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[ "WJMWorld Journal of Mechanics2160-049XScientific Research Publishing10.4236/wjm.2014.47023WJM-48290ArticlesENGINEERINGPHYSICS & MATHEMATICSAn Overset Grid Method for Fluid-Structure InteractionScottT. Miller1*R.L. Campbell1C.W. Elsworth1J.S. Pitt1D.A. Boger1Applied Research Laboratory, The Pennsylvania State University, State College, PA, USA* E-mail:[email protected](STM);11072014040721723712 April 201411 May 2014 8 June 2014© Copyright 2014 by authors and Scientific Research Publishing Inc. 2014This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/\n\nAn overset grid methodology is developed for the fully coupled analysis of fluid-structure interaction (FSI) problems. The overset grid approach alleviates some of the computational geometry difficulties traditionally associated with Arbitrary-Lagrangian-Eulerian (ALE) based, moving mesh methods for FSI. Our partitioned solution algorithm uses separate solvers for the fluid (finite volume method) and the structure (finite element method), with mesh motion computed only on a subset of component grids of our overset grid assembly. Our results indicate a significant reduction in computational cost for the mesh motion, and element quality is improved. Numerical studies of the benchmark test demonstrate the benefits of our overset mesh method over traditional approaches.\n\nOverset Grid Fluid-Structure Interaction Arbitrary-Lagrangian Eulerian Finite Volume Finite Element Moving Mesh OpenFOAM\n1. Introduction\n\nWe present a fully-coupled, arbitrary Lagrangian-Eulerian (ALE) fluid-structure interaction (FSI) algorithm that uses overset meshes around moving bodies to alleviate the difficulties and computational costs asso- ciated with moving mesh algorithms. Overset meshes allow us to accommodate very large structural displace- ments, including problems where no displacement constraints exist on the solid (e.g., the advection of deforma- ble bodies). The fluid domain is comprised of a stationary background mesh and body-fitted overset meshes for the structural components. It is only these overset meshes that need to be modified in a mesh motion procedure. The overset methodology does bring some computational overhead with it in terms of the computation of inter- polations stencils and weights. In this work, we study the benefits associated with the use of overset grids for FSI computations and compare with a standard approach within a single software framework. The benchmark problem of Turek and Hron is used to demonstrate the method and showcase the improvements that overset grids can offer.\n\nFluid-structure interaction modeling describes the complex interactions between a deformable solid structure with external and/or internal fluid flow. The fluid flow exerts forces on the wetted solid surface to cause defor- mation, and the resulting structural motion impacts the fluid flow. For such interaction, a two-way coupled model must be used, wherein the fluid flow and the solid deformations mutually affect each other. Moreover, for time-accurate transient models, a fully-coupled approach must be used such that all governing equations are si- multaneously satisfied (at least in the appropriate approximate sense) at each discrete time level.\n\nNumerical simulations of transient, fully coupled1 FSI phenomena have been performed by many authors, us- ing a variety of approaches. The common problem that all approaches must overcome is the disparity in the “natural” coordinate frames of the materials: the equations of solid mechanics are cast in the Lagrangian (refer- ence) frame, while fluid dynamics equations are traditionally written in a fixed Eulerian (spatial) configuration. All computational schemes for coupled FSI problems must bridge these two coordinate frames.\n\nOne approach to resolving this mathematical discrepancy in the descriptions is to cast all of the governing equations into an Eulerian framework - . This approach is used when very large structural deformations are expected, as the solid can move freely throughout the domain without changing the topology of the discretization. FSI methods of this type are inherently interface-capturing rather than interface-resolving; that is, the fluid- solid interface is not explicitly part of the discretization. Rather, the interface is captured by solving for its position as part of the numerical solution algorithm. The lack of a sharply defined interface makes the method inherently difficult to use for high Reynolds number flows where boundary layer resolution is an important aspect of the simulation.\n\nFixed grid methods for FSI have a fixed Eulerian grid, and the solid-fluid interface position is solved for as part of the solution procedure. Gerstenberger et al. applied a fixed grid method for moving interfaces with the use of h-adaptive mesh refinement. They also considered hybrid method that is a combination of fixed-grid and ALE formulations, which allowed for different discretizations and solution strategies for the fluid and solid domains. Wall et al. described both advances in ALE methods and new fixed grid methods based on domain decomposition ideas. In particular, advances in fixed-grid methods for FSI through the use of XFEM and Lagrange multiplier techniques was presented in . These methods were applied to higher-order problems in 3D, using either local adaptivity or another method where a layer of deformable (ALE) fluid elements are added to the structures surface. These methods seem to be very promising in terms of computational cost; how- ever, it remains to be seen how the methods work for very high Reynold’s number flows with turbulent bound- ary layers.\n\nExamples of interface-capturing methods include the immersed boundary method - , the immersed interface method , the fictitious domain method , the mortar finite element method , and the extended finite element method (XFEM) - . These methods are categorized as Eulerian-Lagrangian (EL) methods with the basic premise of use an Eulerian background mesh for the fluid, and a Lagrangian mesh for the solid, thus allowing both domains to reside in their natural mathematical framework. The two descriptions are then coupled by a similar variety of approaches, such as via the use of Lagrange multipliers or penalty methods. The interface must be captured as part of the solution procedure, requiring some mathematical description of the moving boundary. The prototypical example for interface representation is the level-set method - . As with the fully Eulerian methods, the fluid-solid interface can cause numerical difficulties as it cuts the background cells, resulting in decreased accuracy. Boundary layer resolution with these techniques has not been satisfactorily shown in the literature.\n\nParticle methods, such as smoothed particle hydrodynamics (SPH) or the immersed particle method, have also been applied to coupled FSI problems; see, e.g., - and the references therein for descriptions of these methods. A meshless finite element method with a purely Lagrangian description of both the solid and the fluid was proposed in .\n\nArbitrary Lagrangian-Eulerian methods, first studied in - and summarized in , allow the mesh topology to remain fixed in an Eulerian manner, move with material particles in a Lagrangian manner, or arbitrarily move to enable capturing of the fluid-solid interface. Tezduyar et al. describe the advantage of the ALE approach over the fixed-mesh alternatives is the ability to maintain high-quality meshes near the structure’s interface, resulting in more accurate fluid mechanics in that region. This reason is especially important for boundary layer resolution. The ALE formulation of the governing equations represents the discretized fluid domain as an arbitrarily deforming mesh, subject to displacement constraints at the fluid-solid interface. The solid equations are solved in Lagrangian coordinates, while the fluid equations are solved on the “moving mesh”. Velocity and traction continuity is enforced across the fluid-solid interface, as well as the kinematic constraint between solid and mesh displacements.\n\nThe ALE approach has been used for problems with large structural displacements , for partitioned - or monolithic - coupling strategies, with space-time finite elements , with discontinuous Galerkin methods , and with many other permutations of structural models and numerical approxima- tion types. Two approaches that seem to be popular are the isogeometric analysis method and space-time finite elements. Bazilevs et al. - use an ALE description for FSI simulations with an isogeometric finite ele- ment method applied to blood flow and wind turbines. Space-time finite elements permit more flexibility with regards to moving the fluid mesh, and they have been studied extensively by Tezduyar et al. - . Their deforming-spatial-domain/stabilized space-time DSD/SST formulations combined with space-time interface projection techniques have been used to solve problems ranging from parachute dynamics to arterial fluid me- chanics.\n\nOur overset grid approach to FSI problems shares similarities with both ALE and EL approaches. We utilize a fixed Eulerian background mesh for our fluid domain as in EL methods. We compute the structural solution on the fixed Lagrangian mesh. The fluid flow on the moving, boundary-conforming composite meshes is computed in the ALE frame. Solution coupling between the fluid and solid regions is done via the ALE approach; however, the flow coupling between the fixed background mesh and the composite meshes surrounding the solids is han- dled through the use of overset interpolation operators, which is somewhat analogous to the use of the coupling schemes that EL methods use to couple the Eulerian and Lagrangian frames. The difference is that in our me- thod we implicitly couple the Eulerian and the ALE frames rather than the Eulerian and Lagrangian frames.\n\nThe overset grid method for fully-coupled FSI simulations has only previously been studied by Wall et al. . In their approach, each fluid grid used was solved sequentially; that is, the overset grid attached to a de- formable body is solved separately from the background grid. Our overset method is similar in the hierarchy of grids used, but differs in that we build the overset grid interpolation directly into the algebraic system for the fluid region. As a result, we do not require any iterations over sequences of fluid grids, and we expect our me- thod to provide a more efficient solution method. The main detriment of the Chimera approach in , as stated by the authors, is the fluid-fluid coupling procedure, where additional computational costs and interpolation errors for convection dominated flows.\n\nOverset grid methods coupling flow fields to rigid solids or reduced order models of solids have been rela- tively popular in the computational fluid dynamics community. Small deformation transonic flutter using an overset, implicit aeroelastic solver were studied in , where they used an algebraic mesh deformation tech- nique for the grid motion. Prescribed helicopter rotor blade motion using first harmonics coupled to unsteady Navier-Stokes using overset was studied in . uses overset in a similar manner, coupling the flow field to a modal description of blade motion. Their work is unique in the choice of an algebraic algorithm for deforming the fluid grid. Overset is used for the pitch and heave of a surface combatant ship in large-scale DES computa- tions in . FSI using patched overset grids for rigid structural motion was accomplished in . The use of overset grids for finite element methods (FEM) was explored in . Kato et al. uses the overset FEM approach for LES, turbo-machinery and aeroacoustics with multiple dynamic frames of reference.\n\nOur approach is similar to in the use of overset grids; however, we allow for arbitrarily large structural movement. Our formulation and implementation removes the need for element deletion/addition that is com- monly used to accommodate large topological changes in moving mesh simulations (see, e.g., ). Rather, only the interpolation stencils and weights change in the overset interpolation step. This feature allows our method to handle situations including free moving deformable objects, and the possibility of extending it to include contact is straightforward with available algorithms.\n\nAnother drawback of moving mesh ALE methods is the need to solve for “arbitrary” mesh geometry to accommodate the structural displacements. No physical equation governs the mesh motion, and the only driving parameter is the known displacements of the fluid-structure boundary. There have been numerous proposed methods on what equations will yield quasi-optimal mesh topology (see, e.g., ). One important aspect when calculating the mesh motion is that the chosen equations are typically solved over the entire computational fluid domain. The result is a non-trivial computation that can contribute significantly to the overall computational cost of an FSI algorithm. Our overset FSI method circumvents the need for a “global” mesh motion solution; we simply solve for updated mesh positions on the composite grids that surround deformable bodies. This results in a greatly reduced computational load for the mesh motion, as only a subset of the grid positions are involved in the computation. Moreover, motion of the composite grids is generally simplified because they typically have no outer constraints, resulting in improved mesh quality.\n\nThe objective of the present work is to implement and demonstrate the advantages of coupling the overset mesh technology and an ALE, partitioned FSI solution algorithm. The governing equations, which are also outlined by Campbell and Paterson but provided here for completeness, are described and the discretization approach is presented. We briefly overview the standard numerical methods used, and we provide a description of how the overset mesh method is implemented within our solvers. A sample numerical benchmark test case based on the work of Turek and Hron is presented to demonstrate the improved mesh quality and solver performance.\n\n2. Governing Equations\n\nOne of the main challenges for coupling fluid and solid domains arises from the “natural” mathematical descriptions of the physics. The governing equations for a fluid flow are cast in an Eulerian (spatial) description, while the equations for a solid are written in Lagrangian (referential) form. Aside from that, the balance laws governing the behavior of both the fluid and solid domains are identical. We introduce the general continuum mechanics balance laws in an arbitrary Lagrangian-Eulerian (ALE) frame which provides the framework to describe the Eulerian, Lagrangian, or an arbitrary frame of reference.\n\nWe first consider the balance of mass:\n\nwhere is mass density, is the (fluid or solid) particle velocity, and is the velocity of the reference frame (the mesh velocity in an ALE method, which is required in this work to deform the fluid mesh to accom- modate structural deformation). For a Lagrangian description, , and for an Eulerian description on a stationary domain,.\n\nPerforming a force balance and making use of the continuity equation leads to the momentum equation:\n\nwhere is the Cauchy stress tensor and is the body force per unit mass.\n\nAn additional constraint for the ALE approach is that the mesh velocity satisfy the Geometric Conservation Law (GCL) - :\n\nwhere is the volume of a control element. The GCL requires the change in volume of each control ele- ment between two adjacent time steps equal the volume swept by the cell boundary during the time step. Farhat et al. have shown that satisfying a discrete version of the GCL is a necessary and sufficient condition for a scheme to preserve the nonlinear stability of a scheme’s fixed grid counterpart.\n\nEquations (1) and (2) are referred to as the governing equations. Application of constitutive relationships provides the necessary closure of the governing equations. The constitutive relationships and resulting equations for the fluid and solid domains are provided next, followed by the procedure used to couple these domains at the fluid/solid interface and details of the implementation.\n\n2.1. Fluid Equations in Eulerian Frame\n\nWe consider only incompressible Newtonian fluids in this work. The constitutive equation for the Cauchy stress tensor is\n\nwhere is the thermodynamic pressure, is the absolute viscosity, and is the symmetric strain-rate tensor. The incompressibility constraint is written as\n\nSubstitution of (4) into the momentum Equation (2) and utilizing (5) yields the Navier-Stokes equations:\n\nwhere is the kinematic viscosity.\n\nWe deal with three types of boundary conditions for our simulations: inflow, outflow, and solid wall. Boundary conditions are specified as\n\nEquations (5) and (6) will be solved for pressure and velocity using an ALE formulation in the present work. The ALE formulation is required to accommodate the structural deformations, thus imparting a non-trivial mesh velocity into the fluid region. We describe the numerical method used and its implementation in Section 3.1.\n\n2.2. Solid Equations in Lagrangian Frame\n\nThe Lagrangian frame-of-reference specifies the material velocity is equal to the frame velocity. Balan- ce of mass thus reduces to, which is independent of time. The momentum Equation (2) becomes\n\nwhere are the material displacements. The divergence of the first Piola-Kirchhoff stress with respect to material coordinates has been used in place of the spatial divergence of the Cauchy stress .\n\nThe numerical benchmarks published in Turek and Hron use a St. Venant-Kirchhoff hyper elastic model, which we also use here. The second Piola-Kirchhoff stress tensor is\n\nwhere are the Lamé parameters, is the identity tensor, and\n\nis the Green-Lagrange strain. The Piola-Kirchhoff stresses are related by, where is the deformation gradient.\n\nBoundary conditions for (10) on the Dirichlet and Neumann boundaries are specified as\n\nIn this work, it happens that the Neumann partition of the boundary is coincident with the fluid-structure boundary.\n\n2.3. Fluid-Structure Coupling\n\nThe fluid-structure interaction is accomplished by imposing fluid stresses on the solid (i.e., the tractions in (14)) and imparting the solid displacements and velocities to the fluid. The requirements for compatibility and the no-slip condition require the following:\n\nwhere is the unit normal on the interface in the spatial configuration and the superscripts on the Cauchy stress denote either the fluid or solid domain.\n\n2.4. Mesh Motion\n\nOur FSI approach requires changes to the spatial discretization (“mesh”) to accommodate the structural displacements in the fluid domain. The solution of the governing equations for the solid provides the interfacial displacement; however, there is no physical specification of the manner in which the mesh should deform away from the interface. The only requirement is that the mesh points on move with the interface. Additionally, it is the time derivative of the mesh displacement that enters the fluid’s governing equations as the mesh velocity.\n\nThere have been numerous methods proposed to solve for the mesh motion; see the reviews in . We employ two methods in our work: 1) diffusion of the interface displacements into the mesh using the Laplace equation:\n\nwhere is the mesh displacement from the original position and is a variable diffusion coefficient, and 2) a linear-elastic solid analogy that requires the divergence of Cauchy stress be zero everywhere:\n\nEquation (17) is similar to Equation (10) for the solid, but without the inertial or body force terms and with Cauchy stress instead of the first Piola-Kirchhoff stress. The mesh is represented by a linear-elastic solid\n\nand uses a small-strain approximation\n\nIn either choice, the mesh motion equation governs the fluid mesh position, and the fluid solver approximates the mesh velocity based on the solution time step and the mesh displacement. For instances where the interface motion is a small fraction of the smallest characteristic length of the interface cells, only the boundary points of the fluid mesh are moved and the remainder of the mesh remains stationary.\n\n3. Numerical Method\n\nCommercial software packages for Computer Aided Engineering (CAE) have recently been developing “multi- physics” capabilities, one of which is FSI. Most, if not all, of the available packages implement an ALE ap- proach. The ADINA System supports FSI calculations in a monolithic solution framework based solely on finite elements. Comsol Multiphysics offers a similar finite element-based monolithic FSI solver. The Star-CCM+ software suite by CD-Adapco offers an overset capability for finite volume-based CFD simu- lations, with the possibility of implicitly coupling rigid structural motions with a six degree-of-freedom solver. They also offer a deformable solid FSI solution procedure by coupling to the commercial finite element package ABAQUS ; however, the overset and deformable solid FSI capabilities can not yet be combined into an overset FSI method. While these commercial softwares are able to solve a small subset of FSI problems, they represent “black boxes” that cannot be user-modified to achieve our current goals. Thus, we have developed our overset FSI method through the use of open-source and in-house software tools.\n\nWe utilize a finite volume method (FVM) for the fluid equations and a finite element method (FEM) for the solid equations. The overset capability is added through the use of the foamed Over library . The need to communicate solution information between solvers, preferably in memory and without the need for file I/O op- erations, has resulted in the use of an open-source flow solver and an in-house structural solver. Additionally, we need to be able to couple the flow solver to our overset grid tools (described in Section 3.4). These require- ments have resulted in a customized FSI solver that will be expanded to larger and more challenging problems in the future.\n\n3.1. Finite Volume Method for the Fluid Region\n\nThe governing fluid mechanics equations are solved using the open source software OpenFOAM - . OpenFOAM is the flow solver of choice for this effort because it facilitates custom integration with third-party solvers, has a pre-existing mesh motion capability that satisfies the GCL, and its source code is freely available through the GNU General Public License. OpenFOAM is an object-oriented library for numerical simulations in continuum mechanics, written in the C++ language. OpenFOAM offers co-located, cell-centered finite volume numerics of second order accuracy for a variety of continuum physics. It offers a segregated solution procedure, whereby each equation is solved independently and sequentially. OpenFOAM version 2.1.x has been used for our implementation.\n\nThe flow problems considered herein are transient and incompressible, and on moving meshes; therefore OpenFOAM’s icoDyMFoam solver provides a baseline for development. The only modifications necessary for our overset-FSI method were adding the overset grid capability (see Section 3.4 for details). The icoDyMFoam solver uses the PISO (Pressure Implicit Splitting of Operators) algorithm to solve for the pressure and velocity fields. The general idea is to use the momentum equation to advance the velocity solution in time, and then a pressure-Poisson equation is derived such that the pressure solution enforces the incompressibility con- straint in a Lagrange-multiplier fashion.\n\n3.2. Finite Element Method for the Solid Region\n\nThe structural mechanics governing equations are solved using the finite element approach, implemented in an author-written C++ program called feanl (finite element analysis non-linear). The governing Equation (10) is discretized via a Bubnov-Galerkin weighted residual method to obtain the weak form - ; as such, details will be omitted here. The application of Dirichlet boundary conditions (13) occurs by elimination of equations from the governing system of equations that result after discretization of the structural domain and application of the finite element method. The geometric-nonlinearity present due to the Green-Lagrange strain is handled with a Newton-Raphson solution scheme.\n\n3.3. Mesh Motion\n\nThe governing mesh motion equations are solved using either OpenFOAM or feanl, depending on the type of mesh motion chosen at run time. Both approaches require a Dirichlet condition on the fluid/solid interface and the fluid mesh motions are computed. The Laplace mesh motion, represented by (16), uses a finite volume ap- proach within OpenFOAM to determine mesh deformation. Either a constant or a variable diffusivity is chosen and mesh motion is computed based on the motion of the interface vertices. Equation (16) is discretized using the fluid mesh and thus the mesh motion solution requires a separate equation solution but does not require a separate mesh.\n\nThe linear-elastic solid analogy, described by Equations (17)-(19), employs a finite element approach and is solved using feanl. This approach requires a finite element mesh that overlays the fluid mesh in the moving region, which can be the entire fluid domain, or a subset of the domain. This mesh in general is substantially coarser than the fluid mesh, and is limited only by 1) maintaining sufficient resolution at the fluid-solid interface to preserve the physical boundary, and by 2) producing sufficient quality of the morphed fluid mesh. An inter- polation scheme is employed within the finite element solver to prescibe motion of all fluid verticies that fall within the elements. The ability to employ a vastly coarser mesh reduces solution times. All aspects of the general-purpose finite element solver are applicable to the mesh motion solver, including variation of material properties to mimmic the variable diffusivity option of the Laplace mesh motion approach.\n\n3.4. Overset Grid Method\n\nIn the present study, the grid deformation that results from solving the coupled fluid-structure interaction is facilitated through the use of overset grids. The capability in this case is provided by an overset grid library named foamedOver that was previously added to OpenFOAM by one of the current authors (Boger) . FoamedOver itself is essentially a bridge between OpenFOAM and several other software packages, including DiRTlib , Suggar++ - , and PETSc . DiRTlib simplifies the addition of the overset ca- pability to an existing flow solver by encapsulating commonly needed operations, such as the gathering and scattering of the flow data at the interpolation locations . Suggar++ provides the overset assembly or domain connectivity information, which includes designation of out cells (hole cutting) and fringe cells as well as the determination of the interpolation stencils and weights . Other packages such as Pegasus provide simi- lar capability, but Suggar++ is particularly suited for the present case since it has native capability for dynamic and/or deforming cell-centered unstructured grids. Finally, PETSc is a suite of data structures and routines for the parallel solution of large systems of linear and non-linear equations . In this case, PETSc was used to facilitate the construction and solution of the linear systems of equations, which were modified to account im- plicitly for the intergrid boundary conditions. So for example, the pressure equation is normally solved using the default preconditioned GMRES solver in PETSc. The momentum equations, on the other hand, are normally solved using a weighted Jacobi scheme .\n\nSeveral hole-cutting methods and interpolation schemes are available in Suggar++. The domain connectivity information for the cases presented here result from an octree-based hole cutting method and use a least-squares method for interpolation.\n\n3.5. Fully Coupled, Partitioned FSI Algorithm\n\nWe employ the partitioned FSI approach of Campbell et al. in this work. In particular, we utilize an iden- tical partitioned iteration procedure, relaxation, and convergence checks. We shall summarize here for com- pleteness.\n\nFigure 1 shows the solution algorithm for our tightly coupled partitioned FSI method using a fixed-point iteration. The fixed-point iteration uses (Aitken’s) under-relaxation to control the structural displacements passed to the fluid, thereby improving robustness and accelerating convergence. The fluid solver (OpenFOAM) passes force information to the solid solver (feanl), which in turn passes the interfacial displacements to the fluid mesh solver. When overset meshes are used, the domain connectivity information (DCI) must be updated every time the mesh is moved.\n\n4. Numerical Results\n\nWe present numerical results for a single FSI validation problem defined by Turek and Hron . We do so in the context of comparing different strategies for the mesh motion component of the simulation. In particular, we compare a non-overset FSI method with several variants of our overset mesh FSI method and demonstrate improved mesh quality and performance during the simulations.\n\nPartitioned approach to FSI showing a fixed-point iteration with under-relaxation for tightly coupled solutions\n\n4.1. Types of Mesh Motion\n\nThe results presented herein demonstrate the behavior of three distinct mesh motion assemblies, as listed below. The name in bold type is used from this point forward to reference a mesh motion scheme.\n\n1. Non-overset: A single body-fitted fluid mesh which is deformed throughout the entire fluid domain. This is the legacy approach.\n\n2. Full Overset: A body-fitted overset mesh assembly where the motion of the entire assembly is computed over the entire fluid domain. This is the naive implementation of overset mesh technology into the existing algorithm.\n\n3. Subset Overset: A body-fitted overset mesh assembly where the background mesh is assumed static and only the motion of the overset grid components attached to the deformable structure is computed.\n\nIn all of the above cases, the mesh motion displacement is computed by solving a vector-valued Laplace equation with boundary conditions prescribed by the exterior of the fluid domain and the deformation of the solid structure. As described in Section 3.3, we have implemented an additional solver option that can be used with any of the aforementioned mesh assemblies. Therefore, the two mesh motion solver options are:\n\n1. Standard isotropic vector Laplace equation solver with variable diffusivity.\n\n2. An overlay solver (described in Section 3.3) that uses an auxiliary finite element mesh that overlays the moving fluid region and is solved using feanl; variable mesh stiffness is accomplished through mesh property variation.\n\n4.2. Benchmark Problem of Turek and Hron\n\nThe reference test case proposed by Turek and Hron was selected to benchmark and validate the proposed overset grid FSI solver presented in this work. The case was developed as an improvement on Ramm and Wall’s test case from 1998 , in order to compare the speed and accuracy of newly developed FSI codes, schemes, and approaches. Goals of the reference case were reproducible dynamic steady state solutions and the generation and presentation of this solution data. The resulting two-dimensional case consists of a slightly off-center cylinder immersed in channel flow, with a flexible trailing structure, as shown in Figure 2. The flow over the cylinder sheds vortices which then impinge on the flexible tail and cause it to oscillate. Details of domain dimensions are included in Table 1, and the ramped parabolic inlet velocity is defined by Equations (20) and\n\nTable 1\n\n. Dimensions of the Turek benchmark test case .\n\nDimensionValue [m]\nChannel Width. Dimensions of the Turek benchmark test case .0.41\nChannel Length. Dimensions of the Turek benchmark test case .2.5\nCylinder Radius. Dimensions of the Turek benchmark test case .0.05\nFlag Length. Dimensions of the Turek benchmark test case .0.35\nFlag Width. Dimensions of the Turek benchmark test case .0.02\nCylinder Center. Dimensions of the Turek benchmark test case .(0.2, 0.2)\n\nDiagram of the Turek and Hron FSI benchmark test case geometry \n\n(21). Physical constants, such as fluid velocity and material properties, were chosen to support simple periodic oscillations of the tail. We will compare our calculations with those of Turek and Hron in their “FSI2” case, which uses the physical properties included in Table 2.\n\n4.3. Mesh Generation and Validation\n\nThe implementation of an overset grid FSI case requires the generation of three separate mesh components: the background fluid mesh, the dynamic overset fluid mesh attached to the deformable structure, and the solid mesh, as seen in Figure 3. The background fluid mesh spans the entire domain, while the overset fluid and solid domains are specific to the immersed geometry being modeled. The interpolation between the background and\n\nDecomposition of Overset FSI meshes: static background (gray), dynamic overset (blue), solid (red). Note the disparate number of cells between the solid and fluid meshes along the fluid-structure interface. The lower images demonstrate the ease with which the solid geometry can be changed\n\nTable 2\n\n. Physical Properties of the Turek benchmark test case .\n\nParameterValueUnits\nFluid\n. Physical Properties of the Turek benchmark test case .. Physical Properties of the Turek benchmark test case .. Physical Properties of the Turek benchmark test case .\n. Physical Properties of the Turek benchmark test case .. Physical Properties of the Turek benchmark test case .. Physical Properties of the Turek benchmark test case .\n. Physical Properties of the Turek benchmark test case .1. Physical Properties of the Turek benchmark test case .\nSolid\n. Physical Properties of the Turek benchmark test case .. Physical Properties of the Turek benchmark test case .. Physical Properties of the Turek benchmark test case .\n. Physical Properties of the Turek benchmark test case .0.4[ ]\n. Physical Properties of the Turek benchmark test case .. Physical Properties of the Turek benchmark test case .[Pa]\n\noverset fluid meshes is performed by Suggar++, as described in Section 3.4. The result of the overset approach is a solver with the ability to easily add and modify solid features in a given fluid domain, as illustrated by Figure 3. Note that the nodes of the cells in the solid and overset fluid meshes do not need to be coincidental on the fluid-structure interface. This feature arises naturally from the partitioned nature of this FSI algorithm, and allows for different meshing requirements to be met for each constituent part of the domain.\n\nBefore delving into the formal study, we present in Figure 4 a sample calculation of the motion of the flexible tail and the flow field during several time steps of our simulation of the FSI2 case by Turek and Hron . The interaction between the shed vortices propagating down the channel, from left to right, and the flexible tail’s deformation is easily observed. We also note that the deformation of the tail is not amplified in these images, demonstrating that we are in fact simulating a case with large solid deformations that subsequently interact with the flow field. The solution is not stationary but does eventually reach a steady state.\n\nTo address the issue of verification and validation, we extract from our simulations the displacement of the vertical midpoint of the the trailing end of the flexible tail and compare it to the values reported by Turek and Hron . The position of this measurement is denoted by a black dot on the tip of the tail in Figure 2.\n\nIn Figure 5 we show two results. The left image shows the tip displacement components over a scaled time period of two steady state oscillations, for all three of our mesh assembly approaches. The values presented were calculated with all numerical schemes and tolerances held constant, except for the method of grid assembly and mesh motion. We have confirmed that all three methods of grid assembly produce the same tip displacements.\n\nThe right image in Figure 5 is a comparison of our calculated horizontal displacements with those from the Turek and Hron FSI2 case. With our initial coarse mesh, we obtain values within a few percent of the reported results, and after appropriately refining the fluid and solid meshes our results agree very well with the previously reported values. Because we have verified that all three approaches match each other, and that refining the mesh brings the solution as close to the Turek and Hron data as we desire, we feel comfortable that our algorithms are implemented correctly and functioning as designed.\n\n4.4. Mesh Motion Comparison Study\n\nThis section contains the primary result of this research effort, namely the demonstration of significant improvement in mesh quality during large deformation FSI simulations via the implementation of overset grid methods. We compare three reproductions of the FSI2 test case in this section: the legacy non-overset mesh approach, the overset mesh approach, and the overset mesh approach with the overlay mesh motion solver. We note that there is no difference in the solution between the full and subset overset techniques, and as such we only report results of the subset overset approach here.\n\nFigure 6 shows the results of running the FSI2 Turek case with each of the aforementioned mesh assembly approaches. We see many differences in the resulting meshes at a given time step of maximum deflection. Most\n\nStill images of our reproduction of the FSI2 case from Turek and Hron , starting at the upper left and moving right then down and left and so on. The grey scale represents velocity magnitude, with contours showing re- gions of equal value\n\nVerification of the overset FSI algorithms. We compare the cal- culated tip displacement between all three mesh assembly approaches (left) and our calculated displacements to those from Turek and Hron (right). All of the approaches produce the same results and match the previously re- ported results\n\nnotably, cell deformations are distributed through the domain in the non-overset case. This leads to stretched cells at the top of the channel and compressed cells at the bottom. Concerns in cell skewness and aspect ratio occur in regions that would be important for boundary layers in this case, but in general the motion of the mesh in the entire domain is undesirable for preserving accuracy. However, in the overset case, background mesh quality is maintained due to the fact that the overset mesh is moved independently. This leads to a predictable background mesh in FSI problems, which is important for preserving mesh quality in areas of importance away from the fluid-structure interface.\n\nIn the overset fluid mesh (middle, Figure 6), cell deformation at the tip of the tail is similar to the non-overset case due to the use of the same standard mesh motion solver for both cases. This is seen more clearly in Figure 7, which shows a zoomed-in region around the deformed overset and non-overset meshes at the tip of the tail. Despite this, it is noted in the overset case that all poor quality cells are confined to the overset mesh.\n\nOne way to resolve this involves stiffening the mesh around the tail, which results in the mesh remaining tangent to the tip of the tail. This is precisely what is done in the overlay mesh motion solver. As shown in the\n\nComparison of mesh motion strategies: the legacy non-overset approach (top), the overset approach with the same mesh motion solver as the legacy approach (middle), and the overset approach with the overlay mesh motion solver (bottom). While all three approaches find the same deflection, the mesh quality clearly improves from top to bottom. The introduction of overset mitigates much of the mesh distortion throughout the domain, and the improved non-uniform stiffness mesh motion solver greatly improves the mesh quality in the deformed overset mesh\n\nZoomed view of the fluid mesh surrounding the tail in Figure 6. The non-overset case (left) and overset case (middle) show similar mesh distortion at the tip of the tail, as is expected since they were computed with the same standard mesh motion solver. The overset case with the non-uniform stiffness overlay mesh motion solver (right) corrects this issue and creates a large displacement mesh with very good cell quality\n\nbottom image of Figure 6 and in Figure 7, this results in a much better quality mesh at the tip of the tail, ef- fectively maintaining the original quality of the entire mesh. In addition, it can be noted that with this improve- ment in cell quality, there was also an improvement in overset communication, leading to a shorter trailing mesh.\n\nIn summary, all of the mesh assembly methods we have proposed are capable of reproducing the results in the FSI2 case from Turek and Hron . The use of overset mesh assemblies improves the mesh quality away from the fluid-structure interface by maintaining a static background mesh, but it does not alleviate the issue of mesh distortion near the interface. We demonstrate that overset meshing combined with a non-uniform stiffness overlay mesh motion solver can preserve mesh quality even during large deformation simulations.\n\n4.5. Timing and Performance Improvements\n\nIn the previous section, we address and demonstrate the improvement in mesh quality during large deformation simulations that is enabled via overset mesh techniques. In the present section we explore the computational cost of this added capability. To do so, we track the time required to run the FSI2 case from the Turek and Hron study for the three mesh assembly approaches given in Section 4.1.\n\nFigure 8 shows the average wall-time per timestep that was needed by the solver to compute the mesh motion component of the FSI algorithm. The average wall-time is the wall-time for the entire timestep divided by the number of FSI subiterations during that timestep. As we can see, the naive implementation of the overset mesh technology into the legacy solver, where the motions of all points in the grid assembly are calculated, increases the run time of the algorithm. However, when we consider the background mesh of the overset grad assembly to be fixed, and calculate the motion of only the grid components attached to the flexible interface, then we see a substantial reduction in the mesh motion solver time as compared to both the full overset and non-overset cases.\n\nIn order to judge the net effect of reducing the mesh motion solver time on the entire simulation time, we include in Figure 9 the average wall-time per timestep of the fluid and solid solver (top) and average wall-time per timestep of the entire FSI algorithm (bottom). The results in this figure, for this example problem, clearly show the wall time for the solid solver is less then the mesh motion solver, but that the fluid solver wall-time dominates the run time of the problem. However, there is a small overall reduction in the total run time by using the subset overset mesh motion approach.\n\nThis is an important observation, given that we have added functionality, i.e., improved mesh quality for large deformations, while retaining or reducing the run-time of the problem. This benefit is expected to be amplified for three dimensional domains, providing further advantage of the overset approach.\n\nAverage wall-time for mesh motion solution per timestep plotted as a func- tion of simulation time. The naive addition of overset mesh technology into the solver increases the mesh motion wall-time, while the optimization for moving only the sub- set of the overset assembly attached to the deforming structure results in reduced wall- time\n\nFigure 9\n\nAverage wall-time for the fluid and structural solutions per timestep (a) plotted as a function of simulation time, and the total solver average wall- time (b). The fluid solver dominates the run-time of this problem, but the over- ball simulation time does not increase with the addition of the overset meshing technology\n\n5. Conclusions\n\nWe have developed and demonstrated an FSI simulation method based on the ALE formulation of the governing equations. Our partitioned algorithm allows for the modular introduction of separate, optimized fluid and structural solvers that are joined by a custom framework to pass information between them and perform the necessary mesh motion. The focus of this work is on the mesh motion component of the problem, as it is the source of many difficulties in FSI simulations where large deformation occurs.\n\nTo this end, we have proposed to use overset grid technology to alleviate some of the mesh motion difficulties. We have implemented overset technology into the FSI algorithm, verified it against the legacy mesh motion technique, and validated it against previously published computational results. When only the motions of the overset mesh components attached to the deforming immersed structure are calculated, we are able to simulta- neously preserve mesh quality without expensive re-meshing, but also fundamentally maintain or reduce the runtime of the algorithm. A key component of this achievement is the use of the non-uniform stiffness overlay solver to compute the mesh motion in a manner that optimizes deformation of the mesh away from the fluid- structure interface.\n\nWhile the authors are excited about the results contained in this work, we are also optimistic that when this algorithm is applied to more complex geometries and three dimensional domains, where mesh motion can be a large fraction of the computation time, we will see an even more pronounced improvement in mesh quality and performance. We plan to extend this solver and apply it to three dimensional RANS simulations in the near fu- ture.\n\nAcknowledgements\n\nThe authors would like to acknowledge support for this research from the Applied Research Laboratory at The Pennsylvania State University, especially the student support from the ARL Undergraduate Honors Program." ]

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[ "Cody\n\n# Problem 1129. Reverse the elements of an array\n\nSolution 2042451\n\nSubmitted on 2 Dec 2019 by maya abu fowdah\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\n### Test Suite\n\nTest Status Code Input and Output\n1   Pass\nx = []; y_correct = []; assert(isequal(your_fcn_name(x),y_correct))\n\n2   Pass\nx = 1; y_correct = 1; assert(isequal(your_fcn_name(x),y_correct))\n\n3   Pass\nx = [1:5]; y_correct = [5:-1:1]; assert(isequal(your_fcn_name(x),y_correct))\n\n4   Pass\nx = [1:5;6:10]; y_correct = [10:-1:6;5:-1:1]; assert(isequal(your_fcn_name(x),y_correct))\n\n5   Pass\nx = [1:5;6:10;11:15]; y_correct = [15:-1:11;10:-1:6;5:-1:1]; assert(isequal(your_fcn_name(x),y_correct))\n\n6   Pass\nx = ones(5); y_correct = ones(5); assert(isequal(your_fcn_name(x),y_correct))\n\n7   Pass\nx = magic(3); y_correct = [2 9 4;7 5 3;6 1 8]; assert(isequal(your_fcn_name(x),y_correct))\n\n8   Pass\nx = [2 9 -4;7 -5 3;-6 1 8]; y_correct =[8 1 -6;3 -5 7;-4 9 2] ; assert(isequal(your_fcn_name(x),y_correct))\n\n### Community Treasure Hunt\n\nFind the treasures in MATLAB Central and discover how the community can help you!\n\nStart Hunting!" ]

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[ "## On the ubiquity of modular forms and Apery-like numbers\n\nSpeaker: Armin Straub\nDate: 09/10/2013\nTime: 14:00 - 16:00\n\nLocation: RISC Seminar room\n\nIn the first part of this talk, we give examples from the theories of short random walks, binomial congruences, positivity of rational functions and series for $1/\\pi$, in which modular forms and Apery-like numbers appear naturally (though not necessarily obviously). Each example is taken from personal research of the speaker. The second part, which is based on joint work with Bruce C. Berndt, is motivated by the secant Dirichlet series $\\psi_s(\\tau) = \\sum_{n = 1}^{\\infty} \\frac{\\sec(\\pi n \\tau)}{n^s}$, recently introduced and studied by Lalin, Rodrigue and Rogers as a variation of results of Ramanujan. We review some of its properties, which include a modular functional equation when $s$ is even, and demonstrate that the values $\\psi_{2 m}(\\sqrt{r})$, with $r > 0$ rational, are rational multiples of $\\pi^{2 m}$. These properties are then put into the context of Eichler integrals of general Eisenstein series. In particular, we determine the period polynomials of such Eichler integrals and indicate that they appear to give rise to unimodular polynomials, an observation which complements recent results on zeros of period polynomials of cusp forms by Conrey, Farmer and Imamoglu." ]

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[ "", null, "# 06.07.2015\n\n## Informatik-Kolloquium\n\nIm Sommersemester 2015 findet im Rahmen des Informatik-Kolloquiums der folgende Vortrag statt:\n\nMontag, 6. Juli 2015, 16.15 Uhr, Turing-Hörsaal\n\n### Finding an Approximate Shortest Path amid Weighted Regions\n\nGiven a triangulated region R that consists of n triangles each associated with a positive weight, two points s and t in R, and 0 < epsilon < 1, we want to find a path between s and t whose cost is at most (1+epsilon) times the cost of an optimal path between s and t. The cost of a polygonal path in R is the weighted sum of the line segments that it comprises of. A shortest (or, an optimal) path between s and t is a path that has the least cost among all the paths between s and t.\n\nThe talk starts with presenting various properties of geodesic shortest paths in weighted regions from Mitchell and Papadimitriou ’(1991), and details their polynomial-time algorithm. Their algorithm progresses the intervals of optimality (a variant of a discrete Dijkstra wavefront) in the geometric domain from s to t. Then, we give an overview over practical but pseudo-polynomial-time algorithms; these algorithms primarily reduce the geometric least cost-path finding problem to a graph-theoretic single-source shortest path problem (rooted at s). Finally, we present an own recent result: the first polynomial-time algorithm since the result of Mitchell and Papadimitriou. Our algorithm initiates a discrete Dijkstra wavefront from s and expands it over R. We decrease the running time by a cubic factor while optimizing the number of events points involved." ]

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[ "# What is Percent of Change? Definition and Examples\n\nWhat is percent of change? Suppose the price of a \\$100 Android tablet increases by \\$20. You can express the increase as a percent as shown below.", null, "20% is an example of percent of change.\n\nGenerally speaking, the percent of change is the ratio of the amount of change to the original amount.\n\nWhen a value increases from its original amount, it is called the percent of increase.\n\nWhen a value decreases from its original amount, it is called the percent of decrease.\n\n## A couple of examples showing how to find the percent of change\n\nExample #1\n\nThe price of a T-shirt decreased from \\$25 to \\$21. Find the percent of change, called in this case the percent of decrease.\n\nPercent of decrease = amount of change / original amount\n\nThe amount of change is 25 - 21 = 4 and the original amount is 25.\n\nPercent of decrease = 4 / 25 = 16 / 100 = 16%\n\nExample #2\n\nIn 1997, 1 share in Amazon was worth about \\$18. By the end of 2020, 1 share in Amazon was worth about 3200. Find the percent of change, called in this case the percent of increase.\n\nPercent of increase = amount of change / original amount\n\nThe amount of change is 3200 - 18 = 3182 and the original amount is 18.\n\nPercent of increase = 3182 / 18 = 176.77 ≈ 177\n\n177 / 1 = 17700 / 100 = 17700%\n\nThe price of 1 share in Amazon increased by about 17700%" ]

