL divergence. Comparing different models means changing the values for $\\theta$. However, when changing $\\theta$ the term $E_\\theta[lnQ(\\theta)]$ also changes. Why do we neglect the effect of this term to the KL divergence ?\n3. Is not the predictive density also used to calculate the prediction for unseen $\\bar{y}$ ? The book also says,\n\nThe ideal measure of a model’s fit would be its out-of-sample predictive performance for new data produced from the true data-generating process (external validation).\n\nTherefore, choosing the model with maximum predictive density for new data points means that we choose the model that gives maximum value for the predictions. How could a model gives maximum value for the prediction is better than other models?\n\nI appreciate if someone can help me to understand these connections. Thanks", null, "" ]

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[ " Mathematical biography of Lawrence Wilson\nsin^2x + cos^2x = 1\ny = frac (-b +- sqrt(b^2 - 4ac)) (2a)\n(x + 2)^2 + (y - 3)^2 = 16\nslope = m = frac (\\text(change in y)) (\\text(change in x)) = frac (Deltay) (Deltax)\n\n# Get Math Help!\n\n### Teaching Experience\n\n##### College Level\n• Mathematics Adjunct Faculty member at Harford Community College (June 2016 - present)\n• Math 212 - Calculus with Applications\n• Math 206 - Calculus III\n• Math 101 - College Algebra\n• Teaching Assistant, Georgia Tech\n• Teaching assistant in the School of Mathematics for Calculus I & II while an undergraduate and graduate student at Georgia Tech.\n##### Tutor\n\nTutored mathematics students 1-on-1 for more than 40 years in algebra I & II, geometry, calculus I, II & III, trigonometry, pre-calculus, statistics, SAT & ACT mathematics.\n\nDeveloped a program to prepare students for the SAT Mathematics section and tutored students to improve their SAT Math scores for more than 8 years with very good results.\n\nAt Georgia Tech, I tutored in the Math Lab for the School of Mathematics and in the tutoring lab for the College of Engineering.\n\n### Education\n\n##### Degrees\n• MS Operations Research, Georgia Institute of Technology (Ga. Tech), 1983\n• BS Applied Mathematics, Georgia Institute of Technology, 1982 (with Highest Honor)\n##### Related Awards\n• Senior Mathematics Prize, 1982, Ga. Tech\n• Pi Mu Epsilon Mathematics Award, 1982, Ga. Tech\n• Pi Mu Epsilon National Mathematics Honor Society\n• Freshman Mathematics Prize, 1979, Univ. of Tenn. Chattanooga\n\n### Professional Mathematician\n\n##### Department of Defense\n\nMore than 38 years of experience as a Mathematician, Operations Research Analyst, and Computer Scientist for the Department of Defense and private defense contractors." ]

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[ "# Incontri di Analisi Matematica tra Firenze, Pisa e Siena\n\n## MathAnalysis(at)UniFIPISI, I\n\n### Venerdì 17 Maggio 2019 Università degli Studi di Firenze Dipartimento di Matematica e Informatica (DiMaI) sede di Viale Morgagni 67/A (Aula Tricerri)\n\n#### PROGRAMMA\n\n11:00 Apertura\n11:10  Matteo Novaga (Università di Pisa): Anisotropic mean curvature flow\n12:00 Alaa Elshorbagy (SISSA e ICTP, Trieste): On the square distance function from a manifold with boundary\n\npausa pranzo\n\n14:30 Stefano Galatolo (Università di Pisa): The existence of Noise Induced Order, a computer aided proof\n15:20 M. Patrizia Pera (Università degli Studi di Firenze)\nExistence and global bifurcation of periodic solutions for retarded functional differential equations on manifolds\n\npausa caffé\n\n16:30 Massimo Gobbino (Università di Pisa)\nNon-local characterizations of Sobolev spaces and bounded variation functions\n17:20 Chiusura\n\n#### ABSTRACTS\n\nAlaa Elshorbagy (SISSA e ICTP, Trieste)\nOn the square distance function from a manifold with boundary\n\nIn this talk we aim to characterize arbitrary codimensional smooth manifolds M with boundary embedded in Rn using the square distance function and the signed distance function from M and from its boundary. The results are localized in an open set.\n\nStefano Galatolo (Università di Pisa)\nThe existence of Noise Induced Order, a computer aided proof\n\nDynamical systems perturbed by noise appear naturally as models of physical systems. In several interesting cases it can be approached rigorously by computational methods.\nAs a nontrivial example of this, we show a computer aided proof to rigorously show the existence of noise induced order in the model of chaotic chemical reactions where it was first discovered numerically by Matsumoto and Tsuda in 1983. We show that in this random dynamical system the increase of noise causes the Lyapunov exponent to decrease from positive to negative, stabi-\nlizing the system. The method is based on a certified approximation of the stationary measure in the L1 norm. This is done by an efficient algorithm which is general enough to be adapted to any dynamical system with additive noise on the interval. Time permitting we will also talk about linear response of such systems when the deterministic part of the system is perturbed deterministically.\n\nMassimo Gobbino (Università di Pisa)\nNon-local characterizations of Sobolev spaces and bounded variation functions\n\nWe present two approximations of the p-norm of the gradient of a function u(x) through double integrals that do not involve derivatives. In the first one, the so called “horizontal approximation”, the gradient is replaced by finite differences. In the second one, the so called “vertical approximation”, the double integral measures some sort of interaction between the sublevels of u(x). In both cases, the integrand penalizes the pairs of points (x, y) such that\nx and y are close to each other, while the difference between u(x) and u(y) is large. We describe a common approach that in both cases leads to compute the pointwise limit and the Γ-limit of these functionals. The main steps are first reducing to dimension one, then localizing the result to an interval, and finally reducing the analysis to the asymptotic behavior of suitable multi-variable inequalities.\n(Based on some joint works with M.G. Mora (horizontal approach) and with C. Antonucci, M. Migliorini, and N. Picenni (vertical approach))\n\nMatteo Novaga (Università di Pisa)\nAnisotropic mean curvature flow\n\nI will present existence and uniqueness results for the anisotropic mean curvature flow with arbitrary mobility. This is achieved by introducing a new notion of solution to the corresponding level set formulation. Such a solution satisfies the comparison principle and a stability property with respect to the approximation by suitably regularized problems. The results are valid in any dimension and for arbitrary, possibly unbounded, initial closed sets. The approach accounts for the possible presence of a time-dependent bounded forcing term, with spatial Lipschitz continuity. As a byproduct of the analysis, the problem of the convergence of the Almgren-Taylor-Wang minimizing movements scheme to a unique “flat flow” in the case of general, possibly crystalline, anisotropies is settled.\n\nM. Patrizia Pera (Università degli Studi di Firenze)\nExistence and global bifurcation of periodic solutions for retarded functional differential equations on manifolds\n\nIn this talk, I will present some results on the existence and global bifurcation\nof periodic solutions to first and second order retarded functional differential equations on boundaryless smooth manifolds. I will consider both cases of a topologically nontrivial compact manifold (e.g., an even dimensional sphere) and of a possibly noncompact constraint, assuming in the latter case that the topological degree of a suitable tangent vector field is nonzero. The approach is topological and based on the fixed point index theory for locally compact maps on metric Absolute Neighborhood Retracts (ANRs). Finally, I will show how to deduce from our results a Rabinowitz-type global bifurcation result as well as a Mawhin-type continuation principle." ]

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[ "# [beginner]Type error at Fine tuning\n\nHi! I’m trying to fine-tune some network, like vgg, alexnet, resnet, to meet with my dataset.\ninput: image, ByteTensor(3×200×200)\noutput: hot vector of labels, ByteTensor(1×98)\n\nI checked the transfer learning tutorial (http://pytorch.org/tutorials/beginner/transfer_learning_tutorial.html)\nand changed the last layer and the calculation part with resnet18 as follows, but the error is happened.\n\n``````#model change\ntrain_resnet = models.resnet18(pretrained=True)\nnum_ftrs = pretrain_resnet.fc.in_features\npretrain_resne.fc = nn.Liear(num_ftrs,98)\n#forward + backward + optimize\nm = nn.LogSoftmax()\noutputs = pretrain_resnet(inputs)\n_, preds = torch.max(outputs.data,1)\nloss = criterion(m(outputs), labels)\n\n#error\noutputs = pretrain_resnet(inputs)\n→RuntimeError: expexted Byte tensor (got Float tensor)\n``````\n\nBest regards,\nhana\n\nByte is discrete. Your image tensor should be floating point type.\n\nThank you.\n\nI changed image, byte tensor to float tensor\nand lables, byte tensor to long tensor like\n\n``````data['image'].float()\ndata['labels'].long()\n``````\n\nbut another Run time error happened at loss calculation.\n\n``````Runtime Error: multi-target not supported at /opt/conda/conda-bld/pytorch_1503965122592/work/torch/lib/THNN/generic/ClassNLLCriterion.c:22\n``````\n\noutputs : FloatTensor 1×98\nlabels: FloatTensor 1×98\n\nhmmm, What it is caused by?\n\nI just changed at loss function like that and it worked!\n\n``````criterion = MultiLabelMarginLoss()\nfor i in epoch:\nloss = criterion(outputs, labels)\n``````\n\nThank you so much!\n\nIf your label vector is one-hot, using MultiLabelMarginLoss is doing the wrong thing, although it won’t give error. Pytorch convention directly uses indices, so your target should be `[batch_size x 1]`. With MultiLabelMarginLoss, you are essentially saying that your target labels contain a lot of label 0s and one label 1.\n\nThank you for telling me that.\n\nMy each target vector has a lot of label 0s and some 1s. ex）[0,0,0,1,0,0,1,…,0]\n\nSo what should I do is to convert 1×98\ntensor to 98×1 tensor and to change the loss function…\nI’m glad if you let me know the suitable loss function.\n\nIt seems that each image belongs to more than one target class. Am I understanding correctly?\n\nyes.\nEach data has labeled at least with 5 classes." ]