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[ "# graph_tool.inference.nested_partition_overlap#\n\ngraph_tool.inference.nested_partition_overlap(x, y, norm=True)[source]#\n\nReturns the hierarchical maximum overlap between nested partitions, according to an optimal recursive label alignment.\n\nParameters:\nxiterable of iterables of int values\n\nFirst partition.\n\nyiterable of iterables of int values\n\nSecond partition.\n\nnorm(optional, default: True)\n\nIf True, the result will be normalized in the range $$[0,1]$$.\n\nReturns:\nwfloat or int\n\nMaximum hierarchical overlap value.\n\nNotes\n\nThe maximum overlap between partitions $$\\bar{\\boldsymbol x}$$ and $$\\bar{\\boldsymbol y}$$ is defined as\n\n$\\omega(\\bar{\\boldsymbol x},\\bar{\\boldsymbol y}) = \\sum_l\\underset{\\boldsymbol\\mu_l}{\\max}\\sum_i\\delta_{x_i^l,\\mu_l(\\tilde y_i^l)},$\n\nwhere $$\\boldsymbol\\mu_l$$ is a bijective mapping between group labels at level $$l$$, and $$\\tilde y_i^l = y^i_{\\mu_{l-1}(i)}$$ are the nodes reordered according to the lower level. It corresponds to solving an instance of the maximum weighted bipartite matching problem for every hierarchical level, which is done with the Kuhn-Munkres algorithm [kuhn_hungarian_1955] [munkres_algorithms_1957].\n\nIf norm == True, the normalized value is returned:\n\n$1 - \\frac{\\left(\\sum_lN_l\\right) - \\omega(\\bar{\\boldsymbol x}, \\bar{\\boldsymbol y})}{\\sum_l\\left(N_l - 1\\right)}$\n\nwhich lies in the unit interval $$[0,1]$$, where $$N_l=\\max(N_{{\\boldsymbol x}^l}, N_{{\\boldsymbol y}^l})$$ is the number of nodes in level l.\n\nThis algorithm runs in time $$O[\\sum_l N_l + (B_x^l+B_y^l)E_m^l]$$ where $$B_x^l$$ and $$B_y^l$$ are the number of labels in partitions $$\\bar{\\boldsymbol x}$$ and $$\\bar{\\boldsymbol y}$$ at level $$l$$, respectively, and $$E_m^l \\le B_x^lB_y^l$$ is the number of nonzero entries in the contingency table between both partitions.\n\nReferences\n\n[peixoto-revealing-2021]\n\nTiago P. Peixoto, “Revealing consensus and dissensus between network partitions”, Phys. Rev. X 11 021003 (2021) DOI: 10.1103/PhysRevX.11.021003 [sci-hub, @tor], arXiv: 2005.13977\n\nH. W. Kuhn, “The Hungarian method for the assignment problem,” Naval Research Logistics Quarterly 2, 83–97 (1955) DOI: 10.1002/nav.3800020109 [sci-hub, @tor]\n\nJames Munkres, “Algorithms for the Assignment and Transportation Problems,” Journal of the Society for Industrial and Applied Mathematics 5, 32–38 (1957). DOI: 10.1137/0105003 [sci-hub, @tor]\n\nExamples\n\n>>> x = [np.random.randint(0, 100, 1000), np.random.randint(0, 10, 100), np.random.randint(0, 3, 10)]\n>>> y = [np.random.randint(0, 100, 1000), np.random.randint(0, 10, 100), np.random.randint(0, 3, 10)]\n>>> gt.nested_partition_overlap(x, y)\n0.140018..." ]

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[ "## DEV Community is a community of 623,823 amazing developers\n\nWe're a place where coders share, stay up-to-date and grow their careers.\n\n# Simple and Effective Collision Resolution of an Axis Aligned Bounding Box to an Immovable Plane\n\nRecently here at Wooden H Studio we have uncovered a way to create some simple Axis Aligned Bounding Box, or AABB for short, to plane resolution, so let’s get started with how we did it!\n\n## Standard Variables\n\nAs a standard AABB’s have a couple variables that when added together create an AABB, these include a position, and minimum value, a maximum value, additionally we made a simple plane that consists of a position, and a normal vector. So, let’s assume we already know that the AABB and the Plane are colliding and now we need to figure out how to move the AABB back up to where it isn’t inside the plane.\n\n## The Calculations\n\nWhat we did is we started off by using the closest point to a line test. Originally, we didn’t have a line to use so we needed to make one. We used the normal value of our plane and added it to the plane's position to give us the endpoint for our line, this way the plane could be facing any direction and we will always have a valid line to start. From here you can find the closest point using the closest point on a line test. To do this test you need to subtract the lines end position by the lines starting position and normalize it, I’ll call this the \"Start To End\" vector. Then you take the point you are trying to find, in this case, it is the AABB’s position, and subtract it by the lines start position. Next, we want to find the dot product of both of these values and multiply it with the \"Start To End\" vector. Lastly, we need to add this new vector to the plane's position and that is how you find the closest point!\n\nNext up we need to find the extents of the AABB, which is simply the AABB’s maximum value subtracted by its position and that will give us the extents of our cube. We can use the extents to get a radius in coherence with the plane. To get this radius we once again use the dot product with the planes normal vector and our extents.\n\nSo now that we essentially have the AABB’s position projected onto our line and we have the \"radius\" of our cube all that is left is to perform a distance check. We can use the distance formula to see how far our closest point on the line is from the plane's position. From here we need to find how much overlap occurs between the plane and the AABB, well we have the distance the object is from the plane, and we have the \"radius\" of the cube, and we know the object is already colliding, so we can take the radius and subtract the distance from it to get the overlap. Now you can multiply this overlap by the planes normal and that will give you the force needed to keep it above the plane and not colliding with it, and that is how we have done AABB to Plane Resolution.\n\nBy Gage Dietz\n\n## Discussion (0)", null, "" ]

[ null, "https://res.cloudinary.com/practicaldev/image/fetch/s--RmY55OKL--/c_limit,f_auto,fl_progressive,q_auto,w_256/https://practicaldev-herokuapp-com.freetls.fastly.net/assets/devlogo-pwa-512.png", null ]

[ "# Train Deep Learning Network to Classify New Images\n\nThis example shows how to use transfer learning to retrain a convolutional neural network to classify a new set of images.\n\nPretrained image classification networks have been trained on over a million images and can classify images into 1000 object categories, such as keyboard, coffee mug, pencil, and many animals. The networks have learned rich feature representations for a wide range of images. The network takes an image as input, and then outputs a label for the object in the image together with the probabilities for each of the object categories.\n\nTransfer learning is commonly used in deep learning applications. You can take a pretrained network and use it as a starting point to learn a new task. Fine-tuning a network with transfer learning is usually much faster and easier than training a network from scratch with randomly initialized weights. You can quickly transfer learned features to a new task using a smaller number of training images.", null, "Unzip and load the new images as an image datastore. This very small data set contains only 75 images. Divide the data into training and validation data sets. Use 70% of the images for training and 30% for validation.\n\n```unzip('MerchData.zip'); imds = imageDatastore('MerchData', ... 'IncludeSubfolders',true, ... 'LabelSource','foldernames'); [imdsTrain,imdsValidation] = splitEachLabel(imds,0.7);```\n\nTo try a different pretrained network, open this example in MATLAB® and select a different network. For example, you can try `squeezenet`, a network that is even faster than `googlenet`. You can run this example with other pretrained networks. For a list of all available networks, see Load Pretrained Networks.\n\n`net =", null, "googlenet;`\n\nUse `analyzeNetwork` to display an interactive visualization of the network architecture and detailed information about the network layers.\n\n`analyzeNetwork(net)`", null, "The first element of the `Layers` property of the network is the image input layer. For a GoogLeNet network, this layer requires input images of size 224-by-224-by-3, where 3 is the number of color channels. Other networks can require input images with different sizes. For example, the Xception network requires images of size 299-by-299-by-3.\n\n`net.Layers(1)`\n```ans = ImageInputLayer with properties: Name: 'data' InputSize: [224 224 3] Hyperparameters DataAugmentation: 'none' Normalization: 'zerocenter' NormalizationDimension: 'auto' Mean: [224×224×3 single] ```\n`inputSize = net.Layers(1).InputSize;`\n\n### Replace Final Layers\n\nThe convolutional layers of the network extract image features that the last learnable layer and the final classification layer use to classify the input image. These two layers, `'loss3-classifier'` and `'output'` in GoogLeNet, contain information on how to combine the features that the network extracts into class probabilities, a loss value, and predicted labels. To retrain a pretrained network to classify new images, replace these two layers with new layers adapted to the new data set.\n\nConvert the trained network to a layer graph.\n\n`lgraph = layerGraph(net);`\n\nFind the names of the two layers to replace. You can do this manually or you can use the supporting function findLayersToReplace to find these layers automatically.\n\n```[learnableLayer,classLayer] = findLayersToReplace(lgraph); [learnableLayer,classLayer] ```\n```ans = 1×2 Layer array with layers: 1 'loss3-classifier' Fully Connected 1000 fully connected layer 2 'output' Classification Output crossentropyex with 'tench' and 999 other classes ```\n\nIn most networks, the last layer with learnable weights is a fully connected layer. Replace this fully connected layer with a new fully connected layer with the number of outputs equal to the number of classes in the new data set (5, in this example). In some networks, such as SqueezeNet, the last learnable layer is a 1-by-1 convolutional layer instead. In this case, replace the convolutional layer with a new convolutional layer with the number of filters equal to the number of classes. To learn faster in the new layer than in the transferred layers, increase the learning rate factors of the layer.\n\n```numClasses = numel(categories(imdsTrain.Labels)); if isa(learnableLayer,'nnet.cnn.layer.FullyConnectedLayer') newLearnableLayer = fullyConnectedLayer(numClasses, ... 'Name','new_fc', ... 'WeightLearnRateFactor',10, ... 'BiasLearnRateFactor',10); elseif isa(learnableLayer,'nnet.cnn.layer.Convolution2DLayer') newLearnableLayer = convolution2dLayer(1,numClasses, ... 'Name','new_conv', ... 'WeightLearnRateFactor',10, ... 'BiasLearnRateFactor',10); end lgraph = replaceLayer(lgraph,learnableLayer.Name,newLearnableLayer);```\n\nThe classification layer specifies the output classes of the network. Replace the classification layer with a new one without class labels. `trainNetwork` automatically sets the output classes of the layer at training time.\n\n```newClassLayer = classificationLayer('Name','new_classoutput'); lgraph = replaceLayer(lgraph,classLayer.Name,newClassLayer);```\n\nTo check that the new layers are connected correctly, plot the new layer graph and zoom in on the last layers of the network.\n\n```figure('Units','normalized','Position',[0.3 0.3 0.4 0.4]); plot(lgraph) ylim([0,10])```", null, "### Freeze Initial Layers\n\nThe network is now ready to be retrained on the new set of images. Optionally, you can \"freeze\" the weights of earlier layers in the network by setting the learning rates in those layers to zero. During training, `trainNetwork` does not update the parameters of the frozen layers. Because the gradients of the frozen layers do not need to be computed, freezing the weights of many initial layers can significantly speed up network training. If the new data set is small, then freezing earlier network layers can also prevent those layers from overfitting to the new data set.\n\nExtract the layers and connections of the layer graph and select which layers to freeze. In GoogLeNet, the first 10 layers make out the initial 'stem' of the network. Use the supporting function freezeWeights to set the learning rates to zero in the first 10 layers. Use the supporting function createLgraphUsingConnections to reconnect all the layers in the original order. The new layer graph contains the same layers, but with the learning rates of the earlier layers set to zero.\n\n```layers = lgraph.Layers; connections = lgraph.Connections; layers(1:10) = freezeWeights(layers(1:10)); lgraph = createLgraphUsingConnections(layers,connections);```\n\n### Train Network\n\nThe network requires input images of size 224-by-224-by-3, but the images in the image datastore have different sizes. Use an augmented image datastore to automatically resize the training images. Specify additional augmentation operations to perform on the training images: randomly flip the training images along the vertical axis and randomly translate them up to 30 pixels and scale them up to 10% horizontally and vertically. Data augmentation helps prevent the network from overfitting and memorizing the exact details of the training images.\n\n```pixelRange = [-30 30]; scaleRange = [0.9 1.1]; imageAugmenter = imageDataAugmenter( ... 'RandXReflection',true, ... 'RandXTranslation',pixelRange, ... 'RandYTranslation',pixelRange, ... 'RandXScale',scaleRange, ... 'RandYScale',scaleRange); augimdsTrain = augmentedImageDatastore(inputSize(1:2),imdsTrain, ... 'DataAugmentation',imageAugmenter);```\n\nTo automatically resize the validation images without performing further data augmentation, use an augmented image datastore without specifying any additional preprocessing operations.\n\n`augimdsValidation = augmentedImageDatastore(inputSize(1:2),imdsValidation);`\n\nSpecify the training options. Set `InitialLearnRate` to a small value to slow down learning in the transferred layers that are not already frozen. In the previous step, you increased the learning rate factors for the last learnable layer to speed up learning in the new final layers. This combination of learning rate settings results in fast learning in the new layers, slower learning in the middle layers, and no learning in the earlier, frozen layers.\n\nSpecify the number of epochs to train for. When performing transfer learning, you do not need to train for as many epochs. An epoch is a full training cycle on the entire training data set. Specify the mini-batch size and validation data. Compute the validation accuracy once per epoch.\n\n```miniBatchSize = 10; valFrequency = floor(numel(augimdsTrain.Files)/miniBatchSize); options = trainingOptions('sgdm', ... 'MiniBatchSize',miniBatchSize, ... 'MaxEpochs',6, ... 'InitialLearnRate',3e-4, ... 'Shuffle','every-epoch', ... 'ValidationData',augimdsValidation, ... 'ValidationFrequency',valFrequency, ... 'Verbose',false, ... 'Plots','training-progress');```\n\nTrain the network using the training data. By default, `trainNetwork` uses a GPU if one is available. This requires Parallel Computing Toolbox™ and a supported GPU device. For information on supported devices, see GPU Computing Requirements (Parallel Computing Toolbox). Otherwise, `trainNetwork` uses a CPU. You can also specify the execution environment by using the `'ExecutionEnvironment'` name-value pair argument of `trainingOptions`. Because the data set is so small, training is fast.\n\n`net = trainNetwork(augimdsTrain,lgraph,options);`", null, "### Classify Validation Images\n\nClassify the validation images using the fine-tuned network, and calculate the classification accuracy.\n\n```[YPred,probs] = classify(net,augimdsValidation); accuracy = mean(YPred == imdsValidation.Labels)```\n```accuracy = 0.9000 ```\n\nDisplay four sample validation images with predicted labels and the predicted probabilities of the images having those labels.\n\n```idx = randperm(numel(imdsValidation.Files),4); figure for i = 1:4 subplot(2,2,i) I = readimage(imdsValidation,idx(i)); imshow(I) label = YPred(idx(i)); title(string(label) + \", \" + num2str(100*max(probs(idx(i),:)),3) + \"%\"); end```", null, "Szegedy, Christian, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed, Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich. \"Going deeper with convolutions.\" In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 1-9. 2015." ]

[ null, "https://se.mathworks.com/help/examples/nnet/win64/TransferLearningUsingGoogLeNetExample_01.png", null, "https://se.mathworks.com/help/examples/nnet/win64/TransferLearningUsingGoogLeNetExample_06.png", null, "https://se.mathworks.com/help/examples/nnet/win64/TransferLearningUsingGoogLeNetExample_02.png", null, "https://se.mathworks.com/help/examples/nnet/win64/TransferLearningUsingGoogLeNetExample_03.png", null, "https://se.mathworks.com/help/examples/nnet/win64/TransferLearningUsingGoogLeNetExample_04.png", null, "https://se.mathworks.com/help/examples/nnet/win64/TransferLearningUsingGoogLeNetExample_05.png", null ]

[ "# How to Calculate MSE in R\n\nOne of the most common metrics used to measure the prediction accuracy of a model is MSE, which stands for mean squared error. It is calculated as:\n\nMSE = (1/n) * Σ(actual – prediction)2\n\nwhere:\n\n• Σ – a fancy symbol that means “sum”\n• n – sample size\n• actual – the actual data value\n• prediction – the predicted data value\n\nThe lower the value for MSE, the more accurately a model is able to predict values.\n\n## How to Calculate MSE in R\n\nDepending on what format your data is in, there are two easy methods you can use to calculate the MSE of a regression model in R.\n\n### Method 1: Calculate MSE from Regression Model\n\nIn one scenario, you may have a fitted regression model and would simply like to calculate the MSE of the model. For example, you may have the following regression model:\n\n```#load mtcars dataset\ndata(mtcars)\n\n#fit regression model\nmodel <- lm(mpg~disp+hp, data=mtcars)\n\n#get model summary\nmodel_summ <-summary(model)\n```\n\nTo calculate the MSE for this model, you can use the following formula:\n\n```#calculate MSE\nmean(model_summ\\$residuals^2)\n\n 8.85917```\n\nThis tells us that the MSE is 8.85917.\n\n### Method 2: Calculate MSE from a list of Predicted and Actual Values\n\nIn another scenario, you may simply have a list of predicted and actual values. For example:\n\n```#create data frame with a column of actual values and a column of predicted values\ndata <- data.frame(pred = predict(model), actual = mtcars\\$mpg)\n\n#view first six lines of data\n\npred actual\nMazda RX4 23.14809 21.0\nMazda RX4 Wag 23.14809 21.0\nDatsun 710 25.14838 22.8\nHornet 4 Drive 20.17416 21.4\n```#calculate MSE" ]

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[ "Lemma 74.7.1. Let $S$ be a scheme. Let $\\{ f_ i : T_ i \\to T\\} _{i \\in I}$ be an fpqc covering of algebraic spaces over $S$. Suppose that for each $i$ we have an open subspace $W_ i \\subset T_ i$ such that for all $i, j \\in I$ we have $\\text{pr}_0^{-1}(W_ i) = \\text{pr}_1^{-1}(W_ j)$ as open subspaces of $T_ i \\times _ T T_ j$. Then there exists a unique open subspace $W \\subset T$ such that $W_ i = f_ i^{-1}(W)$ for each $i$.\n\nProof. By Topologies on Spaces, Lemma 73.9.5 we may assume each $T_ i$ is a scheme. Choose a scheme $U$ and a surjective étale morphism $U \\to T$. Then $\\{ T_ i \\times _ T U \\to U\\}$ is an fpqc covering of $U$ and $T_ i \\times _ T U$ is a scheme for each $i$. Hence we see that the collection of opens $W_ i \\times _ T U$ comes from a unique open subscheme $W' \\subset U$ by Descent, Lemma 35.13.6. As $U \\to X$ is open we can define $W \\subset X$ the Zariski open which is the image of $W'$, see Properties of Spaces, Section 66.4. We omit the verification that this works, i.e., that $W_ i$ is the inverse image of $W$ for each $i$. $\\square$\n\nThere are also:\n\n• 1 comment(s) on Section 74.7: Fpqc coverings\n\nIn your comment you can use Markdown and LaTeX style mathematics (enclose it like $\\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar)." ]

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[ "English | Español\n\n# Try our Free Online Math Solver!", null, "Online Math Solver\n\n Depdendent Variable\n\n Number of equations to solve: 23456789\n Equ. #1:\n Equ. #2:\n\n Equ. #3:\n\n Equ. #4:\n\n Equ. #5:\n\n Equ. #6:\n\n Equ. #7:\n\n Equ. #8:\n\n Equ. #9:\n\n Solve for:\n\n Dependent Variable\n\n Number of inequalities to solve: 23456789\n Ineq. #1:\n Ineq. #2:\n\n Ineq. #3:\n\n Ineq. #4:\n\n Ineq. #5:\n\n Ineq. #6:\n\n Ineq. #7:\n\n Ineq. #8:\n\n Ineq. #9:\n\n Solve for:\n\n Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:\n\nWhat our customers say...\n\nThousands of users are using our software to conquer their algebra homework. Here are some of their experiences:\n\nThanks so much for the explanation to help solve the problems so I could understand the concept. I appreciate your time and effort.\nChristian Terry, ID.\n\nThis algebra software has an exceptional ability to accommodate individual users. While offering help with algebra homework, it also forces the student to learn basic math. The algebra tutor part of the software provides easy to understand explanations for every step of algebra problem solution.\nJonathan McCue, OH\n\nAs a teacher, much of my time was taken up by creating effective lesson plans. Algebrator allows me to create each lesson in about half the time. My kids love it because I can spend more time with them! Once they are old enough, I hope they will find this program useful as well.\nG.O., Kansas\n\nAs the parent of an ADD child, Ive tried many different tutors and learning programs, and none have really worked. So, I must admit, I was skeptical about using yours. So soon after, when my sons math teacher called me to setup a meeting, I thought, Great, what now? But, to my delight, she wanted to know what my secret was because, as she put it, my son had done a complete 180 and was now one of her best students! So I told her what my secret was: your software!\n\nSearch phrases used on 2014-11-02:\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 searchers used to find our site. Can you find yours among them?\n\n• worksheet substitution variables\n• what is the formula for ratio\n• on line t1 calculator\n• number sequence solver\n• ti calculator scale by pi\n• mcdougal littell algebra 2 online\n• how do you foil on a TI 83 calculator\n• linear mappings homeworks exercices problems solutions pdf\n• find lowest common denominator +\"type in\"\n• interactive pre-algebra expressions\n• \"summation notation\" worksheet with solutions\n• free algebra story problem solver\n• Adding and Subtracting Integers Worksheet\n• prealgebra introductory algebra\n• A simple explanation of how to do basic Trigonomotry\n• addition of trigonometric functions examples\n• free online calculator for adding or subtracting integers\n• example of permutation on our real life\n• McDougal Littell Poetry Grade 9\n• how to solve 3rd degree polynomial\n• nonlinear differential equations with Maple\n• put in simplified radical form\n• simple dividing calculator\n• convert decimal to mixed fraction java\n• mix numbers\n• math trivia for kids\n• solving non homogenous differential equations in matlab\n• nth power calculator\n• solving third order equations\n• factoring binomials practice\n• math slope paper\n• sehgal introduction to group rings solutions to exercises\n• second order nonlinear differential equation+matlab\n• matlab solve system of equations nonlinear\n• worksheet problems involving non linear inequalities\n• solving 3rd order polynomials using TI-83\n• solving quadratics by completing the square powerpoint\n• simplifying radical expressions program for ti 83\n• free decimal place value worksheets\n• 5th grade math fun +printout\n• Nomenclature to Balance Chemical Equations calculator\n• the easiest explanation of finding highest common factor\n• fortran program to solve quadratic equation\n• exponent square root calculator\n• how to solve abstract test\n• input and java and reverse and sum\n• 8th grade slope intercept form\n• partial differential non homogeneous boundaries\n• simple aptitude questions\n• plotting+points+pictures\n• Freshmen+Geometry+word+area+problems+free+worksheets\n• solving equations with radicals and exponents\n• plotting points with pictures\n• how to do 3rd root on calculator\n• polynominals calculator foil\n• addition and subtraction integers worksheets\n• solving trinomials calcuaotr\n• engineering aptitude questions and solving answer\n• solving second order differential equations non-linear\n• glencoe Chapter 8 Section 8 Simple Interest Pre-Student Parent Study Guide teacher\n• onliny simpify calculator\n• equations of lines solver\n• graphing calculator slope\n• List of Fourth Roots\n• multiplying and dividing with decimals mixed review\n• multiply rational expressions calculator\n• free algebra 2 problem solver\n• Permutations worksheet\n• online math for 2 grade" ]

[ null, "http://www.softmath.com/images/video-pages/solver-top.png", null ]

[ "##### https://github.com/tensorly/tensorly\nTip revision: 72174be\ntt_matrix.py\n``````\"\"\"Module for matrices in the TT format\"\"\"\n\nimport tensorly as tl\n\n# Note how tt_matrix_to_tensor is implemented in tenalg to allow for more efficient implementations\n# (e.g. using the einsum backend)\nfrom .tenalg import _tt_matrix_to_tensor as tt_matrix_to_tensor\n\nfrom ._factorized_tensor import FactorizedTensor\nimport numpy as np\n\ndef validate_tt_matrix_rank(tensorized_shape, rank=\"same\"):\n\"\"\"Returns the rank of a TT-Matrix Decomposition\n\nParameters\n----------\ntensor_shape : tupe\nshape of the tensorized matrix to decompose\nrank : {'same', float, tuple, int}, default is same\nway to determine the rank, by default 'same'\nif 'same': rank is computed to keep the number of parameters (at most) the same\nif float, computes a rank so as to keep rank percent of the original number of parameters\nif int or tuple, just returns rank\nconstant_rank : bool, default is False\n* if True, the *same* rank will be chosen for each modes\n* if False (default), the rank of each mode will be proportional to the corresponding tensor_shape\n\n*used only if rank == 'same' or 0 < rank <= 1*\n\nrounding = {'round', 'floor', 'ceil'}\n\nReturns\n-------\nrank : int tuple\nrank of the decomposition\n\"\"\"\n\nn_dim = len(tensorized_shape) // 2\n\nif n_dim * 2 != len(tensorized_shape):\nmsg = (\nf\"The order of the give tensorized shape is not a multiple of 2.\"\n\"However, there should be as many dimensions for the left side (number of rows)\"\n\" as of the right side (number of columns). \"\n\" For instance, to convert a matrix of size (8, 9) to the TT-format, \"\n\" it can be tensorized to (2, 4, 3, 3) but NOT to (2, 2, 2, 3, 3).\"\n)\nraise ValueError(msg)\n\nleft_shape = tensorized_shape[:n_dim]\nright_shape = tensorized_shape[n_dim:]\n\nfull_shape = tuple(i * o for i, o in zip(left_shape, right_shape))\nreturn tl.tt_tensor.validate_tt_rank(full_shape, rank)\n\ndef _tt_matrix_n_param(tensorized_shape, rank):\n\"\"\"Number of parameters of a TT-Matrix decomposition for a given `rank` and full `tensor_shape`.\n\nParameters\n----------\ntensorized_shape : int tuple\nshape of the full tensorized matrix to decompose (or approximate)\n\nrank : tuple\nrank of the TT-Matrix decomposition\n\nReturns\n-------\nn_params : int\nNumber of parameters of a TT-Matrix decomposition of rank `rank` of a full tensor of shape `tensor_shape`\n\"\"\"\nn_dim = len(tensorized_shape) // 2\n\nif n_dim * 2 != len(tensorized_shape):\nmsg = (\nf\"The order of the give tensorized shape is not a multiple of 2.\"\n\"However, there should be as many dimensions for the left side (number of rows)\"\n\" as of the right side (number of columns). \"\n\" For instance, to convert a matrix of size (8, 9) to the TT-format, \"\n\" it can be tensorized to (2, 4, 3, 3) but NOT to (2, 2, 2, 3, 3).\"\n)\nraise ValueError(msg)\n\nleft_shape = tensorized_shape[:n_dim]\nright_shape = tensorized_shape[n_dim:]\n\nfactor_params = []\nfor i, (ls, rs) in enumerate(zip(left_shape, right_shape)):\nfactor_params.append(rank[i] * ls * rs * rank[i + 1])\n\nreturn np.sum(factor_params)\n\ndef tt_matrix_to_matrix(tt_matrix):\n\"\"\"Reconstruct the original matrix that was tensorized and compressed in the TT-Matrix format\n\nRe-assembles 'factors', which represent a tensor in TT-Matrix format\ninto the corresponding matrix\n\nParameters\n----------\nfactors: list of 4D-arrays\nTT-Matrix factors (known as core) of shape (rank_k, left_dim_k, right_dim_k, rank_{k+1})\n\nReturns\n-------\noutput_matrix: 2D-array\nmatrix whose TT-Matrix decomposition was given by 'factors'\n\"\"\"\nin_shape = tuple(c.shape for c in tt_matrix)\nreturn tl.reshape(tt_matrix_to_tensor(tt_matrix), (np.prod(in_shape), -1))\n\ndef tt_matrix_to_unfolded(tt_matrix, mode):\n\"\"\"Returns the unfolding matrix of a tensor given in TT-Matrix format\n\nReassembles a full tensor from 'factors' and returns its unfolding matrix\nwith mode given by 'mode'\n\nParameters\n----------\nfactors : list of 3D-arrays\nTT-Matrix factors\nmode : int\nunfolding matrix to be computed along this mode\n\nReturns\n-------\n2-D array\nunfolding matrix at mode given by 'mode'\n\"\"\"\nreturn tl.unfold(tt_matrix_to_tensor(tt_matrix), mode)\n\ndef tt_matrix_to_vec(tt_matrix):\n\"\"\"Returns the tensor defined by its TT-Matrix format ('factors') into\nits vectorized format\n\nParameters\n----------\nfactors : list of 3D-arrays\nTT factors\n\nReturns\n-------\n1-D array\nformat of tensor defined by 'factors'\n\"\"\"\nreturn tl.tensor_to_vec(tt_matrix_to_tensor(tt_matrix))\n\ndef _validate_tt_matrix(tt_tensor):\nfactors = tt_tensor\nn_factors = len(factors)\n\nif n_factors < 1:\nraise ValueError(\n\"A Tensor-Train (MPS) tensor should be composed of at least one factor.\"\nf\"However, {n_factors} factor was given.\"\n)\n\nrank = []\nleft_shape = []\nright_shape = []\nfor index, factor in enumerate(factors):\ncurrent_rank, current_left_shape, current_right_shape, next_rank = tl.shape(\nfactor\n)\n\n# Check that factors are third order tensors\nif not tl.ndim(factor) == 4:\nraise ValueError(\n\"A TTMatrix expresses a tensor as fourth order factors (tt-cores).\\n\"\nf\"However, tl.ndim(factors[{index}]) = {tl.ndim(factor)}\"\n)\n# Consecutive factors should have matching ranks\nif index and tl.shape(factors[index - 1])[-1] != current_rank:\nraise ValueError(\n\"Consecutive factors should have matching ranks\\n\"\n\" -- e.g. tl.shape(factors)[-1]) == tl.shape(factors))\\n\"\nf\"However, tl.shape(factor[{index-1}])[-1] == {tl.shape(factors[index - 1])[-1]} but\"\nf\" tl.shape(factor[{index}]) == {current_rank} \"\n)\n# Check for boundary conditions\nif (index == 0) and current_rank != 1:\nraise ValueError(\n\"Boundary conditions dictate factor.shape == 1.\"\nf\"However, got factor.shape = {current_rank}.\"\n)\nif (index == n_factors - 1) and next_rank != 1:\nraise ValueError(\n\"Boundary conditions dictate factor[-1].shape == 1.\"\nf\"However, got factor[{n_factors}].shape = {next_rank}.\"\n)\n\nleft_shape.append(current_left_shape)\nright_shape.append(current_right_shape)\n\nrank.append(current_rank)\n\n# Add last rank (boundary condition)\nrank.append(next_rank)\n\nreturn tuple(left_shape) + tuple(right_shape), tuple(rank)\n\nclass TTMatrix(FactorizedTensor):\ndef __init__(self, factors, inplace=False):\nsuper().__init__()\n\n# Will raise an error if invalid\nshape, rank = _validate_tt_matrix(factors)\n\nself.shape = tuple(shape)\nself.order = len(self.shape) // 2\nself.left_shape = self.shape[: self.order]\nself.right_shape = self.shape[self.order :]\nself.rank = tuple(rank)\nself.factors = factors\n\ndef __getitem__(self, index):\nreturn self.factors[index]\n\ndef __setitem__(self, index, value):\nself.factors[index] = value\n\ndef __iter__(self):\nfor index in range(len(self)):\nyield self[index]\n\ndef __len__(self):\nreturn len(self.factors)\n\ndef __repr__(self):\nmessage = (\nf\"factors list : rank-{self.rank} TT-Matrix of tensorized shape {self.shape}\"\nf\" corresponding to a matrix of size {np.prod(self.left_shape)} x {np.prod(self.right_shape)}\"\n)\nreturn message\n\ndef to_tensor(self):\nreturn tt_matrix_to_tensor(self)\n\ndef to_matrix(self):\nreturn tt_matrix_to_matrix(self)\n\ndef to_unfolding(self, mode):\nreturn tt_matrix_to_unfolded(self, mode)\n\ndef to_vec(self):\nreturn tt_matrix_to_vec(self)\n``````" ]

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[ "In this post, I will take a brief look at how using type lists can help optimize certain applications. Some of the optimizations in Vlinder Sofwtare’s more special-purpose parsers are possible because they are written in C++ and can therefore use template meta-programming for parts of their work. We’ve recently folded part of the code we use for template meta-programming into a separate library we’ve baptized “meta” and which we will be progressively introducing into our other libraries, picking the meta-parts out of those libraries and moving them into the new library as we go.\n\nOne of the adverse effects of this migration/consolidation/refactoring is that some of the configuration headers of some of our libraries will need to be changed client-side, but in return for that we get faster parsers.\n\nOne of the basic building blocks of the meta library is the type list. Type lists are just that: lists of types. One thing they’re used for is to determine the types of the allocators to be used by the µpool2 allocator allocator – which is one of the places user-level configuration headers will need to be changed. A level of indirection was removed from the TypeList class such that the TypeList class now looks like this:\n\nstruct Nil {};\n\ntemplate < typename T, typename TL >\nstruct TypeList\n{\ntypedef TL tail;\n};\n\n\nIt comes with a few meta-functions, called MakeTypeList, Length, At, Splice, FoldR, etc. and it thus allows you to do various things at compile-time that you would normally do at run-time.\n\nFor example, one of our allocators can be configured (at compile-time) with a block size and a pool size. One common use is to use various pool sizes for various block sizes, using an optimal allocator for each block size and using only as much memory as you are going to need for the pool. The way this is done is by creating a type list of pairs of constants, in which the first is the block size and the second is the preferred pool size. Such a list might look like this:\n\ntypedef MakeTypeList<\nPair< Constant< 8 >, Constant< 512 > >\n, Pair< Constant< 32 >, Constant< 32768 > >\n, Pair< Constant< 1024 >, Constant< 32768 > >\n/* ... */\n>::type PoolSizesByBlockSize;\n\n\nOne thing you can do with such a list is create a list of appropriate allocator types from it. Taking an allocator class template < unsigned int block_size__, unsigned int block_count__ > class Allocator; we’d need to transform the first type list into a second type-list of preferred allocator types. We can do that with our Transform meta-function, which looks like this:\n\ntemplate < typename TL1, template < class > class F >\nstruct Transform;\n\ntemplate < template < class > class F >\nstruct Transform< Nil, F >\n{\ntypedef Nil type;\n};\ntemplate < typename TL1, template < class > class F >\nstruct Transform\n{\ntypedef TypeList< typename F< typename TL1::head >::type, typename Transform< F, typename TL1::tail >::type > type;\n};\n\n\nwhich means we can define a meta-function to create our Allocator type instance as follows:\n\ntemplate < typename Sizes >\nstruct MakeAllocator\n{\ntypedef Allocator< Sizes::first::value, Sizes::second::value / Sizes::first::value > type;\n};\n\n\nand make our list like this:\n\ntypedef Transform< MakeAllocator, PoolSizesByBlockSize >::type AllocatorTypes;\n\n\nUsing type lists like this makes it easier to reason about the types that are going to be used by the program – especially because we’ve chosen a few simple rules to be applied throughout the meta library:\n\n1. All meta-functions return a type using a type typedef\n\n2. meta-functions that return values return them with a value constant but still return a type typedef\n\n3. Type lists end with the Nil type\n\n4. As much as possible, meta-functions carry the same names they do as functions in Haskell, but in UpperCamelCase\n\n(the fourth of these simple rules is why the GetSize meta-function was renamed Length\n\nThe reason why this makes reasoning about type list meta-programs easier is because they can first be modeled in Haskell if need be – as I did when I translated the KMP algorithm to Haskell before creating a C++ template for it.\n\nEnding a type list in Nil makes it possible to break out of the Transform meta-function with a simple specialization. In Haskell, the Transform meta-function would look like this:\n\ntransform :: (a -> b) -> [a] -> [b]\ntransform _ [] = []\ntransform f x:xs = f x : transform f xs\n\n\nThe underscore wild-card being modeled in C++ as the remaining specializable template parameter in the partial specialization of the Transform template (the other one being the type list parameter, which was specialized as Nil).\n\nHence, by adding a type list to a configuration header, which contains only the user-interesting information (namely the block sizes and the preferred pool sized to go with those) we accomplish three things:\n\n1. we present the user with only the information relevant to the user\n\n2. we use only those types that are actually interesting for us to use (namely those the user is interested in)\n\n3. the details of the types of allocators used remain hidden from the user (i.e. we can use different allocation algorithms for different allocation sizes – using a slightly different MakeAllocator meta-function – without imposing that choice on the user\n\nI should note, though, that while the user does not have to choose the exact allocator type, he could if he wanted to (by just replacing the AllocatorTypes typedef with the list of allocator types he wants to use rather than a meta-function." ]

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[ "Delta integral from t to sigma(t)\n\n(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)\nThe following formula holds: $$\\int_t^{\\sigma(t)} f(\\tau) \\Delta \\tau = \\mu(t)f(t),$$ where $\\int$ denotes the delta integral, $\\sigma$ denotes the forward jump, and $\\mu$ denotes the forward graininess." ]

[ null ]

[ "# An arcpy solution for randomizing overlapping points within a shape?\n\n298\n2\n01-21-2022 05:18 PM", null, "New Contributor\n\nI have a shapefile layer with polygons for the 50 U.S. states (\"States\"). I also have a point featureclass with potentially many overlapping points at the centroid of each state polygon (\"Dots\").\n\nI want to use the CreateRandomPoints_management() function to find new placements for all the points in each state, essentially creating a 1:1 dot density map with clickable point features.\n\nHere's the workflow I have envisioned:\n\n1. Loop through and select each state, one by one\n2. Get the count of points contained within each state polygon boundary\n3. Use CreateRandomPoints_management to generate count number of randomized points within each state boundary\n4. Move the original points to the new random locations and then delete the random points layer -or- Add fields and assign values to the newly created random points layer from the original points [Whichever's simpler and more reliable]\n\nI've tried several times to write this code, but my arcpy chops aren't that great yet. Any ideas or examples would be greatly appreciated!\n\nTags (3)\n1 Solution\n\nAccepted Solutions", null, "by", null, "MVP Esteemed Contributor\n\nSolved: Re: Dispersing geocoded points within a Polygon - Esri Community\n\nHope the following script works for you (Courtesy @XanderBakker and ArcPy Team)\n\n``````#-------------------------------------------------------------------------------\n# Name: Disperse3.py\n# Purpose: Disperse points in multiple polygons\n# Author: arcpy Team\n# http://arcpy.wordpress.com/2013/06/07/disperse-overlapping-points/\n# Created: 02-dec-2013\n#-------------------------------------------------------------------------------\n\nimport arcpy\nimport random\n\ndef main():\nfcPoints = r\"C:\\Project\\_Forums\\Disperse\\test.gdb\\points3\"\nfcPolygon = r\"C:\\Project\\_Forums\\Disperse\\test.gdb\\Polygons\"\narcpy.env.overwriteOutput = True\n\nwith arcpy.da.SearchCursor(fcPolygon, (\"SHAPE@\")) as cursor:\nfor row in cursor:\npolygon = row\ndisperse_points(fcPoints, polygon)\ndel row\n\ndef point_in_poly(poly, x, y):\npg = arcpy.PointGeometry(arcpy.Point(x, y), poly.spatialReference)\nreturn poly.contains(pg)\n\ndef disperse_points(in_points, polygon):\nlenx = polygon.extent.width\nleny = polygon.extent.height\nwith arcpy.da.UpdateCursor(in_points, \"SHAPE@XY\") as points:\nfor p in points:\nif point_in_poly(polygon, p, p):\n# I changed code here!\nx = (random.random() * lenx) + polygon.extent.XMin\ny = (random.random() * leny) + polygon.extent.YMin\ninside = point_in_poly(polygon, x, y)\nwhile not inside:\nx = (random.random() * lenx) + polygon.extent.XMin\ny = (random.random() * leny) + polygon.extent.YMin\ninside = point_in_poly(polygon, x, y)\npoints.updateRow([(x, y)])\nelse:\npass # don't update location if point doesn't originally falls inside current polygon\n\nif __name__ == '__main__':\nmain()‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍``````\n\n*Change the path of the point and polygon feature classes in Line No. 13/14.\n\nThink Location\n2 Replies", null, "by", null, "MVP Esteemed Contributor\n\nSolved: Re: Dispersing geocoded points within a Polygon - Esri Community\n\nHope the following script works for you (Courtesy @XanderBakker and ArcPy Team)\n\n``````#-------------------------------------------------------------------------------\n# Name: Disperse3.py\n# Purpose: Disperse points in multiple polygons\n# Author: arcpy Team\n# http://arcpy.wordpress.com/2013/06/07/disperse-overlapping-points/\n# Created: 02-dec-2013\n#-------------------------------------------------------------------------------\n\nimport arcpy\nimport random\n\ndef main():\nfcPoints = r\"C:\\Project\\_Forums\\Disperse\\test.gdb\\points3\"\nfcPolygon = r\"C:\\Project\\_Forums\\Disperse\\test.gdb\\Polygons\"\narcpy.env.overwriteOutput = True\n\nwith arcpy.da.SearchCursor(fcPolygon, (\"SHAPE@\")) as cursor:\nfor row in cursor:\npolygon = row\ndisperse_points(fcPoints, polygon)\ndel row\n\ndef point_in_poly(poly, x, y):\npg = arcpy.PointGeometry(arcpy.Point(x, y), poly.spatialReference)\nreturn poly.contains(pg)\n\ndef disperse_points(in_points, polygon):\nlenx = polygon.extent.width\nleny = polygon.extent.height\nwith arcpy.da.UpdateCursor(in_points, \"SHAPE@XY\") as points:\nfor p in points:\nif point_in_poly(polygon, p, p):\n# I changed code here!\nx = (random.random() * lenx) + polygon.extent.XMin\ny = (random.random() * leny) + polygon.extent.YMin\ninside = point_in_poly(polygon, x, y)\nwhile not inside:\nx = (random.random() * lenx) + polygon.extent.XMin\ny = (random.random() * leny) + polygon.extent.YMin\ninside = point_in_poly(polygon, x, y)\npoints.updateRow([(x, y)])\nelse:\npass # don't update location if point doesn't originally falls inside current polygon\n\nif __name__ == '__main__':\nmain()‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍``````\n\n*Change the path of the point and polygon feature classes in Line No. 13/14.\n\nThink Location", null, "New Contributor\n\nThanks, Jayanta! That function does look like it might do what I need.", null, "" ]