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[ "## How to increase score in python\n\nfor support. pity, that now can..\n\n# How to increase score in python\n\nLast Updated on December 31, Predicting probabilities instead of class labels for a classification problem can provide additional nuance and uncertainty for the predictions.\n\nThe added nuance allows more sophisticated metrics to be used to interpret and evaluate the predicted probabilities. In general, methods for the evaluation of the accuracy of predicted probabilities are referred to as scoring rules or scoring functions.\n\nIn this tutorial, you will discover three scoring methods that you can use to evaluate the predicted probabilities on your classification predictive modeling problem. Discover bayes opimization, naive bayes, maximum likelihood, distributions, cross entropy, and much more in my new bookwith 28 step-by-step tutorials and full Python source code.\n\nEach predicted probability is compared to the actual class output value 0 or 1 and a score is calculated that penalizes the probability based on the distance from the expected value. The penalty is logarithmic, offering a small score for small differences 0.\n\nIn order to summarize the skill of a model using log loss, the log loss is calculated for each predicted probability, and the average loss is reported. In the binary classification case, the function takes a list of true outcome values and a list of probabilities as arguments and calculates the average log loss for the predictions. Given a specific known outcome of 0, we can predict values of 0.\n\nThe result is a curve showing how much each prediction is penalized as the probability gets further away from the expected value. We can repeat this for a known outcome of 1 and see the same curve in reverse. Running the example creates a line plot showing the loss scores for probability predictions from 0. This helps to build an intuition for the effect that the loss score has when evaluating predictions.\n\n## T-test using Python and Numpy\n\nAs an average, we can expect that the score will be suitable with a balanced dataset and misleading when there is a large imbalance between the two classes in the test set. This is because predicting 0 or small probabilities will result in a small loss. We can demonstrate this by comparing the distribution of loss values when predicting different constant probabilities for a balanced and an imbalanced dataset. First, the example below predicts values from 0.\n\nRunning the example, we can see that a model is better-off predicting probabilities values that are not sharp close to the edge and are back towards the middle of the distribution. We can repeat this experiment with an imbalanced dataset with a ratio of class 0 to class 1. Here, we can see that a model that is skewed towards predicting very small probabilities will perform well, optimistically so.\n\nThe result suggests that model skill evaluated with log loss should be interpreted carefully in the case of an imbalanced dataset, perhaps adjusted relative to the base rate for class 1 in the dataset. The Brier score, named for Glenn Brier, calculates the mean squared error between predicted probabilities and the expected values.Although popular statistics libraries like SciPy and PyMC3 have pre-defined functions to compute different tests, to understand the maths behind the process, it is imperative to understand whats going on in the background.\n\nThis series will help you understand different statistical tests and how to perform them in python using only Numpy. A t-test is one of the most frequently used procedures in statistics. The t test also tells you how significant the differences are; In other words it lets you know if those differences could have happened by chance. Your cold lasts a couple of days.\n\nThe next time you have a cold, you buy an over-the-counter pharmaceutical and the cold lasts a week. You survey your friends and they all tell you that their colds were of a shorter duration an average of 3 days when they took the homeopathic remedy.\n\nWhat you really want to know is, are these results repeatable? A t test can tell you by comparing the means of the two groups and letting you know the probability of those results happening by chance. For example, a drug company may want to test a new cancer drug to find out if it improves life expectancy. It would seem that the drug might work. But it could be due to a fluke. The t score is a ratio between the difference between two groups and the difference within the groups.\n\n808#16 camera\n\nThe larger the t score, the more difference there is between groups. The smaller the t score, the more similarity there is between groups. A t score of 3 means that the groups are three times as different from each other as they are within each other. When you run a t test, the bigger the t-value, the more likely it is that the results are repeatable.\n\nEvery t-value has a p-value to go with it. A p-value is the probability that the results from your sample data occurred by chance. They are usually written as a decimal. Low p-values are good ; They indicate your data did not occur by chance. For example, a p-value of. In most cases, a p-value of 0. There are three main types of t-test: 1. An Independent Samples t-test compares the means for two groups.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.\n\nData Science Stack Exchange is a question and answer site for Data science professionals, Machine Learning specialists, and those interested in learning more about the field. It only takes a minute to sign up. I have provided a sample data, but mine has thousands of records distributed in a similar way.\n\nCsgo time command\n\nHence prediction should be 1,2,3 or 4 as these are my values for target variable. I have tried using algorithms such as random forest, decision tree etc.\n\nHere if you see, values 1,2 and 3 are occurring more times as compared to 4. Hence while predicting, my model is more biased towards 1 2 and 3 whereas I am getting only less number of predictions for 4 Got only 1 predicted for policy4 out of thousands of records when I saw the confusion matrix.\n\nIn order to make my model generalize, I removed equal percentage of data that belongs to 1,2 and 3 value randomly.", null, "I grouped by each value in Col5 and then removed certain percentage, so that I brought down the number of records. Now I could see certain increase in percentage of accuracy and also reasonable increase in predictions for value 4 in confusion matrix.\n\nIs this the right approach to deal with removing the data randomly from those groups on which the model is biased? I tried for in-built python algorithms like Adaboost, GradientBoost techniques using sklearn.\n\nI read these algorithms are for handling imbalance class. But I couldnt succeed in improving my accuracy, rather by randomly removing the data, where I could see some improvements. Is there are any pre-defined packages in sklearn or any logic which I can implement in python to get this done, if my random removal is wrong?\n\nShould I try this for value 4? And can we do this using any in-built packages in python? It would be great if someone helps me in this situation. This paper suggests using ranking I wrote it.\n\nSince rankers compare observation against observation, training is necessarily balanced. There are two \"buts\" however: training is much slower, and, in the end, what these models do is rank your observations from how likely they are to belong to one class to how likely they are to belong to another so you need to apply a threshold afterwards.\n\nText graphics in video\n\nIf you are going to use pre-processing to fix your imbalance I would suggest you look into MetaCost. This algorithm involves building a bagging of models and then changing the class priors to make them balanced based on the hard to predict cases. It is very elegant.\n\nThe cool thing about methods like SMOTE is that by fabricating new observations, you might making small datasets more robust. Anyhow, even though I wrote some things on class imbalance, I am still skeptic that it is an important problem in the real world. I would think it is very uncommon that you have imbalance priors in your training set, but balanced priors in your real world data.\n\nDo you? What usually happens is that type I errors are different than type II errors and I would bet most people would be better off using a cost matrix, which most training methods accept or you can apply it by pre-processing using MetaCost or SMOTE. I think many times \"fixing imbalance\" is short to \"I do not want to bother thinking about the relative trade-off between type I and II errors.\n\nAdaBoost gives better results for class imbalance when you initialize the weight distribution with imbalance in mind. I can dig the thesis where I read this if you want. Anyhow, of course, those methods won't give good accuracies. Do you have class imbalance in both your training and your validation dataset?\n\nYou should use metrics such as F1 score, or pass a cost matrix to the accuracy function.R squared value increase if we increase the number of independent variables.\n\nAdjusted R-square increases only if a significant variable is added. Look at this example. As we are adding new variables, R square increases, Adjusted R-square may not increase. We may have to see the variable impact test and drop few independent variables from the model. Build a model, Calculate R-square is near to adjusted R-square. If not, use variable selection techniques to bring R square near to Adj- R square. No, if observe the formula carefully then we can see Adj-R square is influenced by k number of variables and n number of observations.\n\nFinally either reduce number of variables or increase the number of observations to bring Adj-R Square close to R Square. You must be logged in to post a comment.", null, "In :. In :. In :. Build a model to predict y using x1,x2 and x3. In :. Variable: Y R-squared: 0. R-squared: 0. Observations: 12 AIC: In :. Build a model to predict y using x1,x2,x3,x4,x5 and x6. In :. In :. In :. Model R 2. Model1 0. The next post is a practice session on multiple regression issues.\n\nSearch for:. All rights reserved.There are many ways to keep the score in a game, we will show you how to write a score onto the canvas. The syntax for writing text on a canvas element is different from drawing a rectangle.\n\nTherefore we must call the component constructor using an additional argument, telling the constructor that this component is of type \"text\". In the component constructor we test if the component is of type \"text\", and use the fillText method instead of the fillRect method:.\n\nAt last we add some code in the updateGameArea function that writes the score onto the canvas. We use the frameNo property to count the score:. If you want to report an error, or if you want to make a suggestion, do not hesitate to send us an e-mail:. HOW TO. Your message has been sent to W3Schools. W3Schools is optimized for learning, testing, and training. Examples might be simplified to improve reading and basic understanding.\n\nPhonetics list\n\nWe all may have faced this problem of identifying the related features from a set of data and removing the irrelevant or less important features with do not contribute much to our target variable in order to achieve better accuracy for our model. Feature Selection is one of the core concepts in machine learning which hugely impacts the performance of your model. The data features that you use to train your machine learning models have a huge influence on the performance you can achieve.\n\nIrrelevant or partially relevant features can negatively impact model performance. Feature selection and Data cleaning should be the first and most important step of your model designing.\n\nIn this post, you will discover feature selection techniques that you can use in Machine Learning.", null, "Feature Selection is the process where you automatically or manually select those features which contribute most to your prediction variable or output in which you are interested in. Having irrelevant features in your data can decrease the accuracy of the models and make your model learn based on irrelevant features.\n\nHow to select features and what are Benefits of performing feature selection before modeling your data? I want to share my personal experience with this. Now you know why I say feature selection should be the first and most important step of your model design. Feature Selection Methods:. I will share 3 Feature selection techniques that are easy to use and also gives good results.\n\nHow to Code: Collision Detection — Part I\n\nCorrelation Matrix with Heatmap. Description of variables in the above file. Univariate Selection. Statistical tests can be used to select those features that have the strongest relationship with the output variable. The scikit-learn library provides the SelectKBest class that can be used with a suite of different statistical tests to select a specific number of features.\n\nYou can get the feature importance of each feature of your dataset by using the feature importance property of the model. Feature importance gives you a score for each feature of your data, the higher the score more important or relevant is the feature towards your output variable. Feature importance is an inbuilt class that comes with Tree Based Classifiers, we will be using Extra Tree Classifier for extracting the top 10 features for the dataset.\n\nCorrelation states how the features are related to each other or the target variable. Correlation can be positive increase in one value of feature increases the value of the target variable or negative increase in one value of feature decreases the value of the target variable. Heatmap makes it easy to identify which features are most related to the target variable, we will plot heatmap of correlated features using the seaborn library.\n\nHave a look at the last row i. In this article we have discovered how to select relevant features from data using Univariate Selection technique, feature importance and correlation matrix. If you found this article useful give it a clap and share it with others. Sign in. Raheel Shaikh Follow. Towards Data Science A Medium publication sharing concepts, ideas, and codes.Boosting is a technique in machine learning in which multiple models are developed sequentially.\n\nEach new model tries to successful predict what prior models were unable to do. The average for regression and majority vote for classification are used. For classification, boosting is commonly associated with decision trees. However, boosting can be used with any machine learning algorithm in the supervised learning context. Since several models are being developed with aggregation, boosting is associated with ensemble learning. Ensemble is just a way of developing more than one model for machine-learning purposes." ]