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[ "# 1.MD.B.3 Worksheets\n\n#### CCSS.maths.CONTENT.1.MD.B.3\n\n:\n\"Tell and write time in hours and half-hours using analog and digital clocks.\"\n\nOur Take:Year two students should be able to read both an analog and digital clock within the hour and half-hour. A typical practise exercise involves reading and recording the times on a series of analog clocks.\n\nThese worksheets can help students practise this Common Core State Standards skill.\n\n## Worksheets\n\nTime Review: Time Match\nWorksheet\nTime Review: Time Match\nYear 2\nMaths\nWorksheet\nTime Review: Tell Time with Carlos Cat\nWorksheet\nTime Review: Tell Time with Carlos Cat\nYear 2\nMaths\nWorksheet\nBe on Time\nWorksheet\nBe on Time\nThese busy bees need some help getting their honey delivered in time.\nYear 2\nMaths\nWorksheet\nOn the Hour\nWorksheet\nOn the Hour\nGive your first grader a head start on time by practising telling time on the hour. Match each clock to the correct time it tells.\nYear 2\nMaths\nWorksheet\nOn the Hour: Write the Time #1\nWorksheet\nOn the Hour: Write the Time #1\nYear 2\nMaths\nWorksheet\nOn the Hour: Write the Time #2\nWorksheet\nOn the Hour: Write the Time #2\nIntroduce your first grader to telling time on the hour with this simple worksheet.\nYear 2\nMaths\nWorksheet\nHour Hand\nWorksheet\nHour Hand\nThese clocks are missing their hands. Can your first grader fix the problem by drawing new hands on the clocks?\nYear 2\nMaths\nWorksheet\nOn the Half Hour: Telling Time with Malcolm Mouse\nWorksheet\nOn the Half Hour: Telling Time with Malcolm Mouse\nHelp young Malcolm Mouse learn how to tell time on the half hour by circling the time shown on each clock.\nYear 2\nMaths\nWorksheet\nHalf Hour\nWorksheet\nHalf Hour\nPractise telling time to the half hour with your first grader with this matching worksheet.\nYear 2\nMaths\nWorksheet\nTime to the Half Hour\nWorksheet\nTime to the Half Hour\nLet's practise keeping track of the time by writing the time shown on each clock.\nYear 2\nMaths\nWorksheet\nOn the Half Hour: Telling Time with Clockwork Cat\nWorksheet\nOn the Half Hour: Telling Time with Clockwork Cat\nLearners tell time to the half hour by reading the faces of 11 analog clocks in this fun practise worksheet.\nYear 2\nMaths\nWorksheet\nDraw the Hour Hand\nWorksheet\nDraw the Hour Hand\nGive the clock maker a hand by drawing the hour hands back on the clocks following the times shown.\nYear 2\nMaths\nWorksheet\nElapsed Time: One Hour Later\nWorksheet\nElapsed Time: One Hour Later\nIf your first grader is ready for a new time challenge, have her try her hand at calculating elapsed time.\nYear 2\nMaths\nWorksheet\nTime Review: On the Hour and Half Hour\nWorksheet\nTime Review: On the Hour and Half Hour\nOffering lots of time telling practise on the hour and half hour, this worksheet is a great refresher.\nYear 2\nMaths\nWorksheet\nTelling Time: Crazy Clocks\nWorksheet\nTelling Time: Crazy Clocks\nFor this year two maths worksheet, kids look at each analog clock, determine the time, and write the time in the spaces provided.\nYear 2\nMaths\nWorksheet\nTelling Time: Showtime!\nWorksheet\nTelling Time: Showtime!\nFor this year two maths worksheet, kids practise telling time by reading digital time and converting it to analog by drawing hands on the face of a clock.\nYear 2\nMaths\nWorksheet\nTelling Time: Tick-tock\nWorksheet\nTelling Time: Tick-tock\nFor this year two maths worksheet, kids look at each analog clock, determine the time, and write the time in the spaces provided.\nYear 2\nMaths\nWorksheet\nTick Tock: Learning to Tell the Time\nWorksheet\nTick Tock: Learning to Tell the Time\nIn this worksheet, all the clocks are missing their hands. Your child will need to look at what time it is and draw in the clock hands.\nYear 2\nMaths\nWorksheet\nNight or Day?\nWorksheet\nNight or Day?\nHere's a fun sheet to help first graders learning to tell time. Your child will practise determining what time of day it is: morning, day, evening or night!\nYear 2\nMaths\nWorksheet\nNight Time or Day Time?\nWorksheet\nNight Time or Day Time?\nCan your child tell what time of day it is just by looking at the clock? Help him practise telling time of day with a fun worksheet!\nYear 2\nMaths\nWorksheet\nTelling Time: A.M. or P.M.?\nWorksheet\nTelling Time: A.M. or P.M.?\nHelp your child understand a.m. and p.m. by having her read each sentence, then determine if the event happened before noon (a.m.) or after noon (p.m.).\nYear 2\nMaths\nWorksheet\nTime Quiz\nWorksheet\nTime Quiz\nWhat time is it? Review time telling skills on the analog clock with this fill-in-the-bubbles quiz.\nYear 2\nMaths\nWorksheet\nTime to the Hour\nWorksheet\nTime to the Hour\nGet some great practise telling time to the hour by drawing in the time you see below each blank face.\nYear 2\nMaths\nWorksheet\nTelling Time to the Hour\nWorksheet\nTelling Time to the Hour\nDon't get lost in a digital world! practise telling time to the hour on an analog clock using this colorful worksheet.\nYear 2\nMaths\nWorksheet\nTicking Clock\nWorksheet\nTicking Clock\nNow that your child has a grasp of telling time to the hour, have her practise writing out the time using words instead of numbers!\nYear 2\nMaths\nWorksheet\nTime Mix Up\nWorksheet\nTime Mix Up\nUh oh, it looks like there's been a time mix up! Have some fun figuring out analog clocks with your student.\nYear 2\nMaths\nWorksheet\nFind the Time\nWorksheet\nFind the Time\nLet's find the time with this beginner's worksheet on reading analog clocks.\nYear 2\nMaths\nWorksheet\nTime practise\nWorksheet\nTime practise\nPractise telling time with an analog clock using this great practise sheet.\nYear 2\nMaths\nWorksheet\nTell the Time\nWorksheet\nTell the Time\nDraw the hands of a rotary clock to tell the correct time.\nYear 2\nMaths\nWorksheet\nTelling Time\nWorksheet\nTelling Time\nWhat time is it? Does your kid know? Make sure your child knows how to tell time precisely on a rotary clock with this worksheet.\nYear 2\nMaths\nWorksheet\n\nCreate new collection\n\n0\n\n### New Collection>\n\n0Items\n\nWhat could we do to improve Education.com?" ]

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[ "### How to Create Sample Excel file with Sheet from each table with Top 1000 Rows per sheet in SSIS Package - SSIS Tutorial\n\nYou are working as an ETL Developer / SSIS developer. You are asked to create an Excel file with date time on each execution and load the top X rows from each table to new excel sheet to newly created Excel File. There should be new Excel Sheet for each Table from Database.\n\nThe excel file can be used for data analysis or test purpose.\n\n## Solution:\n\nWe are going to use Script Task in SSIS Package to dump data from SQL Server Database tables to Excel file. Let's create variables so we can change the Top X anytime we like, also the location where the file should be created and name of the file.\n\nFolderPath: Where you would like to create an Excel File\nExcelFileName: The name of Excel file you would like to create\nTopRowCount : Provide the values for Top clause, I am using Top 1 from each table\n\nHow to Export top X rows from each table to Excel File Dynamically in SSIS Package\n\nStep 2: Create ADO.NET Connection in SSIS Package to use in Script Task\nCreate ADO.NET Connection Manager so we can use in Script Task to get tables data to export to Excel. This ADO.Net connection should be pointing to Database that we want to export to an Excel File.\n\nCreate ADO.NET Connection in SSIS Package to use in Script Task to Export All Tables from Database to Excel File with Top X Rows\n\nBring the Script Task on Control Flow Pane in SSIS Package and open by double clicking Check-box in front of variable to add to Script Task.\n\nHow to Export Top X Rows from each Table to Excel File to create sample data in SSIS Package\n\nStep 4: Add Script to Script task Editor in SSIS Package to Export Top X Rows from  All Tables from SQL Server Database to Excel File\nClick Edit Button and it will open Script Task Editor.\nUnder #region Namespaces, I have added below code\n```using System.IO;\nusing System.Data.OleDb;\nusing System.Data.SqlClient;```\n\nUnder public void Main() {\n\nstring datetime = DateTime.Now.ToString(\"yyyyMMddHHmmss\");\n``` try\n{\n\n//Declare Variables\nstring ExcelFileName = Dts.Variables[\"User::ExcelFileName\"].Value.ToString();\nstring FolderPath = Dts.Variables[\"User::FolderPath\"].Value.ToString();\nstring TopRowCount = Dts.Variables[\"User::TopRowCount\"].Value.ToString();\nExcelFileName = ExcelFileName + \"_\" + datetime;\n\nOleDbConnection Excel_OLE_Con = new OleDbConnection();\nOleDbCommand Excel_OLE_Cmd = new OleDbCommand();\n\n//Construct ConnectionString for Excel\nstring connstring = \"Provider=Microsoft.ACE.OLEDB.12.0;\" + \"Data Source=\" + FolderPath + ExcelFileName\n+ \";\" + \"Extended Properties=\\\"Excel 12.0 Xml;HDR=YES;\\\"\";\n\n//drop Excel file if exists\nFile.Delete(FolderPath + \"\\\\\" + ExcelFileName + \".xlsx\");\n\n//USE ADO.NET Connection from SSIS Package to get data from table\n\n//Read list of Tables with Schema from Database\nstring query = \"SELECT Schema_name(schema_id) AS SchemaName,name AS TableName FROM sys.tables WHERE is_ms_shipped = 0\";\n\n//MessageBox.Show(query.ToString());\nSqlCommand cmd = new SqlCommand(query, myADONETConnection);\nDataTable dt = new DataTable();\n\n//Loop through datatable(dt) that has schema and table names\n\nforeach (DataRow dt_row in dt.Rows)\n{\nstring SchemaName = \"\";\nstring TableName = \"\";\nobject[] array = dt_row.ItemArray;\nSchemaName = array.ToString();\nTableName = array.ToString();\n\n//Load Data into DataTable from SQL ServerTable\n// Assumes that connection is a valid SqlConnection object.\nstring queryString =\n\"SELECT top \"+TopRowCount+\" * from \" + SchemaName + \".\" + TableName;\nDataSet ds = new DataSet();\n\nstring TableColumns = \"\";\n\n// Get the Column List from Data Table so can create Excel Sheet with Header\nforeach (DataTable table in ds.Tables)\n{\nforeach (DataColumn column in table.Columns)\n{\nTableColumns += column + \"],[\";\n}\n}\n\n// Replace most right comma from Columnlist\nTableColumns =(\"[\"+ TableColumns.Replace(\",\", \" Text,\").TrimEnd(','));\nTableColumns = TableColumns.Remove(TableColumns.Length - 2);\n//MessageBox.Show(TableColumns);\n\n//Use OLE DB Connection and Create Excel Sheet\nExcel_OLE_Con.ConnectionString = connstring;\nExcel_OLE_Con.Open();\nExcel_OLE_Cmd.Connection = Excel_OLE_Con;\nExcel_OLE_Cmd.CommandText = \"Create table [\" + SchemaName+\"_\"+TableName + \"] (\" + TableColumns + \")\";\nExcel_OLE_Cmd.ExecuteNonQuery();\n\n//Write Data to Excel Sheet from DataTable dynamically\nforeach (DataTable table in ds.Tables)\n{\nString sqlCommandInsert = \"\";\nString sqlCommandValue = \"\";\nforeach (DataColumn dataColumn in table.Columns)\n{\nsqlCommandValue += dataColumn + \"],[\";\n}\n\nsqlCommandValue=\"[\"+sqlCommandValue.TrimEnd(',') ;\nsqlCommandValue = sqlCommandValue.Remove(sqlCommandValue.Length - 2);\nsqlCommandInsert = \"INSERT into [\" + SchemaName+\"_\"+TableName + \"] (\" + sqlCommandValue +\") VALUES(\";\n\nint columnCount = table.Columns.Count;\nforeach (DataRow row in table.Rows)\n{\nstring columnvalues = \"\";\nfor (int i = 0; i < columnCount; i++)\n{\nint index = table.Rows.IndexOf(row);\ncolumnvalues += \"'\" + table.Rows[index].ItemArray[i] + \"',\";\n\n}\ncolumnvalues = columnvalues.TrimEnd(',');\nvar command = sqlCommandInsert + columnvalues + \")\";\nExcel_OLE_Cmd.CommandText = command;\nExcel_OLE_Cmd.ExecuteNonQuery();\n}\n\n}\nExcel_OLE_Con.Close();\n}\n}\n\ncatch (Exception exception)\n{\n\n// Create Log File for Errors\nusing (StreamWriter sw = File.CreateText(Dts.Variables[\"User::FolderPath\"].Value.ToString() + \"\\\\\" +\nDts.Variables[\"User::ExcelFileName\"].Value.ToString() + datetime + \".log\"))\n{\nsw.WriteLine(exception.ToString());\n\n}\n\n}```\n\nStep 5:\nSave the script in Script Task Editor and then run your SSIS Package to export top X rows from each of the table to new Excel Sheet in Excel File.\n\nI ran my SSIS Package with Top 1 and here is my output Excel file.\n\nCreate Sample Excel file with Top X rows from each table in a database by using SSIS Package" ]

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[ "Primality proof for n = 31002614113816567181:\n\nTake b = 2.\n\nb^(n-1) mod n = 1.\n\n66721073718023 is prime.\nb^((n-1)/66721073718023)-1 mod n = 28399559369264978603, which is a unit, inverse 17080331612411478219.\n\n(66721073718023) divides n-1.\n\n(66721073718023)^2 > n.\n\nn is prime by Pocklington's theorem." ]

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[ "# 去分母，去括号，移项，合并同类项，系数化为1.\n\n(8)(1.8-7x)/1.2-(1.3-3x)/0.2=-(5x-0.4)/0.3通分:(1.8-7x)-6(1.3-3x)=-4(5x-0.4)去括号:1.8-7x-7.8+18x=-20x+1.6合并:-6+11x=-20x+1.6移项:11x+20x=6+1.631x=7.6x=7.6/31=76/310=38/155如果不懂,请追问,祝学习愉快!\n\n3(x/2-7)=3x-6去括号3x/2-21=3x-6去分母3x-42=6x-12移项3x-6x=-12+42合并同类项-3x=30系数化为一x=-10\n\n1)去分母,依据等式性质2,注意每一项都要乘以最小公倍数2)去括号,依据乘法对加法的分配律,注意符号问题,别漏乘3)移项,依据等式性质1,注意要变号4)合并同类项,依据乘法对加法的分配律或合并同类项法则5)系数化为1,依据等式性质2\n\n①5(x+8)-5=0 去括号得5x+40-5=0移项得5x=5-40合并同类项得5x=-35系数化为1得x=-7②-3(x+3)=24去括号得-3x-9=24移项得-3x=24+9合并同类项得-3x=33系数化为1得x=-11\n\nAll rights reserved Powered by www.xcxd.net\ncopyright ©right 2010-2021。" ]

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[ "# #27f519 Color Information\n\nIn a RGB color space, hex #27f519 is composed of 15.3% red, 96.1% green and 9.8% blue. Whereas in a CMYK color space, it is composed of 84.1% cyan, 0% magenta, 89.8% yellow and 3.9% black. It has a hue angle of 116.2 degrees, a saturation of 91.7% and a lightness of 52.9%. #27f519 color hex could be obtained by blending #4eff32 with #00eb00. Closest websafe color is: #33ff00.\n\n• R 15\n• G 96\n• B 10\nRGB color chart\n• C 84\n• M 0\n• Y 90\n• K 4\nCMYK color chart\n\n#27f519 color description : Vivid lime green.\n\n# #27f519 Color Conversion\n\nThe hexadecimal color #27f519 has RGB values of R:39, G:245, B:25 and CMYK values of C:0.84, M:0, Y:0.9, K:0.04. Its decimal value is 2618649.\n\nHex triplet RGB Decimal 27f519 `#27f519` 39, 245, 25 `rgb(39,245,25)` 15.3, 96.1, 9.8 `rgb(15.3%,96.1%,9.8%)` 84, 0, 90, 4 116.2°, 91.7, 52.9 `hsl(116.2,91.7%,52.9%)` 116.2°, 89.8, 96.1 33ff00 `#33ff00`\nCIE-LAB 84.896, -81.137, 78.479 33.663, 65.803, 11.847 0.302, 0.591, 65.803 84.896, 112.881, 135.954 84.896, -77.651, 101.925 81.119, -67.884, 48.124 00100111, 11110101, 00011001\n\n# Color Schemes with #27f519\n\n• #27f519\n``#27f519` `rgb(39,245,25)``\n• #e719f5\n``#e719f5` `rgb(231,25,245)``\nComplementary Color\n• #95f519\n``#95f519` `rgb(149,245,25)``\n• #27f519\n``#27f519` `rgb(39,245,25)``\n• #19f579\n``#19f579` `rgb(25,245,121)``\nAnalogous Color\n• #f51995\n``#f51995` `rgb(245,25,149)``\n• #27f519\n``#27f519` `rgb(39,245,25)``\n• #7919f5\n``#7919f5` `rgb(121,25,245)``\nSplit Complementary Color\n• #f51927\n``#f51927` `rgb(245,25,39)``\n• #27f519\n``#27f519` `rgb(39,245,25)``\n• #1927f5\n``#1927f5` `rgb(25,39,245)``\n• #f5e719\n``#f5e719` `rgb(245,231,25)``\n• #27f519\n``#27f519` `rgb(39,245,25)``\n• #1927f5\n``#1927f5` `rgb(25,39,245)``\n• #e719f5\n``#e719f5` `rgb(231,25,245)``\n• #13b908\n``#13b908` `rgb(19,185,8)``\n• #16d209\n``#16d209` `rgb(22,210,9)``\n• #18ea0a\n``#18ea0a` `rgb(24,234,10)``\n• #27f519\n``#27f519` `rgb(39,245,25)``\n• #3ef631\n``#3ef631` `rgb(62,246,49)``\n• #55f74a\n``#55f74a` `rgb(85,247,74)``\n• #6cf862\n``#6cf862` `rgb(108,248,98)``\nMonochromatic Color\n\n# Alternatives to #27f519\n\nBelow, you can see some colors close to #27f519. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #5ef519\n``#5ef519` `rgb(94,245,25)``\n• #4cf519\n``#4cf519` `rgb(76,245,25)``\n• #39f519\n``#39f519` `rgb(57,245,25)``\n• #27f519\n``#27f519` `rgb(39,245,25)``\n• #19f51d\n``#19f51d` `rgb(25,245,29)``\n• #19f530\n``#19f530` `rgb(25,245,48)``\n• #19f542\n``#19f542` `rgb(25,245,66)``\nSimilar Colors\n\n# #27f519 Preview\n\nThis text has a font color of #27f519.\n\n``<span style=\"color:#27f519;\">Text here</span>``\n#27f519 background color\n\nThis paragraph has a background color of #27f519.\n\n``<p style=\"background-color:#27f519;\">Content here</p>``\n#27f519 border color\n\nThis element has a border color of #27f519.\n\n``<div style=\"border:1px solid #27f519;\">Content here</div>``\nCSS codes\n``.text {color:#27f519;}``\n``.background {background-color:#27f519;}``\n``.border {border:1px solid #27f519;}``\n\n# Shades and Tints of #27f519\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #020e01 is the darkest color, while #fbfffb is the lightest one.\n\n• #020e01\n``#020e01` `rgb(2,14,1)``\n• #032101\n``#032101` `rgb(3,33,1)``\n• #053402\n``#053402` `rgb(5,52,2)``\n• #074703\n``#074703` `rgb(7,71,3)``\n• #095a04\n``#095a04` `rgb(9,90,4)``\n• #0b6c05\n``#0b6c05` `rgb(11,108,5)``\n• #0d7f06\n``#0d7f06` `rgb(13,127,6)``\n• #0f9206\n``#0f9206` `rgb(15,146,6)``\n• #11a507\n``#11a507` `rgb(17,165,7)``\n• #13b808\n``#13b808` `rgb(19,184,8)``\n• #15ca09\n``#15ca09` `rgb(21,202,9)``\n• #17dd0a\n``#17dd0a` `rgb(23,221,10)``\n• #19f00a\n``#19f00a` `rgb(25,240,10)``\n• #27f519\n``#27f519` `rgb(39,245,25)``\n• #39f62c\n``#39f62c` `rgb(57,246,44)``\n• #4af73f\n``#4af73f` `rgb(74,247,63)``\n• #5cf751\n``#5cf751` `rgb(92,247,81)``\n• #6ef864\n``#6ef864` `rgb(110,248,100)``\n• #7ff977\n``#7ff977` `rgb(127,249,119)``\n• #91fa8a\n``#91fa8a` `rgb(145,250,138)``\n• #a3fb9d\n``#a3fb9d` `rgb(163,251,157)``\n• #b4fcaf\n``#b4fcaf` `rgb(180,252,175)``\n• #c6fcc2\n``#c6fcc2` `rgb(198,252,194)``\n• #d8fdd5\n``#d8fdd5` `rgb(216,253,213)``\n• #e9fee8\n``#e9fee8` `rgb(233,254,232)``\n• #fbfffb\n``#fbfffb` `rgb(251,255,251)``\nTint Color Variation\n\n# Tones of #27f519\n\nA tone is produced by adding gray to any pure hue. In this case, #808f7f is the less saturated color, while #1ffe10 is the most saturated one.\n\n• #808f7f\n``#808f7f` `rgb(128,143,127)``\n• #789975\n``#789975` `rgb(120,153,117)``\n• #70a26c\n``#70a26c` `rgb(112,162,108)``\n• #67ab63\n``#67ab63` `rgb(103,171,99)``\n• #5fb45a\n``#5fb45a` `rgb(95,180,90)``\n• #57be50\n``#57be50` `rgb(87,190,80)``\n• #4fc747\n``#4fc747` `rgb(79,199,71)``\n• #47d03e\n``#47d03e` `rgb(71,208,62)``\n• #3fd935\n``#3fd935` `rgb(63,217,53)``\n• #37e32b\n``#37e32b` `rgb(55,227,43)``\n• #2fec22\n``#2fec22` `rgb(47,236,34)``\n• #27f519\n``#27f519` `rgb(39,245,25)``\n• #1ffe10\n``#1ffe10` `rgb(31,254,16)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #27f519 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]

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[ "# Asia's Blog\n\n### Math 9\n\nThe 5 most important things I learned in math 9 would be addition, subtraction, multiplication and division of rational numbers. Adding and subtracting with polynomials. Linear equations , linear inequalities algebraically and graphically and proportion. Addition, subtraction, multiplication and division… Continue Reading →\n\nEnlargements and reductions When the dimensions of an object (length, width, height etc) of an object are changed by multiplying by a scale factor. This can be in 2D or 3D objects. Object must stay proportional to each other. Angles… Continue Reading →\n\nI wanted to measure the height of my trampoline using similar triangles and a mirror. The distance between the mirror and I was 2ft and the distance between the trampoline and the mirror was 6ft. Next I measured my height… Continue Reading →\n\nThese are the numbers I started with to get my 6 point shape. To reduce my shape by the scale factor of .3 I divided each one of my numbers from the original chart by 3 to get these numbers:… Continue Reading →\n\nInequalities   A linear inequalities is almost the same as a linear equation except the = is replace with a <,>,≥ ,≤ To solve a linear inequality you first have to make zero pairs on either sides of the inequality… Continue Reading →\n\nVocab: Equation – A statement that the values of two mathematical expressions are equal. Equivalent Equation – When the only solution to the problem is the same. Coefficient – A number used to multiply a variable. Constant – A number… Continue Reading →\n\nIf you have a pattern that starts at  1 and increases by 2 then your chart would be X=1,2,3,4,5 and Y=1,3,5,7,9 In which case the rule would be 2X-1. When putting numbers on to a graph you refer to the… Continue Reading →\n\nIn grade 9 polynomials I have learned how to add, subtract, multiply and divide with polynomials. I have also learned about terms, coefficients, constants and degree. Addition – When adding  polynomials you group all like terms and the get rid… Continue Reading →" ]

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[ "###### Abstract\n\nWe constrain the spectrum of primordial curvature perturbations by using recent Cosmic Microwave Background (CMB) and Large Scale Structure (LSS) data. Specifically, we consider CMB data from the COBE, Boomerang and Maxima experiments, the real space galaxy power spectrum from the IRAS PSCz survey, and the linear matter power spectrum inferred from Ly forest spectra, where we for simplicity assume the absence of appreciable covariances. We study the case of single field slow roll inflationary models, and we extract bounds on the scalar spectral index, , the tensor to scalar ratio, , and the running of the scalar spectral index, , for various combinations of the observational data. We find that CMB data, when combined with data from Lyman forest, place strong constraints on the inflationary parameters. Specifically, we obtain , and , indicating that big n, big r models (often referred to as hybrid models) are ruled out.\n\nConstraints on inflation from CMB and Lyman- forest\n\nNORDITA, Blegdamsvej 17, DK-2100 Copenhagen, Denmark\n\nS. H. Hansen 222e-mail:\n\nNAPL, University of Oxford, Keble road, OX1 3RH, Oxford, UK\n\nF. L. Villante 333e-mail:\n\nDipartimento di Fisica and Sezione INFN di Ferrara, Via del Paradiso 12, 44100 Ferrara, Italy\n\nA. J. S. Hamilton 444e-mail:\n\nJILA and Dept. Astrophys. & Planet. Sci., Box 440, U. Colorado, Boulder CO 80309, USA\n\nPACS: 98.62.Ra, 98.65.-r, 98.70.Vc, 98.80.Cq\n\n## 1 Introduction\n\nInflation is generally believed to provide the initial conditions for the evolution of large scale structure (LSS) and the cosmic microwave background radiation (CMB). The garden of inflation offers a bounty of models, each of which predicts a certain power spectrum of primordial curvature perturbations, , a function of the wavenumber . This power spectrum can be Taylor-expanded about some wavenumber and truncated after a few terms \n\n lnP(k)=lnP(k0)+(n−1)lnkk0+12dndlnk∣∣∣k0ln2kk0+⋯ (1)\n\nin which the first term is a normalization constant, the second is a power-law approximation, with the case corresponding to a scale invariant Harrison-Zel’dovich spectrum, and the third term is the running of the spectral index.\n\nAn important class of models is given by single field slow roll (SR) inflationary models, which can be treated perturbatively. The properties of SR models are well known (see e.g. ref.  for review and a list of references), and we will here classify the different models by the 3 parameters , where is the scalar spectral index at the pivot scale , the parameter is the tensor to scalar perturbation ratio at the quadrupole scale, and . The reason for using these 3 variables instead of the normal SR parameters (defined in the appendix) is simply that the former 3 variables are more closely related to what is measured from observations.\n\nIn SR models the tensor spectral index and its derivative can be expressed [2, 3]\n\n nT=−rκanddnTdlnk=rκ[(n−1)+rκ] . (2)\n\nThe factor in the above equations depends on the model, and in particular is different for different  . In our analysis we use the parametrisation from ref. , which for the models considered here means .\n\nThe different SR models are traditionally  categorised into 3 main groups according to the relationship between the first and second derivative of the inflaton potential, and they are distributed in and space as in Fig. 1 (see details in the appendix or in ref. ), where the dashed lines on the borders between the different models are the two attractors found in ref. , and . For large values of and , SR models “naturally” predict sizeable deviations from a power law approximation (i.e. ), so when comparing to observations it is important to include the third parameter , in addition to the parameters and commonly considered.", null, "Figure 1: The various slow-roll models in (n,r) and (n,∂lnk) space. The dashed lines are the two attractors (here we have used κ=5 which is a typical value for a flat universe with a large cosmological constant). The figure (n,∂lnk) is for ξ2=0. The hatched regions move up and down by inclusion of the third derivative, ξ2≠0 (see Eq. 10 in the appendix).\n\nThe purpose of this paper is to ascertain what constraints currently available observational data can place on the parameters of SR inflation. Of course the universe could lie outside the hatched regions of Fig. 1, indicating that one should look beyond SR inflation; but it seems reasonable to explore the simplest models in the first instance. In ref. , CMB data were used to put bounds on inflationary parameters, and indications were found towards a negative bend of the primordial power spectrum (). However, the scales probed by CMB are limited, and the constraint on was weak.\n\nIn the present paper we extend the analysis of  by including information not only from the CMB, but also from the linear galaxy power spectrum measured from the IRAS Point Source Catalogue Redshift (PSCz) survey , and from the linear matter power spectrum inferred from the Ly forest in quasar spectra . Even though it is not completely clear that the correlations in the 3d matter power spectrum are negligible, we treat them as such for simplicity. The size of and effect from such covariances might be essential, and should be considered more carefully in a future investigation. As we will show, these data, probing different ranges of scales, yield much tighter constraints on the inflationary parameters than CMB data alone.\n\n## 2 The data\n\nRecently observational data on both the CMB and LSS have improved dramatically. The balloon-borne experiments Boomerang  and MAXIMA  have determined the CMB angular power spectrum beyond the first acoustic peak, whose position near indicates a flat universe, hence seemingly confirming the inflationary paradigm. The two experiments, together with COBE-DMR , provide a high signal-to-noise determination of the CMB power spectrum for , thus testing the structure formation paradigm on scales roughly of the order Mpc.\n\nLSS data, probing smaller scales, provide complementary information. In this paper we consider the real space galaxy power spectrum from IRAS Point Source Catalogue Redshift (PSCz) survey which probes scales in the range Mpc [9, 17]. In order to avoid problems with the interpretation of non-linear effects, we use data only at scales Mpc.\n\nFurther, we consider the information on the linear matter spectrum at redshift which can be inferred from the Ly- forest in quasar spectra. The fact that the nonlinear scale is smaller at higher redshift makes it possible to probe the linear power spectrum to smaller scales ( Mpc) than are accessible to galaxy surveys at low redshift. In this paper we use a recent determination of the linear matter power spectrum from the Lyman- forest at redshift , based on a large sample of Keck HIRES and Keck LRIS quasar spectra. To convert the measured power spectrum of Ly- flux into the matter power spectrum, apply a correction factor obtained from -body computer simulations. To allow for possible systematic uncertainty in this correction factor, we will repeat the analysis excluding the data at the smallest scales.\n\n### 2.1 Data analysis\n\nIn order to investigate how the CMB, PSCz and Ly- data constrain the SR parameter space , we performed a likelihood analysis of the data sets from COBE , Boomerang  and MAXIMA , together with the decorrelated linear power spectrum of PSCz galaxies for Mpc [9, 17], and the Ly- data from Table 4 of ref. . The likelihood function is\n\n L∝exp(−χ2/2), (3)\n\nwhere\n\n χ2=χ2CMB+χ2PSCz+χ2Ly−α. (4)\n\nFor the CMB data\n\n χ2CMB=∑i(Cl,i(θ)−Cl,i)2σ2(Cl,i), (5)\n\nwhile for PSCz and Ly- data\n\n χ2PSCz,Ly−α=∑i(Pk,i(θ)−Pk,i)2σ2(Pk,i), (6)\n\nthe sum being taken over published values of band-powers and . The quantity is a vector of cosmological parameters, taken here to be\n\n θ={Ωm,ΩΛ,Ωb,H0,τ,Q,n,r,∂lnk} . (7)\n\nThe parameters are: the matter density ; the baryon density ; the Hubble parameter ; the optical depth to reionization; the normalizations , , and of the CMB, LSS, and Ly- power spectra; and the inflationary parameters . We have assumed that the universe is flat, , as predicted by standard inflationary models. For all the figures we marginalize over all other parameters. We consider only two values for the baryon density, and , however, as we will see, the results are very similar in those two cases, suggesting that the results will be similar if allowing as a free parameter.\n\nThe CMB, LSS, and Ly- data are all subject to uncertainties in their overall normalizations. The CMB groups quote estimated calibration errors for their experiments, which we account for by allowing the data points to shift up or down, by 10% for Boomerang , and by 4% for MAXIMA . Because of uncertainty in the linear galaxy-to-mass bias for PSCz galaxies , we conservatively treat the normalization as an unconstrained parameter. Ref. quotes uncertainties in the overall normalization of the matter power spectrum inferred from the Ly- forest, but these uncertainties are based on simulations with , so to avoid possible bias we again conservatively treat the normalization as an unconstrained parameter.\n\nFor simplicity all data points have been treated as uncorrelated in the likelihood functions, eqs. (5,6). For the CMB data, correlations between estimates of angular power at different harmonics are induced by finite sky coverage, but in practice the CMB teams quote band-powers at sufficiently well-separated bands of that the correlations are probably small. For the PSCz data, the published band-powers are explicitly decorrelated. For the Ly- data, the covariances between estimates of the flux power spectrum are small, according to Fig. 12 of , and this may translate into small statistical covariances in the inferred matter power spectrum. As mentioned earlier, it is not completely clear how good this translation from flux power to matter power is, and we leave this question for future investigation.\n\nWe have chosen the pivot scale in Eq. (1) as . This choice is made for convenience, since is the scale at which wave-numbers are normalised in the CMBFAST code. Our results are independent of the value of .", null, "Figure 2: The 1 and 2 σ allowed regions for the two slow roll parameters n and ∂lnk. The left panels assume a BBN prior on Ωbh2=0.019, whereas the right panels are for Ωbh2=0.030, the value which best fits the CMB data. The top row is for CMB data alone, the middle row is for Lyman-α data alone, and the bottom row is for the combined analysis.\n\n### 2.2 Results\n\nThe analysis of the constraints from CMB data was presented in detail in ref.  (see also ). Here we extend the analysis in by including the reionization optical depth, , as a free parameter. This is potentially important since there is a well-known degeneracy between and the scalar spectral index . However, the analysis turns out to prefer models with , so including leaves the main conclusions of essentially unchanged, as can be seen in the upper panels of Figs. 2 and 3. We recall here the main conclusions from : (1) if we allow the primordial power spectrum to bend, , then CMB data do not constrain the tensor to scalar perturbation ratio ; (2) if we assume a BBN prior, , then CMB data favour a negative bend, , corresponding to a bump-like feature centered at scales .\n\nLet us now discuss the information on the inflationary parameters which emerges from PSCz and Ly- data. The first observation is that PSCz data do not provide relevant constraints in the plane. This is easily understood, because the PSCz data at large scales (say ) have large errors and therefore play little role in the evaluation. This implies that PSCz data effectively span only one decade in . Considering that the overall normalization of the data is taken as a free parameter, it is evident that one cannot obtain strong constraints from such a small range of scales.\n\nThe situation is quite different with Ly- data, which have small error bars and span almost two decades in . This is shown in Fig. 2, where we present the allowed regions corresponding to 1 and 2 (we define the region as and the 2 region as ) for both as suggested by BBN (left column), and as suggested by CMB (right column). The top graphs are from CMB data alone, the middle graphs are obtained using Ly- data alone, and the bottom graphs are from the combined analysis.\n\nIt is straightforward to understand how Ly- data select the allowed regions shown in the middle panels of Fig. 2. At the small scales probed by Ly- data, the theoretical linear matter power spectrum is roughly proportional to\n\n P(k)∝ln2(αk/Γh)kn′−4 (8)\n\nwhere , and is expressed in . The parameter is the effective spectral index of primordial density perturbation at the scale Mpc representative of Ly- data 555The observational units for wavenumbers are . The conversion to Mpc is model-dependent since it requires the evaluation of the Hubble constant at redshift .. On the other hand the Ly- data, as discussed in , are well fitted by a power law, , with spectral index . This means that\n\n dlnP(kα)dlnk=(n′−4)+2ln(αkα/Γh)=−2.47±0.06 . (9)\n\nIf we consider that\n\nIt is important to note that the regions constrained by Ly- data are “orthogonal” to the regions constrained by CMB data. This means that the combined analysis (CMB+Ly-) gives much stronger bounds than any of the two alone. Moreover, since CMB data provide a bound on , the degeneracy between and in Eq. (9) is removed, and therefore the Ly- observation of can be directly translated into a constraint on . This is clearly shown in the lower panels of Fig. 2, from which one obtains the following conclusions: (1) the combined analysis strongly indicates that the bend of the primordial power spectrum is close to zero, being at the 2 level; (2) the spectral index is constrained to be fairly close to . One notes that the limits obtained do not crucially depend on the assumed values of , indicating that the inclusion of Lyman- data avoids the problem with CMB data alone, that different extend the allowed range of the spectral index beyond  . However, one should note that, due essentially to CMB data, the goodness of the fit is quite sensitive to the assumed value of , the being substantially smaller for high .", null, "Figure 3: The 1 and 2 σ allowed regions in the (n,r) plane. The left panels assume a BBN prior on Ωbh2=0.019, whereas the right panels are for Ωbh2=0.030, the value which best fits the CMB data. The top panels are for CMB data alone, while the bottom panels are for the combined analysis. Hybrid models are to the right of the full line.\n\nIn Fig. 3 we present the constraints obtained for the remaining SR parameter . Specifically, we show the 1 and 2 allowed regions in the plane, for both low and high . The top panels are from CMB data alone, while the bottom ones are from the combined analysis. It is clear that in the combined analysis is constrained to be smaller than about 0.3 at 2 . This is substantially different from the analysis of CMB data alone, where no constraints on could be obtained, since a strong bend, e.g. , could allow the tensor component to be big . It is worth noting, that Ly- data don’t probe directly; they fix to be less than 1, and close to zero. In this way strong constraint on can be obtained from CMB data. This result is extremely important when we compare to theoretical models, since different classes of models predict different relationships between the scalar spectral index and the tensor to scalar ratio (see Fig. 1). The combined analysis, indicating and , favours small field models and seems to exclude hybrid models. This is clear from the lower panels of Fig. 3, where the big n, big r (often referred to as hybrid models, to the right of the full line), are excluded at 2666We have used (see Eq. 2), and for larger the hybrid models move to bigger . It is worth pointing out, that the classification of hybrid models  as in Fig. 1, and as the models to the right of the full line in Fig. 3 is oversimplified. In this paper we follow ref. , and by ”hybrid models” we refer to potentials for which (see appendix for details). When considering more general potentials, or F-term hybrid inflation , more complicated behaviour results, and a simplified classification is impossible.\n\nAn important caveat to this analysis concerns possible systematic uncertainties in the inference of a linear matter power spectrum from the Ly- data. What measure directly from observations is the power spectrum of transmitted Ly- flux. The conversion to a linear matter power spectrum involves a fairly large, scale-dependent correction which extract from collisionless computer simulations, with the Ly- optical depth taken proportional to a certain power of the dark matter density . It has been suggested that the relation between baryonic and dark matter densities could introduce significant uncertainty in the flux-to-mass correction at small scales. Specifically, pressure effects cause the baryonic density to be smoothed compared to the dark matter density , an effect that can be parametrized as , with comoving filter scale . The procedure considered by is to treat the filter scale as a free parameter constrained only by the shape of the power spectrum of Ly- flux. However, argue that treating as a free parameter is overly pessimistic, and that if takes values suggested by hydrodynamic simulations, then the effect on the power spectrum is minor.\n\nTo allow for the possibility that the systematic errors are underestimated at small scales, we repeated the analysis neglecting the last 3 data-points from the Ly- data , both for and for free. The upper panels in Fig. 4 show the case where . Here, the results are essentially unchanged by the removal of the data points. However, the lower panels show the full case. Here, the tight constraint on disappears completely, and the constraint on is significantly weakened. The reason is that the small scale data points are the most important for constraining . When these points are removed, is not nearly as tightly constrained as before, and as seen for the case where only CMBR data is used, a large can be compensated by a negative bend of the spectrum.\n\nThus, the very tight constraint derived above depends on the correctness of the small scale Ly- data. Therefore, it is highly desirable that a better understanding of the possible systematic errors in determining matter power spectra from Ly- forest observations is developed.", null, "Figure 4: The 1 and 2 σ allowed regions in the (n,r) plane. These results are obtained from the combined analysis, neglecting the last 3 data-points from . The left panels assume a BBN prior on Ωbh2=0.019, whereas the right panels are for Ωbh2=0.030, the value which best fits the CMB data. The top panels assume ∂lnk=0, whereas the lower panels have ∂lnk as a free parameter. Hybrid models are to the right of the full line.\n\nAnother worry is that the error ellipses for CMB and Ly- are only marginally overlapping. This might indicate that the two data sets are mutually inconsistent, and that other physical effects should be taken into account. For the Ly- data one might think of massive neutrinos or warm dark matter, where both would suppress power on small scales, potentially allowing bigger or bigger positive .\n\n## 3 Conclusions\n\nWe have considered data from both CMB and LSS to place constraints on the parameters of single field slow roll inflationary models. We have found that, by combining CMB data with the power spectrum inferred from Lyman forest, one obtains strong constraints on the inflationary parameters. We obtain , and\n\n## Acknowledgements\n\nWe are pleased to thank A. Dolgov, A. Linde, A. Melchiorri and J. Silk for comments and discussions. SHH is supported by a Marie Curie Fellowship of the European Community under the contract HPMFCT-2000-00607. We acknowledge the use of CMBFAST .\n\n## Appendix A Notation\n\nWe use the notation: , where\n\n ϵ=M22(V′V)2 ,η=M2V′′V−M22(V′V)2andξ2=M4V′V′′′V2\n\nsee [7, 21] for details. The notation with , used e.g. in , simply corresponds to the substitution . The 3 classes of SR models are small fields , large fields , and hybrid models . One finds\n\n r=2κϵ ,∂lnk=−2ξ2+8ϵ2(2α−1)andn−1=2ϵ(α−2) . (10)" ]