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[ "# Is this suggested solution for the below mentioned erratum correct?\n\n5-2.Do a topological sort of the following graph G", null, "This problem is from \"The Algorithm Design Manual (2nd Edition)\" by Steven Skiena. Since, this graph is not a DAG topological sorting can't be done. In the errata list for this book it is suggested to reverse the edge (F,H) but this will make the vertex \"H\" unreachable. Then how this solution is possible \"A, B, D, E, C, H, G, I, J, F\".\n\n• You mean `H` becomes unreachable? May 26 '15 at 18:13\n• The solution is valid because all predecessors of H (none!) are mentioned before H. May 26 '15 at 18:15\n• ya i made mistake. That should be \"H\" instead of \"F\". May 26 '15 at 18:17\n\nThe solution is valid since `H` has no successors that mentioned before `H` and no predecessors that are mentioned after `H`.\n\nIt's not any stranger than the fact that the graph\n\n``````A <- B -> C\n``````\n\n(where `B` is \"unreachable\") can be topologically sorted as\n\n``````B, A, C\n``````\n• when i have solved the above question i got this answer A,B,D,E,C,G,F,I,J,H. here i have just placed H in the last because it is not violating the rule that all the predecessors of a vertex should be processed first. is my answer valid? May 26 '15 at 18:55\n• Hmm.. No, because `H` would then come after `G`. You should be ok if you put `H` first. (In fact you just showed that my answer was incomplete. Answer updated.) May 26 '15 at 19:26\n• would yu like to verify my new answer \"A, B, D, E, H, G, I, J, C, F\". Thanks in advance May 27 '15 at 15:40" ]

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[ "# Calculate the volume of carbon dioxide gas lost at 25 degrees and 100kPa?\n\n## Initial mass (g) = 125.5 Final mass (g) = 124.8 Change in mass (g) = 0.7\n\nFeb 3, 2018\n\n$0.38 L$, or $380 c {m}^{3}$ lost.\n\n#### Explanation:\n\nUse the Ideal Gas Law:\n\n$P V = n R T$\n\nFor the initial mass of $C {O}_{2}$:\n\nRemember, the formula for moles, $n$, is $n = \\frac{m}{M}$, where $m$ is the given mass and $M$ the molar mass.\n\n$M = 44.01 \\frac{g}{\\text{mol}}$\n\nHere, $m = 125.5 g$.\n\nSo $n = \\frac{125.5}{44.01} = 2.85 \\text{mol}$.\n\nSo now, we can rearrange the gas law:\n\n$V = \\frac{n R T}{P}$\n\n$V = \\frac{2.85 \\cdot 8.314 \\cdot 298.15}{100}$\n\n$V = 70.65 L$ of carbon dioxide before the loss.\n\nFor the final mass of $C {O}_{2}$:\n\nHere, $m = 124.8 g$\n\nSo $n = \\frac{124.8}{44.01} = 2.835 \\text{mol}$\n\n$V = \\frac{n R T}{P}$\n\n$V = \\frac{2.835 \\cdot 8.314 \\cdot 298.15}{100}$\n\n$V = 70.27 L$ of carbon dioxide after loss.\n\nTherefore, the total loss must be ${V}_{\\text{final\"-V_\"initial}}$.\n\nSo the loss is equal to $70.65 - 70.27 = 0.38 L$." ]

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[ "We begin by obtaining TARGET low-pass neuroblastoma data (NBL) from the GDC archive. Please note: TARGET_NBL_WGS_CNVLOH.tsv is a clinical metadata file and therefore not compatible with the ensuing functions to extract segment data. We have also chosen to use only a single comparison type (NormalVsPrimary) to ensure comparability and compatibility with the data. Users can download the tar.gz file and remove the tsv files into a single folder. We have already done that here. The source for these files is located here", null, "The user simply chooses to add all the files to the cart, then click the black cart button in the top right hand corner.", null, "You can untar it with R, but the files will be in a complex set of directories. It is best to list the files recursively with criteria that will obtain the segment files in tsv format, with that single comparison of interest.\n\n``````if(!dir.exists(\"extracted_nbl_data\")){dir.create(\"extracted_nbl_data\")}\ntarget_files_nbl<-list.files(path = \"extracted_nbl_data\",pattern=glob2rx(\"*NormalVsPrimary.tsv\"),recursive=T,full.names = T)\nprint(target_files_nbl)``````\n\nWith the full list of input files from the GDC, these can then be simply loaded into a function that will read all of them, sample match them, and aggregate the data into a bin-sample matrix. This matrix can then be saved into the fast, space efficient, RDS filetype.\n\n``````sample_aggregated_segvals_output_full<-CNVScope::formSampleMatrixFromRawGDCData(tcga_files = target_files_nbl,format = \"TARGET\")\nsaveRDS(sample_aggregated_segvals_output_full,\"NBL_sample_matched_input_matrix.rds\")``````\n\n#Custom Data For those who have a desire to add custom data, we have provided a series of options that allow custom data, provided that a CSV file has a single column with copy number values. We will show that the same result can be obtained with the correct options, specifying the column of interest, using a completely different section of the function. Use the format=“custom” option and be sure to specify the names following columns in your text file: copy number column chromosome, start position end position. In this case, we have also selected freadskip=14 as there are 14 lines before the tabular data begins. The sample pattern is a regular expression set to grab the sample name within the filename, setting sample_pat=“” will grab the complete filename and let this denote unique samples. We suggest shorter sample than this, however. A sample column name (sample_col) can also be specified to specify samples on each line of the input files instead of using the filename or a portion thereof.\n\nFor further information, please review the help files by typing: help(“CNVScope::formSampleMatrixFromRawGDCData”)\n\n``````nbl_custom_input_matrix<-CNVScope::formSampleMatrixFromRawGDCData(tcga_files = target_files_nbl,\nformat = \"custom\",binsize = 1e6,freadskip = 14,parallel=F,debug=F,\nsample_pat = \"(?<=30-)(.*?)(?=_)\",sample_col = \"sample\",chrlabel=\">chr\",\nstartlabel = \"begin\",endlabel = \"end\",cnlabel = \"relativeCvg\")\nsaveRDS(nbl_custom_input_matrix,\"NBL_custom_sample_matched_input_matrix.rds\")``````\n\nWith this, your input matrix is complete.\n\nNext, please look at the next vignette that details recursive linear regression and postprocessing.\n\nOptional example for advanced Use: A high definition version is quite simple to do, using the above options, on TARGET, TCGA, or custom format data. Simply decrease the binsize to increase the resolution.\n\nIn chromosome 2, we have found that the median bin size is 731069 and that smaller chromosomes benefit from binsize reduction more than larger chromosomes (except for chromosome 1). In this case, we decrease our binsize by a factor of 4, making the total number of values in the matrix increase by a factor of 16. It will take longer than the typical time.\n\n``````nbl_custom_input_matrix_hd<-CNVScope::formSampleMatrixFromRawGDCData(tcga_files = target_files_nbl,\nformat = \"custom\",binsize = 2.5e5,freadskip = 14,parallel=T,debug=F,\nsample_pat = \"(?<=30-)(.*?)(?=_)\",sample_col = \"sample\",chrlabel=\">chr\",\nstartlabel = \"begin\",endlabel = \"end\",cnlabel = \"relativeCvg\")\nsaveRDS(nbl_custom_input_matrix_hd,\"NBL_custom_sample_matched_input_matrix_2.5e5binsize_parallel.rds\")``````\n\nIn the opposite manner, if you wanted to quickly create a low density version, this would be the way to go about it. It will make the input matrix creation process proceed a great deal faster and will require less RAM to display an interactive map.\n\n``````nbl_custom_input_matrix_ld<-CNVScope::formSampleMatrixFromRawGDCData(tcga_files = target_files_nbl,\nformat = \"custom\",binsize = 1e8,freadskip = 14,parallel=F,debug=F,\nsample_pat = \"(?<=30-)(.*?)(?=_)\",sample_col = \"sample\",chrlabel=\">chr\",\nstartlabel = \"begin\",endlabel = \"end\",cnlabel = \"relativeCvg\")\nsaveRDS(nbl_custom_input_matrix,\"NBL_custom_sample_matched_input_matrix_1e8binsize.rds\")``````\n\nA demonstration is below of varying resolutions, using correlation based maps (for space reasons): Examples of chr11 are shown below, in increasing order of resolution (1e8,1e7,1e6,2.5e5,1e5 binsize). Note that the resolution doesn’t dramatically improve after 1e6, despite the time and computational effort required to generate it.", null, "", null, "chr11_1e7" ]