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[ "# Information Processing\n\nJust another WordPress.com weblog\n\n## Sign problem in QCD\n\nThe revised version of our paper 0808.2987 is up on arXiv now. Special thanks to Kim Splittorff, Mark Alford, Bob Sugar, Phillippe de Forcrand and many others for comments. See earlier discussion.\n\nOn the sign problem in dense QCD\n\nS. Hsu and D. Reeb\n\nWe investigate the Euclidean path integral formulation of QCD at finite baryon density. We show that the partition function Z can be written as the difference between two sums Z+ and Z-, each of which defines a partition function with positive weights. If the ratio Z-/Z+ is nonzero in the infinite volume limit the sign problem is said to be severe. This occurs only if, and generically always if, the associated free energy densities F+ and F- are equal in this limit. In an earlier version of this paper we conjectured that F- is bigger than F+ in some regions of the QCD phase diagram, leading to domination by Z+. However, we present evidence here that the sign problem may be severe at almost all points in the phase diagram, except in special cases like exactly zero chemical potential (ordinary QCD), which requires a particular order of limits, or at exactly zero temperature and small chemical potential. Finally, we describe a Monte Carlo technique to simulate finite-density QCD in regions where Z-/Z+ is small.\n\nWritten by infoproc\n\nOctober 2, 2008 at 6:41 pm\n\nPosted in physics, qcd" ]

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[ "# What is iso cost line. What is isocost curve? 2019-01-13\n\nWhat is iso cost line Rating: 8,8/10 669 reviews\n\n## Iso", null, "This is known as the stage of diminishing returns. There is perfect competition in the factor market. The firm aims at profit maximisation. If the distance between those isoquants increases as output increases, the firm's production function is exhibiting decreasing returns to scale; doubling both inputs will result in placement on an isoquant with less than double the output of the previous isoquant. Subsidiary industries crop up to help the main industry. In an isocost line shows all combinations of inputs which cost the same total amount.\n\nNext\n\n## Iso", null, "In the typical case shown in the top figure, with smoothly curved isoquants, a firm with fixed unit costs of the inputs will have isocost curves that are linear and downward sloped; any point of tangency between an isoquant and an isocost curve represents the cost-minimizing input combination for producing the output level associated with that isoquant. You all have never eaten chocolates. The absolute value of the slope of the isocost line, with capital plotted vertically and labour plotted horizontally, equals the ratio of unit costs of labour and capital. In the upper dotted portion, more capital and in the lower dotted portion more labour than necessary is employed. This causes the isocost line to become steeper. Each such point shows the equilibrium factor combination for maximising output subject to cost constraint, i.\n\nNext\n\n## Difference between isocost and isoquant", null, "Finally, any combination of inputs above or to the right of an isoquant results in more output than any point on the isoquant. I'm not sure they are from my experiences. To find the least cost combination of inputs to produce a given output, we need to construct such equal cost lines or isocost lines. It is because the slope of an isocost line is calculated as Since we assume that no changes are made in the prices of either of the inputs, the slope remain the same for all budget line at any given outlay. Let us also suppose that the price of labor was decreased by certain amount, as a result of which the producer became able to purchase more units of labor at the same outlay.\n\nNext\n\n## What is isocost curve?", null, "A linear isoquant implies that either factor can be used in proportion. It will be slightly bigger if the extractor puts a header on the file, like Nero. Analyzing these three things will help produce the best maximum output in the most cost-friendly way possible. Thus, profit maximisation and cost minimisation are the two sides of the same coin. The decision to supply an extra unit depends on the marginal cost of producing that unit.\n\nNext\n\n## Economics: The Isocost Line", null, "Examples: I will read the book that is written by my favorite author. Decreasing Returns to Scale: Figure 24. But for your production function your output can have different values so you'd have multiple isoquant curves and multiple isoquant curves already describe an isoquant map Isoquant map - shows a number of isoquant curves in a single graph, describing a production function. Thus the least cost combination of factors refers to a firm producing the largest volume of output from a given cost and producing a given level of output with the minimum cost when the factors are combined in an optimum manner. Finally, any combination of inputs above or to the right of an isoquant results in more output than any point on the isoquant. With the help of isoquant and iso-cost lines, a producer can determine the point at which inputs yield maximum profit by incurring minimum cost.\n\nNext\n\n## What is iso cost line", null, "There are two essential or second order conditions for the equilibrium of the firm. The slope of iso cost line indicates the ratio of the factor prices. In agriculture, most materials used to create many products are farmed. Specifically, the point of tangency between any isoquant and an isocost line gives the lowest-cost combination of inputs that can produce the level of output associated with that isoquant. The least cost factor combination can be determined by imposing the isoquant map on isocost line. Finally, suppose that the firm wished to use capital and labour in equal proportions. In other words, isoquant shows all the input points required to produce same level of output.\n\nNext\n\n## Difference between isocost and isoquant", null, "Iso quant map shows all the possible combinations of labour and capital that can produce different levels of output. Effect of a wage increase on isocost line? Short or long run costs can change. This can easily be confirmed because. The new cost equation becomes: Again we can re-write this with K on the y-axis, such that: We can see now that the wage-rent ratio has increased. This can directly affect agriculture production because farmers have to know what they can spend on a certain input in order to be able to profit from the production. As we move down along an isoquant the absolute value of its slope or Marginal Rate of Technical Substitution declines and the isoquant is convex. A change in factor price makes changes in the slope of isocost lines as shown in the figure.\n\nNext\n\n## Post 6: What is the ISO", null, "Its legs are made of hand-lathed maple and its surface is oak, with maple inlay. An isoquant map can also indicate decreasing or increasing returns to scale based on increasing or decreasing distances between the isoquant pairs of fixed output increment, as output increases. Again, less expensive is better. This really affects agriculture with the grain market. Production isoquant strictly convex and curve linear An isoquant shows that extent to which the firm in question has the ability to substitute between the two different inputs at will in order to produce the same level of output. This shows all the possible cost and the consumers budget to get the most money out of the product you are promoting to sell. Isoquants: An isoquant is a locus of points showing all the technically efficient ways of combining factors of production to produce a fixed level of output.\n\nNext" ]

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[ "", null, "One-way ANOVA Power Analysis IDRE Stats Conduct and Interpret a Sequential One-Way Discriminant Analysis; Conduct and Interpret a One-Way ANOVA . Examples for typical questions the ANOVA answers are\n\n## ANOVA kean.edu\n\nSample Size Calculation for One-Way ANOVAs in. This tutorial will help you set up and interpret contrasts following a one-way Analysis of Variance (ANOVA) in Excel using the XLSTAT software., Subjects One-Way ANOVA example : one another, but she can't know which specific mean pairs significantly differ until she conducts a post-hoc analysis (e.g.,.\n\nFor example, a one-way Analysis of Variance could have one IV A repeated measures ANOVA is almost the same as one-way ANOVA, with one main difference: Subjects One-Way ANOVA example : one another, but she can't know which specific mean pairs significantly differ until she conducts a post-hoc analysis (e.g.,\n\nANOVA Testing Example. we can calculate the variance between the groups or s^2BETWEEN. One Way ANOVA By Hand; One-Tailed z-test Hypothesis Test By Hand; Analysis of variance (ANOVA) is an analysis tool used in For example, a researcher might variables in your Analysis of Variance test. A one-way ANOVA\n\nFor example, in a t-test we calculate S x, S Which treatments differ from one another? The Analysis of Variance has told us only that there (One-way ANOVA) Let us understand One Way ANOVA with an example. As we have already seen that there are three types of Anova analysis or analysis of variance which we can use\n\nExample 2: Analyzing Power, Sample Size, and Effect Size One possible way of characterizing is in relation to a The 1-Way ANOVA: Power Calculation 1/07/2012В В· How To Calculate and Understand Analysis of Variance (ANOVA) F Test. statisticsfun. The Anova example is for a one way anova test.\n\nSubjects One-Way ANOVA example : one another, but she can't know which specific mean pairs significantly differ until she conducts a post-hoc analysis (e.g., Watch videoВ В· How to calculate a one way ANOVA by hand (in Excel) and comparing the results to SPSS.\n\nThe one-way Analysis of Variance (ANOVA) is used with one categorical independent variable and one continuous variable. The independent variable can Estimation for the one-way layout can be performed one of two ways. First, we can calculate the The one-way ANOVA is useful when we want to compare Example\n\nFor example, in a t-test we calculate S x, S Which treatments differ from one another? The Analysis of Variance has told us only that there (One-way ANOVA) For example, a one-way Analysis of Variance could have one IV A repeated measures ANOVA is almost the same as one-way ANOVA, with one main difference:\n\nHow to perform one-way analysis of variance (ANOVA) in Excel, including planned and unplanned comparisons, effect size, and homogeneity of variances testing. Conduct and Interpret a Sequential One-Way Discriminant Analysis; Conduct and Interpret a One-Way ANOVA . Examples for typical questions the ANOVA answers are\n\nOne-way ANOVA Power Analysis we can do some simply calculation to see that the grand mean will be 598. For example, we might not have a This tutorial will help you set up and interpret contrasts following a one-way Analysis of Variance (ANOVA) in Excel using the XLSTAT software.\n\nLet us understand One Way ANOVA with an example. As we have already seen that there are three types of Anova analysis or analysis of variance which we can use Introduction to ANOVA. There are commonly two types of ANOVA tests for univariate analysis – One-Way ANOVA The results for two-way ANOVA test on our example\n\n### ONE-WAY ANOVA University of Edinburgh", null, "1.3.5.4. One-Factor ANOVA itl.nist.gov. Methods and formulas for One-Way ANOVA. The calculation for the mean square for the factor follows: For example, if the calculated p, One-way ANOVA Power Analysis we can do some simply calculation to see that the grand mean will be 598. For example, we might not have a.\n\n### 1.3.5.4. One-Factor ANOVA itl.nist.gov", null, "Power for One-way ANOVA Real Statistics Using Excel. Stats: Two-Way ANOVA. The two-way analysis of variance is an extension to the one-way analysis of variance. For example, if the first factor Stats: Two-Way ANOVA. The two-way analysis of variance is an extension to the one-way analysis of variance. For example, if the first factor.", null, "• One Way Anova (Analysis of Variance) Calculator\n• QMSS e-Lessons The One-Way ANOVA\n• One Way ANOVA Calculation Example on Vimeo\n\n• Describes how to calculate the power and sample size requirements for a one-way ANOVA. Includes examples and Excel add-in. For example, in a t-test we calculate S x, S Which treatments differ from one another? The Analysis of Variance has told us only that there (One-way ANOVA)\n\nThese include one-way ANOVA, two-way ANOVA and multiple ANOVA, All except equation [A] appear in the ANOVA calculation table. Discussion and conclusions Estimation for the one-way layout can be performed one of two ways. First, we can calculate the The one-way ANOVA is useful when we want to compare Example\n\n1/07/2012В В· How To Calculate and Understand Analysis of Variance (ANOVA) F Test. statisticsfun. The Anova example is for a one way anova test. ANOVA Testing Example. we can calculate the variance between the groups or s^2BETWEEN. One Way ANOVA By Hand; One-Tailed z-test Hypothesis Test By Hand;\n\nStats: Two-Way ANOVA. The two-way analysis of variance is an extension to the one-way analysis of variance. For example, if the first factor For example, a one-way Analysis of Variance could have one IV A repeated measures ANOVA is almost the same as one-way ANOVA, with one main difference:\n\n1/07/2012В В· How To Calculate and Understand Analysis of Variance (ANOVA) F Test. statisticsfun. The Anova example is for a one way anova test. In one-way ANOVA, the interest lies in We can refer back to the data table used in Two way ANOVA example to illustrate analysis of covariance.\n\nSummary Table for the One-way ANOVA Summary ANOVA Source Sum of Squares Degrees of Freedom Hand Calculation of ANOVA Sample size calculation for ANOVAs can be complicated, so we'll start with sample size calculation for one-way ANOVAs. Contact Statistics Solutions.\n\nThis tutorial will help you set up and interpret contrasts following a one-way Analysis of Variance (ANOVA) in Excel using the XLSTAT software. Types of ANOVA. One-way between groups. The example For example, the grades by tutorial analysis It is unlikely that you would do an analysis of variance\n\nThus, One way ANOVA calculator is used to test the equality of samples by using variance. ANOVA - short for Analysis Of Variance Simple Example - One-Way ANOVA. A scientist wants to know if all children from schools A, B and C have equal mean IQ scores.\n\nHow to calculate an ANOVA table Calculations by Hand We look at the following example: Similar as for a T-test we calculate the critical value for the level = 5% For example, a one-way Analysis of Variance could have one IV A repeated measures ANOVA is almost the same as one-way ANOVA, with one main difference:\n\nExample of a Three-group ANOVA . The following is a hypothetical example comparing satisfaction ratings of teachers randomly Definitional Formulas for One-way ANOVA Analysis of variance (ANOVA) I’ll use concepts and graphs to answer these questions about F-tests in the context of a one-way ANOVA example.\n\nOne factor analysis of variance, also known as ANOVA, gives us a way to make multiple comparisons of several population means. Rather than doing this in a pairwise For example, a one-way Analysis of Variance could have one IV A repeated measures ANOVA is almost the same as one-way ANOVA, with one main difference:\n\n## One Way Anova (Analysis of Variance) Calculator", null, "ONE-WAY ANOVA University of Edinburgh. A bit of background and a detailed example of an ANOVA Calculation, An Explanation and an ANOVA Calculation Example. It is another common tool and one that is, One-way ANOVA with post-hoc Tukey HSD Calculator for multiple comparison.\n\n### One Way Analysis of Variance (ANOVA)\n\nQMSS e-Lessons The One-Way ANOVA. ANOVA Testing Example. we can calculate the variance between the groups or s^2BETWEEN. One Way ANOVA By Hand; One-Tailed z-test Hypothesis Test By Hand;, Sample size calculation for ANOVAs can be complicated, so we'll start with sample size calculation for one-way ANOVAs. Contact Statistics Solutions..\n\nExample of a Three-group ANOVA . The following is a hypothetical example comparing satisfaction ratings of teachers randomly Definitional Formulas for One-way ANOVA One-Way Analysis of Variance For example, suppose we had 7 groups. One Way Anova: Computational Procedures Formula Explanation\n\nAnalysis of variance (ANOVA) I’ll use concepts and graphs to answer these questions about F-tests in the context of a one-way ANOVA example. For example, in a t-test we calculate S x, S Which treatments differ from one another? The Analysis of Variance has told us only that there (One-way ANOVA)\n\nOne-Way Analysis of Variance for Independent or Correlated Samples. The logic and computational details of the one-way ANOVA for independent and correlated samples How to perform one-way analysis of variance (ANOVA) in Excel, including planned and unplanned comparisons, effect size, and homogeneity of variances testing.\n\nOne-way Anova Power Analysis SAS Data Analysis Examples. Overall F Test for One-Way ANOVA Fixed Scenario Elements Method Exact Alpha 0.05 ANOVA Testing Example. we can calculate the variance between the groups or s^2BETWEEN. One Way ANOVA By Hand; One-Tailed z-test Hypothesis Test By Hand;\n\nHow to calculate an ANOVA table Calculations by Hand We look at the following example: Similar as for a T-test we calculate the critical value for the level = 5% ANOVA Testing Example. we can calculate the variance between the groups or s^2BETWEEN. One Way ANOVA By Hand; One-Tailed z-test Hypothesis Test By Hand;\n\nConduct and Interpret a Sequential One-Way Discriminant Analysis; Conduct and Interpret a One-Way ANOVA . Examples for typical questions the ANOVA answers are 30/01/2016В В· One-Way ANOVA Calculation Roger Morrissette. 11 5 One Way ANOVA Comparing Several Sample Means Two-Way Chi Square Calculation Example\n\nEstimation for the one-way layout can be performed one of two ways. First, we can calculate the The one-way ANOVA is useful when we want to compare Example Stats: Two-Way ANOVA. The two-way analysis of variance is an extension to the one-way analysis of variance. For example, if the first factor\n\nOne-Way Analysis of Variance For example, suppose we had 7 groups. One Way Anova: Computational Procedures Formula Explanation Stats: Two-Way ANOVA. The two-way analysis of variance is an extension to the one-way analysis of variance. For example, if the first factor\n\nDescribes how to calculate the power and sample size requirements for a one-way ANOVA. Includes examples and Excel add-in. One-way Anova Power Analysis SAS Data Analysis Examples. Overall F Test for One-Way ANOVA Fixed Scenario Elements Method Exact Alpha 0.05\n\nEstimation for the one-way layout can be performed one of two ways. First, we can calculate the The one-way ANOVA is useful when we want to compare Example Subjects One-Way ANOVA example : one another, but she can't know which specific mean pairs significantly differ until she conducts a post-hoc analysis (e.g.,\n\nHow to perform one-way analysis of variance (ANOVA) in Excel, including planned and unplanned comparisons, effect size, and homogeneity of variances testing. One Way Analysis of Variance (ANOVA) Example: Researchers wish to see if there is difference in average BMI among three .different populations.\n\nOne Way ANOVA Calculation Example on Vimeo. Example of a Three-group ANOVA . The following is a hypothetical example comparing satisfaction ratings of teachers randomly Definitional Formulas for One-way ANOVA, Estimation for the one-way layout can be performed one of two ways. First, we can calculate the The one-way ANOVA is useful when we want to compare Example.\n\n### 3 Types of ANOVA analysis SixSigmaStats", null, "One Way ANOVA Calculation Example on Vimeo. A bit of background and a detailed example of an ANOVA Calculation, An Explanation and an ANOVA Calculation Example. It is another common tool and one that is, 30/01/2016В В· One-Way ANOVA Calculation Roger Morrissette. 11 5 One Way ANOVA Comparing Several Sample Means Two-Way Chi Square Calculation Example.\n\n### ANOVA kean.edu", null, "One-Way ANOVA Calculation YouTube. One-Way Analysis of Variance for Independent or Correlated Samples. The logic and computational details of the one-way ANOVA for independent and correlated samples One application of the one-way ANOVA that might be of interest has to do with students' performance in in this example, This calculation is relatively.", null, "One application of the one-way ANOVA that might be of interest has to do with students' performance in in this example, This calculation is relatively Describes how to calculate the power and sample size requirements for a one-way ANOVA. Includes examples and Excel add-in.\n\nOne-way ANOVA treatments. You may, of course, overwrite the demo example data, but \\(k=4\\) When the number of contrasts to be estimated is small, The one-way Analysis of Variance (ANOVA) is used with one categorical independent variable and one continuous variable. The independent variable can\n\nThese include one-way ANOVA, two-way ANOVA and multiple ANOVA, All except equation [A] appear in the ANOVA calculation table. Discussion and conclusions One application of the one-way ANOVA that might be of interest has to do with students' performance in in this example, This calculation is relatively\n\n30/01/2016В В· One-Way ANOVA Calculation Roger Morrissette. 11 5 One Way ANOVA Comparing Several Sample Means Two-Way Chi Square Calculation Example This tutorial will help you set up and interpret contrasts following a one-way Analysis of Variance (ANOVA) in Excel using the XLSTAT software.\n\nOne-Way Analysis of Variance For example, suppose we had 7 groups. One Way Anova: Computational Procedures Formula Explanation One-Way Analysis of Variance for Independent or Correlated Samples. The logic and computational details of the one-way ANOVA for independent and correlated samples\n\nFor example, in a t-test we calculate S x, S Which treatments differ from one another? The Analysis of Variance has told us only that there (One-way ANOVA) Watch videoВ В· How to calculate a one way ANOVA by hand (in Excel) and comparing the results to SPSS.\n\nTypes of ANOVA. One-way between groups. The example For example, the grades by tutorial analysis It is unlikely that you would do an analysis of variance One way ANOVA (Analysis Of Variance) R Two way ANOVA calculation BY HAND We will do two way ANOVA with example, lets start the calculation. Example:\n\nIn one-way ANOVA, the interest lies in We can refer back to the data table used in Two way ANOVA example to illustrate analysis of covariance. The main difference between one way and two way ANOVA is that there is only one factor or independent Key Differences; One way Analysis of Variance (ANOVA)\n\nThe one-way analysis of variance (ANOVA), basic principle of the one-way ANOVA test and provides practical anova test examples in R One-way ANOVA Test in What is ANOVA? Analysis of Variance(ANOVA) helps you test differences between two or more group means. ANOVA test is centered around the different sources of\n\nAnalysis of variance (ANOVA) I’ll use concepts and graphs to answer these questions about F-tests in the context of a one-way ANOVA example. 1/07/2012В В· How To Calculate and Understand Analysis of Variance (ANOVA) F Test. statisticsfun. The Anova example is for a one way anova test.", null, "For example, in a t-test we calculate S x, S Which treatments differ from one another? The Analysis of Variance has told us only that there (One-way ANOVA) A bit of background and a detailed example of an ANOVA Calculation, An Explanation and an ANOVA Calculation Example. It is another common tool and one that is" ]

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[ "# Find How to Assign Weights to Interfaces\n\nIf you use Fireware with a Pro upgrade, you can assign a weight to each interface used in your round-robin multi-WAN configuration. By default, each interface has a weight of 1. The weight refers to the proportion of load that the Firebox sends through an interface.\n\nYou can use only whole numbers for the interface weights; no fractions or decimals are allowed. For optimal load balancing, you might have to do a calculation to know the whole-number weight to assign for each interface. Use a common multiplier so that the relative proportion of the bandwidth given by each external connection is resolved to whole numbers.\n\nFor example, suppose you have three Internet connections. One ISP gives you 6 Mbps, another ISP gives you 1.5 Mbps, and a third gives you 768 Kbps. Convert the proportion to whole numbers:\n\n• First convert the 768 Kbps to approximately .75 Mbps so that you use the same unit of measurement for all three lines. Your three lines are rated at 6, 1.5, and .75 Mbps.\n• Multiply each value by 100 to remove the decimals. Proportionally, these are equivalent: [6 : 1.5 : .75] is the same ratio as [600 : 150 : 75]\n• Find the greatest common divisor of the three numbers. In this case, 75 is the largest number that evenly divides all three numbers 600, 150, and 75.\n• Divide each of the numbers by the greatest common divisor.\n\nThe results are 8, 2, and 1. You could use these numbers as weights in a round-robin multi-WAN configuration." ]

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[ "### second line of balmer series\n\nIn spectral line series …the ultraviolet, whereas the Paschen, Brackett, and Pfund series lie in the infrared. (b) 20 27 × 4861 A o. Chemistry Bohr Model of the Atom Atoms and Electromagnetic Spectra. The wavelength of the first line is (a) $\\displaystyle \\frac{27}{20}\\times 4861 A^o$ What is the frequency of limiting line in Balmer series? \"No two electrons in an atom can have the same four quantum numbers\" is a statement of E. the Pauli exclusion principle. Q: The wavelength of the second line of Balmer series in the hydrogen spectrum is 4861 Å. (a) The second line in the Balmer series corresponds to an electronic transition between which Bohr orbits in a hydrogen atom? Favorite Answer. (A) 364.8 nm (B) 729.6 nm To which transition can we attribute this line? When any integer higher than 2 was squared and then divided by itself squared minus 4, then that number multiplied by 364.50682 nm (see equation below) gave the wavelength of another line in the hydrogen spectrum. Explanation: The second line of the Balmer series occurs at wavelength of 486.13 nm. The second line of the Balmer series occurs at a wavelength of 486.1 nm. To which transition can we attribute this line? Why did Rutherford defer to the idea of many electrons in rings? In terms of Bohr radius , the radius of the second Bohr orbit of a hydrogen atom is given by (1) 4 (2) 8 (3) (4) 2 15. Learn about this topic in these articles: spectral line series. Further, this series shows the spectral lines for emissions of the hydrogen atom, and it has several prominent ultraviolet Balmer lines … 1.6. If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. (c) 20 × 4861 A o. Balmer series is the spectral series emitted when electron jumps from a higher orbital to orbital of unipositive hydrogen like-species. Join Yahoo Answers and get 100 points today. • Contact Number: 9667591930 / 8527521718 13. Find an answer to your question The wavelength of the second line of the balmer series in the hydrogen spectrum is 4861 A calculate the wavelength of … We get Balmer series of the hydrogen atom. How many grams of ammonia, NH3, are produced in the reaction with 50.0 g of N2, nitrogen. The Balmer equation could be used to find the wavelength of the absorption/emission lines and was originally presented as follows (save for a notation change to give Balmer's constant as B): 1 Answer Ernest Z. Sep 5, 2017 #f = 8.225 × 10^14color(white)(l)\"Hz\"# Explanation: The Balmer series corresponds to all electron transitions from a higher energy level to #n = 2#. 4.09 × 10-19 J C. 4.09 × 10-22 J D. 4.09 × 10-28 J E. 1.07 × 10-48 J asked Dec 23, 2018 in Physics by Maryam ( … Please explain your work. What is the energy difference between the initial and final levels of the hydrogen atom in this emission process? Still have questions? The Balmer series is a series of emission lines or absorption lines in the visible part of the hydrogen spectrum that is due to transitions between the second (or first excited) state and higher energy states of the hydrogen atom. Name of Line nf ni Symbol Wavelength Balmer Alpha 2 3 Hα 656.28 nm Calculate\n(a) The wavelength and the frequency of the line of the Balmer series for hydrogen. :) If your not sure how to do it all the way, at least get it going please. So, for your answer C, 1/wavelength = 1.096776X10^7 m^-1 (1/2^2 - 1/4^2), 1/wavelength = 1.096776X10^7 m^-1(0.25 - 0.0625), If you do the calculation for any of the other transitions, you will not get that same wavelength, 1/wavelength = 1.096776X10^7 m^-1 (1/4 - 1/25), and D gives 1/wavelength = 1.096776X10^7 (1/4-1/9). The wave number for the second line of H- atom of Balmer series is 20564.43 cm-1 and for limiting line is 27419 cm-1. second) line isAssuming f to be You may need to download version 2.0 now from the Chrome Web Store. Table 1. Performance & security by Cloudflare, Please complete the security check to access. The wavelength of the first line of Lyman series is 1215 Å, the wavelength of first line of Balmer series will be (A) 4545 Å (B) 5295 Å (C) 6561 Å #n_i = 5 \" \" -> \" \" n_f = 3# This time, you have #1/(lamda_2) = R * (1/3^2 - 1/5^2)# Now, to get the ratio of the first line to that of the second line, you need to divide the second equation by the first one. Cloudflare Ray ID: 60e1eee3683d1ea5 Answered by Expert 21st August 2018, 1:33 PM By this formula, he was able to show that some measurements of lines made in his time by spectroscopy were slightly inaccurate and his formula predicted lines that were later found although had not yet been observed. What is the energy difference between the initial and final levels of the hydrogen atom in this emission process? N2+ 3H2→2NH3 The second line of the Balmer series occurs at a wavelength of 486.1 nm. Match the correct pairs. The equation is: In the equation RH is the Rydberg constant (1.096776X10^7 m^-1) and nf and ni are the two levels. 2.44 x 1018 J B. Solution for B. The electronic transition corresponding to this line is (a) n = 4 → n = 2 (b) n = 8 → n = 2 Balmer had done no physics before, and made his great discovery when he was almost sixty. Slain veteran was fervently devoted to Trump, Georgia Sen.-elect Warnock speaks out on Capitol riot, Capitol Police chief resigning following insurrection, New congresswoman sent kids home prior to riots, Coach fired after calling Stacey Abrams 'Fat Albert', $2,000 checks back in play after Dems sweep Georgia, Kloss 'tried' to convince in-laws to reassess politics, Serena's husband serves up snark for tennis critic, CDC: Chance of anaphylaxis from vaccine is 11 in 1M, Michelle Obama to social media: Ban Trump for good. There is a nice equation that lets you calculate the wavelength of the photon emitted by any electron transition. Q. The wave number for the second line of H- atom of Balmer series is 20564.43 cm -1 and for limiting line is 27419 cm -1. In star: Line spectrum. The second line of the Balmer series occurs at wavelength of 486.13 nm. The frequency of 1st line Balmer series in atom is . 9. 2.44 × 1018 J B. VITEEE 2007: Assuming f to be the frequency of first line in Balmer series, the frequency of the immediate next (i.e. What is the energy difference between the initial and final levels of the hydrogen atom in this emission process? line indicates transition from 4 --> 2. line indicates transition from 3 -->2. The composition of a compound with molar mass 93 g/mol has been measured as:? stellar spectra. These lines are emitted when the electron in the hydrogen atom transitions from the n = 3 or greater orbital down to the n = 2 orbital. 800+ VIEWS. In what region of the electromagnetic spectrum does this series lie ? The wavelengths of these lines are given by 1/λ = R H (1/4 − 1/n 2), where λ is the wavelength, R H is the Rydberg constant, and n is the level of the original orbital. • Balmer noticed that a single wavelength had a relation to every line in the hydrogen spectrum that was in the visible light region. 1 decade ago. let λ be represented by L. Using the following relation for wavelength; For 4-->2 transition. The second line of the Balmer series occurs at a wavelength of 486.13 nm. That wavelength was 364.50682 nm. The individual lines in the Balmer series are given the names Alpha, Beta, Gamma, and Delta, and each corresponds to a ni value of 3, 4, 5, and 6 respectively. …visible hydrogen lines (the so-called Balmer series; see spectral line series), however, are produced by electron transitions within atoms in the second energy level (or first excited state), which lies well above the ground level in energy. (3 marks) (c) Draw an energy level diagram of a hydrogen atom and indicate the clectronic transition of the first line and the second line of the Balmer series. a) n = 6 to n = 2 b) n = 5 to n = 2 15. The red line at the right is the $$H_{\\alpha}$$ line and the two leftmost lines are considered to be ultraviolet as they have wavelengths less than 400 nm. To which transition can we attribute this line?a) n = 6 to n = 2b) n = 5 to n = 2c) n = … The second line of the Balmer series occurs at a wavelength of 486.13 nm. 4.09 x 10-19 J C. 4.09 x 10-22 J D. 4.09 x 10-28 J E. 1.07 x 10-48 J Problem: The second line of the Balmer series occurs at wavelength of 486.13 nm. The Balmer series includes the lines due to transitions from an outer orbit n > 2 to the orbit n' = 2. (d) 4861 A o. (b) Find the longest and shortest wavelengths in the Lyman series for hydrogen. Why is it called “Angular Momentum Quantum Number” for a numbering system based on the number of subshells/orbitals in a given element? My teacher says the answer is \"C\" n = 4 to n = 2, but why is this the correct answer? If the moon and planets shine with their own light, then the spectral analysis of light from these heavenly bodies should be individual and different to the spectral analysis of light from the Sun. What is the energy difference between the initial and final levels of the hydrogen atom in this emission process? When electron jumps from n = 4 to n = 2 orbit, we get (1) second line of Lyman series (2) second line of Balmer series (3) second line of Paschen series (4) an absorption line of Balmer series 14. Values of $$n_{f}$$ and $$n_{i}$$ are shown for some of the lines (CC BY-SA; OpenStax). what is the wave length of the first line of lyman series ? The Balmer series in a hydrogen atom relates the possible electron transitions down to the n = 2 position to the wavelength of the emission that scientists observe.In quantum physics, when electrons transition between different energy levels around the atom (described by the principal quantum number, n ) they either release or absorb a photon. spontaneous combustion - how does it work? The second level, which corresponds to n = 2 has an energy equal to − 13.6 eV/2 2 = −3.4 eV, and so forth. The wavelength of the second line of the balmer series in the hydrogen spectrum is 4861 A calculate - Brainly.in. )HZ Calculate the wavelength (in nm) of light emitted in the above transition. 4 Answers. n]2 122. A. The wavelength of the second line of Balmer series in the hydrogen spectrum is 4861 Å…. The second line of the Balmer series occurs at a wavelength of 486.1 nm. (c) Whenever a photon is emitted by hydrogen in Balmer series, it is followed by another photon in LYman series. His number also proved to be the limit of the series. Get your answers by asking now. Who was the man seen in fur storming U.S. Capitol? Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. Your IP: 128.199.55.74 13.6k VIEWS. 2.44* 1018J A) 4.09 x 10-19 J B) C) 4.09 x 10-22 J 4.09 x 10-28 J D) 1.07x 10-48 J E) The frequency of line emitted by single ionised He atom is 2:25 600+ LIKES. If the transition of electron takes place from any higher orbit (principal quantum number = 3, 4, 5, …) to the second orbit (principal quantum number = 2). A) 2.44 ×1018J B) 4.09 × 10–19 J C) 4.09 × 10–22 J D) 4.09 × 10–28 J E) 1.07 × 10–48 J If the wavelength of the first line of the Balmer series of hydrogen is$6561 \\, Å\\$, the wavelength of the second line of the series should be 8. To which transition can we attribute this line? C. Can Bohr's explain why there are stable orbits without radiating any energy?… Figure $$\\PageIndex{4}$$: The visible hydrogen emission spectrum lines in the Balmer series. Calculate the wavelengths of the first three lines in the Balmer series for hydrogen. Wavelengths of these lines are given in Table 1. analysis of light from the Sun. Which transition emits photon of maximum frequency :- (1) second spectral line of Balmer series (2) second spectral line of Paschen series (3) fifth spectral line of Humphery series the shortest line of Lyman series p = 1 and n = ∞ Balmer Series: If the transition of electron takes place from any higher orbit (principal quantum number = 3, 4, 5, …) to the second orbit (principal quantum number = 2). The Balmer series of atomic hydrogen. The second line of the Balmer series of a single-ionized helium atom will have a wavelength: 4:36 100+ LIKES. A. 800+ SHARES. Relevance. Balmer decided that the most likely atom to show simple spectral patterns was the lightest atom, hydrogen. Al P. Lv 7. Balmer series is a hydrogen spectral line series that forms when an excited electron comes to the n=2 energy level. Answer Save. What is the energy difference between the initial and final levels of the hydrogen atom in this emission process? Please enable Cookies and reload the page. The colour of the second line of Balmer series is(a) Blue(b) Yellow(c) Red(d) Violet - 7885352 HARL3780 HARL3780 29.01.2019 Physics Secondary School The colour of the second line of Balmer series is(a) Blue(b) Yellow(c) Red(d) Violet 2 See answers aryangupta78901234in aryangupta78901234in (a) 27 20 × 4861 A o. Answer: 486.13 nm.. One of the lines in the emission spectrum of Li 2+ has the same wavelength as that of the second line of Balmer series in hydrogen spectrum. The second line of the Balmer series occurs at a wavelength of 486.13 nm. The transitions, which are responsible for the emission lines of the Balmer, Lyman, and Paschen series, are also shown in Fig. This formula gives a wavelength of lines in the Balmer series of the hydrogen spectrum. Another way to prevent getting this page in the future is to use Privacy Pass. Balmer Series – Some Wavelengths in the Visible Spectrum. N2+ 3H2→2NH3How many grams of hydrogen, H2, are necessary to react completely with 50.0g of nitrogen, N2? Answered by Expert 21st August 2018, 1:33 PM Rate this answer Q: The wavelength of the second line of Balmer series in the hydrogen spectrum is 4861 Å. The second line of the Balmer series occurs at a wavelength of 486.1 nm. Part of the Balmer series is in the visible spectrum, while the Lyman series is entirely in the UV, and the Paschen series and others are in the IR. (2 marks) 1 (b) Given the following equation, 1 v = 3.288 x 10456 where nl and n2 represent principal quantum numbers. 14. Thank you! The wavelength of the first line is. It is obtained in the visible region. Their formulas are similar to Balmer’s except that the constant term is the reciprocal of the square of 1, 3, 4, or 5, instead of 2, and the running number n begins at 2, 4, 5, or… 25. a) If you examine the spectral lines in the Balmer series, they seem to bunch up closely at one end. L=4861 = For 3-->2 transition =6562 A⁰ If you are on a personal connection, like at home, you can run an anti-virus scan on your device to make sure it is not infected with malware." ]

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[ "# Units of mean decrease accuracy on a variable importance plot obtained from a Random Forests classifier?\n\nTo know the importance variable in a Random Forest I used The mean decrease accuracy and mean decrease Gini.\n\nI would like to understand what are the x-axis units of the mean decrease accuracy and mean decrease Gini on a variable importance plot obtained from a random forests classifier. For example the mean decrease accuracy and gini values range between 0,000 - 0,012 and 0-600 respectively.", null, "Thanks\n\n• Please give more details, we can't answer without any context. – Erwan Jun 20 '20 at 0:13\n• I shared my plots. Mean decrease accuracy and mean decrease gini are used to know the variables importance in a RF but i don't understand the x-axis. What is the meaning of this values? How can I interpreter? – joan llano Jun 20 '20 at 0:32\n• Logically the mean decrease accuracy must be by how much the accuracy decreases when training the model without the feature. But if you want a detailed answer you should explain why you are using these measures, what is the task etc. – Erwan Jun 20 '20 at 12:44\n\nGini decrease is calculated based on the mean decrease in Gini i.e. $$p_i(i-p_i)$$ each time when the Tree is splitted on that Feature. Value is so high because the r package weight the impurities by the raw counts, not the proportions." ]

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[ "### Currying function in Kotlin Android12.08.2018\n\nCurrying is a common technique in functional programming. It allows transforming a given function that takes multiple arguments into a sequence of functions, each having a single argument. Each of the resulting functions handles one argument of the original (uncurried) function and returns another function.\n\nSo, currying is a way to translate a function that takes a number of arguments into a chain of functions that each take a single argument. This may sound confusing, so let's look at a simple example:\n\n```fun subtract(x: Int, y: Int): Int {\nreturn x - y\n}\nprintln(subtract(50, 8))\n```\n\nThis is a function that returns two arguments. The result is quite obvious. But maybe we would like to invoke this function with the following syntax instead:\n\n```subtract(50)(8)\n```\n\nWe can return a function from another function:\n\n```fun subtract(x: Int): (Int) -> Int {\nreturn fun(y: Int): Int {\nreturn x - y\n}\n}\n```\n\nHere it is in the shorter form:\n\n```fun subtract(x: Int) = fun(y: Int): Int {\nreturn x - y\n}\n```\n\nAnd here it is in an even shorter form:\n\n```fun subtract(x: Int) = {y: Int -> x - y}\n```\n\nAlthough not very useful by itself, it's still an interesting concept to grasp.\n\n###### Quote\nMan supposes, God disposes.\n-" ]

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[ "Question about Texas Instruments TI-86 Calculator\n\n# What button do you push on the TI-86 calculator to do the inv log function?\n\nPosted by on\n\n### kakima\n\n• Level 3:\n\nAn expert who has achieved level 3 by getting 1000 points\n\nOne Above All:\n\nThe expert with highest point at the last day of the past 12 weeks.\n\nTop Expert:\n\nAn expert who has finished #1 on the weekly Top 10 Fixya Experts Leaderboard.\n\nSuperstar:\n\nAn expert that got 20 achievements.\n\n• Texas Instru... Master\n\nFor the inverse natural log, press 2nd LN. For the inverse common log, press 2nd LOG.\n\nFor example, to calculate the inverse natural log of 2, press 2nd LN 2 ENTER and you'll get about 7.389 .\n\nPosted on Jan 25, 2011\n\n×\n\nmy-video-file.mp4\n\n×", null, "## Related Questions:\n\n### How to calculate inv logs on casio fx-82 au plus?\n\nThe inverse of log functions are power functions.\nInv of ln is exponential (e^x)\nA function and its inverse usually share the same physical key. One function is accessed directly, the other by using the SHIFT or 2ndF key.", null, "Aug 18, 2014 | Casio Office Equipment & Supplies\n\n### How do I calculate inverse logs on casio fx-82au plus?\n\nThe inverse of log functions are power functions.\nInv of ln is exponential (e^x)\nA function and its inverse usually share the same physical key. One function is accessed directly, the other by using the SHIFT or 2ndF key.", null, "Aug 18, 2014 | Casio Office Equipment & Supplies\n\n### Change base log\n\nThe TI 86 has two logarithmic functions: natural logarithm (ln) and common (decimal) logarithms (log). If you need the logarithm in any other base than e or 10 you need to use one of the two equivalent expressions\nlog_b(x) =ln(x)/ln(b) =log(x)/log(b)\nHere b is the value of the base of the logarithm and x is the argument (the value whose logarithm you are seeking). Of course the argument x must be a positive number.\nNote: On the TI 86 the log function can calculate the logarithm of a complex number, according to the manual.\n\nSep 22, 2013 | Texas Instruments TI-86 Calculator\n\n### Inverse log function\n\nFor the common antilog, use the 10^x function available as the shifted function of the log key. For example, to calculate the common antilog of 2, press SHIFT log 2 =\n\nIf you want the natural (base-e) antilog, use e^x available as the shifted function of the ln key.\n\nAug 05, 2013 | Casio fx-115ES Plus Scientific Calculator\n\n### How do i get inv on my TI-84 Plus caculator\n\nTo get the inverse trigonometric functions press the 2nd key then the trig function key. If you'll look at the key legends above the SIN, COS, and TAN keys you'll see the standard math notations for their inverse function.\n\nApr 05, 2012 | Texas Instruments TI-84 Plus Calculator\n\n### I can not find the arc key or the INV key\n\nThe INV key that you may find on some scientific calculators has, on the TI 83/84/ Plus calculators, an equivalent key marked [2nd].\n\nOn the TI83/84 Plus, each trigonometric function has a second marking [SIN^-1], [COS^-1] or [TAN^-1]. To calculate the inverses of trigonometric functions ( arc sine, arc cosine, arc tangent) you press [2nd] followed by the relevant trigonometric function key For example, [2nd] [SIN] displays sin^-1( on the command line.\n\nUnfortunately the hyperbolic functions and their inverses are only accessed through the CATALOG. You press [2nd] to open the CATALOG. Then you scroll down the CATALOG list to reach cosh(, cosh^-(, sinh(, sinh^-1(, tanh(, or tanh^-1(.\nTo speed the search in the catalog, you use the ALPHA keyboard: To reach cosh(, press[PRGM] and you scroll down from there.\n\nFeb 27, 2012 | Texas Instruments TI-84 Plus Calculator\n\n### I'm using the original TI-30 SOL calculator. Is there any way to do inverse sine or cosine?\n\nOf course. Just press the INV key before pressing the appropriate trig function key. For example, to calculate the inverse sine, press INV then sin.\n\nApr 05, 2011 | Texas Instruments TI-30XA Calculator\n\n### There is no shift key or 2nd button on my TI-30 SLR how do i access the functions above function keys\n\nUse the INV button to access the secondary functions show above each button. Not very intuitive, unfortunately!\n\nOct 02, 2010 | Texas Instruments Scientific Calculator\n\n#### Related Topics:\n\n469 people viewed this question\n\nLevel 3 Expert\n\nLevel 3 Expert" ]