[ null, 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", null, 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null, 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[ "Through 45 32 and -25 02. Copyright GlencoeMcGraw-Hill a division of The McGraw-Hill Companies Inc.\n\n### HIKING Naomi left from an elevation of 7400 feet at.", null, "2-3 skills practice rate of change and slope. X -2 3 8 13 7. Nd the rate of change and explain what it represents. 3-3 Rate of Change and Slope.\n\nHOMES Find the slope of the roof of a home that rises 8 feet for every horizontal change of 24 feet. Express as a fraction in simplest form. Practice Slope Find the slope of each line.\n\n6 3 8 4 Determine the rate ofchange each graph. Use the information in the diagram to determine Üthe initial height of the airplane. -2 -4 3 2 Graph the line passing through the given point with the given slope.\n\nNAME _ DATE_ PERIOD _ 3-3 Skills Practice Rate of Change and Slope Find the slope of Study Resources. 5-1 Practice Form G Rate of Change and Slope Determine whether each rate of change is constant. If it is nd the rate of change and explain what it represents.\n\n3 8 7 34 5 6 2. 10 3 7 2 3. -2 -2 10 -2 o 8.\n\nLesson 3 Skills Practice Constant Rate of Change and Slope Find the constant rate of change for each linear function and interpret its meaning. Find the average rate of change in value of the machine between the end of three years and the end of eight years. 1 5 -1 -3 2.\n\nNAME _____ DATE _____ PERIOD _____ Chapter 2 20 Glencoe Algebra 2 2-3 Practice Rate of Change and Slope Find the slope of the line that passes through each pair of points. 23 Rate of Change and Slopepdf – NAME DATE PERIOD 2-3 Practice Rate of Change and Slope Find the slope of the line that passes through each pair of. Its the same thing as slope in all cases.\n\n-3 -5 m 2 11. The points given in each table lie on a line. -5 -8 -8 1.\n\n7 6 3 6 4. Express as a fraction in simplest form. 0 2 3 0 3.\n\n3 8 5 2 2. 0 4 m 1 12. -2 3 2 undefined Determine the rate of change of each graph.\n\nRate of Change and Slope Rate of Change Rate of change is a ratio that compares how much one quantity changes on average relative to the change in another quantity. Width ft Height in xy 210 414 618 822. Its the slope of the graph of the equation at.\n\nThe same machine has a value of 2800 at the end of eight years. Express as a fraction in simplest form. Practice Form G Rate of Change and Slope Determine whether each rate of change is constant.\n\nWhat is the rate of change. 628721 To find the rate of change use the coordinates 1 15 and 2 9. 2 1 0 0 8.\n\nLeave answers as Improper Fractions. Class Size Teachers 2 3 1 0 4 5 6 Students 20 40 60 80 100 120 4. 4 3 7 2 6.\n\nThen graph the line. -2 -2 10 -2 7. Find the slope of the line that passes through each pair of points.\n\n3 8 5 2 2. 85-5 4 -2 Determine the slope of each graph using rise over run or the slope formula. Change in y rate of change change in x change in height change in time 60-20 The rate of change is mmday.\n\n2-3 Word Problem Practice Rate of Change and Slope 1. Its the slope of the graph from 00 to the endpoint. 2-3 Skills Practice Rate of Change and Slope DATE PERIOD Find the slope of the line that passes through each pair of points.\n\nSo the rate of change is. A machine that originally cost 15600 has a value of 7500 at the end of three years. 2 1 0 0 8.\n\nTETHER A tether is tied tautly to the top of a pole as shown. Skills Practice Rate of Change and Slope DATE PERIOD Find the slope of the line that passes through each pair of points. What is the slope of the tether.\n\nFind the slope of the line that passes through 10 1 and 5 2. View Lesson 3-3 Skills_Practice_Rate_of_Change_and_Slopedocx from BIOLOGY 112 at Lawrence Central High School. Graph and describe the basic shape of the graphs and analyze the general form of the equations for the following families of functions.\n\nSo the rate of change is í6. Find the rate of change in terms of inches per month. 2-3 Skills Practice Slope Find the slope of the line that passes through each pair of points.\n\nFind the rate of change represented in each table or graph. NAME _____ DATE _____ PERIOD _____ Chapter 2 20 Glencoe Algebra 2 2-324 Practice Rate of Change and Slope Writing Linear Equations Find the slope of the line that passes through each pair of points. Lesson 2-3 NAME DATE PERIOD PDF Pass Chapter 2 19 Glencoe Algebra 2 Find the slope of the line that passes through each pair of points.\n\nLinear quadratic exponential piece-wise and absolute value use technology when appropriate. Video Guide Section 2-3. Find the average rate of change for the data in the table.\n\nFind the slope of the line. If it is. Gallons Quarts xy 14 28 312 416 2.\n\nThrough 3 3 and 10 0 2 After 2 months a bamboo plant was 175 inches tall. 3 8 7 3. -2 -1 m -2 5 parallel to the.\n\n8 -5 4 -2 5. Find the slope of the line that passes through each pair of points. Average Rate of Change change in ì change in ë Elevation of the.\n\nV 3 0 2-4 y L-H x-H4zW 2- 12 0 2 41 6X ITrZZ 13. Watch the video and complete the accompanying notesIf you forgot your notes page at school you can print them at home using the link in the assignment. 160 140 40 -8-64-20 2 change in y Rate of change change in x change in height change in time 30-120 The average rate of change or a rider between I and 3 seconds is 30 fts.\n\n4 5 2 7 8. NAME 3-3 Skills Practice Rate of Change and Slope DATE PERIOD Find the slope of the line that passes through each pair of points. AVIATION An airplane descends along a straight-line path with a slope of 01 to land at an airport.\n\n-3 5 -3 -1 6. Find the slope of each line. Section 23 Find Slope and Rate of Change A252.\n\n628721 To find the rate of change use the coordinates 10 3 and 5 2. 1 9 0 6 4. 2 m -1 13.\n\nFind the slope of each line. 19 Glencoe Algebra 2. After 8 months the same plant was 124 inches tall.\n\nPlay this game to review Algebra I. 10 3 7 2 3. Predict how tall it will be after one year.\n\nAllowance Allowance 12 18 6 0 24 30 36 Age years 3156 9 12 18 3. MOUNTAINS Find the slope of a. Find the slope of the line that passes through 10 1 and 5 2 Preview this quiz on Quizizz.\n\nUse the ordered pairs 3 20 and 9 60. Rate of Change and Slope Find theslope of line that passes through each pair of points. 4 5 6 2 9.", null, "1 3 Skills Practice Rate Of Change And Slope Ans Key Pdf Name Date Period 1 3 Skills Practice Rate Of Change And Slope Find The Slope Of The Line That Course Hero", null, "This Is Such A Fun Way For My 8th Grade Math And Algebra 1 Student To Practice Matching Line Algebra Activities Linear Equations Maths Activities Middle School", null, "Standard Form Of A Line Matching Cards Activity Teaching Math Teaching Algebra Algebra Activities", null, "Linear Equation Card Match Activity Slope Intercept Form Pdf Digital Slope Intercept Form High School Math Classroom 8th Grade Math", null, "Students Will Be Able To Determine The Rate Of Change Or Slope And Initial Value Or Y Intercept From A Relationship Worksheets Teaching Algebra Task Cards", null, "2 3 Rate Of Change And Slope Key Pdf Name Date Period 2 3 Practice Rate Of Change And Slope Find The Slope Of The Line That Passes Through Each Pair Course Hero", null, "Slope Frayer Model Junior High Math Math Notes 7th Grade Math", null, "Mathhooks Expressions And Equations 8 Which Of The Pilot S Instruments Is Not Working Base Education Math Maths Activities Middle School Middle School Math", null, "Linear Graphs Slope Y Intercept And Equations Equations Math Algebra I", null, "Students Will Be Able To Determine The Rate Of Change Or Slope And Initial Value Or Y Intercept From A Relationship Worksheets Teaching Algebra Task Cards", null, "Slope Four Ways Finding Slope Task Card Activity School Algebra Algebra Activities Teaching Algebra", null, "Slope Four Ways Finding Slope Task Card Activity Learning Math Teaching Algebra Teaching Math", null, "Solving Systems Of Equations Maze Slope Intercept Form Solve By Graphing Systems Of Equations Teaching Algebra Equations" ]

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[ "# Read from BRAM and write into 2D array in VHDL\n\nI have initialized a single port BRAM (clk,din,dout,addr,we) 8X10 with .coe file. I want to read from BRAM and write into the 2D array of dimension 10X8. As the dout of BRAM is 8 bit but the width of array is 10 basically, I want to do transpose. Kindly suggest me some solution. Please zoom the image below for better details.\n\nentity dummy_handle is\nPort ( clk : in STD_LOGIC;\n--test : out STD_LOGIC_VECTOR(7 DOWNTO 0);\n\nrst : in STD_LOGIC);\nend dummy_handle;\n\narchitecture Behavioral of dummy_handle is\n\ntype array2D is array (0 to 7,0 to 9) of STD_LOGIC;\nsignal M: array2D;\nsignal addr_array : STD_LOGIC_VECTOR(2 DOWNTO 0) := \"000\";\n\nsignal we_A: STD_LOGIC_VECTOR(0 DOWNTO 0) := \"0\";\nsignal addr : STD_LOGIC_VECTOR(3 DOWNTO 0) := \"0000\";\nsignal din : STD_LOGIC_VECTOR(7 DOWNTO 0);\nsignal test : STD_LOGIC_VECTOR(7 DOWNTO 0);\nsignal dout : STD_LOGIC_VECTOR(7 DOWNTO 0);\nsignal i : integer:= 0;\nsignal j : integer:= 0;\n\nCOMPONENT array_print\nPORT (\nclka : IN STD_LOGIC;\nwea : IN STD_LOGIC_VECTOR(0 DOWNTO 0);\naddra : IN STD_LOGIC_VECTOR(3 DOWNTO 0);\ndina : IN STD_LOGIC_VECTOR(7 DOWNTO 0);\ndouta : OUT STD_LOGIC_VECTOR(7 DOWNTO 0)\n);\nEND COMPONENT;\n\nbegin\n\ntest <= dout;\n\nprint_array : array_print\nPORT MAP (\nclka => clk,\nwea => we_A,\ndina => din,\ndouta => dout\n);\n\nbegin\nif rising_edge(clk) then\n\nif j = 9 and addr = \"1001\" then\nj <= 0;\ni <= 0;\n\nelse\n\ni <= i + 1;\n\nj <= j + 1;\nend if;\n\nend if;\n\nend if;\n\nend process dat_process;\nend Behavioral;\n\n\nThis is my code,it works ok for 0th column of array , but rest of the column upto 9 is showing undefined. It is not updating j.\n\nThis is the test bench.\n\nENTITY dummy_handle_test IS\nEND dummy_handle_test;\n\nARCHITECTURE behavior OF dummy_handle_test IS\n\n-- Component Declaration for the Unit Under Test (UUT)\n\nCOMPONENT dummy_handle\nPORT(\nclk : IN std_logic;\nrst : IN std_logic\n);\nEND COMPONENT;\n\n--Inputs\nsignal clk : std_logic := '0';\nsignal rst : std_logic := '0';\n\n-- Clock period definitions\nconstant clk_period : time := 20 ns;\n\nBEGIN\n\n-- Instantiate the Unit Under Test (UUT)\nuut: dummy_handle PORT MAP (\nclk => clk,\nrst => rst\n);\n\n-- Clock process definitions\nclk_process :process\nbegin\nclk <= '0';\nwait for clk_period/2;\nclk <= '1';\nwait for clk_period/2;\nend process;\n\n-- Stimulus process\nstim_proc: process\nbegin\n-- hold reset state for 100 ns.\nwait for 100 ns;\n\nwait for clk_period*10;\n\n-- insert stimulus here\n\nwait;\nend process;\n\nEND;\n\n\ndout is the out of BRAM, and it is of 8 bit ,how can we make it as a 10 bit and also I am not able to understand the long and short vector point, it will corrupt the original data ,i think.Pls help me in that.\n\nlibrary IEEE;\nuse IEEE.STD_LOGIC_1164.ALL;\nuse ieee.std_logic_unsigned.all;\nuse IEEE.NUMERIC_STD.ALL;", null, "• Comments are not for extended discussion; this conversation has been moved to chat. Dec 11, 2020 at 14:30\n\nAnswering your first question. I'll edit this as more information is provided. To add a short vector to the contents of a longer vector you can do this:\n\nsignal vector_long : std_logic_vector(9 downto 0);\nsignal vector_short : std_logic_vector(7 downto 0);\n\n#place statement below in process\nvector_long <= \"00\" & vector_short\n\n\nThis snippet will place 00 in vector_long at index 9 & 8 while the value of vector_short is placed in the lower 8 bits.\n\nIn your case it would be more convenient to do this:\n\nsignal dout : std_logic_vector(9 downto 0) := (others => '0');\n\n#move to component declaration\nprint_array : array_print\nPORT MAP (\nclka => clk,\nwea => we_A,\ndina => din,\ndouta => dout(7 downto 0)\n);\n\n\nAs you can see, we can assign individual bits in the port map. There is also an initial setting on the dout signal so the two uppermost bits are not undefined. This is a simulation only construct and will be removed for synthesis. That is not a problem as in the real world, there are only 2 states in a register.\n\nOther Errors\n\nYou have also made an error in the sensitivity list of your process. You only need clock in the sensitivity list (and rst too, if you intend to use it). This will cause very erratic behaviour as the process is run when one of the items in your sensitivity list changes.\n\nAs regards your use statements you should remove std_logic_unsigned as a library. It is a deprecated library and is no longer supported. Also, it contains functions with the same name as Numeric_std which will conflict. You need to do type conversions on the signals you are adding to or if you absolutely have to do vector arithmetic then you should use the VHDL-2008 library numeric_std_unsigned.\n\nThe next error is that you allow i to count past 7. This will cause a fatal error in simulation when you try to read from test(8) which does not exist. This means that j will never be updated as the simulation will stop. You should have got an error message about this in your simulator. Adding an elsif to check the value of i before reading from test(i) will prevent this. You then need to set i back to 0.\n\nI'm assuming that you only intend to read from BRAM once? As it stands, this process will run over and over as you have not added any controls such as enable.\n\n• I had set the BRAM to always enable mode. And want to read from BRAM for every address like first I read from address 0 and put the value to the array at 0th column and for the next column of array I want to read the next i.e. address 1of the BRAM and so on. Dec 11, 2020 at 13:28\n• You misunderstand. I was referring to you custom process. Once it has looped through and read the bram, it will begin again, and again, and again. Dec 11, 2020 at 14:54\n• once it reads the last address of BRAM and placed the data to last column of array, i need to stop the process then, for that i am using NULL,Is it correct? Dec 12, 2020 at 7:01" ]

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[ " Sample Problems > Usage > Mesh_Control > front\n\n# front\n\nNavigation:  Sample Problems > Usage > Mesh_Control >\n\n# front", null, "", null, "", null, "{ FRONT.PDE\n\nThis example demonstrates the use of the FRONT statement\n\nto create a dense mesh at a moving front.\n\nThe FRONT command is used to force mesh refinement wherever the\n\nconcentration variable passes through a value of 0.5.\n\nThe problem is the same as CHEMBURN.PDE.\n\n}\n\n title 'FRONT statement in Chemical Reactor'   select   painted     { make color-filled contour plots }   variables  Temp (threshold=1)  C (threshold=1)   definitions  Lz = 1  r1=1  heat=0  gamma = 16  beta = 0.2  betap = 0.3  BI = 1  T0 = 1  TW = 0.92 { the very nasty reaction rate: }  RC = (1-C)*exp(gamma-gamma/Temp)    xev=0.96   { some plot points }  yev=0.25   initial value  Temp=T0  C=0", null, "equations\n\nTemp:  div(grad(Temp)) + heat + betap*RC = dt(Temp)\n\nC:  div(grad(C)) + beta*RC = dt(C)\n\nboundaries\n\nregion 1\n\nstart (0,0)\n\n{ a mirror plane on X-axis }\n\nnatural(Temp) = 0\n\nnatural(C) = 0\n\nline to (r1,0)\n\n{ \"Strip Heater\" at fixed temperature }\n\n{ ramp the boundary temp in time, because  discontinuity is costly to diffuse }\n\nvalue(Temp)=T0 + 0.2*uramp(t,t-0.05)\n\nnatural(C)=0               { no mass flow on strip heater }\n\narc(center=0,0) angle 5\n\n{ convective cooling and no mass flow on outer arc }\n\nnatural(Temp)=BI*(TW-Temp)\n\nnatural(C)=0\n\narc(center=0,0) angle 85\n\n{ a mirror plane on Y-axis }\n\nnatural(Temp) = 0\n\nnatural(C) = 0\n\nline to (0,0) to close\n\ntime 0 to 1\n\n{ FORCE CELLS TO SPAN NO MORE THAN 0.1 ACROSS C=0.5 }\n\nfront(C-0.5, 0.1)\n\nplots\n\nfor cycle=10                 { watch the fast events by cycle }\n\ngrid(x,y)\n\ncontour(Temp)\n\ncontour(C) as \"Completion\"\n\nfor t= 0.2 by 0.05 to 0.3       { show some surfaces during burn }\n\nsurface(Temp)\n\nsurface(C) as \"Completion\"\n\nhistories\n\nhistory(Temp,C) at (0,0) (xev/2,yev/2) (xev,yev) (yev/2,xev/2) (yev,xev)\n\nend" ]