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[ "# How do you solve 14> - 2x + 2> - 4?\n\nApr 19, 2018\n\n$x \\in \\left(- 6 , 3\\right)$\n\n#### Explanation:\n\n$\\text{subtract 2 from each interval}$\n\n$14 \\textcolor{red}{- 2} > - 2 x \\cancel{+ 2} \\cancel{\\textcolor{red}{- 2}} > - 4 \\textcolor{red}{- 2}$\n\n$\\Rightarrow 12 > - 2 x > - 6$\n\n$\\text{divide all 3 intervals by } - 2$\n\n$\\textcolor{red}{\\text{Remembering to reverse the inequality signs}}$\n\n$\\Rightarrow - 6 < x < 3$\n\n$x \\in \\left(- 6 , 3\\right) \\leftarrow \\textcolor{b l u e}{\\text{in interval notation}}$" ]

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[ "stdev() Function\n\nReturns the standard deviation of the specified number(s).\n\n## Syntax\n\nstdev( number, … )\n\nnumber: (Decimal Array) A member or array of members of the set from which the standard deviation will be calculated.\n\nDecimal\n\n## Examples\n\nYou can experiment with this function in the test box below.\n\nTest Input\n\n`stdev(1,2,3,4)` returns `1.290994`\n\nOpen in Github" ]

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[ "# FNGR 1 | Lesson 4 | Explore (Vertical Translations)", null, "# Vertical Translations\n\nA vertical transformation occurs when we add or subtract a constant value from the outputs, or the function itself. It is represented as either $$f(x)+k$$ or $$f(x)-k$$.\n\nExample:\n\nThe parent function for the exponential is $$f(x)=2^x$$:", null, "If we translate this graph up 3 units we end up with this graph:", null, "The new equation for the function is $$f(x)=2^x+3$$.\n\nExamine the table of values for the original and the new functions:\n\n$$x$$ $$f(x)=2^x$$\n$$-2$$ $$\\dfrac{1}{4}$$\n$$-1$$ $$\\dfrac{1}{2}$$\n$$0$$ $$1$$\n$$1$$ $$2$$\n$$2$$ $$4$$\n$$x$$ $$f(x)=2^x+3$$\n$$-2$$ $$3 \\dfrac{1}{4}$$\n$$-1$$ $$3 \\dfrac{1}{2}$$\n$$0$$ $$4$$\n$$1$$ $$5$$\n$$2$$ $$7$$\n\nWhat do you notice? What do you wonder? Describe what you think is happening in your own words. How does this compare to the graphs above?" ]

[ null, "https://i2.wp.com/mdtpmodules.org/wp-content/uploads/2017/09/Explore.png", null, "https://i2.wp.com/mdtpmodules.org/wp-content/uploads/2018/01/fngr1-l4-explore2-1.png", null, "https://i1.wp.com/mdtpmodules.org/wp-content/uploads/2018/01/fngr1-l4-explore2-2.png", null ]

[ "# Different definition of Cox rings\n\nDefinition: Let $$X$$ be a normal projective variety with finitely generated Picard group. Define the Cox ring of $$X$$ as the multisection ring $$\\text{Cox}(X)=\\bigoplus_{(m_1,\\ldots,m_k)\\in \\mathbb{N}^k} \\text{H}^0(X,m_1L_1+\\ldots+m_kL_k),$$ where $$L_1,\\ldots,L_k$$ are a basis of $$\\text{Pic}(X)_{\\mathbb{Q}}$$ and whose affine hull contains $$\\overline{\\text{Eff}(X)}$$.\n\nThis is the Hu-Keel defintion of Cox ring, and I would like to understand why the second extra property is required, since by looking at the literature it looks like there are very few cases in which this condition is asked, and there is no explanation to that. In particular, these are my doubts:\n\n• Why do they add this condition: I know it's vague, and it is a definition so it is not correct or wrong a priori, but for istance can we always find such a basis?\n• What do they mean by affine hull: I suspect they mean the convex hull, but these are two different notions.\n\nI apologize in advance for this low-level (and probably not research-oriented) question, I've asked the same question on MSE without receving an proper answer (I've then deleted since they were equal, and here there are some comments), thus I understand if you want to delete it. Thanks in advance!\n\n• Welcome to MO. I suggest that you wait a bit more (2-3 days) for answers on MSE before cross-posting your question here. Maybe the downvote (that I do not understand) is due to this. Mar 22, 2022 at 8:47\n• I think they just mean the space consisting of all positive linear combinations of the $L_i$. $Eff(X)$ is a convex cone in $Pic(X)_{\\mathbb R}$, so one can always find a basis so that this cone is contained in the \"first quadrant\". Mar 22, 2022 at 14:52\n• Also, the Cox ring is supposed to be a ring which contains all sections of all line bundles, so it would be strange to not contain all effective line bundles in the direct sum. (Up to numerical equivalence). Mar 22, 2022 at 14:52\n• Dear @wnx, thanks for the reply! So if I understand correctly you're basically saying that, among all the possible basis for $\\text{Pic}(X)_{\\mathbb{Q}}$, we simply choose one such that the $\\text{Eff}(X)$ is contained in $\\sum_{i=1}^k \\mathbb{Q}_+L_i$, right? (which looks like the convex cone generated by $L_1,\\ldots,L_k$, and not the affine hull) Mar 22, 2022 at 15:53\n• Yes, I think that's right! Mar 22, 2022 at 16:02\n\nI believe that the main point is that the pseudo-effective cone may not be a rational polyhedral cone. If the pseudo-effective cone is $$\\ell$$-dimensional, then there may be an extremal ray $$\\rho$$ of the pseudo-effective cone such that $$\\rho$$ is not equal to $$\\mathbb{R}_{+} u$$ where $$u \\in \\mathbb{Z}^{\\ell}$$. It would be meaningless to speak of $$H^{0}(X, D)$$ where $$D \\in N^{1}(X)_{\\mathbb{R}} \\setminus N^{1}(X)_{\\mathbb{Q}}$$.\nHowever, it is very fruitful to talk about the Cox ring in such cases. For an example of a Cox ring which does not have finitely generated support look at An Introduction to Invariants and Moduli and Counterexample to Hilbert's fourteenth Problem for the 3-dimensional additive group, both by Shigeru Mukai. In the second reference, he discusses Nagata's construction of a representation of a vector group of dimension $$n-r$$ of dimension $$2n$$ such that the ring of invariants is isomorphic to the Cox ring of the blow-up of $$\\mathbb{P}^{r-1}_{k}$$ at $$n$$-points. In the first reference he proves that for appropriately chosen $$n$$ and $$r$$, that the pseudo-effective cone is not a finitely generated semigroup.\nBecause of this difficulty, I suspect they added the latter condition. This condition is indeed what @wnx said that $$\\operatorname{Eff}(X) \\subseteq \\mathbb{Q}_{+} \\mathcal{L}_{i}$$. They were forced to do this because $$\\operatorname{Eff}(X)$$ may not be generated by elements of $$N^{1}(X)_{\\mathbb{Q}}$$." ]

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[ "", null, "# Question: What Is The HCF Of 5 And 15?\n\n## What is the HCF of 5 and 25?\n\nThe hcf(25,35) is 5 ..\n\n## What is the HCF of 18 and 24?\n\nWe found the factors and prime factorization of 18 and 24. The biggest common factor number is the GCF number. So the greatest common factor 18 and 24 is 6.\n\n## What is the HCF of 13 23 and 14?\n\nGiven that other two factors in the LCM are 13 and 14. We have seen that the numbers are (23 × 13) and (23 × 14). Clearly we get HCF as 23 and the factors in the LCM as 13, 14 and 23.\n\n## What is the LCM of 5 10 and 15?\n\nThe LCM of 5,10,15 5 , 10 , 15 is the result of multiplying all prime factors the greatest number of times they occur in either number. The LCM of 5,10,15 5 , 10 , 15 is 2⋅3⋅5=30 2 ⋅ 3 ⋅ 5 = 30 .\n\n## What is the HCF of 4 and 6?\n\nWe found the factors and prime factorization of 4 and 6. The biggest common factor number is the GCF number. So the greatest common factor 4 and 6 is 2.\n\n## How is HCF calculated?\n\nThe highest common factor is found by multiplying all the factors which appear in both lists: So the HCF of 60 and 72 is 2 × 2 × 3 which is 12. The lowest common multiple is found by multiplying all the factors which appear in either list: So the LCM of 60 and 72 is 2 × 2 × 2 × 3 × 3 × 5 which is 360.\n\n## What is the HCF of 5 10 15?\n\nFactors of 15 = 1, 3, 5 and 15. Factors of 10 = 1, 2, 5 and 10. Therefore, common factor of 15 and 10 = 1 and 5. Highest common factor (H.C.F) of 15 and 10 = 5.\n\n## What is the HCF of 0 and 6?\n\nStep-by-step explanation: The common factor of 0. We cann’t divide any number by 0 as is it in undefined. Thus, the highest common factor of 0 and 6 is “undefined”.\n\n## What is the HCF of 20?\n\nFor example, find the HCF of 20 and 35. The common factors of the given numbers are : 1,2,4,5,10,20. The greatest among all other numbers is 20, so it shall be the HCF of both the numbers.\n\n## What is the LCM of 5 15 and 30?\n\nLeast common multiple (LCM) of 15 and 30 is 30.\n\n## What is the HCF and LCM of 5 and 15?\n\nLeast common multiple (LCM) of 5 and 15 is 15.\n\n## What is the HCF of 15?\n\nFactors of 15 (Fifteen) = 1, 3, 5 and 15. Factors of 35 (Thirty five) = 1, 5, 7 and 35. Therefore, common factor of 15 (Fifteen) and 35 (Thirty five) = 1 and 5. Highest common factor (H.C.F) of 15 (Fifteen) and 35 (Thirty five) = 5.\n\n## Whats the HCF of 15 and 20?\n\n5Greatest common factor (GCF) of 15 and 20 is 5. We will now calculate the prime factors of 15 and 20, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15 and 20.\n\n## What is the HCF of 6 and 15?\n\nGreatest common factor (GCF) of 6 and 15 is 3. We will now calculate the prime factors of 6 and 15, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6 and 15.\n\n## What is the HCF of 16 and 24?\n\n8Example 21 Consider the highest common factor of 16 and 24 again. The common factors are 1, 2, 4 and 8. So, the highest common factor is 8.\n\n## What is the HCF of 20 and 30?\n\nWe found the factors and prime factorization of 20 and 30. The biggest common factor number is the GCF number. So the greatest common factor 20 and 30 is 10.\n\n## What is the HCF of 36 and 48?\n\n12Greatest common factor (GCF) of 36 and 48 is 12. We will now calculate the prime factors of 36 and 48, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36 and 48." ]

[ null, "https://mc.yandex.ru/watch/66676336", null ]

[ "My watch list\nmy.chemeurope.com\n\n# Photoelectric effect\n\nThe photoelectric effect is a quantum electronic phenomenon in which electrons are emitted from matter after the absorption of energy from electromagnetic radiation such as x-rays or visible light. The emitted electrons can be referred to as photoelectrons in this context. The effect is also termed the Hertz Effect, due to its discovery by Heinrich Rudolf Hertz, although the term has generally fallen out of use.\n\nStudy of the photoelectric effect led to important steps in understanding the quantum nature of light and electrons and influenced the formation of the concept of wave–particle duality.\n\n## Introduction\n\nWhen a metallic surface is exposed to electromagnetic radiation above a certain threshold frequency (which is specific to the surface of the material), the photons are absorbed and current is produced. No electrons are emitted for radiation with a frequency below that of the given threshold because the electrons are unable to gain sufficient energy to overcome the electrostatic barrier presented by the termination of the crystalline surface (the material's work function). In 1905 it was known that the energy of the photoelectrons increased with increasing frequency of incident light. However, the manner of the increase was not experimentally determined to be linear until 1915 when Robert Andrews Millikan showed that Einstein was correct.\n\nBy the law of conservation of energy, the electron absorbs the energy of the photon and if sufficient, the electron can escape the material with a finite kinetic energy. A single photon can only eject a single electron because the energy of one photon can only be absorbed by one electron. The electrons that are emitted are often termed photoelectrons.\n\nThe photoelectric effect helped further wave-particle duality, whereby physical systems (such as photons, in this case) display both wave-like and particle-like properties, a concept that was used in quantum mechanics. Albert Einstein mathematically explained the photoelectric effect and extended the work on quanta that Max Planck developed.\n\n## Explanation\n\nThe photons of the light beam have a characteristic energy determined by the frequency of the light. In the photoemission process, if an electron absorbs the energy of one photon and has more energy than the work function, it is ejected from the material. If the photon energy is too low, the electron is unable to escape the surface of the material. Increasing the intensity of the light beam does not change the energy of the constituent photons, only the number of photons. Thus the energy of the emitted electrons does not depend on the intensity of the incoming light, but only on the energy of the individual photons.\n\nElectrons can absorb energy from photons when irradiated, but they follow an \"all or nothing\" principle. All of the energy from one photon must be absorbed and used to liberate one electron from atomic binding, or the energy is re-emitted. If the photon energy is absorbed, some of the energy liberates the electron from the atom, and the rest contributes to the electron's kinetic energy as a free particle.\n\n### Laws of photoelectric emission\n\n1. For a given metal and frequency of incident radiation, the rate at which photoelectrons are ejected is directly proportional to the intensity of the incident light.\n2. For a given metal, there exists a certain minimum frequency of incident radiation below which no photoelectrons can be emitted. This frequency is called the threshold frequency.\n3. Above the threshold frequency, the maximum kinetic energy of the emitted photoelectron is independent of the intensity of the incident light but depends on the frequency of the incident light.\n4. The time lag between the incidence of radiation and the emission of a photoelectron is very small, less than 10-9 seconds.\n\n### Equations\n\nIn analysing the photoelectric effect quantitatively using Einstein's method, the following equivalent equations are used:\n\nEnergy of photon = Energy needed to remove an electron + Kinetic energy of the emitted electron\n\nAlgebraically:", null, "$hf = \\phi + E_{k_{max}} \\,$\n\nwhere\n\n• h is Planck's constant,\n• f is the frequency of the incident photon,\n•", null, "$\\phi = h f_0 \\$ is the work function (sometimes denoted W instead), the minimum energy required to remove a delocalised electron from the surface of any given metal,\n•", null, "$E_{k_{max}} = \\frac{1}{2} m v_m^2$ is the maximum kinetic energy of ejected electrons,\n• f0 is the threshold frequency for the photoelectric effect to occur,\n• m is the rest mass of the ejected electron, and\n• vm is the velocity of the ejected electron.\n\nNote: If the photon's energy (hf) is less than or equal to the work function (φ), no electron will be emitted. The work function is sometimes denoted W.\n\nSince an emitted electron cannot have negative kinetic energy, the equation implies that if the photon's energy is less than the work function, no electron will be emitted.\n\nAccording to Einstein's special theory of relativity the relation between energy (E) and momentum (p) of a particle is", null, "$E = \\sqrt{(pc)^2 + (mc^2)^2}$, where m is the rest mass of the particle and c is the velocity of light in a vacuum.\n\n### Three-step model\n\nThe photoelectric effect in crystalline material is often decomposed into three steps:\n\n1. Inner photoelectric effect (see photodiode below). The hole left behind can give rise to auger effect, which is visible even when the electron does not leave the material. In molecular solids photons are excited in this step and may be visible as lines in the final electron energy. The inner photoeffect has to be dipole allowed. The transition rules for atoms translate via the tight-binding model onto the crystal. They are similar in geometry to plasma oscillations in that they have to be transversal.\n2. Ballistic transport of half of the electrons to the surface. Some electrons are scattered.\n3. Electrons escape from the material at the surface.\n\nIn the three-step model, an electron can take multiple paths through these three steps. All paths can interfere in the sense of the path integral formulation. For surface states and molecules the three-step model does still make some sense as even most atoms have multiple electrons which can scatter the one electron leaving.\n\n## History\n\n### Early observations\n\nIn 1839, Alexandre Edmond Becquerel observed the photoelectric effect via an electrode in a conductive solution exposed to light. In 1873, Willoughby Smith found that selenium is photoconductive.\n\n### Hertz's spark gaps\n\nIn 1887, Heinrich Hertz observed the photoelectric effect and the production and reception of electromagnetic (EM) waves. He published these observations in the journal Annalen der Physik. His receiver consisted of a coil with a spark gap, where a spark would be seen upon detection of EM waves. He placed the apparatus in a darkened box to see the spark better. However, he noticed that the maximum spark length was reduced when in the box. A glass panel placed between the source of EM waves and the receiver absorbed ultraviolet radiation that assisted the electrons in jumping across the gap. When removed, the spark length would increase. He observed no decrease in spark length when he substituted quartz for glass, as quartz does not absorb UV radiation. Hertz concluded his months of investigation and reported the results obtained. He did not further pursue investigation of this effect, nor did he make any attempt at explaining how this phenomenon was brought about.\n\n### JJ Thomson: electrons\n\nIn 1899, Joseph John Thomson investigated ultraviolet light in Crookes tubes. Influenced by the work of James Clerk Maxwell, Thomson deduced that cathode rays consisted of negatively charged particles, later called electrons, which he called \"corpuscles\". In the research, Thomson enclosed a metal plate (a cathode) in a vacuum tube, and exposed it to high frequency radiation. It was thought that the oscillating electromagnetic fields caused the atoms' field to resonate and, after reaching a certain amplitude, caused a subatomic \"corpuscle\" to be emitted, and current to be detected. The amount of this current varied with the intensity and color of the radiation. Larger radiation intensity or frequency would produce more current.\n\nNikola Tesla described the photoelectric effect in 1901. He described such radiation as vibrations of aether of small wavelengths which ionized the atmosphere. On November 5, 1901, he received the patent US685957 (Apparatus for the Utilization of Radiant Energy) that describes radiation charging and discharging conductors (e.g., a metal plate or piece of mica) by \"radiant energy\". Tesla used this effect to charge a capacitor with energy by means of a conductive plate (i.e., a solar cell precursor). The radiant energy threw off with great velocity minute particles (i.e., electrons) which were strongly electrified. The patent specified that the radiation (or radiant energy) included many different forms. These devices have been referred to as \"Photoelectric alternating current stepping motors\".\n\nIn practice, a polished metal plate in radiant energy (e.g. sunlight) will gain a positive charge as electrons are emitted by the plate. As the plate charges positively, electrons form an electrostatic force on the plate (because of surface emissions of the photoelectrons), and \"drain\" any negatively charged capacitors. As the rays or radiation fall on the insulated conductor (which is connected to a capacitor), the condenser will indefinitely charge electrically.\n\n### Von Lenard's observations\n\nIn 1902, Philipp von Lenard observed the variation in electron energy with light frequency. He used a powerful electric arc lamp which enabled him to investigate large changes in intensity, and had sufficient power to enable him to investigate the variation of potential with light frequency. His experiment directly measured potentials, not electron kinetic energy: he found the electron energy by relating it to the maximum stopping potential (voltage) in a phototube. He found that the calculated maximum electron kinetic energy is determined by the frequency of the light. For example, an increase in frequency results in an increase in the maximum kinetic energy calculated for an electron upon liberation - ultraviolet radiation would require a higher applied stopping potential to stop current in a phototube than blue light. However Lenard's results were qualitative rather than quantitative because of the difficulty in performing the experiments: the experiments needed to be done on freshly cut metal so that the pure metal was observed, but it oxidised in a matter of minutes even in the partial vacuums he used. The current emitted by the surface was determined by the light's intensity, or brightness: doubling the intensity of the light doubled the number of electrons emitted from the surface. Lenard did not know of photons.\n\n### Einstein: light quanta\n\nAlbert Einstein's mathematical description in 1905 of how the photoelectric effect was caused by absorption of quanta of light (now called photons), was in the paper named \"On a Heuristic Viewpoint Concerning the Production and Transformation of Light\". This paper proposed the simple description of \"light quanta,\" or photons, and showed how they explained such phenomena as the photoelectric effect. His simple explanation in terms of absorption of single quanta of light explained the features of the phenomenon and the characteristic frequency. Einstein's explanation of the photoelectric effect won him the Nobel Prize (in Physics) of 1921.\n\nThe idea of light quanta began with Max Planck's published law of black-body radiation (\"On the Law of Distribution of Energy in the Normal Spectrum\". Annalen der Physik 4 (1901)) by assuming that Hertzian oscillators could only exist at energies E proportional to the frequency f of the oscillator by E = hf, where h is Planck's constant. By assuming that light actually consisted of discrete energy packets, Einstein wrote an equation for the photoelectric effect that fit experiments (it explained why the energy of the photoelectrons was dependent only on the frequency of the incident light and not on its intensity: a low intensity, high frequency source could supply a few high energy photons, whereas a high intensity, low frequency source would supply no photons of sufficient individual energy to dislodge any electrons). This was an enormous theoretical leap but the reality of the light quanta was strongly resisted. The idea of light quanta contradicted the wave theory of light that followed naturally from James Clerk Maxwell's equations for electromagnetic behavior and more generally, the assumption of infinite divisibility of energy in physical systems. Even after experiments showed that Einstein's equations for the photoelectric effect were accurate resistance to the idea of photons continued, since it appeared to contradict Maxwell's equations, which were well understood and verified.\n\nEinstein's work predicted that the energy of the ejected electrons increases linearly with the frequency of the light. Perhaps surprisingly, that had not yet been tested. In 1905 it was known that the energy of the photoelectrons increased with increasing frequency of incident light -- and independent of the intensity of the light. However, the manner of the increase was not experimentally determined to be linear until 1915 when Robert Andrews Millikan showed that Einstein was correct.\n\n### Effect on wave-particle question\n\nThe photoelectric effect helped propel the then-emerging concept of the dualistic nature of light, that light exhibits characteristics of waves and particles at different times. The effect was impossible to understand in terms of the classical wave description of light, as the energy of the emitted electrons did not depend on the intensity of the incident radiation. Classical theory predicted that the electrons could 'gather up' energy over a period of time, and then be emitted. For such a classical theory to work a pre-loaded state would need to persist in matter. The idea of the pre-loaded state was discussed in Millikan's book Electrons (+ & -) and in Compton and Allison's book X-Rays in Theory and Experiment. These ideas were abandoned.\n\n## Uses and effects\n\n### Photodiodes and phototransistors\n\nSolar cells (used in solar power) and light-sensitive diodes use a variant of the photoelectric effect, but not ejecting electrons out of the material. In semiconductors, light of even relatively low energy, such as visible photons, can kick electrons out of the valence band and into the higher-energy conduction band, where they can be harnessed, creating electric current at a voltage related to the bandgap energy.\n\n### Image sensors\n\nVideo camera tubes in the early days of television used the photoelectric effect; newer variants used photoconductive rather than photoemissive materials.\n\nSilicon image sensors, such as charge-coupled devices, widely used for photographic imaging, are based on a variant of the photoelectric effect, in which photons knock electrons out of the valence band of energy states in a semiconductor, but not out of the solid itself.\n\n### Electroscopes\n\nElectroscopes are fork-shaped, hinged metallic leaves placed in a vacuum jar, partially exposed to the outside environment. When an electroscope is charged positively or negatively, the two leaves separate, as charge distributes evenly along the leaves causing repulsion between two like poles. When ultraviolet radiation (or any radiation above threshold frequency) shines onto the metallic outside of the electroscope, a negatively charged scope will discharge and the leaves will collapse, while nothing will happen to a positively charged scope (besides charge decay). The reason is that electrons will be liberated from the negatively charged one, gradually making it neutral, while liberating electrons from the positively charged one will make it even more positive, keeping the leaves apart\n\n### Photoelectron spectroscopy\n\nSince the energy of the photoelectrons emitted is exactly the energy of the incident photon minus the material's work function or binding energy, the work function of a sample can be determined by bombarding it with a monochromatic X-ray source or UV source (typically a helium discharge lamp), and measuring the kinetic energy distribution of the electrons emitted.\n\nUsing lasers, different photon energies are available. This method allows looking into the bulk, or into nanostructures on the top, or with 50 eV at the topmost atomic layer. Laser pulses can be used for time-resolved two-photon PES to monitor dynamics. They also allow the use of time-of-flight spectrometers for 10 eV ranges, using fewer electrons.\n\nPhotoelectron spectroscopy is done in a high vacuum environment, since the electrons would be scattered by air.\n\nA typical electron energy analyzer is a concentric hemispherical analyser (CHA), which uses an electric field to divert electrons different amounts depending on their kinetic energies. For every element and core atomic orbital there will be a different binding energy. The many electrons created from each will then show up as spikes in the analyzer, and can be used to determine the elemental composition of the sample.\n\n### Spacecraft\n\nThe photoelectric effect will cause spacecraft exposed to sunlight to develop a positive charge. This can get up to the tens of volts. This can be a major problem, as other parts of the spacecraft in shadow develop a negative charge (up to several kilovolts) from nearby plasma, and the imbalance can discharge through delicate electrical components. The static charge created by the photoelectric effect is self-limiting, though, because a more highly-charged object gives up its electrons less easily.\n\n### Moon dust\n\nLight from the sun hitting lunar dust causes it to become charged through the photoelectric effect. The charged dust then repels itself and lifts off the surface of the Moon by electrostatic levitation. This manifests itself almost like an \"atmosphere of dust\", visible as a thin haze and blurring of distant features, and visible as a dim glow after the sun has set. This was first photographed by the Surveyor program probes in the 1960s. It is thought that the smallest particles are repelled up to kilometers high, and that the particles move in \"fountains\" as they charge and discharge.\n\n### Night Vision Devices\n\nPhotons hitting a gallium arsenide plate in Night Vision Devices cause the ejection of photoelectrons due to the photoelectric effect. These are then then amplified into a cascade of electrons that light up a phosphor screen.\n\n## References\n\n### Notes\n\n1. ^ a b Serway, Raymond A. (1990). Physics for Scientists & Engineers. Saunders, p. 1150. ISBN 0030302587.  Describes the photoelectric effect as the \"emission of photoelectrons from matter\", and describes the original usage as the \"emission of photoelectrons from metallic surfaces\" after the experiments of Milikan, and others.\n2. ^ The American journal of science. (1880). New Haven: J.D. & E.S. Dana. Page 234\n3. ^ Wolfram Scienceworld describes the terminology of the photoelectric effect and the previous usage of the term Hertz Effect.\n4. ^ Millikan, Robert Andrews (1916). \"A Direct Photoelectric Determination of Planck's \"h\"\". Physical Review VII: 362.\n5. ^ Stefan Hüfner (2003). Photoelectron Spectroscopy: Principles and Applications. Springer. ISBN 3540418024.\n6. ^ http://www.phys.virginia.edu/classes/252/photoelectric_effect.html\n7. ^ http://spiff.rit.edu/classes/phys314/lectures/photoe/photoe.html\n8. ^ Photoelectron spectroscopy\n9. ^ Spacecraft charging\n10. ^ - Moon fountains\n11. ^ - Dust gets a charge in a vacuum\n\n### Book References\n\nSerway, R. A. (1990). Physics for engineers and scientists, 3rd ed. Saunders Publishing" ]

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[ "### How fast is 800 meters per second?\n\nConvert 800 meters per second. How much is 800 meters per second? What is 800 meters per second in other units? Convert to kmh, mph, feet per second, cm per second, knots, and meters per second. To calculate, enter your desired inputs, then click calculate.\n\n### Summary\n\nConvert 800 meters per second to kmh, mph, feet per second, cm per second, knots, and meters per second.\n\n#### 800 meters per second to Other Units\n\n 800 meters per second equals 80000 centimeters per second 800 meters per second equals 2624.671916 feet per second 800 meters per second equals 2879.97696 kilometers per hour\n 800 meters per second equals 1555.089029 knots 800 meters per second equals 800 meters per second 800 meters per second equals 1789.549034 miles per hour" ]

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[ "# [FOM] ACA\n\npax0 at seznam.cz pax0 at seznam.cz\nMon Jul 9 10:09:52 EDT 2012\n\n```Suppose we have the comprehention scheme in Z_2\nEXAn(n in X <--> phi(n))\nand phi is not Arithmetical.\n\nAre there some trivial cases in which we can make phi arithmetical by pushing\nsome quantifiers in front of the whole formula, especially this:\nphi(n) is prefixed by a string of universally quantified 2nd order variables.\nCan we push them in front of the whole formula thus making them parameters\nand the whole formula arithmetical, and yet the two formulas left equivalent?\nThank you, Jan Pax\n```" ]

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[ "English\n\n# Php Array sizeof Function\n\nWhat is sizeof Function?\n\n## Explanation\n\nThe \"size of\" function is the alias of count() function.\n\n### Syntax:\n\nsizeof(array1,array2)\n\nIn the above syntax \"array\" is the array to count, there is a parameter \"mode\" which can have \"0\" by default doesnt detect a multi dimensional array, if \"1\" is selected will detect the length of multi dimensional array.\n\n#### Example :\n\n<?php\n\\$b=array(\"Grapes\", \"Apple\", \"Cherry\");\n\\$a=sizeof(\\$b);\nprint_r(\\$a);\n?>\nResult :\n\n3\n\nIn the above example the size of the array \"\\$b\" is displayed as \"4\".\n\nAsk Question" ]

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[ "# Line Plot Worksheets For 3rd Grade Grade Math Line Plots Fractions Plot Measurement And Data Worksheets Fraction Line Plot Worksheets 3rd Grade", null, "line plot worksheets for 3rd grade grade math line plots fractions plot measurement and data worksheets fraction line plot worksheets 3rd grade.\n\nfraction line plot worksheets 3rd grade worksheet for all download and,statistics for grade 3 solutions examples videos worksheets line plot 3rd fraction,fraction line plot worksheets 3rd grade statistics, line plot worksheets 3rd grade fraction for learning a free,line plot worksheets 3rd grade fraction reading charts and graphs showing data on a graph, free worksheets library download and print on fraction line plot 3rd grade,line graph worksheets grade plot 3rd fraction,plot worksheets grade fraction line 3rd, grade math line plots fractions plot measurement and data fraction worksheets 3rd,fraction line plot worksheets 3rd grade create a bar graph template how to make double in creating." ]

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[ "An intuitive grasp of free energy\n\nFree energy is a mathematical function that can be employed in statistical inference. This post offers a few different ways to understand its definition.\n\n### Free energy guides statistical inference\n\nYou perform statistical inference when you observe some data $$\\class{mj_red}{x}$$, and update your degrees of belief $$\\class{mj_yellow}{q(\\class{mj_blue}{w})}$$ in unobservable states of the world $$\\class{mj_blue}{w}$$.\n\nIn order for this kind of inference to be useful, the unobservable states must be statistically related to the observable data. In other words there must be a statistical relationship $$\\class{mj_grey}{p(\\class{mj_blue}{w},\\class{mj_red}{x})}$$ between $$\\class{mj_blue}{w}$$ and $$\\class{mj_red}{x}$$.\n\nFree energy, which we will label $$F$$, is a function of $$\\class{mj_grey}{p},\\class{mj_yellow}{q}$$ and $$\\class{mj_red}{x}.$$ One way free energy can guide inference is via the following rule: upon observing $$\\class{mj_red}{x}$$, and assuming $$\\class{mj_grey}{p}$$, your degree of belief $$\\class{mj_yellow}{q}$$ should be chosen so that $$F$$ is as small as possible.\n\nFor an accessible treatment of free energy in statistical inference see my post The simplest possible model of the free energy principle. If you haven’t read it yet, and if you are unfamiliar with statistical inference, you might want to give it a go before reading on.\n\nIn the rest of this post, we will be trying to understand how to interpret $$F$$. Our target is an intuitive understanding of why minimising it is a desirable goal of statistical inference. The following example will help illustrate the discussion, but go to the post linked above to see the example worked through to its conclusion.\n\n### Example: where’s my cat?\n\nYou have a cat that spends its time in either the $$\\class{mj_blue}{\\text{kitchen}}$$ or the $$\\class{mj_blue}{\\text{bedroom}}$$. When it’s in the kitchen, it often $$\\class{mj_red}{\\text{meows}}$$ for food; when it’s in the bedroom, it often $$\\class{mj_red}{\\text{purrs}}$$ loudly.\n\nSuppose you tally the proportion of the times your cat is in each place and making each noise. The results might look something like this:\n\n$$\\begin{equation*} \\begin{array}{cc} & & \\class{mj_red}{\\text{Cat noise}}\\\\ & & \\begin{array}{cc} \\class{mj_red}{\\text{meow}} & \\ \\class{mj_red}{\\text{purr}} \\end{array}\\\\ \\class{mj_blue}{\\text{Cat location}}& \\begin{array}{c} \\class{mj_blue}{\\text{kitchen}}\\\\ \\class{mj_blue}{\\text{bedroom}}\\end{array} & \\left(\\begin{array}{c|c} 40\\% & 20\\%\\\\ \\hline 10\\% & 30\\% \\end{array}\\right) \\end{array} \\end{equation*}$$\n\nNow suppose you are in the living room and you hear a $$\\class{mj_red}{\\text{meow}}$$. You can’t tell whether the sound came from the $$\\class{mj_blue}{\\text{kitchen}}$$ or $$\\class{mj_blue}{\\text{bedroom}}$$, but you do know the statistics given in the table above. Statistical inference is the process of answering the question: what is the probability of the cat being in one location or the other, given that we heard it $$\\class{mj_red}{\\text{meowing}}$$?\n\n### Inputs to the free energy function\n\nFree energy takes three inputs, and gives a real number as output. For clarity, here are those inputs again, with reference to the cat example:\n\n• $$\\class{mj_red}{x}$$: the observable data on the basis of which you will perform inference. In the example above, we said that we heard the cat $$\\class{mj_red}{\\text{meowing}}$$, so $$\\class{mj_red}{x=\\text{meowing}}.$$\n• $$\\class{mj_yellow}{q(\\class{mj_blue}{w})}$$: your degree of belief in unobservable parts of the world, after having performed inference. This is a probability vector (mathematician-speak for “a list of numbers that add up to $$1$$\"). For example, $$\\class{mj_yellow}{q(\\class{mj_blue}{w})} = \\left(\\frac{6}{10},\\frac{4}{10}\\right)$$ means you are $$60\\%$$ sure the cat is in the $$\\class{mj_blue}{\\text{kitchen}}$$ and $$40\\%$$ sure the cat is in the $$\\class{mj_blue}{\\text{bedroom}}.$$ (We’re assuming the cat can only be in one of those two places.)\n• $$\\class{mj_grey}{p(\\class{mj_blue}{w},\\class{mj_red}{x})}$$: the statistical connection assumed to hold between observed data $$\\class{mj_red}{x}$$ and unobserable parts of the world $$\\class{mj_blue}{w}$$. This is defined by the table above. To make it mathematically correct, we convert the percentages to fractions, so $$\\class{mj_grey}{p(\\class{mj_blue}{\\text{kitchen}},\\class{mj_red}{\\text{meow}})}=\\frac{4}{10}$$ and so on.\n\nWhen we say the statistical connection $$\\class{mj_grey}{p}$$ is “assumed” to hold, we mean both that you are operating under the assumption that $$\\class{mj_grey}{p}$$ is the correct statistical connection, and that this assumption is correct. In other words: $$\\class{mj_grey}{p}$$ is true and you make inferences as though it were true. (More complex forms of inference weaken this assumption, and describe how to update $$\\class{mj_grey}{p}$$ on the basis of multiple observations $$\\class{mj_red}{x_t}, \\class{mj_red}{x_{t+1}},…$$. In this post we will ignore those more difficult ideas.)\n\nAll right. Free energy has three inputs. But what does it do with them?\n\n### Free energy: Compact form\n\nThere are three useful ways to write free energy, as far as I know. Here is the first, which I call “compact form”, because it’s shorter than the other two:\n\n$$F= \\class{mj_green}{\\sum_{\\class{mj_blue}{w}} \\left( \\class{mj_yellow}{q(\\class{mj_blue}{w})} \\class{mj_lavender}{\\log \\left( \\frac{\\class{mj_yellow}{q(\\class{mj_blue}{w})}} {\\class{mj_grey}{p(\\class{mj_blue}{w},\\class{mj_red}{x})}} \\right)} \\right)}$$\n\nIn a somewhat futile attempt to mimic this incredible colourised explanation of the discrete Fourier transform, I offer the following definition:\n\nFree energy is the average value (weighted by your degree of belief in hidden states) of the log ratio of your degree of belief in hidden states to the assumed statistical relationship between hidden states and observed data.\n\nOr, in the language of cats:\n\nFree energy is the average value (weighted by your degree of belief in where the cat currently is) of the log ratio of your degree of belief in where the cat currently is to the assumed statistical relationship between where the cat currently is and what sound the cat is currently making.\n\nThis description might be correct, but it isn’t particularly enlightening.\n\nThe main benefits of the compact form are that it’s relatively easy to remember, and the other two forms can be derived from it. Other than that, it doesn’t provide a great deal of insight into what $$F$$ is actually for, and why minimising it is a useful thing to do. For that, we turn to the Bayesian form.\n\n### Free energy: Bayesian form\n\nIf you ask me, the best way to think of free energy is as a measure of the cost of inaccuracy in your degrees of belief. Intuitively, there are two ways your degrees of belief can be inaccurate, and so two kinds of cost they might incur. Free energy describes how these two costs should be balanced against each other.\n\nOn the one hand, you shouldn’t hold degrees of belief $$\\class{mj_yellow}{q(\\class{mj_blue}{w})}$$ that are inordinately far away from what you know the true statistics to be, $$\\class{mj_grey}{p(\\class{mj_blue}{w})}.$$ In short: Don’t overfit. You overfit when you believe something that makes the currently observed data very probable, at the expense of a wider set of possible data.\n\nOn the other hand, you shouldn’t hold degrees of belief $$\\class{mj_yellow}{q(\\class{mj_blue}{w})}$$ that fail to explain the data you are presently observing, $$\\class{mj_grey}{p(\\class{mj_red}{x}|\\class{mj_blue}{w})}$$. In short: Don’t be conservative when accounting for new data.\n\nFree energy is equal to a sum of two terms that represent these costs:\n\n$$F= \\underbrace{ \\class{mj_green}{\\sum_{\\class{mj_blue}{w}} \\left( \\class{mj_yellow}{q(\\class{mj_blue}{w})} \\class{mj_lavender}{\\log \\left( \\frac{\\class{mj_yellow}{q(\\class{mj_blue}{w})}} {\\class{mj_grey}{p(\\class{mj_blue}{w})}} \\right)} \\right)}}_{ \\substack{ \\text{Don’t overfit} \\\\ \\text{(i.e. Don’t stray from your prior beliefs)} } } + \\quad \\underbrace{ \\class{mj_green}{\\sum_{\\class{mj_blue}{w}} \\left( \\class{mj_yellow}{q(\\class{mj_blue}{w})} \\class{mj_lavender}{\\log \\left( \\frac{1} {\\class{mj_grey}{p(\\class{mj_red}{x}|\\class{mj_blue}{w})}} \\right)} \\right)}}_{ \\substack{ \\text{Don’t be conservative} \\\\ \\text{(i.e. Don’t make the data too surprising)} } }$$\n\nThe first term is relative entropy from $$\\class{mj_grey}{p}$$ to $$\\class{mj_yellow}{q}$$. This is a standard way to measure the distance between two probability distributions. (There’s a lot to be said about relative entropy – eventually I’ll write another post on it.) Because it can be treated as a measure of how far away your degrees of belief are from your prior expectations, it penalises you for straying too far.\n\nThe second term measures how surprising the data you just observed, $$\\class{mj_red}{x}$$, would be if you were to believe $$\\class{mj_yellow}{q(\\class{mj_blue}{w})}$$. You shouldn’t believe something that makes the data you just saw too surprising.\n\nThis is sometimes described as “explaining” the data, and that sort of makes sense: if you believe the cat is in the $$\\class{mj_blue}{\\text{kitchen}},$$ for example, and it turns out that $$\\class{mj_grey}{p(\\class{mj_red}{\\text{meowing}}|\\class{mj_blue}{\\text{kitchen}})}$$ is high, you can explain why you heard $$\\class{mj_red}{\\text{meowing}}$$ by appealing to the cat being in the $$\\class{mj_blue}{\\text{kitchen}}$$. Mathematically, higher values of $$\\class{mj_grey}{p(\\class{mj_red}{x}|\\class{mj_blue}{w})}$$ should be matched with high values of $$\\class{mj_yellow}{q(\\class{mj_blue}{w})}$$ to make that right-hand term low.\n\nIn short: the fact that proposed degrees of belief $$\\class{mj_yellow}{q(\\class{mj_blue}{w})}$$ stay close to prior expectations, at the same time as explaining your data, justifies you in adopting $$\\class{mj_yellow}{q(\\class{mj_blue}{w})}$$.\n\nWhy do I call this “Bayesian form”? Because it exemplifies the trade-off at the heart of Bayesian inference. In Bayesian inference, we calculate the correct degrees of belief by multiplying our prior belief in $$\\class{mj_blue}{w}$$ by a term that describes how probable the observed data $$\\class{mj_red}{x}$$ would be if $$\\class{mj_blue}{w}$$ were true. Bayes' rule\n\n$$\\class{mj_yellow}{q_{}(\\class{mj_blue}{w})} \\quad\\text{ought to be equal to}\\quad \\underbrace{ \\class{mj_grey}{p(\\class{mj_blue}{w})} \\vphantom{\\frac{\\class{mj_grey}{p(\\class{mj_red}{x}|\\class{mj_blue}{w})}}{\\class{mj_grey}{p(\\class{mj_red}{x})}}} }_{ \\substack{ \\text{Prior belief}\\\\ \\text{in }\\class{mj_blue}{w} } } \\quad \\underbrace{ . \\vphantom{\\frac{\\class{mj_grey}{p(\\class{mj_red}{x}|\\class{mj_blue}{w})}}{\\class{mj_grey}{p(\\class{mj_red}{x})}}} }_{ \\substack{ \\text{multiplied}\\\\ \\text{by} } } \\quad \\underbrace{ \\frac{\\class{mj_grey}{p(\\class{mj_red}{x}|\\class{mj_blue}{w})}} {\\class{mj_grey}{p(\\class{mj_red}{x})}} }_{ \\substack{ \\text{Relative probability}\\\\ \\text{of data given }\\class{mj_blue}{w} } }$$\n\n– tells you implicitly what $$F$$ tells you explicitly: that you ought to balance these two kinds of costs in this particular way. On the other hand, Bayes' rule tells you something explicitly that $$F$$ reveals only implicitly: what $$\\class{mj_yellow}{q_{}(\\class{mj_blue}{w})}$$ ought to be! Fortunately, the next formulation of free energy makes that important piece of information a bit more explicit.\n\n### Free energy: Upper bound form\n\n$$F= \\underbrace{ \\class{mj_green}{\\sum_{\\class{mj_blue}{w}} \\left( \\class{mj_yellow}{q(\\class{mj_blue}{w})} \\class{mj_lavender}{\\log \\left( \\frac{\\class{mj_yellow}{q(\\class{mj_blue}{w})}} {\\class{mj_grey}{p(\\class{mj_blue}{w}|\\class{mj_red}{x})}} \\right)} \\right)}}_{ \\substack{ \\text{How far you are from} \\\\ \\text{the correct posterior} } } + \\underbrace{ \\frac{1} {\\class{mj_grey}{p(\\class{mj_red}{x})}} }_{ \\substack{ \\text{How surprising} \\\\ \\text{is the observed data} } }$$\n\nAgain the first term is a relative entropy measure. However, this time it’s from the correct posterior $$\\class{mj_grey}{p(\\class{mj_blue}{w}|\\class{mj_red}{x})}$$ to your degree of belief $$\\class{mj_yellow}{q(\\class{mj_blue}{w})}$$. This term penalises you for straying from the correct posterior – which makes perfect sense, given that you want to believe the truth.\n\n(A wrinkle: relative entropy is usually invoked by putting the “correct” distribution and the “approximating” distribution the other way round than they are written here. The question raises itself: how should relative entropy be interpreted when its component distributions are swapped? Although it still counts as a measure of the penalty of failing to believe the truth, it’s a slightly different penalty than we’re used to. I don’t yet have an answer to this question. Drop me a line if you have any ideas.)\n\nThe second term is the overall surprise of the data $$\\class{mj_red}{x}$$. Importantly, this second term doesn’t depend on $$\\class{mj_blue}{w}$$. Two conclusions can therefore be drawn:\n\n1. $$\\class{mj_yellow}{q(\\class{mj_blue}{w})}$$ ought to be as close to $$\\class{mj_grey}{p(\\class{mj_blue}{w}|\\class{mj_red}{x})}$$ as possible. There are no other constraints on your degree of belief. In this form, $$F$$ is no longer telling you to balance two costs, it’s telling you just to believe the truth!\n2. $$F$$ is always greater than or equal to $$\\frac{1}{\\class{mj_grey}{p(\\class{mj_red}{x})}}$$. This is a consequence of the fact that relative entropy is always greater than or equal to zero.\n\nThe second point justifies the name “upper bound form”. It shows that free energy is an upper bound on surprise.\n\n### Why not just always use upper bound form?\n\nBayesian form gave circuitous advice about what degrees of belief to hold, entreating you to balance the costs of overfitting and being too conservative. But upper bound form is much more explicit, telling you exactly what your degrees of belief ought to be. Surely upper bound form is all we need when doing statistical inference?\n\nThere is a significant problem with this idea. The problem arises when you try to compute $$\\class{mj_yellow}{q(\\class{mj_blue}{w})}$$ from $$\\class{mj_grey}{p(\\class{mj_blue}{w},\\class{mj_red}{x})}$$ and $$\\class{mj_red}{x}$$. Bayes' rule tells you how to do it, but requires an intermediate step in which you calculate $$\\class{mj_grey}{p(\\class{mj_red}{x})}$$. For mathematical reasons I won’t go into here, it is not always possible to calculate $$\\class{mj_grey}{p(\\class{mj_red}{x})}$$ from $$\\class{mj_grey}{p(\\class{mj_blue}{w},\\class{mj_red}{x})}$$.\n\nIf you cannot calculate $$\\class{mj_grey}{p(\\class{mj_red}{x})}$$, you cannot follow Bayes' rule. You also cannot use the upper bound form of free energy: without $$\\class{mj_grey}{p(\\class{mj_red}{x})}$$, you cannot calculate $$\\class{mj_grey}{p(\\class{mj_blue}{w}|\\class{mj_red}{x})}$$. You need to use a different procedure to choose your degrees of belief.\n\nIt turns out that in these situations, it is still sometimes possible to calculate the ingredients of the Bayesian form, $$\\class{mj_grey}{p(\\class{mj_blue}{w})}$$ and $$\\class{mj_grey}{p(\\class{mj_red}{x}|\\class{mj_blue}{w})}$$. In other words, there are situations in which you have all the components of the Bayesian form of free energy, but lack components of the upper bound form.\n\nIn these kinds of situations, you cannot follow Bayes' rule and you cannot use the upper bound form. But you have all the ingredients required to calculate the Bayesian form of free energy. You can therefore test different candidate degrees of belief, until you find the $$\\class{mj_yellow}{q(\\class{mj_blue}{w})}$$ that makes $$F$$ smallest.\n\nIn sum, Bayesian form is useful when you can calculate $$\\class{mj_grey}{p(\\class{mj_blue}{w})}$$ and $$\\class{mj_grey}{p(\\class{mj_red}{x}|\\class{mj_blue}{w})}$$, but not $$\\class{mj_grey}{p(\\class{mj_red}{x})}$$. Of course, you can use compact form too, but that doesn’t reveal the rationale behind using free energy for statistical inference." ]

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[ "# Function Pointers\n\n### Introduction\n\nFunction pointers, pointers are just a block of memory that point to another block of memory that actually hold the data, class, function etc. but the pointer can be altered to point to a dfferent block of memory. The best thing about pointers is that are capable of doing the same thing on the data referenced in the pointer.\n\nA function pointer, is able to point to a function and call that function with the same similar parameters but then if the pointer reference is re-directed to another method it will still call in a same way and have the same parameters passed to it but just calling a different function.\n\n### Declaring a function pointer\n\nTo declare a function pointer\n\n``````returntype (*functionpointername)(parameters);\n``````\n\nas you can tell the declaration is very similar to a standard function, return type function name and parameters but in this case you have a * (pointer) to a function.\n\nThe return type and parameters example\n\n``````int (*intAddSum)(int value1, int value2) = NULL;\n``````\n\nIn the above it will return a int with adding the two int parameters,it is always a good idea to set the function pointer to a NULL, you may not know where the default memory reference may goto!!!.\n\n### Basic example of a function pointer\n\nHere is a basic example of a function pointer, it will point to a method that will take 2 parameters and add them up to return there sumed valued.\n\n``````int addTwo(int value1, int value2)\n{\nreturn (value1 + value2);\n}\n\nint (*fPointer)(int , int) = NULL;\n\nint main()\n{\n// the function pointer will take the address/reference (&) of the funtion addTwo\n// call just a normal function.\nfPointer(3,5);\nreturn 0;\n}\n\n``````\n\n### Full code of changing the pointer\n\nHere is some full code that will change the pointer reference and also pass the function pointer to another method to be called from within there, so you can also pass function pointers, c++ is a great language to code in.\n\n``````#include <iostream>\n\nusing namespace std;\n\nvoid normalHi()\n{\ncout << \"hi\" << endl;\n}\n\nvoid normalBye()\n{\ncout << \"bye\" << endl;\n}\n\n// always set the function pointer to NULL.\nvoid (*func)() = NULL;\n\n// to pass a function pointer to a function.\nvoid callFunc( void (*function)())\n{\nfunction();\n}\n\nint main(int argc, char* argv[])\n{\n// setup as the normalHi function\nfunc=&normalHi;\nfunc();\n// change to the other function\nfunc=&normalBye;\nfunc();\n\n// call the function pointed to within another function.\ncallFunc(func);\nreturn 0;\n}\n``````\n\n### Conclusion\n\nFunction pointers are very helpfully and you can setup a list a function pointers at run time which would not be know at compile time. Hopefully, this will help with better understanding of what a pointer and function pointers are.\n\nI do really like to have any feedback regarding any tutorial/post, just reply or PM me.. glad to help, better to share knowledge." ]

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[ "## Saturday, January 22, 2011\n\n### Quantized Redshifts. II. The Fourier Series\n\nThe Tools\nThe mathematical tool commonly used in reports of redshift quantization is the power spectral density (PSD) (Wikipedia).  You've seen simple versions of the PSD in the form of a graphic equalizer in computer applications such as iTunes.  Sound engineers use a graphic equalizer to adjust audio power in multiple frequency bands (Wikipedia).  While the PSD is an excellent tool for identifying well-defined frequencies, broadband signals which cover many frequencies, require considerably more effort to interpret.  To understand this requires a bit more exploration of just what the PSD is and does.\n\nHistory\nCharles Fourier was the father of what we now call the set of transformations that bear his name.  Why did Fourier develop these transformations?  Fourier was working on the problem of heat transfer, examining solutions of the equation (Wikipedia).", null, "For very simple cases of conduction between two planar surfaces, the solution to the equation seemed intractable.   But Fourier decided to approach the problem in a standard reductionist way - can the big problem that is unsolvable be broken down into a set of simpler problems that can be solved by the existing techniques.  Because the heat transfer equation was a differential equation of 2nd-order, one possible set of simpler solutions might be a weighted sum of sines and cosines.  Fourier explored the idea that any function f(x) in a range of position, x, from -L to +L, might have an alternative representation as a sum of sines and cosines.  In mathematical notation, this is written,\nwhere n is an integer ranging from one to infinity.  Fourier found that this equation would be true if the coefficients, an, and bn, were given by the integrals:\n\nThe technique provided the means for Fourier to re-write the heat transport equation into a sum of 2nd-order differential equations where the individual terms did have simple solutions.  Then the method would allow him to recombine the simple solutions into the complete solution to the problem.\n\nCaveat: Care should be exercised as some sources define a0 and the normalization of an and bn different than defined here.  So long as a consistent set of series and coefficients are used, there should be no problem.\n\nFourier Series: Frequencies Everywhere!\nThe technique would prove to be incredibly powerful, and would open the door to the more generalized methods of orthogonal functions (wikipedia).  These techniques would become very important for solving the more complex equations that would be developed for electromagnetism (Maxwell's Equations) and quantum mechanics (Schrodinger Equation).\n\nBut the Fourier series has another implications important for our story\n\nAll functions of a finite range could be expressed as a sum of sine and cosine waves.  The cosine wave is equivalent to a sine wave shifted in phase by 90 degrees (pi/2 radians).\n\nCaveat: I say 'All functions', but there are some limitations, called Dirichlet conditions (Wikipedia).  However, it is easy to see that in a practical sense, it means that almost any function that can represent a physical system will have a Fourier Series.\n\nLet's look at a function and its Fourier series.\n\nWe'll start with a square wave (Wikipedia).  The square wave can be expressed mathematically as\n\nand graphically, we'll show two periods of the wave.\n\nFrom the 'recipe' above, we can compute the Fourier coefficients for this profile, a & b:\n\nWe plot the amplitude of these coefficients, using different colors for the sine and cosine components.  The dot represents the actual amplitude of the coefficient (vertical axis) for a given integer, n (the horizontal axis).\n\nIn this example, we see that for the cosine terms in blue, only the first coefficient, a0, is non-zero.  All other cosine terms are zero.  The sine terms, in red, are very different - we see that the even frequencies are zero and the odd frequencies are non-zero.\n\nAs a check on our result, and to illustrate that the Fourier series really does work, we can plug these coefficients into the Fourier series and add them up and see how they compare to the original function.  To examine how the result behaves when we include more terms, we'll use multiple colors to distinguish the curves with a different number of terms.  The black curve is the original square wave.  The cyan curve is constructed from only two terms, red includes four terms, blue includes eight terms, and green is 32 terms..", null, "Click to Enlarge\n\nNotice that the more terms we include, the more closely the series value matches the original function in black.  There is only one discrepancy, and that is the Gibbs phenomena (wikipedia) visible at the top of the square where it turns down.  This occurs at strong discontinuities in the function.  The more terms we include, that overshoot will get narrower in width, but it is an unfortunate artifact of the discontinuity in the square wave.\n\nNext Weekend: The PSD connection" ]

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[ "# Secure MultiParty Computation with secret inputs for secret outputs\n\nI want to know if it’s possible to use a SMPC (Secure Multi-Party Computation) to have $N$ entities compute the outcome of a known mathematical operation with two or more secret inputs, where each secret input is only known by one entity in the $N$-sized group.\n\nI’m asking, because I want to define a protocol where two network nodes take part in a virtual money transfer – with $k$ witness nodes – where the balance of each node taking part in the transaction is kept secret to itself. After the transaction is calculated, each part can verify with the outputs whether the operation was successful or not." ]

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[ "Remember Me?", null, "September 25th 07, 07:54 PM posted to microsoft.public.excel.worksheet.functions\n UB", null, "external usenet poster First recorded activity by ExcelBanter: Jan 2007 Posts: 120", null, "Error type mismatch in writing macro\n\nHi\nI have a formula in cell - =IF(J45=\"\",\"\",(J45+181)), where if j45 is blank,\nthe cell h45 is blank or h45 has a new date, the format of the coloumn \"H\"\nis date.\n\nI my VB code I am using this column to satify a condition and my code is\nFor rwIndex = 4 To 40\nYear(Worksheets(\"Sheet1\").Cells(rwIndex, 12).Value) = Year(Mydate)\nThen\nWorksheets(\"Sheet1\").Cells(rwIndex, 12).Interior.Color = RGB(0, 0, 255)\n\nI am getting Runtime error '13' - Type Mismatch, because few cells blank,\nbecause of the cell formula IF(J45=\"\",\"\",(J45+181))\n\nPlease advise how can I correct the VB code", null, "September 25th 07, 08:07 PM posted to microsoft.public.excel.worksheet.functions\n JE McGimpsey", null, "external usenet poster First recorded activity by ExcelBanter: Jul 2006 Posts: 4,624", null, "Error type mismatch in writing macro\n\nYour cell isn't blank. It has a formula in it that's returning a null\nstring as a value... One alternative:\n\nDim rCell As Range\nFor Each rCell in Worksheets(\"Sheet1\").Range(\"L4:L40\")\nWith rCell\nIf IsDate(.Value) Then\nIf Year(.Value) = Year(Mydate) Then\n.Interior.Color = RGB(0, 0, 255)\nEnd If\nEnd If\nEnd With\nNext rCell\n\nIn article ,\nub wrote:\n\nHi\nI have a formula in cell - =IF(J45=\"\",\"\",(J45+181)), where if j45 is blank,\nthe cell h45 is blank or h45 has a new date, the format of the coloumn \"H\"\nis date.\n\nI my VB code I am using this column to satify a condition and my code is\nFor rwIndex = 4 To 40\nYear(Worksheets(\"Sheet1\").Cells(rwIndex, 12).Value) = Year(Mydate)\nThen\nWorksheets(\"Sheet1\").Cells(rwIndex, 12).Interior.Color = RGB(0, 0, 255)\n\nI am getting Runtime error '13' - Type Mismatch, because few cells blank,\nbecause of the cell formula IF(J45=\"\",\"\",(J45+181))\n\nPlease advise how can I correct the VB code", null, "September 26th 07, 12:48 PM posted to microsoft.public.excel.worksheet.functions\n UB", null, "external usenet poster First recorded activity by ExcelBanter: Jan 2007 Posts: 120", null, "Error type mismatch in writing macro\n\nHi\nIt worked, Thanks\n\n\"JE McGimpsey\" wrote:\n\nYour cell isn't blank. It has a formula in it that's returning a null\nstring as a value... One alternative:\n\nDim rCell As Range\nFor Each rCell in Worksheets(\"Sheet1\").Range(\"L4:L40\")\nWith rCell\nIf IsDate(.Value) Then\nIf Year(.Value) = Year(Mydate) Then\n.Interior.Color = RGB(0, 0, 255)\nEnd If\nEnd If\nEnd With\nNext rCell\n\nIn article ,\nub wrote:\n\nHi\nI have a formula in cell - =IF(J45=\"\",\"\",(J45+181)), where if j45 is blank,\nthe cell h45 is blank or h45 has a new date, the format of the coloumn \"H\"\nis date.\n\nI my VB code I am using this column to satify a condition and my code is\nFor rwIndex = 4 To 40\nYear(Worksheets(\"Sheet1\").Cells(rwIndex, 12).Value) = Year(Mydate)\nThen\nWorksheets(\"Sheet1\").Cells(rwIndex, 12).Interior.Color = RGB(0, 0, 255)\n\nI am getting Runtime error '13' - Type Mismatch, because few cells blank,\nbecause of the cell formula IF(J45=\"\",\"\",(J45+181))\n\nPlease advise how can I correct the VB code\n\n Thread Tools Search this Thread", null, "Show Printable Version Search this Thread: Advanced Search Display Modes", null, "Linear Mode", null, "Switch to Hybrid Mode", null, "Switch to Threaded Mode", null, "Posting Rules Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are On", null, "Similar Threads Thread Thread Starter Forum Replies Last Post Launchnet Excel Worksheet Functions 5 July 20th 07 04:35 AM Jurassien Excel Discussion (Misc queries) 3 February 23rd 07 09:14 PM David Excel Discussion (Misc queries) 2 December 11th 05 05:46 PM Paul Excel Discussion (Misc queries) 0 October 25th 05 07:28 AM Jim May Excel Discussion (Misc queries) 5 January 9th 05 07:45 PM\n\nAll times are GMT +1. The time now is 10:50 AM.", null, "Copyright ©2004-2019 ExcelBanter." ]

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[ "# Printable Basic Math Worksheets\n\nhigh school word problems worksheets basic math printable simple easy practice sheets google search carpentry worksheet problem solving free m.\n\nmath worksheet worksheets for k 6 help free printout samples printable christmas 1st grade download.\n\nkindergarten math worksheet easy sheets free printable worksheets for 1st grade geometry preschool amp simple at sh.\n\nbasic subtraction worksheets to free printable math for 2nd grade pdf.\n\nprintable high school math wo puzzle puzzles for kids nice middle pictures inspiration free maths basic worksheets 1st grade place value h.\n\ngrade middle school math worksheets picture for kindergarten first addition basic exercises fractions free printable 5th multiplic.\n\nmultiplication fast facts worksheets math aids grade sheets medium to large size printable free for.\n\nbasic math worksheets grade printable reading ultimate for first free 2.\n\nmedium to large size of math worksheets the best image printable life worksheet basic facts grade multiplications free for 3rd place value works.\n\nmedium to large size of awesome collection fourth math worksheets basic year maths printable vision free for grade.\n\nmath addition worksheets free printable single digit worksheet download excel compass christmas for 4th grade.\n\nmath worksheets easy for kindergarten basic free printable 7th 8th graders pictures on bridal catalog.\n\nmath riddle puzzle worksheet book worksheets that teach free printable 1st grade money cookie.\n\nmedium to large size of math worksheet free printable addition worksheets for kindergarten basic coloring grade 3 geometry.\n\n6 grade math worksheets word problems best free algebra printable for 6th multiplication single digit worksheet 1 in basic exercise.\n\nsimple math worksheets printable elegant best maths for kids preschoolers free grade 3 subt.\n\nbasic division facts worksheet 4 fact worksheets printable free math for grade 2.\n\nclick to get printable graphic race track math board worksheet for practicing facts free worksheets grade 2 addition.\n\nsimple division worksheets for kids free printable math 3rd grade.\n\nbudgeting spreadsheet for mac simple budget template excel printable helper worksheet math worksheets numbers endowed more printabl.\n\nprintable math worksheets kindergarten for preschool free simple beautiful best k images on and 2nd grade pdf.\n\nmultiplying 2 digit by numbers free math worksheets printable for 8th grade with answers multiplication long no.\n\nsubtraction math puzzle riddle book worksheets that teach free printable for 6th grade exponents over swept worksheet.\n\neasy addition worksheets beginner kindergarten for first grade printable math worksheet and subtraction picture with pictures basic free 6th ord.\n\nfree math printable worksheets for kids 2nd grade multiplication preschool to school age.\n\nprintable college math worksheets free for grade 2 addition 5 basic.\n\nworksheets basic math equations simple algebra true false free printable worksheet skills practice sheet interest col.\n\nideas of fraction worksheet for grade math worksheets 5 fractions free printable 3rd division mat.\n\nsingle digit addition questions with some regrouping free math worksheets printable for 2nd grade measurement.\n\nfun e math worksheets for kindergarten print out grade 1 coloring sheets amusing free printable 8th with answers.\n\nworksheets for kids the simple subtraction problems on this printable worksheet free math 3rd grade divisi.\n\nprintable fractions division work sheet math skills student practice sheets free worksheets for grade 2 addition 1.\n\naddition math worksheets triple digit worksheet free download excel printable christmas for 1st grade home thumb.\n\nalgebra worksheets basic free printable math 6th grade word problems.\n\nbasic math facts test thousands of printable worksheets for home school or multiplication ea.\n\nfree basic math worksheets the best printable maths ideas simple fun for first grade gallery of beginner 2nd multiplication wor.\n\ndomino addition and subtraction worksheet template sample worksheets free documents printable math for grade 3 workshee.\n\nmath worksheets addition regrouping grade multi digit with some free printable for 5th division basic together first pr.\n\nprintable adding worksheets kindergarten addition worksheet free math for kids decorating ideas and fr.\n\nmaths problems worksheets printable the easy multi step word math worksheet from problem for de page free thanksgiving.\n\ninspirational word search printable basic math worksheets kindergarten motivational spelling for grade 3 learning sear.\n\nmath worksheets preschool basic learning printable is so famous but why form letter and free maths fo.\n\nfree printable simple addition worksheet for first grade math worksheets 3 coloring 4th f." ]

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[ "", null, "Top", null, "# How To Make A Balloon Arch", null, "Classic balloon décor will always be the bread and butter of any balloon business, but sometimes calculating a correct quote for your customer can be challenging. The ability to accurately complete a job cost form is the difference between a profitable balloon décor job and a day wasted. This guide will show you how to create a balloon arch, focusing on calculating the distances and number of balloons needed to make a balloon arch.\n\n## How To Make A Balloon Arch\n\nThe number one question our Customer Service team at burton + BURTON® receives is, “How many balloons do I need to create a balloon arch?” This question seems easy enough to answer, but many aspects come into play when calculating the number of balloons needed to make a balloon arch. What does the space look like? How are you going to size your balloons? Will you be using four or five balloon clusters to create the arch?\n\n## Calculate A Balloon Arch\n\nCustomers calling a balloon decorator are usually unaware of the many variables that determine the cost of a design, so it’s important to be ready to give a quick estimate. Balloon arches range in cost based on size and materials used. With a few simple calculations, you will be able to deliver design quotes with ease. Below are examples showing several different types of balloon arches:\n\n## How To Make A Tall Balloon Arch\n\nIf an arch is taller than it is wide–for example, an arch fit for a standard door entrance–you should double the height and add the width to give the approximate total length. For example, an arch 20 feet in height and 10 feet in width will use this formula:Step 1: Total length2(Height) + Width = Total LengthDouble the height, which is 20 feet", null, "2 to get 40 feet. Now add the width of 10 to get an approximate total length of 50 feet.Step 2: Convert length in feet to inches50 feet", null, "12 = 600 inchesStep 3: Total balloons usedFinally, factor in the size of your balloons and the number of balloons in each cluster used in your design. In this example, we will use 11-inch standard latex sized to 10 inches.600 inches/10 inches = 60 clusters needed4 cluster design: 60 clusters", null, "4 = 240 total balloons used5 cluster design: 60 clusters", null, "5 = 300 total balloons used\n\n## Making A Wide Balloon Arch\n\nTo calculate an arch that is wider than it is tall, like an arch over a football field, simply add the height and length to give you the approximate total length. For example, an arch that is 12 feet tall and 20 feet wide will use this formula.Step 1: Total lengthHeight + Width = LengthAdd the 12-foot height to the 20-foot width to give you the approximate total length of 32 feet.Step 2: Convert length in feet to inches32 feet", null, "12 = 384 inchesStep 3: Total balloons usedFinally, you will need to factor in the size of your balloons and the number of balloons in each cluster used in your design. In this example, we will use 11-inch standard latex sized to 10 inches.384 inches/10 inches = 38.4 clusters needed4 cluster design: 38.4 clusters", null, "4 = 153.6 rounded up to 154 total balloons used5 cluster design: 38.4 clusters", null, "5 = 192 total balloons used\n\n## Making An Arch With Equal Lengths and Widths\n\nIf the height and width are the same or similar in measure, multiply one and a half times the height and add the width to get the approximate length. For example, an arch that is both 12 feet tall and 12 feet wide will use this formula.Step 1: Total length1.5(Height) + Width = LengthMultiply the height of 12 feet by 1.5 and then add the width of 12 feet to reach an approximate total length of 30 feet.Step 2: Convert length in feet to inches30 feet", null, "12 = 360 inchesStep 3: Total balloons usedFinally, factor in the size of your balloons and the number of balloons in each cluster used in your design. In this example, we will use 11-inch standard latex sized to 10 inches.360 inches/10 inches = 36 clusters needed4 cluster design: 36 clusters", null, "4 = 144 total balloons used5 cluster design: 36 clusters", null, "5 = 180 total balloons used\n\n##", null, "To determine how many bags of each color balloon will be needed to create the desired effect, use this simple equation for a standard spiral design:Number of clusters/Number of colors = Number of each color balloonRemember to make allowances to accommodate popped balloons and design errors when placing your order. When pricing your design, also factor in added perceived value when special patterns or adornments like twisted shapes or foil balloons are used.The sky is the limit when it comes to what you can create! We can’t wait to see your designs. Make sure to tag us on Instagram @burtonplusburton for a chance to be featured!" ]

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[ "", null, "# How to implement transaction-based attribution\n\nby | Dec 1, 2011\n\nI got an email from someone today asking how to calculate transaction-based attribution. I addressed this during our recent Attribution Week, but will touch on it briefly here, and in greater detail in this month’s newsletter.\n\nRecall that attribution relies on returns and weights.\n\nThe Weights\n\nWith a holdings-based appraoch we use the weight at the start of the period. For example, if the portfolio’s initial value is 100,000, and Technology has 10,000 as its starting value, then its weight is 10% (10,000 / 100,000).\n\nTo have a transaction-based approach, we need to adjust the weight for any buys/sells/income that occur during the month. For example, if we bought another 2,000 at the middle of the month, then we weight the transaction the same way we do with Modified Dietz [(CD-D+1)/CD] and multiply this by the value (and so, 0.5 x 2,000 = 1,000). We add this to the starting value and get a revised weight [(10,000 + 1,000)/100,000 = 11%]\nWe use this weight in our formula.\n\nThe Returns\n\nWith holdings-based, we can simply account for the starting values to derive our returns. With transaction-based, I suggest you use Modified Dietz, so that you capture the activity that occurs. And so for our example above, if we ended with Technology being valued at 14,000, we’d have R = (VE-VB-CF)/(VB+w*CF)=(14,000-10,000-2,000)/(10,000+0.5*2,000).\n[I’ll let you do the math]\n\nThat’s it! Again, I’ll spend a bit more time on this in the newsletter.\n\n# The Journal of Performance Measurement\n\nThe Performance Measurement Resource." ]

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

[ "Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 10 Ordinary Differential Equations Ex 10.6 Textbook Questions and Answers, Notes.\n\n## Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 10 Ordinary Differential Equations Ex 10.6\n\nQuestion 1.\nSolve the following differential equations.\n[x + y cos($$\\frac { y }{ x }$$)] dx = x cos ($$\\frac { y }{ x }$$) dy\nSolution:\nThe given equation can be written as", null, "On integration we obtain", null, "which gives the required solution.", null, "Question 2.\nSolve (x³ + y³)dy – x² ydx = 0\nSolution:\nThe given equation can be written as", null, "", null, "", null, "", null, "Question 3.\nSolve ye$$\\frac { x }{ y }$$ dx = (x$$\\frac { x }{ y }$$ + y)dy\nSolution:\nThe given equation can be written as", null, "", null, "Question 4.\nSolve 2xy dx + (x² + 2y²)dy = 0\nSolve ye$$\\frac { x }{ y }$$ dx = (x$$\\frac { x }{ y }$$ + y)dy\nSolution:\nThe given differential equation can be written as", null, "", null, "$$\\frac { 1 }{ 3 }$$ log (3v + 2v³) + log x = log |C1|\nlog (3v + 2v³) + 3log (x) = 3 log (C1)\nlog (3v + 2v³) + log (x)³ = log (C1\nlog (3v + 2v³)x³ = log C1³\n(3v + 2v³)x³ = C1³", null, "3x²y + 2y³ = C1³\n3x²y + 2y³ = C is a required solution.", null, "Question 5.\n(y² – 2xy) dx = (x² – 2xy) dy\nSolution:\nGiven equation is (y² – 2xy) dx = (x² – 2xy) dy\ny² – 2xy = (x² – 2xy) $$\\frac { dy }{ dx }$$\n∴ The equation can written as", null, "", null, "log (3v² – 3v) = – 3 log x + log C\nlog (3v² – 3v) = – log x³ + log C\n= log c – log x³", null, "", null, "Question 6.\nx $$\\frac { dy }{ dx }$$ = y – x cos²($$\\frac { y }{ x }$$)\nSolution:\nGiven x $$\\frac { dy }{ dx }$$ = y – x cos² $$\\frac { y }{ x }$$\nThe equation can be written as\n$$\\frac { dy }{ dx }$$ = $$\\frac { y-cos^2 \\frac { y }{ x } }{ x }$$ …….. (1)\nThis is a homogeneous differential equation.\ny = vx\n$$\\frac { dy }{ dx }$$ = v (1) + x $$\\frac { dv }{ dx }$$\nSubstituting $$\\frac { dy }{ dx }$$ value in equation (1), we get", null, "Integrating on both sides, we get\n∫ sec² v dx = -∫ $$\\frac { dx }{ x }$$\ntan v = – log x + log C\ntan v = log C – log x\ntan v = log($$\\frac { C }{ x }$$)\netan v = $$\\frac { C }{ x }$$\nC = x etan v\nC = x etan $$\\frac { y }{ x }$$\nIs a required equation.", null, "Question 7.\nSolve (1 + 3e$$\\frac { y }{ x }$$) dy + 3etan $$\\frac { y }{ x }$$ (1 – $$\\frac { y }{ x }$$) dx = 0, given that y = 0 when x = 1.\nSolution:\nThe given differential equation may be", null, "", null, "Given that y = 0 when x = 1\n0 + 3(1) e° = c\n3 = c\n∴ y + 3xey/x = 3 is a required solution.", null, "Question 8.\n(x² + y²) dy = xy dx. It is given that y (1) = y(x0) = e. Find the value of x0.\nSolution:\nThe given differential equation is of the form", null, "", null, "", null, "", null, "" ]

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[ "Assembly Unicoloured $$d=0$$ $$d=1$$ $$d=2$$ $$d=3$$" ]

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[ "# 3390. 线段树：点覆盖\n\n• 操作 $1$：给出参数 $x,d$，令 $a_x = d$\n• 操作 $2$：给出参数 $l,r$，求 $a_l + a_{l+1} + \\ldots + a_r, \\max \\{a_l, a_{l+1}, \\ldots, a_r\\}, \\min \\{a_l, a_{l+1}, \\ldots, a_r\\}$\n\n### 输入格式\n\n• 1 x d，或\n• 2 l r\n\n### 样例\n\nInput\n5\n1 2 3 4 5\n5\n1 1 2\n2 1 2\n1 5 1\n2 1 5\n2 3 3\n\nOutput\n4 2 2\n12 4 1\n3 3 3\n\n\n32 人解决，34 人已尝试。\n\n46 份提交通过，共有 132 份提交。\n\n7.9 EMB 奖励。" ]

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[ "", null, "# How to turn a constant vector into a matrix?\n\nIs there a GAUSS function that would allow me to take a vector and\nturn it into a matrix with constant values in each column (or row)? For\nexample, I say I wanted to take the following:\n\n`X = 1 2 3`\n\nand from the values in X create the matrix\n\n```Y = 1 2 3\n1 2 3\n1 2 3\n1 2 3\n1 2 3```\n\n0\naccepted\n\nYou can use the reshape function for this:\n\n```//Create a row vector\nX = { 1 2 3 };\n\n//Reshape the row vector into a 5x3 matrix\nY = reshape(X, 5, 3);```\n\nNow Y will equal:\n\n``` 1 2 3\n1 2 3\n1 2 3\n1 2 3\n1 2 3```", null, "### Have a Specific Question?\n\nGet a real answer from a real person\n\n### Need Support?\n\nGet help from our friendly experts." ]

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[ "Home\n\nWhat does the left y axis represent?\n\nWhat does the y axis on the left represent. The y axis on the left means the population of the hares. Expert answered|emdjay23|Points 190049| Log in for more information. Question. Asked 5/9/2020 1:05:42 AM. 0 Answers/Comments. This answer has been confirmed as correct and helpful. s What does the left y-axis of the graph represent? birth rate or death rate. What does the green graph line represent? total number of individuals in the population. Which stage in the graph shows the greatest overall decline in death rate? Stage 2 What does the y-axis on the left represent? b. What does the y-axis on the right represent? c. For both y axes, what value do the numbers on the axes need to be multiplied by? (hint: look at the parenthesis) 2. What was the approximate population of snowshoe hares in 1865? 3. What was the approximate pop. ulation of lynx in 1865? 4 The x-axis is usually the horizontal axis, while the y-axis is the vertical axis. They are represented by two number lines that intersect perpendicularly at the origin, located at (0, 0), as shown in the figure below. Specifying a point on the x- and y-axis You can specify a point using an ordered pair of numbers, (x, y)\n\nWhat does the y axis on the left represen\n\n• What does the left y-axis of the graph represent? Interpreting Graphs and Data: Bird Populations During Old-Field Succession. number of breeding pairs per 100 acres. What does the blue graph line represent? number of species. After 20 years, what was the total number of bird species? 14\n• What does the left y-axis show? sea surface temperature anomaly, in degrees Celsius time, in four-year intervals incidence of cholera, as a percentage of the normal rate sea surface temperature anomaly, in degrees Fahrenheit sea surface temperature, in degrees Celsiu\n• The rule for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the -value the same. For example, when point P with coordinates (5,4) is reflecting across the Y axis and mapped onto point P', the coordinates of P' are (-5,4). Notice that the y-coordinate for both points did not change, but the.\n• What does the Y axis on the left represent? Number of Hares. What does the Y axis on the right represent? Number of Lynx. For both Y axes, what value do the numbers on the axes need to be multiplied by? x10 to the 3rd power. What was the approximate population of snowshoe hares in 1865\n\nThe line on a graph that runs vertically (up-down) through zero. It is used as a reference line so you can measure from it The y-axis is like a vertical ruler. It shows you where an object on a Cartesian plane, a two-dimensional mathematical graph, is in the y (vertical) direction. It is also the starting, or zero,..\n\nMastering Biology: Chapter 53 Population Dynamics\n\n1. The left y-axis represents thickness of sea ice and snow, referenced to the top of the ice. Image courtesy of the National Snow and Ice Data Center (NSIDC), University of Colorado, Boulder. Modified from Maykut and Untersteiner (1971)\n2. View science.docx from ENG 163 at University of California, Davis. 1. Refer to the graph in Model 1. a. What does the y axis on the left represent? # of hares (in thousands) b. What does the y axis\n3. 18 1) The y-axis is a measure of closeness of either individual data points or clusters. 2) California and Arizona are equally distant from Florida because CA and AZ are in a cluster before either joins FL. 3) Hawaii does join rather late; at about 50\n4. The normal distribution is the most important probability distribution in statistics because many continuous data in nature and psychology displays this bell-shaped curve when compiled and graphed. For example, if we randomly sampled 100 individuals we would expect to see a normal distribution frequency curve for many continuous variables, such.\n\nYes. The area under the curve is a probability. The x-axis is measured in the units of the thing that has the Normal distribution. So the y-axis has to be measured in units of probability divided by units of the thing with the distribution. For ex.. Motion can be represented by a position-time graph, which plots position relative to the starting point on the y-axis and time on the x-axis. The slope of a position-time graph represents velocity. The steeper the slope is, the faster the motion is changing Compressing and stretching depends on the value of a a. When a a is greater than 1 1: Vertically stretched. When a a is between 0 0 and 1 1: Vertically compressed. Vertical Compression or Stretch: None. Compare and list the transformations. Parent Function: y = x2 y = x 2. Horizontal Shift: None. Vertical Shift: None Y-axis definition, (in a plane Cartesian coordinate system) the axis, usually vertical, along which the ordinate is measured and from which the abscissa is measured. See more 3. Yes, the y axis is the value of the probably density function. The probability is a different thing, it is the area below the curve for the studied interval. The cumulative distribution function is closely related with the probability density function. Its tables are usually used to solve this types of problems and in the graphic of that.\n\na. What does the y - axis on the left represent? b. What ..\n\nA. Absolutely! In Utilities » Application Settings » Simulation Graph Defaults, change Preferred Distribution Format to Relative Frequency. Click OK, and answer Yes to the confirming prompt. This setting will affect all input and output histograms in all your models. Naturally, you can still use the histogram icon at the bottom of any graph. The line on a graph that runs horizontally (left-right) through zero. It is used as a reference line so you can measure from it They are all three the same rotation direction. The thing at play here is orientations of coordinate systems. What right rotation (if you point your right hand thumb along the axis and close your other fingers they will point to the direction of the rotation) around the X-axis does is rotate the Y axis towards the Z axis if XYZ is a right oriented coordinate system (if you take your right hand.", null, "Graph question: different right-and-left y-axis. waveguide. Wed, 11/25/2009 - 12:16 pm. Hello, I would like to plot TWO different functions on ONE plot, using Igor. I want to scale the right axis in accordance to my first plot, and the left axis in accordance to the second one, so scaling must be different Reflections are isometries .As you can see in diagram 1 below, \\$\\$ \\triangle ABC \\$\\$ is reflected over the y-axis to its image \\$\\$ \\triangle A'B'C' \\$\\$. And the distance between each of the points on the preimage is maintained in its imag x-axis definition: 1. the line of figures or coordinates that are arranged from left to right on a graph or map: 2. Learn more\n\nIn mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between.Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers , the set of nonnegative real numbers, the. The probability density function of the sum of two independent random variables U and V, each of which has a probability density function, is the convolution of their separate density functions: + = () = () It is possible to generalize the previous relation to a sum of N independent random variables, with densities U 1, , U N: + + = () This can be derived from a two-way change of variables. Y Axis. more The line on a graph that runs vertically (up-down) through zero. It is used as a reference line so you can measure from it. See: Coordinates. Cartesian Coordinates Customize the Y-axis labels. The Y-axis labels are displayed to the left by default. Right now, they're light grey, small, and difficult to read. Let's change that. Expand the Y-Axis options. Move the Y-Axis slider to On. One reason you might want to turn off the Y-axis, is to save space for more data. Format the text color, size, and font\n\nExam 2 ch6 Flashcards Quizle\n\nRotation around the y axis -- that is, tilting the device toward the left or right -- causes the gamma rotation angle to change:. The gamma angle is 0° when the device's left and right sides are the same distance from the surface of the Earth, and increases toward 90° as the device is tipped toward the right, and toward -90° as the device is tipped toward the left a. What does the y axis on the left represent? It represents number of hares. b. What does the y axis on the right represent? It represents number of lynx c. For both y axes, what value do the numbers on the axes need to be multiplied by? They need to be multiplied by 10 to the third power. 2. What was the approximate population of snowshoe.", null, "The economic (left-right) axis measures one's opinion of how the economy should be run: left is defined as the desire for the economy to be run by a cooperative collective agency (which can mean the state, but can also mean a network of communes) while right is defined as the desire for the economy to be left to the devices of competing. So we should use an equation in x and y where x represents the first coordinate and y represents the second coordinate. We should create a coordinate plane by drawing a horizontal number line called the x-axis, and a vertical line called the y-axis. 1. In this specific model of ball toss. a) What does the x-axis represent? From here, take 4 steps towards the y axis (upwards). As the name ordered pair suggests, the order in which values are written in a pair is very important. The ordered pair (6, 4) is different from the pair (4, 6). Both represent two different points as shown below. Applicatio In the picture seen on the left the b value is positive (y=2x 2 +5x+1),  causing the parabola to move left The c value represents the y-intercept, where the parabola crosses the y-axis\n\nA hydrograph is a graph of the flow in a stream over a period of time. Below is a picture of a hydrograph, with stream flow (discharge) in cubic feet per second on the y-axis and time in months on the x-axis. Peaks in the hydrograph are usually a result of precipitation events, while troughs represent drier times For those that may be having problems with their controller axis and sensitivity settings, here is a breakdown explaining some of the more important settings for axis configuration. At the foot of the guide is an explanation on how to map buttons or keys to axes such as Prop Pitch, Mixture and Ra..\n\nX and y axis - Mat\n\na. What does the y axis on the left represent? The y axis on the left means the population of the hares. b. What does the y axis on the right represent? The y axis on the right means the population of the lynx c. For both y axes, what value do the numbers on the axes need to be multiplied by? It needs to be by multiply by 2. 2 1. Place relative intensity values on the y axis in the tables above. 2. Label each peak on the graphs above with the subshell each represents (1s, etc). 3. Which electron will be removed from a neutral atom of potassium to form K+? _____ Explain, using the information provided by the above spectrum: 4\n\na. What does the y axis on the left represent? # of hares b. What does the y axis on the right represent? # of lynx c. For both y axes, what value do the numbers on the axes need to be multiplied by? 10^3 2. What was the approximate population of snowshoe hares in 1865? 160 3. What was the approximate population of lynx in 1865? 60 4. When the. Post your questions to our community of 350 million students and teachers. Get expert, verified answers. Learn faster and improve your grade The independent variable belongs on the x-axis (horizontal line) of the graph and the dependent variable belongs on the y-axis (vertical line). The x and y axes cross at a point referred to as the origin, where the coordinates are (0,0). In graphs with only positive values for x and y, the origin is in the lower left corner. The Scal In spatial statistics the theoretical variogram (,) is a function describing the degree of spatial dependence of a spatial random field or stochastic process ().The semivariogram (,) is half the variogram.. In the case of a concrete example from the field of gold mining, a variogram will give a measure of how much two samples taken from the mining area will vary in gold percentage depending on. The horizontal x-axis represents the scores on the test, and the vertical y-axis represents the frequencies. The frequencies are plotted as bars. Histogram of Mid-Term Language Arts Exam . A frequency polygon is a line graph representation of a set of scores from a frequency table. The horizontal x-axis is represented by the scores on the scale.\n\nThe most common graphs name the input value x x and the output value y y, and we say y y is a function of x x, or y = f (x) y = f ( x) when the function is named f f. The graph of the function is the set of all points (x,y) ( x, y) in the plane that satisfies the equation y= f (x) y = f ( x). If the function is defined for only a few input. In order to represent this wide range of values in one diagram, the Y-axis of a CMD or HR diagram is usually plotted on a logarithmic scale. What this means is that instead of each tick mark on the y-axis increasing by 1 unit (1,2,3,4,5), the y-axis tick marks increase by a factor of 10 (0.001, 0.01, 0.1, 1, 10, 100, 1000) A more generalized way to represent an equation o f a straight line p arallel to the y-axis is x = k, where 'k' is a real number. Here, 'k' represents the distance from the y-axis to the line 'x=k'. For example, if we have the equation of a line as 'x =2', it says that the line is at a distance of 2 units away from the y-axis Brainly.com - For students. By students. Brainly is the place to learn. The world's largest social learning network for students\n\nChapter 4 evr study guide Flashcards Quizle\n\nAn ordered pair (x, y) represents the position of a point relative to the origin.The x-coordinate represents a position to the right of the origin if it is positive and to the left of the origin if it is negative.The y-coordinate represents a position above the origin if it is positive and below the origin if it is negative.Using this system, every position (point) in the plane is uniquely. In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuthal angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to.\n\nA graph is translated k units vertically by moving each point on the graph k units vertically. can be sketched by shifting f ( x) k units vertically. The value of k determines the direction of the shift. Specifically, if k < 0, the base graph shifts k units downward. (2) g ( x) = 4 x -1. The graphical representation of function (1), f ( x ), is. Turn off the left Y axis, and create a right Y axis to which you assign data set. To use different colors for the two Y axes. It is possible to give the two Y axes different colors. Select one axis, drop the Change menu, choose Selected Object(s), and set the color (and thickness) on the Format Object dialog that appears..\n\nAnalyze the following diagram: In this graph, the y-axis represents price and the x-axis represents quantity. There are two lines, S1 and D1. S1 starts at 0,2 and has an upward slope. D1 starts at approximately 0,16 and has a downward slope. The two lines cross at the point 31,14 We have a normal parabola with the base of the parabola on the y-axis at the value of c. Example 3: Let a = 0 and b = 1. All of these graphs have a slope of 1 (the b value) and cross the y-axis at the c value. Example 4: Let a = 1 and b = 1. We have a series of parabolas whose bases are to the left of the y-axis and that cross the y-axis at the. Finally to your question about points to the left of the y-axis - this space contains information about motion that happened before time t=0. Remember that moment t=0 might be considered as the first instant that we began to record information, or maybe it is just an arbitrary moment. If so, events to the left of the vertical axis make sense\n\nThe horizontal axis is called the x-axis and the vertical axis is called the y-axis. The center of the coordinate system (where the lines intersect) is called the origin. The axes intersect when both x and y are zero. The coordinates of the origin are (0, 0). An ordered pair contains the coordinates of one point in the coordinate system The range of the function does not change when the sign of a is changed. Now that we have seen the affect of changing a, let's take a look at what happens to the graph when b is changed, while a and c are left constant. Below is the graph y = a sin (bx + c) where b = 1/2, 1, and 2, a = 1, and c = 0\n\nEVR Ch 10 (graphit/viewpoints/interpreting graphs\n\nIf a standard right-handed Cartesian coordinate system is used, with the x-axis to the right and the y-axis up, the rotation R(θ) is counterclockwise. If a left-handed Cartesian coordinate system is used, with x directed to the right but y directed down, R(θ) is clockwise. Such non-standard orientations are rarely used in mathematics but are common in 2D computer graphics, which often have. Looking at the expression for this translation, the +1 outside the function tells me that the graph is going to be moved up by one unit.And the -2 inside the argument tells me that the graph is going to be shifted two units RIGHT.(Remember that the left-right shifting is backwards from what you might expect.) Generally, it's better to work from the inside out A graph is said to be symmetric about the origin if whenever (a,b) ( a, b) is on the graph then so is (−a,−b) ( − a, − b). Here is a sketch of a graph that is symmetric about the origin. Note that most graphs don't have any kind of symmetry. Also, it is possible for a graph to have more than one kind of symmetry", null, "", null, "", null, "", null, "", null, "Take a photo of your question and get an answer in as little as 30 mins*. With over 21 million homework solutions, you can also search our library to find similar homework problems & solutions. Try Chegg Study. *Our experts' time to answer varies by subject & question. (we average 46 minutes) But the descendent sign (DC) is located on the left side of a chart, opposite to the ascendent sign (AC). While your ascendent (aka the rising sign) represents your surface-level personality and. Now, we plot the TPR on the y-axis and FPR on the x-axis, draw the curve for various τ and calculate the area under this curve ( AUC ). AUC = ∫1 0TPR(x)dx = ∫1 0P(A > τ(x))dx where x is the FPR. Now, one way to calculate this integral is to consider x as belonging to a uniform distribution vertical axis meaning: 1. the y-axis 2. the y-axis 3. the line of figures that are arranged from top to bottom at the side. Learn more" ]