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[ "", null, "# How to delete DataFrame Row In Pandas Based On Column Value?\n\nA DataFrame is the primary data structure of the Pandas library and is commonly used for storing and working with tabular data. A common operation that could be performed on such data is deleting a DataFrame row in Pandas based on column value to remove unwanted information from the dataframe.\n\nTo start working with Pandas, we first need to import this statement in the Python code :\n\n### Python 3 Code :\n\n``import pandas as pd``\n\n## Running Example\n\nLet us understand this operation with the help of an example. Consider the following DataFrame containing 3 students with names A, B and C and their corresponding marks (out of 10) for two subjects, Mathematics and Physics.", null, "Python code snippet for generating the above DataFrame :\n\n### Python 3 Code :\n\n``````# Importing pandas\nimport pandas as pd\n\n# Dictionary for our data\ndata = {'Name' : ['A', 'B', 'C'], 'Mathematics' : [8, 5, 10], 'Physics' : [7, 9, 8]}\n\n# DataFrame for the dictionary\ndf = pd.DataFrame(data)\n\n# Printing the DataFrame\nprint(df)``````\n\nHere, data is a dictionary we created to initialize the DataFrame. For this, we use the DataFrame() function of the Pandas library which takes the dictionary as an argument and returns the required DataFrame.\n\nNow, let’s say we need to remove the rows of students that have received less than 8 marks in the subject physics. Thus, the student in the first row will be deleted and the resulting DataFrame would look like this :", null, "Let us look at different ways of performing this operation on a given DataFrame :\n\n## Remove DataFrame Rows by Selecting required Rows Only\n\nThis method is pretty straightforward and is the most commonly used one. In this method, we select the required rows instead of deleting the ones that are not required.\n\nSo, instead of deleting the rows with less than 8 marks in physics, we select the rows with greater than or equal to 8 marks in physics.\n\nThis operation is often referred to as boolean masking. Here, df[‘Physics’] is used to access the column with the label Physics in the dataframe. The changes are not made in place so we need to reassign the column.\n\nLet us look at the Python code and corresponding output for this method.\n\n### Python 3 Code :\n\n``````import pandas as pd\n\n# Dictionary for our data\ndata = {'Name' : ['A', 'B', 'C'], 'Mathematics' : [8, 5, 10], 'Physics' : [7, 9, 8]}\n\n# DataFrame for the dictionary\ndf = pd.DataFrame(data)\n\n# Selecting the required rows\ndf = df[df['Physics'] >= 8]\n\n# Printing the updated DataFrame\nprint(df)``````\n\nOutput :", null, "Another way to perform the same operation would be to use df.Physics to access the column labeled as Physics instead of using df[‘Physics’]. The changes are not made in place so we need to reassign the column. Let us look at the Python code and corresponding output for this method -\n\n### Python 3 Code :\n\n``````# Importing pandas\nimport pandas as pd\n\n# Dictionary for our data\ndata = {'Name' : ['A', 'B', 'C'], 'Mathematics' : [8, 5, 10], 'Physics' : [7, 9, 8]}\n\n# DataFrame for the dictionary\ndf = pd.DataFrame(data)\n\n# Selecting the required rows\ndf = df[df.Physics >= 8]\n\n# Printing the updated DataFrame\nprint(df)``````\n\nOutput :", null, "## Remove DataFrame Rows by Using the dataframe.drop() function\n\nIn this method, we use the dataframe.drop() function with the index of rows to be dropped, the first one here, passed as a parameter.\n\nHere, df[‘Physics’] is used to access the column with the label Physics in the dataframe. After selecting the rows to be deleted, i.e the ones with less than 8 marks in physics, we want to get the index of these rows.\n\nFor this, we use the dataframe.index property, which returns 0 in this case, the index of the first row. The changes are not made in place so we need to reassign the column.\n\nLet us look at the python code and corresponding output for this method.\n\n### Python 3 Code :\n\n``````# Importing pandas\nimport pandas as pd\n\n# Dictionary for our data\ndata = {'Name' : ['A', 'B', 'C'], 'Mathematics' : [8, 5, 10], 'Physics' : [7, 9, 8]}\n\n# DataFrame for the dictionary\ndf = pd.DataFrame(data)\n\n# Selecting the required rows\ndf = df.drop(df[df['Physics'] < 8].index)\n\n# Printing the updated DataFrame\nprint(df)``````\n\nOutput :", null, "Another way to perform the same operation would be to use df.Physics to access the column labeled as Physics instead of using df[‘Physics’]. Let us look at the Python code and corresponding output for this method -\n\n### Python 3 Code :\n\n``````# Importing pandas\nimport pandas as pd\n\n# Dictionary for our data\ndata = {'Name' : ['A', 'B', 'C'], 'Mathematics' : [8, 5, 10], 'Physics' : [7, 9, 8]}\n\n# DataFrame for the dictionary\ndf = pd.DataFrame(data)\n\n# Selecting the required rows\ndf = df.drop(df[df.Physics < 8].index)\n\n# Printing the updated DataFrame\nprint(df)``````\n\nOutput :", null, "If we want to make the changes in place to avoid reassigning the dataframe, we need to pass the parameter inplace as True. Let us look at the python code and corresponding output for this method.\n\n### Python 3 Code :\n\n``````# Importing pandas\nimport pandas as pd\n\n# Dictionary for our data\ndata = {'Name' : ['A', 'B', 'C'], 'Mathematics' : [8, 5, 10], 'Physics' : [7, 9, 8]}\n\n# DataFrame for the dictionary\ndf = pd.DataFrame(data)\n\n# Selecting the required rows\ndf.drop(df[df['Physics'] < 8].index, inplace = True)\n\n# Printing the updated DataFrame\nprint(df)``````\n\nOutput :", null, "Another way to perform the same operation would be to use df.Physics to access the column labeled as Physics instead of using df[‘Physics’] along with using inplace = True parameter. Let us look at the Python code and corresponding output for this method -\n\n### Python 3 Code :\n\n``````# Importing pandas\nimport pandas as pd\n\n# Dictionary for our data\ndata = {'Name' : ['A', 'B', 'C'], 'Mathematics' : [8, 5, 10], 'Physics' : [7, 9, 8]}\n\n# DataFrame for the dictionary\ndf = pd.DataFrame(data)\n\n# Selecting the required rows\ndf.drop(df[df.Physics < 8].index, inplace = True)\n\n# Printing the updated DataFrame\nprint(df)``````\n\nOutput :", null, "## Conclusion\n\nIn this topic, we have learned how to delete a DataFrame row in Pandas based on column value from an existing Pandas DataFrame, following a running example of test scores of students in different subjects, thus giving us an intuition of how this concept could be applied in real-world situations. Feel free to reach out to [email protected] in case of any suggestions\n\nTrending" ]

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[ "", null, "# Jacobi Polynomials in an Orthogonal Collocation Method\n\nInitializing live version", null, "Requires a Wolfram Notebook System\n\nInteract on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.\n\nPartial differential equations in rectangular, cylindrical, and spherical coordinates with symmetric boundary conditions occur in many fields of science and engineering. It is often possible to solve such equations using an orthogonal collocation method with roots of Jacobi polynomials as the points of collocation.\n\nContributed by: Jorge Gamaliel Frade Chávez (March 2011)\nOpen content licensed under CC BY-NC-SA\n\n## Snapshots", null, "", null, "", null, "## Details\n\nSymmetric Jacobi polynomials used in the orthogonal collocation method can be obtained from", null, ",\n\nwhere", null, "applies to a rectangular, cylindrical, or spherical coordinate, respectively,", null, "is the hypergeometric function,", null, "is the order in the polynomial,", null, "is the", null, "Jacobi polynomial, and", null, "is the independent variable.\n\nReference: J. V. Villadsen and W. E. Stewart, \"Solution of Boundary-Value Problems by Orthogonal Collocation,\" Chemical Engineering Science, 22, 1967 pp. 3981–3996." ]

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[ "# 3508148614404\n\n## 3,508,148,614,404 is an even composite number composed of six prime numbers multiplied together.\n\nWhat does the number 3508148614404 look like?\n\nThis visualization shows the relationship between its 6 prime factors (large circles) and 144 divisors.\n\n3508148614404 is an even composite number. It is composed of six distinct prime numbers multiplied together. It has a total of one hundred forty-four divisors.\n\n## Prime factorization of 3508148614404:\n\n### 22 × 3 × 7 × 292 × 701 × 70841\n\n(2 × 2 × 3 × 7 × 29 × 29 × 701 × 70841)\n\nSee below for interesting mathematical facts about the number 3508148614404 from the Numbermatics database.\n\n### Names of 3508148614404\n\n• Cardinal: 3508148614404 can be written as Three trillion, five hundred eight billion, one hundred forty-eight million, six hundred fourteen thousand, four hundred four.\n\n### Scientific notation\n\n• Scientific notation: 3.508148614404 × 1012\n\n### Factors of 3508148614404\n\n• Number of distinct prime factors ω(n): 6\n• Total number of prime factors Ω(n): 8\n• Sum of prime factors: 71583\n\n### Divisors of 3508148614404\n\n• Number of divisors d(n): 144\n• Complete list of divisors:\n• Sum of all divisors σ(n): 9702733412736\n• Sum of proper divisors (its aliquot sum) s(n): 6194584798332\n• 3508148614404 is an abundant number, because the sum of its proper divisors (6194584798332) is greater than itself. Its abundance is 2686436183928\n\n### Bases of 3508148614404\n\n• Binary: 1100110000110011011111001110110101000001002\n• Base-36: 18RMD3V2C\n\n### Squares and roots of 3508148614404\n\n• 3508148614404 squared (35081486144042) is 12307106700744705076275216\n• 3508148614404 cubed (35081486144043) is 43175159319539720988274524143765811264\n• The square root of 3508148614404 is 1873005.2360855801\n• The cube root of 3508148614404 is 15194.7185806393\n\n### Scales and comparisons\n\nHow big is 3508148614404?\n• 3,508,148,614,404 seconds is equal to 111,548 years, 14 weeks, 1 day, 22 hours, 13 minutes, 24 seconds.\n• To count from 1 to 3,508,148,614,404 would take you about two hundred seventy-eight thousand, eight hundred seventy years!\n\nThis is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000. (We do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!)\n\n• A cube with a volume of 3508148614404 cubic inches would be around 1266.2 feet tall.\n\n### Recreational maths with 3508148614404\n\n• 3508148614404 backwards is 4044168418053\n• The number of decimal digits it has is: 13\n• The sum of 3508148614404's digits is 48\n• More coming soon!" ]

[ null ]