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[ "# 0.06 kg to lbs - 0.06 kilograms into pounds\n\nDo you want to know how much is 0.06 kg equal to lbs and how to convert 0.06 kg to lbs? Here it is. You will find in this article everything you need to make kilogram to pound conversion - theoretical and practical too. It is also needed/We also want to highlight that all this article is dedicated to only one number of kilograms - that is one kilogram. So if you want to learn more about 0.06 kg to pound conversion - keep reading.\n\nBefore we go to the practice - this is 0.06 kg how much lbs calculation - we will tell you some theoretical information about these two units - kilograms and pounds. So let’s move on.\n\nHow to convert 0.06 kg to lbs? 0.06 kilograms it is equal 0.1322773572 pounds, so 0.06 kg is equal 0.1322773572 lbs.\n\n## 0.06 kgs in pounds\n\nWe are going to begin with the kilogram. The kilogram is a unit of mass. It is a base unit in a metric system, formally known as International System of Units (in abbreviated form SI).\n\nAt times the kilogram is written as kilogramme. The symbol of the kilogram is kg.\n\nThe kilogram was defined first time in 1795. The kilogram was described as the mass of one liter of water. This definition was simply but difficult to use.\n\nThen, in 1889 the kilogram was defined by the International Prototype of the Kilogram (in abbreviated form IPK). The IPK was prepared of 90% platinum and 10 % iridium. The IPK was used until 2019, when it was substituted by a new definition.\n\nToday the definition of the kilogram is build on physical constants, especially Planck constant. The official definition is: “The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of c and ΔνCs.”\n\nOne kilogram is equal 0.001 tonne. It could be also divided into 100 decagrams and 1000 grams.\n\n## 0.06 kilogram to pounds\n\nYou learned some information about kilogram, so now let's go to the pound. The pound is also a unit of mass. It is needed to emphasize that there are not only one kind of pound. What does it mean? For example, there are also pound-force. In this article we want to concentrate only on pound-mass.\n\nThe pound is used in the British and United States customary systems of measurements. Naturally, this unit is in use also in other systems. The symbol of this unit is lb or “.\n\nThe international avoirdupois pound has no descriptive definition. It is defined as exactly 0.45359237 kilograms. One avoirdupois pound could be divided into 16 avoirdupois ounces or 7000 grains.\n\nThe avoirdupois pound was enforced in the Weights and Measures Act 1963. The definition of the pound was placed in first section of this act: “The yard or the metre shall be the unit of measurement of length and the pound or the kilogram shall be the unit of measurement of mass by reference to which any measurement involving a measurement of length or mass shall be made in the United Kingdom; and- (a) the yard shall be 0.9144 metre exactly; (b) the pound shall be 0.45359237 kilogram exactly.”\n\n### How many lbs is 0.06 kg?\n\n0.06 kilogram is equal to 0.1322773572 pounds. If You want convert kilograms to pounds, multiply the kilogram value by 2.2046226218.\n\n### 0.06 kg in lbs\n\nTheoretical section is already behind us. In next part we will tell you how much is 0.06 kg to lbs. Now you know that 0.06 kg = x lbs. So it is high time to know the answer. Let’s see:\n\n0.06 kilogram = 0.1322773572 pounds.\n\nIt is an exact result of how much 0.06 kg to pound. You may also round it off. After rounding off your result will be as following: 0.06 kg = 0.132 lbs.\n\nYou learned 0.06 kg is how many lbs, so let’s see how many kg 0.06 lbs: 0.06 pound = 0.45359237 kilograms.\n\nObviously, in this case it is possible to also round off this result. After it your result is exactly: 0.06 lb = 0.45 kgs.\n\nWe are also going to show you 0.06 kg to how many pounds and 0.06 pound how many kg results in charts. See:\n\nWe want to start with a chart for how much is 0.06 kg equal to pound.\n\n### 0.06 Kilograms to Pounds conversion table\n\nKilograms (kg) Pounds (lb) Pounds (lbs) (rounded off to two decimal places)\n0.06 0.1322773572 0.1320\nNow see a chart for how many kilograms 0.06 pounds.\n\nPounds Kilograms Kilograms (rounded off to two decimal places\n0.06 0.45359237 0.45\n\nNow you know how many 0.06 kg to lbs and how many kilograms 0.06 pound, so we can move on to the 0.06 kg to lbs formula.\n\n### 0.06 kg to pounds\n\nTo convert 0.06 kg to us lbs a formula is needed. We are going to show you two formulas. Let’s begin with the first one:\n\nNumber of kilograms * 2.20462262 = the 0.1322773572 result in pounds\n\nThe first version of a formula will give you the most exact result. Sometimes even the smallest difference could be considerable. So if you need a correct result - first formula will be the best solution to calculate how many pounds are equivalent to 0.06 kilogram.\n\nSo let’s go to the another formula, which also enables conversions to learn how much 0.06 kilogram in pounds.\n\nThe second version of a formula is as following, let’s see:\n\nAmount of kilograms * 2.2 = the result in pounds\n\nAs you can see, the second formula is simpler. It could be the best choice if you need to make a conversion of 0.06 kilogram to pounds in fast way, for example, during shopping. You only have to remember that your result will be not so exact.\n\nNow we want to learn you how to use these two versions of a formula in practice. But before we are going to make a conversion of 0.06 kg to lbs we are going to show you another way to know 0.06 kg to how many lbs totally effortless.\n\n### 0.06 kg to lbs converter\n\nAnother way to know what is 0.06 kilogram equal to in pounds is to use 0.06 kg lbs calculator. What is a kg to lb converter?\n\nConverter is an application. It is based on first formula which we gave you above. Thanks to 0.06 kg pound calculator you can effortless convert 0.06 kg to lbs. You only have to enter amount of kilograms which you want to calculate and click ‘convert’ button. The result will be shown in a second.\n\nSo let’s try to calculate 0.06 kg into lbs with use of 0.06 kg vs pound converter. We entered 0.06 as a number of kilograms. It is the outcome: 0.06 kilogram = 0.1322773572 pounds.\n\nAs you can see, this 0.06 kg vs lbs converter is so simply to use.\n\nNow we are going to our primary topic - how to convert 0.06 kilograms to pounds on your own.\n\n#### 0.06 kg to lbs conversion\n\nWe are going to start 0.06 kilogram equals to how many pounds calculation with the first version of a formula to get the most exact outcome. A quick reminder of a formula:\n\nNumber of kilograms * 2.20462262 = 0.1322773572 the result in pounds\n\nSo what have you do to learn how many pounds equal to 0.06 kilogram? Just multiply amount of kilograms, this time 0.06, by 2.20462262. It gives 0.1322773572. So 0.06 kilogram is exactly 0.1322773572.\n\nYou can also round off this result, for example, to two decimal places. It is equal 2.20. So 0.06 kilogram = 0.1320 pounds.\n\nIt is high time for an example from everyday life. Let’s convert 0.06 kg gold in pounds. So 0.06 kg equal to how many lbs? As in the previous example - multiply 0.06 by 2.20462262. It gives 0.1322773572. So equivalent of 0.06 kilograms to pounds, if it comes to gold, is equal 0.1322773572.\n\nIn this example you can also round off the result. It is the outcome after rounding off, in this case to one decimal place - 0.06 kilogram 0.132 pounds.\n\nNow we can go to examples converted with a short version of a formula.\n\n#### How many 0.06 kg to lbs\n\nBefore we show you an example - a quick reminder of shorter formula:\n\nAmount of kilograms * 2.2 = 0.132 the outcome in pounds\n\nSo 0.06 kg equal to how much lbs? And again, you have to multiply number of kilogram, this time 0.06, by 2.2. Let’s see: 0.06 * 2.2 = 0.132. So 0.06 kilogram is 2.2 pounds.\n\nLet’s do another conversion using this formula. Now calculate something from everyday life, for example, 0.06 kg to lbs weight of strawberries.\n\nSo convert - 0.06 kilogram of strawberries * 2.2 = 0.132 pounds of strawberries. So 0.06 kg to pound mass is equal 0.132.\n\nIf you learned how much is 0.06 kilogram weight in pounds and are able to calculate it using two different versions of a formula, let’s move on. Now we want to show you these results in charts.\n\n#### Convert 0.06 kilogram to pounds\n\nWe realize that outcomes shown in tables are so much clearer for most of you. We understand it, so we gathered all these outcomes in charts for your convenience. Due to this you can quickly make a comparison 0.06 kg equivalent to lbs outcomes.\n\nLet’s start with a 0.06 kg equals lbs chart for the first formula:\n\nKilograms Pounds Pounds (after rounding off to two decimal places)\n0.06 0.1322773572 0.1320\n\nAnd now let’s see 0.06 kg equal pound chart for the second formula:\n\nKilograms Pounds\n0.06 0.132\n\nAs you see, after rounding off, when it comes to how much 0.06 kilogram equals pounds, the results are not different. The bigger number the more considerable difference. Keep it in mind when you need to make bigger number than 0.06 kilograms pounds conversion.\n\n#### How many kilograms 0.06 pound\n\nNow you learned how to calculate 0.06 kilograms how much pounds but we are going to show you something more. Do you want to know what it is? What do you say about 0.06 kilogram to pounds and ounces conversion?\n\nWe are going to show you how you can calculate it step by step. Let’s start. How much is 0.06 kg in lbs and oz?\n\nFirst things first - you need to multiply number of kilograms, in this case 0.06, by 2.20462262. So 0.06 * 2.20462262 = 0.1322773572. One kilogram is 2.20462262 pounds.\n\nThe integer part is number of pounds. So in this case there are 2 pounds.\n\nTo know how much 0.06 kilogram is equal to pounds and ounces you need to multiply fraction part by 16. So multiply 20462262 by 16. It is exactly 327396192 ounces.\n\nSo your result is exactly 2 pounds and 327396192 ounces. It is also possible to round off ounces, for example, to two places. Then your outcome is 2 pounds and 33 ounces.\n\nAs you can see, conversion 0.06 kilogram in pounds and ounces quite simply.\n\nThe last calculation which we will show you is calculation of 0.06 foot pounds to kilograms meters. Both of them are units of work.\n\nTo convert it you need another formula. Before we show you this formula, see:\n\n• 0.06 kilograms meters = 7.23301385 foot pounds,\n• 0.06 foot pounds = 0.13825495 kilograms meters.\n\nNow look at a formula:\n\nNumber.RandomElement()) of foot pounds * 0.13825495 = the result in kilograms meters\n\nSo to calculate 0.06 foot pounds to kilograms meters you need to multiply 0.06 by 0.13825495. It is exactly 0.13825495. So 0.06 foot pounds is 0.13825495 kilogram meters.\n\nIt is also possible to round off this result, for instance, to two decimal places. Then 0.06 foot pounds will be equal 0.14 kilogram meters.\n\nWe hope that this conversion was as easy as 0.06 kilogram into pounds conversions.\n\nWe showed you not only how to make a calculation 0.06 kilogram to metric pounds but also two another calculations - to know how many 0.06 kg in pounds and ounces and how many 0.06 foot pounds to kilograms meters.\n\nWe showed you also other solution to do 0.06 kilogram how many pounds conversions, that is with use of 0.06 kg en pound converter. It will be the best option for those of you who do not like converting on your own at all or this time do not want to make @baseAmountStr kg how lbs calculations on your own.\n\nWe hope that now all of you can make 0.06 kilogram equal to how many pounds calculation - on your own or with use of our 0.06 kgs to pounds converter.\n\nIt is time to make your move! Let’s calculate 0.06 kilogram mass to pounds in the best way for you.\n\nDo you need to make other than 0.06 kilogram as pounds conversion? For example, for 10 kilograms? Check our other articles! We guarantee that calculations for other amounts of kilograms are so simply as for 0.06 kilogram equal many pounds.\n\n### How much is 0.06 kg in pounds\n\nAt the end, we are going to summarize the topic of this article, that is how much is 0.06 kg in pounds , we gathered answers to the most frequently asked questions. Here we have for you the most important information about how much is 0.06 kg equal to lbs and how to convert 0.06 kg to lbs . You can see it down below.\n\nHow does the kilogram to pound conversion look? It is a mathematical operation based on multiplying 2 numbers. How does 0.06 kg to pound conversion formula look? . See it down below:\n\nThe number of kilograms * 2.20462262 = the result in pounds\n\nHow does the result of the conversion of 0.06 kilogram to pounds? The exact answer is 0.1322773572 lb.\n\nThere is also another way to calculate how much 0.06 kilogram is equal to pounds with second, shortened type of the formula. Have a look.\n\nThe number of kilograms * 2.2 = the result in pounds\n\nSo now, 0.06 kg equal to how much lbs ? The result is 0.1322773572 pounds.\n\nHow to convert 0.06 kg to lbs in a few seconds? You can also use the 0.06 kg to lbs converter , which will make whole mathematical operation for you and give you an exact answer .\n\n#### Kilograms [kg]\n\nThe kilogram, or kilogramme, is the base unit of weight in the Metric system. It is the approximate weight of a cube of water 10 centimeters on a side.\n\n#### Pounds [lbs]\n\nA pound is a unit of weight commonly used in the United States and the British commonwealths. A pound is defined as exactly 0.45359237 kilograms." ]

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[ "# Abstract:\n\nThe compressible laminar boundary layer in a pressure gradient with suction, for a Prandtl number of unity and a linear viscosity-temperature relation, is analyzed on the basis of the momentum and thermal integral equations in conjunction with sixth and for separation seventh degree velocity, and seventh degree stagnation enthalpy profiles. For flows over a flat plate, and for flows in a pressure gradient, straightforward and simple methods of calculating the boundary layer for a given Mach number, a given uniform wall temperature, and a given suction distribution are shown. Wherever exact or purportedly accurate solutions for an impermeable or a permeable wall are available, the results obtained by the present analysis agree very well with such solutions, including the general asymptotic suction solutions for compressible flows with a pressure gradient and heat transfer. Finally, the boundary layer with a linearly diminishing external velocity is calculated. Author" ]

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[ "## The Matching Approach\n\nIn their work to establish the best distance indicators among detached and semidetached binaries in the Small Magellanic Cloud, Wyithe & Wilson (2002a,b) and Wilson & Wyithe (2003) obtained starting parameters for the rigorous WD model by comparing each light curve with a set of archived model light curves, and then sending the best match to an automated version of the WD differential corrector program DC.\n\nIn ongoing work, Kallrath & Wilson (2057) are extending this approach by an inner linear regression loop, incorporating a priori information, adding interpolation techniques, and increasing storage and numerical efficiency. This approach now supports all WD parameters.\n\nFor a given binary system, let l0ic be any observed value for observable c, c = 1... C, at phase 0. Correspondingly, l°ick denotes the computed value at the same phase 0i for the archive1 curve k, k = 1... K. Note that K might easily be a large number such as 1010. The matching approach returns the number of the best fitting archive light curve, a scaling parameter, a , and a shift parameter, b, by solving the\n\n7 Synonomously, we use the terms stored, library, or template light curves.\n\nfollowing nested minimization problem:\n\nmin k\n\nNote that the inner minimization problem only requires solution of a linear regression problem. Thus, for each k, there exists an analytic solution for the unknown parameters a and b. Note that the icicn values are obtained by interpolation. The archive light curves are generated in such a way that they are well covered in the eclipses, while a few points will do in those phases that show only small variation. Thus, there is a non-equidistant distribution of grid points that is well interpolated by cubic polynomials.\n\n### 5.3.2.1 Solving Linear Regression Problems\n\nAlthough solving linear regression problems is not difficult as such, one should exploit a priori knowledge of light curve parameters when looping over k. If a priori knowledge is available, for instance, on the mass ratio, q, or the temperatures T1 and T2, then certain k values can be excluded. The analysis of C observables (radial velocity curves and light curves) requires to solve C linear regression problems. If the observable is a radial velocity curve, the additive constant b gives the systemic velocity y . For light curves, a returns the WD scaling quantity L 1 and b is third light, I3\n\n5.3.2.2 Generation and Storage of the Archive Curves\n\nArchive generation requires appropriate looping and proper interfacing to subroutine LC of the WD program. Special attention should be paid to the way the stored sets can be accessed. If a priori knowledge is available in connection with the Roche potentials Ü1 and for instance, on the mass ratio, q, we should exclude unphys-ical configurations and ensure that certain values of k can be excluded.\n\nAn additional aspect is the storage of the computed archive light curves. For each light curve and observable (wavelength), we need rk = 4 x C x Ik bytes, where we consider 4 bytes, Ik phases and C bands. Note that we may have different numbers of phases depending on the shape and amplitude of the light curve (used in our interpolation scheme). The total memory requirement is then R := J2K= 1 rk. Note that R may easily reach the order of 4C ■ 108 light curves if all reasonable combinations of the photometric parameters e,d, i, q,Q1,Q1, T1, T2, and log g are considered.\n\nThe choice of unadjusted parameters A1, A2, g1, and g2 depends on T1 and T2. L1 can be set arbitrarily to L1 = 1 because the matching problem involves the scaling parameter anyway. L2 follows as a function of L1. l3 is covered by the linear regression in the matching problem. Limb-darkening parameters also can be chosen, from, for instance, Van Hamme's (1993) limb-darkening coefficients. As the computation of limb-darkening coefficients depends on log g, we have added this as a parameter. Great care is necessary when involving the eccentric orbit parameters. Both eccentricity, e, and length of the perihel, m, need a very fine grid.\n\nIn addition to the sets generated automatically, we add all the light curve parameters sets for those EBs for which a light curve solution is available. This way, when we find a match to an observed light curve, we are able to provide not only some reasonable light curve parameters but, in addition, also a candidate similar to the current EB.\n\nOne might think to store the library light curves in a type of database. However, database techniques become very poor when talking about 1010 light curves. Therefore, a flat storage scheme is used. In the simplest case, for each k we store the physical and geometric parameters, then those parameters describing observable c, and then the values of the observable.", null, "## Telescopes Mastery\n\nThrough this ebook, you are going to learn what you will need to know all about the telescopes that can provide a fun and rewarding hobby for you and your family!\n\nGet My Free Ebook" ]

[ null, "https://www.fossilhunters.xyz/images/downloads/eJw9yksKgCAQANDbuFTLfgTSUcLPkEPpiBleP9q0easXas2rEA1PbGClnHkkIu4oCk8tXWT8Hk0yBxRxQ_I8h7wZV5GSzujqU4D9Eb0eJ2UXBdPgQHUs6H6UrH2-8wMkXQ.jpg", null ]