[ "", null, "", null, "Our software program is like having your own personal algebra professor on call.", null, "", null, "", null, "Reviews & User Comments Unconditional Guarantee Algebra Prof vs The Rest Features and Benefits Resources and Links About Algebra-Net Our Privacy Policy FAQ - Resources How to Order! Algebra Home Algebra-net 112 Budley Street Denham Springs LA 70726 Ph: (206) 666-3590", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "OUR USERS", null, "", null, "", null, "Thank you so very much! Whoever had the idea of inventing such a useful Algebra siftwaer - it has saved me, now I really understand it now.\nP.W., Louisiana\n\nThis software has been great at helping me with my fractions. Something, Id struggled with for years. I have asked my parents for help, but they say all the math looks different now than when they were in school. Now, I dont need to ask anymore because the software explains everything.\nRobert Davis, CA\n\nI needed to test out of algebra to satisfy the entrance requirements for school. Algebra Professor saved me. Thank you!\nTom Canty, AZ\n\nThank you for the responses. You actually make learning Algebra sort of fun.\nRick Edmondson, TX\n\nStudents struggling with all kinds of algebra problems find out that our software is a life-saver. Here are the search phrases that today's Algebra Buster customers have used to find our site. Can you find yours among them?\n\n free polynomial calculator ti 86 decimal to fraction operations with rational expression similar or different... adding integers games solve math equations for me free how to solve equations involving rational expressions greatest common factor cool math taks math puzzles prentice hall chemistry workbook answers radical expressions on ti-89 math calculators online algebra 1 mcdougal littell answers difference of 2 squares precalculus proofs help equation divider calculator how to solve system of equations algebra multiplier calculator 9th grade math ebook ti-83 plus find cube \"fraction lesson plan\" the steps of algebra 2 problems\n\n Prev Next", null, "", null, "Algebra Homework | Elementary Algebra | Algebra Solver | Pre-Algebra | Mathematical Equation | Math Solver Algebra Factoring | Algebra Graphing | Rational Expression | Algebraic Equation | Algebraic Calculator | Complex Fraction Common Factor | Math Software | Math Help | Math Solve | Inequalities | Algebra Problems | Math Problems | Solving Algebra Problems All Rights Reserved by Algebra-Net.com 2007-2009" ]

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[ "", null, "Open in App\nNot now\n\n# Find minimum changes required in an array for it to contain k distinct elements\n\n• Difficulty Level : Easy\n• Last Updated : 28 Sep, 2022\n\nGiven an array arr of size N and a number K. The task is to find the minimum elements to be replaced in the array with any number such that the array consists of K distinct elements.\nNote: The array might consist of repeating elements.\nExamples:\n\nInput : arr[]={1, 2, 2, 8}, k = 1\nOutput :\nThe elements to be changed are 1, 8\nInput : arr[]={1, 2, 7, 8, 2, 3, 2, 3}, k = 2\nOutput :\nThe elements to be changed are 1, 7, 8\n\nApproach: Since the task is to replace minimum elements from the array so we won’t replace elements which have more frequency in the array. So just define an array freq[] which stores the frequency of each number present in the array arr, then sort freq in descending order. So, first k elements of freq array don’t need to be replaced.\nBelow is the implementation of the above approach :\n\n## C++\n\n `// CPP program to minimum changes required``// in an array for k distinct elements.``#include ``using` `namespace` `std;` `#define MAX 100005` `// Function to minimum changes required``// in an array for k distinct elements.``int` `Min_Replace(``int` `arr[], ``int` `n, ``int` `k)``{``    ``sort(arr, arr + n);` `    ``// Store the frequency of each element``    ``int` `freq[MAX];``    ` `    ``memset``(freq, 0, ``sizeof` `freq);``    ` `    ``int` `p = 0;``    ``freq[p] = 1;``    ` `    ``// Store the frequency of elements``    ``for` `(``int` `i = 1; i < n; i++) {``        ``if` `(arr[i] == arr[i - 1])``            ``++freq[p];``        ``else``            ``++freq[++p];``    ``}` `    ``// Sort frequencies in descending order``    ``sort(freq, freq + n, greater<``int``>());``    ` `    ``// To store the required answer``    ``int` `ans = 0;``    ``for` `(``int` `i = k; i <= p; i++)``        ``ans += freq[i];``        ` `    ``// Return the required answer``    ``return` `ans;``}` `// Driver code``int` `main()``{``    ``int` `arr[] = { 1, 2, 7, 8, 2, 3, 2, 3 };``    ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);``    ` `    ``int` `k = 2;``    ` `    ``cout << Min_Replace(arr, n, k);``    ` `    ``return` `0;``}`\n\n## Java\n\n `// C# program to minimum changes required``// in an array for k distinct elements.``import` `java.util.*;` `class` `GFG``{``    ``static` `int` `MAX = ``100005``;``    ` `    ``// Function to minimum changes required``    ``// in an array for k distinct elements.``    ``static` `int` `Min_Replace(``int` `[] arr,``                           ``int` `n, ``int` `k)``    ``{``        ``Arrays.sort(arr);``    ` `        ``// Store the frequency of each element``        ``Integer [] freq = ``new` `Integer[MAX];``        ``Arrays.fill(freq, ``0``);``        ``int` `p = ``0``;``        ``freq[p] = ``1``;``        ` `        ``// Store the frequency of elements``        ``for` `(``int` `i = ``1``; i < n; i++)``        ``{``            ``if` `(arr[i] == arr[i - ``1``])``                ``++freq[p];``            ``else``                ``++freq[++p];``        ``}``    ` `        ``// Sort frequencies in descending order``        ``Arrays.sort(freq, Collections.reverseOrder());``        ` `        ``// To store the required answer``        ``int` `ans = ``0``;``        ``for` `(``int` `i = k; i <= p; i++)``            ``ans += freq[i];``            ` `        ``// Return the required answer``        ``return` `ans;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main (String []args)``    ``{``        ``int` `[] arr = { ``1``, ``2``, ``7``, ``8``, ``2``, ``3``, ``2``, ``3` `};``        ` `        ``int` `n = arr.length;``        ` `        ``int` `k = ``2``;``        ` `        ``System.out.println(Min_Replace(arr, n, k));``    ``}``}` `// This code is contributed by PrinciRaj1992`\n\n## Python3\n\n `# Python 3 program to minimum changes required``# in an array for k distinct elements.``MAX` `=` `100005` `# Function to minimum changes required``# in an array for k distinct elements.``def` `Min_Replace(arr, n, k):``    ``arr.sort(reverse ``=` `False``)` `    ``# Store the frequency of each element``    ``freq ``=` `[``0` `for` `i ``in` `range``(``MAX``)]``    ` `    ``p ``=` `0``    ``freq[p] ``=` `1``    ` `    ``# Store the frequency of elements``    ``for` `i ``in` `range``(``1``, n, ``1``):``        ``if` `(arr[i] ``=``=` `arr[i ``-` `1``]):``            ``freq[p] ``+``=` `1``        ``else``:``            ``p ``+``=` `1``            ``freq[p] ``+``=` `1` `    ``# Sort frequencies in descending order``    ``freq.sort(reverse ``=` `True``)``    ` `    ``# To store the required answer``    ``ans ``=` `0``    ``for` `i ``in` `range``(k, p ``+` `1``, ``1``):``        ``ans ``+``=` `freq[i]``        ` `    ``# Return the required answer``    ``return` `ans` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``arr ``=` `[``1``, ``2``, ``7``, ``8``, ``2``, ``3``, ``2``, ``3``]``    ` `    ``n ``=` `len``(arr)``    ` `    ``k ``=` `2``    ` `    ``print``(Min_Replace(arr, n, k))``    ` `# This code is contributed by``# Surendra_Gangwar`\n\n## C#\n\n `// C# program to minimum changes required``// in an array for k distinct elements.``using` `System;` `class` `GFG``{``    ``static` `int` `MAX = 100005;``    ` `    ``// Function to minimum changes required``    ``// in an array for k distinct elements.``    ``static` `int` `Min_Replace(``int` `[] arr,``                           ``int` `n, ``int` `k)``    ``{``        ``Array.Sort(arr);``    ` `        ``// Store the frequency of each element``        ``int` `[] freq = ``new` `int``[MAX];``        ` `        ``int` `p = 0;``        ``freq[p] = 1;``        ` `        ``// Store the frequency of elements``        ``for` `(``int` `i = 1; i < n; i++)``        ``{``            ``if` `(arr[i] == arr[i - 1])``                ``++freq[p];``            ``else``                ``++freq[++p];``        ``}``    ` `        ``// Sort frequencies in descending order``        ``Array.Sort(freq);``        ``Array.Reverse(freq);``        ` `        ``// To store the required answer``        ``int` `ans = 0;``        ``for` `(``int` `i = k; i <= p; i++)``            ``ans += freq[i];``            ` `        ``// Return the required answer``        ``return` `ans;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main ()``    ``{``        ``int` `[] arr = { 1, 2, 7, 8, 2, 3, 2, 3 };``        ` `        ``int` `n = arr.Length;``        ` `        ``int` `k = 2;``        ` `        ``Console.WriteLine(Min_Replace(arr, n, k));``    ``}``}` `// This code is contributed by ihritik`\n\n## Javascript\n\n ``\n\nOutput:\n\n`3`\n\nTime Complexity : O(NlogN)\n\nAuxiliary Space: O(1) because it is using constant size freq array\n\nMy Personal Notes arrow_drop_up" ]

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[ "# Pivot Points\n\nPosted in Indicators of technical analysis\n\nPivot Points were created by parket traders on commodity markets. Today they are still used for futures trading, as well as Forex and Indices trading. Their aim is to set the Support and Resistance levels for the traded assets. They are still more and more popular as an indicator of technical analysis.\n\nThe Pivot Points are mainly used on markets with wide High/Low range. Such markets are very volatile.\n\nPivot Points calculation looks like follows:\n\nPP = [(H + L + C) / 3] or[(H + L) / 2] or[(O n+1 + H + L + C) / 4]\n\nR1 = 2*PP – L\n\nR2 = PP + H – L\n\nR3 = 2*PP + H – 2*L\n\nS1 = 2*PP – H\n\nS2 = PP – H + L\n\nS3 = 2*PP + L – 2*H\n\nS1, S2, S3 = First, Second, Third level of Support\n\nR1, R2, R3 = First, Second, Third level of Resistance\n\nO, H, L, C = Open, High, Low, Close\n\nPivot Points can be calculated on any time period. The calculation doesn't have to be in days. It can be based on weeks, months or e.g. 30-minutes graphs. If two Pivot Points, calculated on different time scales, do meet on the same level, such Pivot Point becomes much stronger. That's the reason why it is recommended to calculate them on more time scales, to confirm our trade decisions.\n\nHow to use the Pivot points:\n\nIt is important to realize that Pivot points calculated from today's prices are valid for the next day. Pivot point represents Support or Resisstance. If the price breaks through PP downwards, the crossed PP becomes Resistance. There are 3 basic levels of Support below the Pivot Point. The price can bounce off these supports upwards.  The analogy is true should the price cross the Pivot point upwards. Then the Pivot Point becomes Support for the price and it can bounce downwards mainly on the 3 basic Resistance levels.\n\nWe shouldn't enter trades immediately after the Price/Pivot Point crossing. There is a possibility of testing this Pivot point level and its strength again. The price moves in the desired direction just after such testing.\n\nAs you may understood from the section above, the Pivot Points are primarily used to identify:\n\n• when to enter a trade,\n• where to place our Stop Loss and\n• where to place our Profit Target.\n\nNote: There is more ways how to calculate the Pivot Points. You can choose from Fibonacci, Camarilla, Woodies Pivot Points etc. You don't have to calculate it yourself, just click here.", null, "" ]

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[ "## randomized two blocks (1 and 3) - second block in-between (not...\n\n Author Message LimaHD", null, "", null, "New Member", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Group: Forum Members Posts: 2, Visits: 5 Hi, I'm trying to randomize the order of two blocks. But I also want another block in between those two blocks. Here is what I did before (when I didn't need the block in between):/ preinstructions = (introduction, instructions1)/ blocks = [1-2 =noreplace(vid_1, vid_1_sl); 3= demographics]/ postinstructions = (end)Now I tried this, but I could make it work: / preinstructions = (introduction, instructions1)/ blocks = [1-3 =noreplace(vid_1, vid_1_sl); 2=stroop;  4= demographics]/ postinstructions = (end)I'm trying to randomize block 1 and 3 without randomizing block 2, as it has to come second. Only the order of 1 and 3 have to be randomized. Do you have any idea how I have to change it?Thanks for your help. Dave", null, "", null, "Supreme Being", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Group: Administrators Posts: 9.9K, Visits: 49K +xLimaHD - 11/11/2019Hi, I'm trying to randomize the order of two blocks. But I also want another block in between those two blocks. Here is what I did before (when I didn't need the block in between):/ preinstructions = (introduction, instructions1)/ blocks = [1-2 =noreplace(vid_1, vid_1_sl); 3= demographics]/ postinstructions = (end)Now I tried this, but I could make it work: / preinstructions = (introduction, instructions1)/ blocks = [1-3 =noreplace(vid_1, vid_1_sl); 2=stroop;  4= demographics]/ postinstructions = (end)I'm trying to randomize block 1 and 3 without randomizing block 2, as it has to come second. Only the order of 1 and 3 have to be randomized. Do you have any idea how I have to change it?Thanks for your help. The correct syntax to do this is:/ preinstructions = (introduction, instructions1)/ blocks = [1,3 =noreplace(vid_1, vid_1_sl); 2=stroop;  4= demographics]/ postinstructions = (end) LimaHD", null, "", null, "New Member", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Group: Forum Members Posts: 2, Visits: 5 +xDave - 11/11/2019+xLimaHD - 11/11/2019Hi, I'm trying to randomize the order of two blocks. But I also want another block in between those two blocks. Here is what I did before (when I didn't need the block in between):/ preinstructions = (introduction, instructions1)/ blocks = [1-2 =noreplace(vid_1, vid_1_sl); 3= demographics]/ postinstructions = (end)Now I tried this, but I could make it work: / preinstructions = (introduction, instructions1)/ blocks = [1-3 =noreplace(vid_1, vid_1_sl); 2=stroop;  4= demographics]/ postinstructions = (end)I'm trying to randomize block 1 and 3 without randomizing block 2, as it has to come second. Only the order of 1 and 3 have to be randomized. Do you have any idea how I have to change it?Thanks for your help. The correct syntax to do this is:/ preinstructions = (introduction, instructions1)/ blocks = [1,3 =noreplace(vid_1, vid_1_sl); 2=stroop;  4= demographics]/ postinstructions = (end)Thank you so much", null, "" ]

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[ "When conducting the 2-sample t-test to compare the average of two groups, the data in both groups must be sampled from a normally distributed population. If that assumption does not hold, the nonparametric Mann-Whitney test is a better safeguard against drawing wrong conclusions.\n\nThe Mann-Whitney test compares the medians from two populations and works when the Y variable is continuous, discrete-ordinal or discrete-count, and the X variable is discrete with two attributes. Of course, the Mann-Whitney test can also be used for normally distributed data, but in that case it is less powerful than the 2-sample t-test.\n\n### Uses for the Mann-Whitney Test\n\nExamples for the usage of the Mann-Whitney test include:\n\n• Comparing the medians of manufacturing cycle times (Y = continuous) of two different production lines (X).\n• Comparing the medians of the satisfaction ratings (Y= discrete-ordinal) of customers before and after improving the quality of a product or service.\n• Comparing the medians of the number of injuries per month (Y = discrete count) at two different sites (X).\n\n### Project Example: Reducing Call Times\n\nA team wants to find out whether a project to reduce the time to answer customer calls was successful. Time is measured before and after the improvement. A dot plot (Figure 1) of the data shows a lot of overlap between the lead times – it is hard to tell whether there are significant differences.\n\nTherefore, the team decides to use a hypothesis test to determine if there are “true differences” between before and after. Because the data is not normally distributed (p < 0.05) (Figure 2), the 2-sample t-test cannot be used. The practitioners will use the Mann-Whitney test instead.\n\nFor the test, the null hypothesis (H0) is: The samples come from the same distribution, or there is no difference between the medians in the call times before and after the improvement. The alternative hypothesis (Ha) is: The samples come from different distribution, or there is a difference.\n\n### Passing Mann-Whitney Test Assumptions\n\nAlthough the Mann-Whitney test does not require normally distributed data, that does not mean it is assumption free. For the Mann-Whitney test, data from each population must be an independent random sample, and the population distributions must have equal variances and the same shape.\n\nEqual variances can be tested. For non-normally distributed data, the Levene’s test is used to make a decision (Figure 3). Because the p-value for this test is 0.243, the variances of the before and after groups used in the customer call example are the same.\n\nIdeally the probability plot can be used to look for a similar distribution. In this case, the probability plot (Figure 4) shows that all data follows an exponential distribution (p > 0.05).\n\nIf the probability plot does not provide distribution that matches all the groups, a visual check of the data may help. When examining the plot, a practitioner might ask: Do the distributions look similar? Are they all left- or right-skewed, with only some extreme values?\n\n### Completing the Test\n\nBecause the assumptions are now verified, the Mann-Whitney test can be conducted. If the p-value is below the usually agreed alpha risk of 5 percent (0.05), the null hypothesis can be rejected and at least one significant difference can be assumed. For the call times, the p-value is 0.0459 – less than 0.05. The median call time of 1.15 minutes after the improvement is therefore significantly shorter than the 2-minute length before improvement.\n\n Mann-Whitney Test and Cofidence Interval: Before; After\n\nN Median\nBefore 100 2.000\nAfter 80 1.150\n\nPoint estimate for ETA1 – ETA2 is 0.400\n95.0 percent confidence interval for ETA1 – ETA2 is (0.000;0.900)\nW = 9,743.5\nTest of ETA1 – ETA2 vs. ETA1 not = ETA2 is significant at 0.0460\nThe test is significant at 0.0459 (adjusted for ties)\n\n### How the Mann-Whitney Test Works\n\nAnother name for the Mann-Whitney test is the 2-sample rank test, and that name indicates how the test works.\n\nThe Mann-Whitney test can be completed in four steps:\n\n1. Combine the data from the two samples into one\n2. Rank all the values, with the smallest observation given rank 1, the second smallest rank 2, etc.\n3. Calculate and assign the average rank for the observations that are tied (the ones with the same value)\n4. Calculate the sum of the ranks of the first sample (the W-value)\n\nTable 1 shows Steps 1 through 4 for the call time example.\n\n Table 1: Sum of the Ranks of the First Sample (the W-value) Call time Improvement Rank Rank for ties 0.1 Before 1 4 0.1 Before 2 4 0.1 After 3 4 0.1 After 4 4 0.1 After 5 4 0.1 After 6 4 0.1 After 7 4 0.2 Before 8 11 0.2 Before 9 11 0.2 Before 10 11 0.2 After 11 11 0.2 After 12 11 0.2 After 13 11 0.2 After 14 11 … … … … 7.5 Before 173 173 8 After 174 174 8.5 After 175 175 8.6 Before 176 176 10.3 Before 177 177 11.3 Before 178 178 11.9 After 179 179 18.7 Before 180 180 Sum of ranks (W-value) for before 9,743.5\n\nBecause Ranks 1 through 7 are related to the same call time of 0.1 minutes, the average rank is calculated as (1 + 2 + 3 + 4 + 5 + 6 + 7) / 7 = 4. Other ranks for ties are determined in a similar fashion.\n\nBased on the W-value, the Mann-Whitney test now determines the p-value of the test using a normal approximation, which is calculated as follows:", null, "where,\nW = Mann-Whitney test statistics, here: 9743.5\nn = The size of sample 1 (Before), here: 100\nm = The size of sample 2 (After), here: 80\n\nThe resulting ZW value is 1.995, which translate for a both-sided test (+/- ZW) and a normal approximation into a p-value of 0.046.\n\nIf there are ties in the data as in this example, the p-value is adjusted by replacing the denominator of the above Z statistics by", null, "where,\ni = 1, 2, …, l\nl = The number of sets of ties\nti = The number of tied values in the i-th set of ties\n\nThe unadjusted p-value is conservative if ties are present; the adjusted p-value is usually closer to the correct values, but is not always conservative.\n\nIn this example, the p-value does not vary dramatically through the adjustment; it is 0.0459. This indicates that the probability that such a ZW value occurs if there are actually no differences between the call times before and after the improvement is only 4.59 percent. With such a small risk of being wrong, a practitioner could conclude that the after results are significantly different." ]

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