[ "Impact Factor 6.684 | CiteScore 2.7\nMore on impact ›\n\n# Frontiers in Celland Developmental Biology", null, "## HYPOTHESIS AND THEORY article\n\nFront. Cell Dev. Biol., 08 May 2017 | https://doi.org/10.3389/fcell.2017.00041\n\n# How Cells Can Control Their Size by Pumping Ions\n\n• Department of Biology, University of Iowa, Iowa City, IA, USA\n\nThe ability of all cells to set and regulate their size is a fundamental aspect of cellular physiology. It has been known for sometime but not widely so, that size stability in animal cells is dependent upon the operation of the sodium pump, through the so-called pump-leak mechanism (Tosteson and Hoffman, 1960). Impermeant molecules in cells establish an unstable osmotic condition, the Donnan effect, which is counteracted by the operation of the sodium pump, creating an asymmetry in the distribution of Na+ and K+ staving off water inundation. In this paper, which is in part a tutorial, I show how to model quantitatively the ion and water fluxes in a cell that determine the cell volume and membrane potential. The movement of water and ions is constrained by both osmotic and charge balance, and is driven by ion and voltage gradients and active ion transport. Transforming these constraints and forces into a set of coupled differential equations allows us to model how the ion distributions, volume and voltage change with time. I introduce an analytical solution to these equations that clarifies the influence of ion conductances, pump rates and water permeability in this multidimensional system. I show that the number of impermeant ions (x) and their average charge have a powerful influence on the distribution of ions and voltage in a cell. Moreover, I demonstrate that in a cell where the operation of active ion transport eliminates an osmotic gradient, the size of the cell is directly proportional to x. In addition, I use graphics to reveal how the physico-chemical constraints and chemical forces interact with one another in apportioning ions inside the cell. The form of model used here is applicable to all membrane systems, including mitochondria and bacteria, and I show how pumps other than the sodium pump can be used to stabilize cells. Cell biologists may think of electrophysiology as the exclusive domain of neuroscience, however the electrical effects of ion fluxes need to become an intimate part of cell biology if we are to understand a fundamental process like cell size regulation.\n\n## Introduction\n\nCells in organisms of all phyla are typically small, with diameters of a few tens of microns. This length scale allows for the rapid diffusion of molecules in the cytoplasm (Berg, 1993). If the cells were larger by an order of magnitude the average diffusion time across a cell would rise by two orders of magnitude. It is this rapid growth of transit times that in part sets a very tight limit on absolute cell size.\n\nThere is abundant evidence that cells are able to control their size (Marshall et al., 2012; Amodeo and Skotheim, 2016), but little as to how they do so. Here I will show that there is a tight link between cell size, membrane potential and impermeant intracellular molecules, at least for cells with pliant membranes. At first glance in the huge array of cellular factors, these may seem somewhat remote but they are tied together through the osmotic movement of water across the plasma membrane. This connection can be all but invisible, unless one exposes the forces that drive ion and water fluxes.\n\nThe monovalent inorganic ions, Na+, K+, and Cl are, next to water, the second most abundant components of cells (Frausto da Silva and Williams, 2001). These ions play central roles in the energetics of cells and in determining the osmotic stability of cells. In most cell biology textbooks they are often given short shrift, relegated to counter-ions that play a bystander role. There is perhaps a tendency in cellular biology to locate the drivers of cellular activity in the interactions between macromolecules. The province of ions and potentials is often only seen as germane in neurophysiology; however, I will argue that it is a powerful determinant of cell biology.\n\nThere are conceptually two forms of cell size regulation that can be distinguished. First, the processes that determine the size distributions of various cell types in an animal that I will term cell size regulation (CSR), which for example, makes fibroblasts larger than hepatocytes (Ginzberg et al., 2015). Second, there are mechanisms that stabilize the cell volume when the osmolarity of the extracellular fluid changes, which I will call cell volume regulation (CVR, reviewed in Hoffmann et al., 2009). Although there are likely to be links between these two processes, I will focus on CSR in this paper.\n\nAll cells have a problem that stems from their need for an inventory of impermeant molecules (metabolites, proteins, nucleic acids, etc., Burton, 1983b) that sets up an unstable osmotic condition, which could rupture the plasma membrane if left unattended (Stein, 2002; Armstrong, 2003; Dawson and Liu, 2008). This is the so-called Donnan effect (Sperelakis, 2012). Plants and prokaryotes solve the problem by building cell walls that can resist turgor pressure (Haswell and Verslues, 2015; Wood, 2015). Some single cell eukaryotes pump out excess water (Allen and Naitoh, 2002). All animal cells appear to remedy the problem by pumping Na+ out and K+ in with a Na+/K+ ATPase (NKA), while allowing the passive leak of ions and water down their gradients (Weiss, 1996). The Na+ and K+ gradients also serve as energy reservoirs for transporting other molecules against their concentration gradients and in establishing a negative resting membrane potential.\n\nTosteson and Hoffman (1960) demonstrated how the operation of the NKA can stave off an osmotic catastrophe, where water flows into the cell until it lyses. Although their so-called pump-leak model (PLM) is well established and part of the standard canon of physiology (Boron and Boulpaep, 2016), precisely how it works has not been widely disseminated. I will argue that this is so because, for the most part, the understanding of electrical current flow is not considered a necessary part of a cell biologist's intellectual toolbox. Part of my aim is to show how this omission can hobble our comprehension of a crucial aspect of cell biology and to remedy it by providing the essentials of what one needs to know, to understand the fundamentals of ion and water flow.\n\nPost and Jolly (1957) were the first to show theoretically, how pumping a permeant molecule could stabilize a cell containing impermeant molecules, however their model only considered uncharged molecules. In 1960, Tosteson and Hoffman demonstrated that erythrocyte volume was stabilized by the action of a NKA, which in essence prevents the influx of water induced by the presence of impermeant molecules in the cell. They showed that it was not the NKA alone that was responsible for volume stabilization but a coupled system, which includes Na+, K+, Cl, and water permeability. The action of the NKA can be viewed as making room for the impermeant ions in the cell and equalizing the osmotic pressure across the membrane. The PLM accounts for the asymmetric distribution of Na+ and K+ across animal cells first observed by Schmidt (1850) and Clarke and Fan (2011). This distribution of ions is not just a peculiarity of animal cells but is a universal characteristic of cells in all phyla (Somero et al., 2017).\n\nIt is not my purpose in this paper to examine the experimental evidence for the PLM (Macknight and Leaf, 1977; Hoffmann et al., 2009) in stabilizing cell size but to assess and clarify aspects of its theoretical foundations. I believe that the PLM cannot be understood fully without tackling its mathematics. Here I show how one can set up a system of equations, derived from physical laws (Sterrat et al., 2011; Nelson, 2014), which model the interaction between ion and water fluxes, allowing one to calculate both the membrane potential (V) and cell volume (w). In addition, I introduce an analytical solution derived by Keener and Sneyd (2009), which is useful in making clear how the ionic conductances, pump rate and ion concentrations influence w and V. Using these equations I show that there is direct connection between the number of impermeant molecules (x) in a cell and its volume.\n\nElectrophysiology is often considered to be the province of neuroscience. In this paper I hope to show that it is an essential tool for understanding cells and how they regulate their size.\n\n## Methods\n\nAll simulations and calculations were performed in MATLAB (Mathworks, Natick, MA) and graphs were plotted using Origin (MicroCal, Northampton, MA). Numerical integration of the differential equation was by the simple Euler method with step size 1–100 μs (See Supplementary Material for MATLAB program).\n\n### Symbols and Abbreviations\n\nA, Membrane area\n\nC, Membrane capacitance\n\ngi, Conductance of ion i\n\nn, Number of Na+ pumped per NKA cycle\n\np, Pump rate\n\nPf, Osmotic water permeability coefficient\n\nq, Number of K+ ions pumped per NKA cycle\n\nR, Universal gas constant\n\nT, Absolute temperature\n\nw, Cell volume\n\nx, Number of moles of the impermeant intracellular molecules\n\nz, Average charge of impermeant intracellular molecules\n\nV, Voltage\n\nΠ, The intracellular osmolarity\n\nΠo, The extracellular osmolarity.\n\n### Default Values of Parameters\n\nNote that this parameter set has been used in all figures unless otherwise specified.\n\nClo = 150 mM\n\nCm = unit membrane capacitance = 1 μF cm−2\n\ngCl = 0.2 mS cm−2\n\ngK = 0.3 mS cm−2\n\ngNa = 0.01 mS cm−2\n\nKo = 3 mM\n\nn = 3\n\nNao = 147 mM\n\nq = 2\n\nT = 25°C\n\nx = 2.6 × 10−14 mole\n\nz = −1\n\n### The Pump-Leak Mechanism\n\nThe work presented here derives from a long line of work in cellular physiology. I thought it useful to present it in part as a tutorial, since some of the information is collected in rather specialized publications, often directed at excitable cells. I wanted to present it as one concise narrative rather than as a tedious opera. I hope to make clear that there is a direct connection between the number of impermeant ions in a cell and its size. The elementary physics that is required to understand electrical current flow in biological systems is succinctly covered in the appendices of the following textbooks (Nicholls et al., 2011; Blaustein et al., 2012).\n\nIn what follows I will set up a model that incorporates all the forces and constraints that act on ions and water, both within and outside the cell, to determine how the ions and water will distribute as time moves on. A crucial feature of the model is that the membrane is assumed to be freely distensible, so that as water moves in it will expand correspondingly and shrink if water moves out.\n\nIn addition, I will assume that the composition of the solution in the extracellular space is fixed, which is reasonable since the volume of the extracellular space if far larger than that of a single cell. I will also set aside spatial effects and assume that the cell, for the purposes of this paper, can be considered a single iso-potential sphere (i.e., all points within the cell are at the same potential) and the voltage in the extracellular space is zero.\n\nTo improve the flow of the equations I have adopted the following conventions: capitalized solutes represent concentrations, and lower cases represent amounts in moles. Extracellular ions are denoted by a subscript “o” for “outside,” intracellular ions have no subscript.\n\n### The Donnan Effect\n\nAnimal cell membranes, being somewhat fragile, cannot sustain much transmembrane pressure nor expand much (see however Sachs and Sivaselvan, 2015). Therefore, because membranes are permeable to water, the osmolarity of the extracellular fluid should match closely that of the intracellular fluid. Over 70 years ago Boyle and Conway (1941) realized that the impermeant molecules (metabolites, proteins, nucleic acids etc.) which cells must contain, impose an osmotic load on cells.\n\nTo see how this arises I will consider the effect of impermeant ions on the osmotic balance of cells. Since the osmotic strength of a solution is a colligative property (Atkins and de Paula, 2014), all the impermeant molecules can be lumped together and considered as a single chemical species, without any loss of precision, which I will term x (where X is its osmolarity and x the number of osmoles) with an average charge z. It should be noted that some molecules might have osmotic coefficients less than one.\n\nIt can be shown (see below) that a cell which has a pliant membrane, permeant to monovalent ions and containing impermeant molecules, immersed in a saline solution cannot reach a stable steady state without the input of energy and will burst (Weiss, 1996). Whereas in the absence of impermeant molecules the “cell” is stable if the solution within the cell is identical to that outside.\n\nThe influence of the impermeant molecules is called the Donnan (or Gibbs-Donnan) effect, which has been and continues to be a concept that has been misapplied and misunderstood even in contemporary textbooks. Although a Donnan equilibrium is not possible in a live animal cell, x does exert an effect on the cell and cannot be ignored. Tosteson and Hoffman (1960) showed that the operation of an energy consuming NKA stabilizes cell volume in the presence of x and water permeability. It is this PLM that I will discuss in the rest of this article.\n\n### The Constraint Equation\n\nTo see how x and z, together with the distributions of Na+, K+, and Cl determine cell volume I consider two physico-chemical constraints on cells:\n\n1. Osmotic balance. Since the membrane of animal cells cannot support much of a transmembrane pressure, the osmotic strength of the intracellular solution should be equal to that of the extracellular solution (Πo):\n\n2. Charge Balance. The number of positive charges inside the cell should match that of the intracellular negative charges\n\nWhere w is the cell volume. This also holds true for the extracellular solution.\n\nFrom these two conditions I can derive an expression for the cell volume:\n\nWhere V is the transmembrane potential. The charge imbalance that gives rise to the transmembrane potential is so small as to be chemically undetectable (Burton, 1975). The only assumption for the second part of this equation is that the chloride distribution is at equilibrium.\n\nFrom this equation it is clear that the volume has a simple dependence on x and its charge, z. This equation was derived by Boyle and Conway (1941), and I follow Fraser and Huang (2004) in calling it the “constraint equation.”\n\nThe constraint equation shows for a given z, which values of X and V are consistent with a stable volume (Figure 1, see gray lines). However, it only determines the sum of Na+ and K+. To determine the individual concentrations, I have to consider the forces acting on all the ions.\n\nFIGURE 1", null, "Figure 1. The influence of z and pump rate (p), through the constraint equation, on V and X. The gray lines are from Equation (3) and the blue ones from the KSSs. p in (C mm−2 s−1). The red line represents the trajectory of a system with z = −1 and p = 0.25 C mm−2 s−1, where the pump is turned on and then off after reaching a steady state.\n\nTwo important implications of the constraint equation are that to accommodate x, the voltage needs to be negative, and with a voltage of zero the volume goes to infinity i.e., the cell is unstable. A useful way of thinking about the PLM is that it creates a negative potential and Cl follows its equilibrium making space to accommodate x.\n\n### The Ion Flux Equations\n\nTo complete the model of the cell, equations are required that describe the forces acting on the three mobile ions, Na+, K+, and Cl. These forces are chemical potential (diffusion), electric, and active ion transport. This gives three equations for the rate of change of the intracellular ion concentrations:\n\nWhere A is the membrane area (assumed to be constant) and F Faraday's constant. To break the expressions down into their components, the term ${\\mathrm{\\text{g}}}_{Na}\\left[V-\\frac{RT}{F}ln\\left(\\frac{\\mathrm{\\text{N}}{\\mathrm{\\text{a}}}_{o}}{Na}\\right)\\right]$ is Ohm's law, which combines the chemical and electrical potentials, and $\\frac{RT}{T}ln\\left(\\frac{N{a}_{o}}{Na}\\right)$ is often referred to as the “Nernst potential.” While, the NKA is represented by a constant pump rate p with n and q being the number of Na+ and K+ ions, respectively transported per cycle. As I show in the Appendix (A2, Figure A1) the simplified form of the NKA, where it is represented by constant terms in Equations (4) and (5), has little impact on my overall conclusions. The last term in the equations reflects the influence of volume changes on ion concentrations. This term is very small and can be dropped without incurring much error.\n\nThe assumption of constant area is adopted to reflect the fact that over a short time scale the number of channels and transporters is unlikely to change much.\n\nThe flow of water can be modeled by the following equation (Fettiplace and Haydon, 1980):\n\nWhere Pf is the osmotic water permeability coefficient of the membrane and νw is the partial molar volume of water (18 cm3 mol−1). Water permeability even in the absence of aquaporins is higher than the ionic permeability (Verkman, 1992) and I will assume that water instantaneously equilibrates across the membrane, unless otherwise noted.\n\nFrom the definition of capacitance, the voltage is given by the following equation (Varghese and Sell, 1997):\n\nI shall refer to the system of Equations (1), (2), (4), (5), (6), and (8) as the “pump-leak equations” (PLE). In 1998, Keener and Sneyd found an analytical solution for the steady state of the PLEs, but this important work has as yet not made its way into the biological literature. The advantage of an analytical solution is that it makes evident the influence of the various factors at play in regulating cell volume. Moreover, it offers a convenient check of numerical methods used for solving the PLEs. Keener and Sneyd's solutions (KSS) to the PLEs are given in Appendix A1.\n\n### Integrating the PLEs\n\nNo closed-form solutions are available for the approach of the system to steady-state, hence the system has to be solved by numerical integration.\n\nTo solve numerically the PLEs I integrate Equations (4–7) and use the algebraic Equation (8) to calculate V. Fraser and Huang (2007), termed this the “charge-difference” (CD) method, which explicitly takes into account the impermeant ions, x and their charge, z. I have found that the CD approach converges to the KSS, with reasonable initial conditions (data not shown).\n\nIf I begin the simulation with some arbitrary values of ion concentrations and turn on the NKA the system approaches the steady state given by the KSS. If after reaching steady state the NKA is turned off, the ions equilibrate across the membrane and the volume increases continuously, showing that the system is unstable in the absence of NKA activity (Figure 2). An important feature of the PLM is its robustness; a stable volume can be achieved with a very wide array of combinations of channel conductances and extracellular ion concentrations, so long as $n\\frac{N{a}_{o}}{{g}_{Na}}>q\\frac{{K}_{o}}{{g}_{K}}$ and the p not too high (Keener and Sneyd, 2009; Mori, 2012). The PLM also stabilizes cells against sudden changes in extracellular osmolarity, which is followed by the cell changing to a new stable steady state volume (Figure 3).\n\nFIGURE 2", null, "Figure 2. The effect of turning the NKA on and then off, on ion concentrations, voltage and size. Green arrow, pump on; red, pump off. p = 0.5 C mm−2 s−1. The % of the minimum volume is plotted as function of time on the lowest panel.\n\nFIGURE 3", null, "Figure 3. The PLM stabilizes cells against changes in extracellular osmolarity. The blue rectangles over the figures indicate the period during which the osmolarity was changed from the control value of 300–320 mOsm (left panel) or 280 mOsm (right panel). Water is removed or added respectively to the default extracellular solution. p = 0.5 C mm−2 s−1. The osmotic water permeability = 0.05 cm s−1. The % of the initial volume is plotted as function of time on the lowest panel.\n\nIt is worth noting that if a cell has no impermeant ions, which is clearly impossible, the system is stable in the absence of an NKA. However, with no x, the operation of an NKA has the paradoxical effect of rendering the system unstable (see Appendix A3).\n\n### The Effect of z\n\nThe impermeant molecules x exert an osmotic effect on the system and constrain the size of the cell. The mean charge on these molecules, z, also has a powerful influence on the ion distributions, voltage and volume of the cell. This can be seen by plotting these variables as a function of z with a fixed number of moles of x (Figure 4).\n\nFIGURE 4", null, "Figure 4. The effect of z on ion concentrations, voltage and cell radius. p = pmin and was 0.65 C mm−2 s−1 for all of the values shown. The % of the minimum volume is plotted as function of z on the lowest panel.\n\n### Cp Curves\n\nThe action of the NKA can be made evident by plotting ion concentrations, V and volume as a function of the pump rate, p What I will term, Cp curves, provide a way of visualizing the forces at play as p is ramped up and the effect of p on the apportioning of ions. When one plots the concentration of intracellular ions as a function of pump rate the ion concentrations form a braid (symmetrical for the case of z = −1 because of the osmotic and charge constraints (Figure 5, 2nd panel from the top and see Appendix A4).\n\nFIGURE 5", null, "Figure 5. A Cp plot of ion concentrations, voltage and cell radius. z = −1, n = 3, and q = 2. The case where potassium in not actively transported (q = 0) is shown in gray. The % of the minimum volume is plotted as function of p on the lowest panel.\n\nIf, as in Figure 5 (top panel), the cations and anions in the Cp plots are grouped separately, the preservation of charge and osmotic balance become obvious; the sum of all intracellular species is equal to Πo, while the sum of the positive charges is equal to that of the negative charges. This also holds for z ≠ −1 but relationships between the ion concentrations and p become somewhat more complicated (see Appendix A5, Figure A2).\n\nAs p is increased, although Na+ and K+ are being pumped, it is Cl and X that first respond to this applied force. Why is this so? Because the net action of the NKA during a cycle is to move one positive charge out of the cell, it makes the inside of the cell more negative (i.e., hyperpolarizes), which drives Cl out of the cell passively requiring little energy, while setting up the asymmetric Na+/K+ distribution, which is far out of equilibrium, requires a greater energetic input.\n\nAn alternate way of viewing the PLM is shown in Figure 1 where X vs. V derived from the KSEs is plotted for a given p (blue lines). The intersections between the CE equation and the X vs. V serve as attractor points, so that if the system starts at a nonequilibrium point it will move to the intersection when the pump is turned on. If the pump is turned off the system moves to V = 0 and the volume goes to infinity.\n\n### Mathematical Knockout of Components of the NKA\n\nThe PLEs can be further simplified by assuming that the NKA can actively transport only one of the monovalent cations.\n\nIf Na+ transport is eliminated but all other aspects of the PLM are left intact, no stable solutions are possible (see Appendix A6). This happens because the pump generates an inward current that depolarizes the cell and draws Cl in. Na+ cannot follow the voltage because of its high extracellular concentration and it remains out of register with the V throughout the Cp curve. This mechanism is incapable of generating a stable volume and generates a strong depolarization.\n\nIf K+ transport is eliminated but all other aspects of the PLM are left in place, there is very little difference in the operation of the mechanism as seen in a Cp plot (Figure 5). K+ and Cl can move passively and attempt to follow the voltage. As mentioned above the Na+ pump hyperpolarizes the cell. This drives Cl out and K+ in. For this case, the K+ and Cl follow the Donnan relationship (viz. K Cl = KoClo) exactly and are both in equilibrium with the voltage (see Appendix A6). Because the system requires ATP to sustain a steady-state, the system as whole is not at equilibrium.\n\nThe actual NKA requires both Na+ and K+ to operate, however my analysis shows that Na+ transport is the only necessary component if one thinks of its role in volume regulation. Dropping active K+ transport simplifies the PLEs so that it becomes possible to arrive at analytical solutions to the intersection points on Cp plots and to see how they depend on the systems parameters (see Appendix A4).\n\n### The Effect of Cl− Conductances\n\nThe effect of the Cl conductance on the PLM is entirely passive but it is an essential one, since if the conductance is blocked Cl cannot equilibrate and the mechanism is blocked. In many cells Cl is not passively distributed but is pumped and this will have an effect on the volume regulatory mechanism but is beyond the scope of this paper (Kaila et al., 2014; Vereninov et al., 2016).\n\n### Optimizing the Pump Rate\n\nThe pump rate (p) is a direct measure of the energy needed to sustain the volume and voltage of the cell, since it is directly coupled to ATP hydrolysis. In the PLM, as the pump rate is increased, the volume declines and reaches a minimum at what I will call pmin (Figure 5). If p is increased above this, the volume then increases very slowly. For the case where z = −1, pmin can be found by differentiating Equation (A12) with respect to p, setting this derivative equal to zero and solving for p:\n\nEquation (9) encapsulates how the energy required to maintain cell volume depends on the systems parameters. pmin can be minimized by keeping gNa small but is less sensitive to the magnitude of gK (Figure 6). It is worth noting for the case where q = 0 the volume declines to a minimum but does not increase as p is increased.\n\nFIGURE 6\n\n### An Equivalent Electrical Circuit Representation of the PLM\n\nA standard method for predicting the electrical properties of cells is to build up an equivalent circuit model using capacitors, batteries and conductances; where the latter are often voltage gated (Kay, 2014). Because of ion accumulation and the variable volume, there is no simple way of devising such a circuit to represent the PLM. However a partial circuit representation can be developed, if I use the KSEs to estimate the ion distribution and steady state voltage at a given pump rate. A current-voltage (IV) relationship of the Na+ and K+ currents can then be used to show how current flow is apportioned. This is shown in Figure 7 for two different values of the pump current. The Nernst potentials of the K+ (i.e., $\\frac{RT}{F}ln\\left(\\frac{{K}_{o}}{K}\\right)$) and Na+ (i.e., $\\frac{RT}{F}ln\\left(\\frac{N{a}_{o}}{Na}\\right)$) conductances can be calculated from the their respective intra- and extracellular concentrations. Notice that at the resting potential both the passive Na+ and K+ currents are exactly balanced by an equal and opposite pump current, in the ratio 3:2. The system is stable because deviations from the resting potential will induce currents that restore it to rest.\n\nFIGURE 7", null, "Figure 7. The PLM balances the Na+ and K+ currents to stabilize the membrane potential. For p = 0.1 C mm−2 s−1, EK = −29.5 mV, ENa = 1.155 mV and V = −28.84 mV and for p = 0.5 C mm−2 s−1, EK = −97.43 mV, ENa = 56.41 mV and V = −94.187 mV.\n\n### Pumps Other than the NKA Can Stabilize Cell Volume\n\nThe PLM is not exclusively dependent upon the operation of a NKA; there are other pumps that can substitute. All that is required is a mechanism for pumping Na+ out of the cell, together with passive Na+, K+, and Cl conductances, and water permeability. Mycoplasma, which are bacteria that do not have cell walls, provide a nice example for looking at alternative PLMs. Like other bacteria and archea they do not have a NKA, but they do have a proton pump (Krulwich et al., 2011) and a Na+/H+ transporter (Padan and Landau, 2016), where the proton gradient drives the outward flux of Na+. Figure 8 shows that the operation of a proton pump in conjunction with a Na+/H+ exchanger can stabilize a cell. Blocking the proton pump induces mycoplasma to lyse (Linker and Wilson, 1985).\n\nFIGURE 8", null, "Figure 8. A Cp plot of a PLM model incorporating a Na/H exchanger, a proton pump and conductance (see Appendix A7). The extracellular pH = 7, pNa/H = 105 and gH = 0.007 mS cm−2 and DH = 10−7M. The % of the minimum volume is plotted as function of pH on the lowest panel.\n\n## Discussion\n\nCell size regulation is a fundamental aspect of both single and multi-cellular organisms. Although the link between active and passive ion fluxes and cell size has been known for over 50 years, it seems not to have had much impact in cell biology. In as much as cell biologists, outside of neuroscience, typically do not seem to reach for electrophysiological explanations, in accounting for cellular phenomena.\n\nFrom the components of the PLM it is difficult to discern how it stabilizes cell volume. The mechanism only become evident when one embodies it in a mathematical model and simulates it as a complete system. Although the essentials of the PLM have been around for a long time, its workings have not been widely spread in the form of textbook accounts, with some few exceptions (Stein, 1990; Weiss, 1996). Cell biology textbooks typically only offer verbal explanations that provide a rather superficial understanding of its mechanism of operation. It is perhaps worth noting that inattention to the importance of electrical current flow in cell biology proved a roadblock to the acceptance of a seminal breakthrough in cell biology, viz. Peter Mitchell's chemiosmotic hypothesis (Mitchell, 2004).\n\nA central point to emerge from my analysis of the PLEs is that x determines the cell volume (see Equation 3). Therefore cells can potentially use x to regulate their volume. A plausible mechanism is for cells to continuously monitor their size and use a feedback mechanism to control their size. For example the concentration of an osmolyte like taurine could be increased or decreased depending on whether the size is below or above the size set point. There is evidence for active size sensing in yeast and a number of mechanisms have been proposed to account for it (Pan et al., 2014; Shahrezaei and Marguerat, 2015; Amodeo and Skotheim, 2016). A recent attempt to whittle down the genome of mycoplasma to an essential set of genes has revealed the presence of genes with unknown function (Hutchison et al., 2016). Might some of these be involved in cell size control?\n\nI have not addressed the question of whether the PLM is the only mechanism that controls cell size. Some have claimed that viscoelastic properties of the cell membrane and cytoskeleton play a key role in cell volume regulation (Sachs and Sivaselvan, 2015). It seems to me that it is possible that both factors play a role in cell membrane stabilization.\n\nStarting with Tosteson and Hoffman the PLEs have gone through a number of iterations (Mackey, 1975; Jakobsson, 1980; Lew et al., 1991; Kabakov, 1994; Hernandez and Cristina, 1998; Hoppensteadt and Peskin, 2002; Armstrong, 2003; Fraser and Huang, 2004; Takeuchi et al., 2006; Ataullakhanov et al., 2009; Yurinskaya et al., 2011). Mori (2012) has demonstrated that the PLEs have an asymptotically stable steady state so long as the pump current is not too large. While Vereninov et al. (2014) have shown how to estimate the parameters of a PLE from experimental data.\n\n### The Donnan Effect\n\nThe Donnan effect is frequently introduced in physiological textbooks, however the reader is often left hanging as to its precise implications for cell function. As I have shown, the effect of trapped molecules within the cell has a significant impact on the behavior of the cell; but it should be emphasized that a true (i.e., with no energy input) Donnan equilibrium cannot be attained, unless the membrane can sustain a very high transmembrane pressure. In the hypothetical case where Na+ is pumped actively while K+ and Cl distribute passively, these ions distribute in accord with the Donnan relationship (see above), the system is in a dynamic steady-state. Misunderstanding the Donnan effect, as has been pointed out by others (Voipio et al., 2014), can lead to erroneous ideas about the influence of impermeant ions on ion distributions.\n\nIt is worthwhile making a distinction between the PLM and the so-called Double-Donnan mechanism, because these two are sometimes conflated. The Double-Donnan mechanism (Leaf, 1959) proposes that the asymmetric ion distribution is achieved by the operation of a NKA together with a membrane that is permeable to K+, Cl and water but not to Na+. It is probably best to avoid this term since all membranes have a finite permeability to Na+. Moreover, if the sodium conductance is zero, the system of equations is unstable, with the Na+ concentration becoming negative, which is clearly impossible.\n\nx is a heterogeneous collection of molecules, yet both it and z can be calculated. To do this one needs to have good estimates of the extracellular osmolarity and the intracellular concentrations of the predominant permeable anions and cations. One can then use Equation (1) to estimate x and Equation (2) z. The estimates are of course only as good as the intracellular concentration estimates, which as yet are difficult to obtain, absent sensitive and accurate monovalent ion sensors. Estimates of z have been made for muscle and some cell lines and ranges between −2 and −0.7 (Burton, 1983a; Model, 2014). Both x and z are unlikely to be fixed and will vary as impermeant molecules are metabolized or transported and as the pH changes. A precise accounting for the contributions to z has yet to be done. The contributions of nucleic acids and proteins will depend on how tightly counter ions bind (Raspaud et al., 2000). Some texts refer to x as the “anion gap,” which is sometimes incorrectly attributed to intracellular proteins.\n\n### The Role of Leaks and the Energetics of the PLM\n\nIf one is unaware of the role of the NKA in volume regulation, the presence of Na+, K+, and Cl leaks seems counterproductive as they impose an energetic load on the cell. It is only if one takes into account the central role of the NKA in volume regulation, that the function of the leak conductances become apparent as key components of the PLM. There are a large variety of leak channels (Ren, 2011; Feliciangeli et al., 2015) and it seems likely that they may have evolved to help stabilize cell volume. Moreover, gNa has a profound effect on the energy utilization of a cell, with energy consumption in direct proportion to gNa (Figure 6). Driving the NKA is one of the most energetically costly processes for animals, with an estimated 20% of a cell's energy consumption needed to keep it running (Rolfe and Brown, 1997; Milo and Phillips, 2015). This large energy investment is a clear indication of the importance of the PLM.\n\nAs I have shown, there is a minimum pump rate to achieve a stable volume. Operating above this rate does not change the volume much. As the pump rate declines below pmin, the volume increases monotonically; however, even for very low pump rates, the volume is stable. This constitutes something of a problem for evaluating the PLM experimentally; even with very low pump rates the volume may be stable. In addition it is possible that other pumps may take over and sustain the volume. Moreover, as my simulations show (Figure 2), it may take a long time for ion gradients to dissipate after the application of a pump blocker like ouabain.\n\nIt is worth noting that the leak current is also an essential part of the mechanism that makes cells excitable. If one were to remove all leak currents, which is clearly not possible, from a cell with voltage gated Na+ and K+ channels, there would be no stable resting potential (Kay, 2014). Furthermore the PLM provides a simple explanation for the small changes in axon dimensions induced by action potential propagation (Cohen, 1973; Lee and Kim, 2010).\n\nEquivalent circuit models are often used to simulate neurons, but most models do not, with some exceptions (Kager et al., 2002; Ostby et al., 2009; Ullah et al., 2015), incorporate water and ion fluxes, impermeant molecules and distensible membranes. Cellular swelling occurs after cerebral trauma, stroke, spreading depression and epilepsy (Rungta et al., 2015; Stokum et al., 2016). There is a pressing need for pharmacological interventions that limit swelling and prevent the damage resulting from cells being damaged while expanding into the closed volume of the cranium. Developing such agents requires a detailed understanding of all the factors that play a role in cell volume regulation and the theory that undergirds this mechanism. The operation of the PLM in excitable cells like neurons, with more vigorous passive ion fluxes than in other cells, imposes a more severe energetic demand on neurons and muscle. This by itself may explain why neurons are so sensitive to oxygen deprivation.\n\nThe maintenance and restoration of Na+ and K+ gradients is the most conspicuous function of the NKA, yet its role in volume regulation is seldom recognized. Stein (1995) has argued that the evolution of the NKA and the PLM is a defining characteristic of animal cells. It endows them with an osmoregulatory mechanism that does not require rigid cells and it gives them a negative resting potential, which turned out to be very convenient for evolving excitable cells (Jakobsson, 1980; Armstrong, 2015). The PLM also liberates cells from the straitjacket of cell walls allowing the evolution of contractile mechanisms.\n\n## Author Contributions\n\nAK initiated the project, analyzed the equations, performed simulations and wrote the paper.\n\n## Conflict of Interest Statement\n\nThe author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.\n\n## Acknowledgments\n\nI thank James Keener (Univ. Utah) and David Stewart (Univ. 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Sunderland, MA: Sinauer Associates, Inc.\n\nSperelakis, N. (2012). “Gibbs-donnan equilibrium potentials,” in Cell Physiology Sourcebook, ed N. Sperelakis (Waltham, MA), 147–171. doi: 10.1016/b978-0-12-387738-3.00010-x\n\nStein, W. D. (1990). Channels, Carriers and Pumps: An Introduction to Membrane Transport. New York, NY: Academic Press.\n\nStein, W. D. (1995). The sodium pump in the evolution of animal cells. Philos. Trans. R. Soc. Lond. Biol. 349, 263–269. doi: 10.1098/rstb.1995.0112\n\nStein, W. D. (2002). Cell volume homeostasis: ionic and nonionic mechanisms. The sodium pump in the emergence of animal cells. Int. Rev. Cytol. 215, 231–258. doi: 10.1016/S0074-7696(02)15011-X\n\nSterrat, D., Graham, B., Gillies, A., and Willshaw, D. (2011). Principles of Computational Modelling in Neuroscience. Cambridge University Press. doi: 10.1017/cbo9780511975899\n\nStokum, J. A., Gerzanich, V., and Simard, J. M. (2016). Molecular pathophysiology of cerebral edema. J. Cereb. Blood Flow Metab. 36, 513–538. doi: 10.1177/0271678X15617172\n\nTakeuchi, A., Tatsumi, S., Sarai, N., Terashima, K., Matsuoka, S., and Noma, A. (2006). Ionic mechanisms of cardiac cell swelling induced by blocking Na+/K+ pump as revealed by experiments and simulation. J. Gen. Physiol. 128, 495–507. doi: 10.1085/jgp.200609646\n\nTosteson, D. C., and Hoffman, J. F. (1960). Regulation of cell volume by active cation transport in high and low potassium sheep red cells. J. Gen. Physiol. 44, 169–194. doi: 10.1085/jgp.44.1.169\n\nTruskey, G. A., Yuan, F., and Katz, D. F. (2009). Transport Phenomena in Biological Systems Pearson. Upper Saddle River, NJ: Pearson Education, Inc.\n\nUllah, G., Wei, Y., Dahlem, M. A., Wechselberger, M., and Schiff, S. J. (2015). The role of cell volume in the dynamics of seizure, spreading depression, and anoxic depolarization. PLoS Comput. Biol. 11:e1004414. doi: 10.1371/journal.pcbi.1004414\n\nVarghese, A., and Sell, G. R. (1997). A conservation principle and its effect on the formulation of Na-Ca exchanger current in cardiac cells. J. Theor. Biol. 189, 33–40. doi: 10.1006/jtbi.1997.0487\n\nVereninov, I. A., Yurinskaya, V. E., Model, M. A., Lang, F., and Vereninov, A. A. (2014). Computation of pump-leak flux balance in animal cells. Cell. Physiol. Biochem. 34, 1812–1823. doi: 10.1159/000366382\n\nVereninov, I. A., Yurinskaya, V. E., Model, M. A., and Vereninov, A. A. (2016). Unidirectional flux balance of monovalent ions in cells with Na/Na and Li/Na exchange: experimental and computational studies on lymphoid U937 cells. PLoS ONE 11:e0153284. doi: 10.1371/journal.pone.0153284\n\nVerkman, A. S. (1992). Water channels in cell membranes. Annu. Rev. Physiol. 54, 97–108. doi: 10.1146/annurev.ph.54.030192.000525\n\nVoipio, J., Boron, W. F., Jones, S. W., Hopfer, U., Payne, J. A., and Kaila, K. (2014). Comment on “Local impermeant anions establish the neuronal chloride concentration.” Science 345:1130. doi: 10.1126/science.1252978\n\nWeiss, T. F. (1996). Cellular Biophysics. Vol. 1: Transport. Cambridge, MA: The MIT Press.\n\nWood, J. M. (2015). Bacterial responses to osmotic challenges. J. Gen. Physiol. 145, 381–388. doi: 10.1085/jgp.201411296\n\nYurinskaya, V. E., Rubashkin, A. A., and Vereninov, A. A. (2011). Balance of unidirectional monovalent ion fluxes in cells undergoing apoptosis: why does Na plus /K plus pump suppression not cause cell swelling? J. Physiol. Lond. 589, 2197–2211. doi: 10.1113/jphysiol.2011.207571\n\n## A. Appendix\n\n### A.1. The Keener-Sneyd Solutions\n\nHere I will present the equations that were derived by Keener and Sneyd (2009) with some new extensions that I have deduced (viz. for the case where z = −1, the instability of the system when x = 0 and the effect of knocking out Na+ or K+ transport). The NKA is assumed to operate at a constant rate p, with n and q the number of Na+ and K+ ions transported per pump cycle.\n\nAt steady state each of the current flows is zero and the system of Equations (1, 2, 4–6) can be solved exactly for the five unknowns Na, K, Cl, w, and V:\n\nI follow Keener and Sneyd in defining the following non-dimensional variables:\n\nI define:\n\nwhere $\\gamma {=}^{{g}_{na}}{/}_{{g}_{K}}$\n\nKeener and Sneyd demonstrated that for $n\\frac{N{a}_{o}}{{g}_{Na}}>q\\frac{{K}_{o}}{{g}_{K}}$ there is a range of p for which the system has a finite positive cell volume, with the following solutions:\n\nFor the case where z = −1\n\nFrom Equations (1) and (2):\n\nThen from Equations (A6) and (A7)\n\nsolving for y\n\nfrom (A4) and (A11)\n\n### A.2. A More Realistic Mathematical Representation of the NKA\n\nIn the Keener-Sneyd equations the NKA is represented by as constant term (Equations 4 and 5). To provide a more realistic representation of the NKA I incorporated its dependence on K+ and Na+ concentrations (Truskey et al., 2009). The Na+ flux is:\n\nThe K+ flux is:\n\nwhere: p′ is the maximum Na+ efflux at steady state, DNa and DK are the apparent dissociation constants for Na+ and K+. Figure A1 shows that the form of the Cp curve is maintained even with this nonlinear pump mechanism.\n\nFIGURE A1", null, "Figure A1. Cp plot of PLM with a nonlinear NKA mechanism (Equations A13 and A14). DNa = 0.8 mM and DK = 3.6 mM. The % of the minimum volume is plotted as function of p on the lowest panel.\n\n### A.3. No Impermeant Molecules (x = 0)\n\nAlthough this is clearly an impossible situation it is worth considering because it can provide insight into the action of x in the PLM.\n\nFrom Equations (1) and (2).\n\nWhen the NKA is not operating from Equation (6), V = 0, Na = Nao, K = Ko and the volume is stable. When the pump is on from Equations (4) and (5) one can calculate the distribution of Na+ and K+ as a function of pump rate and from that the membrane potential, which becomes more negative as p increases. However Cl = Clo and there is no way around that. The only thing that can give is the volume, so as one turns on the pump the volume decreases and if it is kept on, the volume will go to zero.\n\n### A.4. The Braided Structure of the Solution to the PLEs with z = −1\n\nFor the case where z = −1 from (1) and (2) as p is increased the following crossovers occur in sequence (see Figure 5 second panel from the top) and it is possible to derive analytical expressions for p at all the intersection points for the case where there is no active K+ transport (i.e., q = 0):\n\nFor Na = Cl and K = X:\n\nfor Cl = X = 0.5Πo:\n\nfor Na = X and K = Cl: For K = Cl\n\nfor Na = K = 0.5Πo:\n\nfor Na = Cl and K = X:\n\n### A.5. PLE with Different z's\n\nFIGURE A2", null, "Figure A2. Cp plots with different zs, noted on the top of each panel. The pump rate p is in C mm−2 s−1.\n\n### A.6. Mathematical Knockout of the Components of the PLE\n\nNo Na+ pumping [z = −1, n = 0]\n\nEquation (A11) becomes:\n\ny ≤ 0 and from Equation (A8) ClClo, which with Equations (1) and (2) implies that X ≤ 0 which means that x cannot be accommodated and hence the system is unstable.\n\nNo K+ pumping [z = −1, q = 0]\n\nFrom Equations (A7) and (A8)\n\nWhich is the Donnan ratio.\n\nFrom Equation (A11)\n\nSubstituting this into Equation (A6) gives:\n\nand substituting Equation (A23) into Equation (A7) gives:\n\n### A.7. Mycoplasma Model\n\nTo model mycoplasma I added an outward directed proton pump, a Na+/H+ exchanger and a proton leak in the PLM model.\n\nTo model the Na+/H+ exchanger I assume that it can be described by the following chemical equilibrium:\n\nWhere H and H0 are the inside and outside proton concentrations respectively.\n\nThe proton flux through the exchanger is then:\n\nWhere pNaH is the permeability of the exchanger. Similarly the Na+ flux though the exchanger is:\n\nThe outward proton pump is represented by the following equation:\n\nwhere pH is the strength of the pump and DH is the dissociation constant for protons.\n\nIn this model the rate of change of intracellular proton concentration is then:\n\nWhere gH is the proton conductance.\n\nThe rate of change of intracellular Na+ is then:\n\nThe proton and hydroxide (calculated assuming that the ionic product of water is 10−14 M2) ion concentrations are included in Equations (1), (2), and (8).\n\nKeywords: osmosis, ion transport, sodium chloride, potassium, impermeant anions, Donnan effect, Na+/K+ ATPase\n\nCitation: Kay AR (2017) How Cells Can Control Their Size by Pumping Ions. Front. Cell Dev. Biol. 5:41. doi: 10.3389/fcell.2017.00041\n\nReceived: 02 February 2017; Accepted: 04 April 2017;\nPublished: 08 May 2017.\n\nEdited by:\n\nSamuel Marguerat, MRC London Institute of Medical Sciences, Imperial College London, UK\n\nReviewed by:\n\nTeuta Pilizota, University of Edinburgh, UK\nAlexey Vereninov, Institute of Cytology (RAS), Russia\n\nCopyright © 2017 Kay. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.\n\n*Correspondence: Alan R. Kay, [email protected]" ]

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[ "# antenna gain, calculating voltage scaling\n\nI am working on a software defined radio project, but I am kind of new to antennas. There's so much info out there on antennas that I'm having trouble finding the answer to my specific question. Hopefully asking here will speed up my understanding.\n\nSuppose I have an Antenna connected to a proper termination load (50 ohms) with all the proper transmission lines with the proper characteristic impedance. We will assume just about everything is 100% efficient for simplicity. I have an ADC that is monitoring the voltage at that termination load. The ADC is much faster than the received carrier frequencies, so I can extract actual waveforms. I emit some RF energy into my antenna at a \"good\" azimuth angle, say 0 degrees, which should have a gain of 0 dB according to my antenna's gain plot. I measure the voltage from my ADC over time and it shows I have a 200mV peak sinusoid. I then rotate my antenna such that the emitter is at an angle, say 45 degrees, in which my antenna's gain plot says it should be -4dB. What is the amplitude of the waveform I will measure now?\n\nHere is my guess: The power received from 0 degrees is : P0 = (0.2/sqrt(2))^2 / R. Note that I used the RMS voltage. My power gain in..non-log(?) will be : PG = (dB/10)^10 = (-4/10)^10 = 0.0001048576. That means the power at 45 degrees will be a scaled version of 0 degrees: P45 = PG*P0. Solve for voltage using power equation: Vans = sqrt(2*P45*R). The R's will cancel when you simplify. I got an answer of 2.048 mV peak sinusoid.\n\n• Where did you get $(-4/10)^2=0.000105$? I get 0.16. – The Photon Mar 14 '16 at 23:25\n• $10^{-0.4}$ is even bigger than that. – The Photon Mar 14 '16 at 23:26\n• Sorry, I mistakenly wrote ^2 instead of ^10. I edited original post. – user2913869 Mar 15 '16 at 1:15\n• You should be taking $10^{x/10}$ instead of $(x/10)^{10}$ to convert from dB to power ratios. – The Photon Mar 15 '16 at 2:00\n\n-4 dB in power is also -4 dB in voltage (since you are comparing voltages across the same impedance, 50 ohms).\n\nIn converting a voltage ratio we use 20log. In converting a power ratio we use 10log. Thus the voltage will be reduced by a factor of 10^(-4/20) = 0.631. Thus the 200 mV peak sinewave, reduced by -4 dB, will become 126 mV peak.\n\n• +1. I hope you think my little tweak is an improvement. If not, feel free to revert. – davidcary Mar 15 '16 at 16:29\n\nI then rotate my antenna such that the emitter is at an angle, say 45 degrees, in which my antenna's gain plot says it should be -4dB. What is the amplitude of the waveform I will measure now?\n\nIf your unrotated-antenna signal is 200 mV then after rotation it is 4 dB lower. 4 dB is a numerical reduction of: -\n\n$10^{\\frac{4}{20}}$ = 1.585\n\nSo your 200 mV signal reduces to 126 mV" ]

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[ "# Excel RATE function: formula examples to calculate interest rate\n\nThis tutorial explains how to calculate interest rate on recurring deposit in Excel by using the RATE function.\n\nFinancial decisions are an important element of business strategy and planning. In everyday life, we also have quite a lot of financial decisions to make. For instance, you are going to apply for a loan to buy a new car. It will surely be helpful to know exactly what interest rate you will have to pay to your bank. For such scenarios, Excel provides the RATE function that is specially designed for calculating interest rate for a specific period.\n\n## Excel RATE function\n\nRATE is an Excel financial function that finds an interest rate per a given period of an annuity. The function calculates by iteration and can have no or more than one solution.\n\nThe function is available in all versions Excel 365, Excel 2019, Excel 2016, Excel 2013, Excel 2010 and Excel 2007.\n\nThe syntax is as follows:\n\nRATE(nper, pmt, pv, [fv], [type], [guess])\n\nWhere:\n\n• Nper (required) - the total number of payment periods such as years, months, quarters, etc.\n• Pmt (required) - the fixed payment amount per period that cannot be changed over the life of the annuity. Usually, it includes principal and interest, but no taxes.\n• Pv (required) - the present value, i.e. the current value of the loan or investment.\n• Fv (optional) - the future value, i.e. the cash balance you wish to have after the last payment. If omitted, it defaults to 0.\n• Type (optional) - indicates when the payments are made:\n• 0 or omitted (default) - payment is due at the end of the period\n• 1 - payment is due at the beginning of the period\n• Guess (optional) - your assumption for what the rate might be. If omitted, it defaults to 10%.\n\n### 6 things you should know about Excel RATE function\n\nTo efficiently use RATE formulas in your worksheets, please pay attention to these usage notes:\n\n1. The RATE function calculates through trial and error. If it fails to converge to a solution after 20 iterations, a #NUM! error is returned.\n2. By default, an interest rate is calculated per payment period. But you can derive an annual interest rate by multiplication as shown in this example.\n3. Use positive numbers to represent cash that you receive (inflows) and negative numbers to represent cash that you pay out (outflows).\n4. Although the RATE syntax describes pv as the required argument, it can actually be omitted if you include the fv argument. Such syntax is typically used for calculating interest rate on a saving account.\n5. The guess argument can be omitted in most cases because it's just a starting value for an iterative procedure.\n6. When calculating RATE for different periods, make sure you are consistent with the values supplied for nper and guess. For example, if you are to make annual payments on a 3-year loan at 8% annual interest, use 3 for nper and 8% for guess. If you are going to make monthly payments on the same loan, then use 3*12 for nper and 8%/12 for guess.\n\n## Basic RATE formula in Excel\n\nIn this example, we'll look at how to make a RATE formula in its simplest form to calculate interest rate in Excel.\n\nLet's say you've borrowed \\$10,000 that should be paid in full over the next three years. You are planning to pay 3 yearly installments of \\$3,800 each. What will the annual interest rate be?\n\nTo find it out, we define the following arguments for the Excel RATE function:\n\n• Nper in C2 (number of payments): 3\n• Pmt in C3 (payment amount): -3,800\n• Pv in C4 (loan amount): 10,000\n\nPlease notice that we specify annual payment (pmt) as a negative number because it's outgoing cash.\n\nIt's assumed that the payment is to be made at the end of each year, so we can omit the [type] argument or set it to the default value (0). The other two optional arguments [fv] and [guess] are also omitted.\n\nAs the result, we get this simple formula:\n\n`=RATE(C2, C3, C4)`", null, "If it is required that the payment be entered as a positive number, then put the minus sign before the pmt argument directly in the formula:\n\n`=RATE(C2, -C3, C4)`", null, "## How to calculate interest rate in Excel - formula examples\n\nNow that you know the essentials of using RATE in Excel, let's explore a couple of specific use cases.\n\n### How to calculate monthly interest rate on a loan\n\nSince most installment loans are paid monthly, it may be helpful to know a monthly interest rate, right? For this, you just need to supply an appropriate number of payment periods to the RATE function.\n\nSuppose the loan is to be paid over 3 years in monthly installments. To get the total number of payments, we multiply 3 years by 12 months (3*12=36).\n\nThe other parameters are shown below:\n\n• Nper in C2 (number of periods): 36\n• Pmt in C3 (monthly payment): -300\n• Pv in C4 (loan amount): 10,000\n\nAssuming the payment is due at the end of each month, you can find a monthly interest rate by using the already familiar formula:\n\n`=RATE(C2, C3, C4)`\n\nCompared to the previous example, the difference is only in the values used for the RATE arguments. Because the function returns an interest rate is for a given payment period, we get a monthly interest rate as the result:", null, "If your source data includes the number of years over which the loan must be repaid, you can do the multiplication inside the nper argument:\n\n`=RATE(C2*12, C3, C4)`", null, "### How to calculate annual interest rate in Excel\n\nTaking our example a little further, how do you find annual interest rate for monthly payments? Simply by multiplying the RATE result by the number of periods per year, which is 12 in our case:\n\n`=RATE(C2, C3, C4) * 12`\n\nThe below screenshot lets you compare the monthly interest rate in C7 and the annual interest rate in C9:", null, "What if the payments are to be made at the end of each quarter?\n\nFirst, you convert the total number of periods into quarterly:\n\nNper: 3 (years) * 4 (quarters per year) = 12\n\nThen, use the RATE function to calculate the quarterly interest rate (C7):\n\n`=RATE(C2, C3, C4)`\n\nAnd multiply the result by 4 to get the annual interest rate (C9):\n\n`=RATE(C2, C3, C4) * 4`", null, "### How to find interest rate on saving account\n\nIn the above examples, we were dealing with loans and calculated the interest rate based on three primary components: loan term, payment amount per period, and loan amount.\n\nAnother common scenario is finding an interest rate on a series of periodic cash flows where we know the future value, not the present value.\n\nAs an example, let's calculate an interest rate required to save up \\$100,000 in 5 years, provided you make the \\$1,500 payment at the end of each month with zero initial investment.\n\nTo have it done, we define the following variables:\n\n• Nper in C2 (total number of payments): 5*12\n• Pmt in C3 (monthly payment): -1,500\n• Fv in C4 (desired future value): 100,000\n\nTo calculate monthly interest rate, the formula in C6 is:\n\n`=RATE(C2*12, C3, ,C4)`\n\nPlease note that C2 contains the number of years. To get the total number of payment periods, we multiply it by 12.\n\nTo get annual interest rate, we multiply the monthly rate by 12. So, the formula in C8 is:\n\n`=RATE(C2*12, C3, ,C4) * 12`", null, "### How to find compound annual growth rate on investment\n\nThe RATE function in Excel can also be used for calculating the compound annual growth rate (CAGR) on an investment over a given period of time.\n\nSupposing you want to invest \\$100,000 for 5 years and receive \\$200,000 in the end. How will your investment grow in terms of CAGR? To find that out, you set up the following arguments for the RATE function:\n\n• Nper (C2): 5\n• Pv (C3): -100,000\n• Fv (C4): 200,000\n\nPlease pay attention that the pmt argument is not used in this case, so we leave it blank in the formula:\n\n`=RATE(C2, ,C3, C4)`\n\nAs the result, the Excel RATE function tells us that our investment has earned the 14.87% compound annual growth rate over 5 years.", null, "## Create interest rate calculator in Excel\n\nAs you may have noticed, the previous examples focused on solving specific tasks. This time, our goal is to create a universal interest rate calculator for annuity, which is a series of equal payments made at regular intervals.\n\nSince we will be using an Excel RANK formula in its full form, we need to provide cells for all the arguments, including the optional ones:\n\n• Total number of payments (nper) - C2\n• Payment amount (pmt) - C3\n• Annuity present value (pv) - C4\n• Annuity future value (fv) - C5\n• Annuity type (type) - C6\n• Estimated interest rate (guess) - C7\n• Number of periods per year - C8\n\nTo test our calculator in practice, let's try to find a monthly and annual interest on a saving account that will ensure \\$100,000 at the end of 5 years with a monthly payment of \\$1,500 made at the beginning of each period.\n\nWe input the variables in corresponding cells like shown in the image below, and enter the following formulas:\n\nIn C10, return a periodic interest rate:\n\n`=RATE(C2, C3, C4, C5, C6, C7)`\n\nIn C11, output an annual interest rate:\n\n`=RATE(C2, C3, C4, C5, C6, C7) * C8`\n\nFor our sample data, the results look as follows:", null, "• For nper, we input 60 (5 years * 12 months = 60 payment periods).\n• For type, we input 1 (payment is due at the beginning of the period). To prevent mistakes, it makes sense to create a drop-down list in C6 to only allow 0 and 1 values for the type argument.\n• If pv is 0 or not defined (like in this example), be sure to specify the fv argument.\n\n## Excel RATE function not working\n\nThe more complex the function, the greater chance of an error. The RATE syntax is quite simple, but it still leaves room for mistakes, especially if you have little experience with Excel financial functions. Below, we will point out a few common errors and how to fix them.\n\n### #NUM! error\n\nReason: occurs when the RANK function fails to find a solution.\n\nMost often, this happens because positive numbers are used to represent outgoing cash flows. Please remember to put the minus sign before any amount that is paid out:", null, "In some cases, you may need to help the RANK function to converge to a solution by providing an initial guess:", null, "When calculating an interest rate with an undefined or zero present value (pv), be certain to specify the future value (fv):", null, "### #VALUE! error\n\nReason: occurs when one or more arguments are non-numeric.\n\nTo fix the error, double check the values used for the RANK arguments and make sure your numbers are not formatted as text.\n\n### RATE function returns incorrect result\n\nSymptom: The result of your RANK formula is a negative percentage, or much lower or higher than expected.\n\nReason: When calculating monthly or quarterly payments, you forgot to convert the number of years to the total number of payment periods. Or a periodic interest rate is not converted to an annual interest rate.\n\nTo resolve this issue, use the following calculations to express the nper argument in appropriate units:\n\nMonthly payments: nper = years * 12\n\nQuarterly payments: nper = years * 4\n\nTo get an annual interest rate, multiply a periodic interest rate returned by the function by the number of periods per year.\n\nMonthly payments: annual interest rate = RATE() * 12\n\nQuarterly payments: annual interest rate = RATE() * 4", null, "### RATE formula returns zero percentage\n\nSymptom: The result of the formula appears as zero percentage with no decimal places (0%).\n\nReason: The calculated interest rate is less than 1%. Because the formula cell is formatted to show no decimal places, the displayed value is \"rounded\" to zero.\n\nTo solve this problem, simply apply the Percentage format with two or more decimal places to the cell containing your formula.", null, "That's how to use RATE function in Excel to calculate interest rate. I thank you for reading and hope to see you on our blog next week!\n\nExamples of RATE formula in Excel (.xlsx file)\n\n## You may also be interested in:\n\n### 3 comments to \"Excel RATE function: formula examples to calculate interest rate\"\n\n1.", null, "Angela says:\n\nHi, I'd really appreciate some help figuring out a way to combine the two formulas below into one. I've tried everything I can think of. They work separately but I need to combine them so that the answer from whichever one has an answer pulls that value into another cell.\n=IF(AND(B4>0,B6>0),B4/B6,0)\n=(IF(AND(B2>0,B3>0),((B2*B3)/B6),0))\n\n2.", null, "Gurinder Singh says:\n\nHi\n\nDo we have any formula to calculate the interest rate if there is a balloon payment at the end of the loan. Please see the below example;\n\nPrinciple: \\$340,876.21\nStart Date: 20/07/2021\nNormal Payments: 60 @ \\$5,575.72\nBallon Payment: \\$63,000\nInterest Payable: \\$56,666.99\n\nPlease provide formula to workout the interest rate so I can prepare the amortisation schedule.\n\nThanks" ]

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[ "-=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- (c) WidthPadding Industries 1987 0|370|0 -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- -=+=- Socoder -> Mystery Boxes Older Topics --> Return of Degustabox Started by Jayenkai Last post by rockford on Tue 17:37, 26-07-22 Monthly Tee Club Started by Jayenkai Last post by Jayenkai on Wed 08:04, 20-01-21 CreationCrate Started by Jayenkai Last post by rockford on Fri 14:24, 28-12-18 LootCrate Started by Jayenkai Last post by Jayenkai on Thu 07:13, 11-10-18 GamerBlock Started by Jayenkai Last post by Jayenkai on Tue 13:51, 17-04-18 NerdBlock Started by Jayenkai Last post by rockford on Sat 09:02, 14-01-17 Older Topics -->" ]

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[ "Author: Oscar Cronquist Article last updated on January 08, 2019", null, "This blog post describes how to insert qualifers to make \"text to columns\" conversion easier.\n\nExample\n\nI copied a table from Wells Fargo annual report (pdf), see image above. Paste it into an excel sheet.", null, "I then used \"Text to Columns\":\n\n1. Select column A\n2. Go to tab \"Data\"\n3. Press with left mouse button on \"Text to Columns\" button.\n\nI got the following result, see image below. Each word is split into a column each, this is not what is wanted.", null, "The table is a mess, however, the \"text to columns\" wizard allows you to select a text qualifer to convert words into a single cell.", null, "This custom function inserts ' (apostrophe) before and after text. The rules are if a character is a number and the next character is a letter then insert an apostrophe before the letter.\n\nThe same thing if a character is a letter and the next character is number then insert a apostrophe before the number.\n\n```Function Ins_text_qualifiers(Str)\nDim TLen As Long\nDim i As Long\nDim j As Long\nTLen = Len(Str)Str = Trim(Str)\nFor i = 1 To TLen\nIf j = TLen + 1 Then Exit For\nIf Asc(Mid(Str, i, 1)) >= 65 And Asc(Mid(Str, i, 1)) <= 90 _\nOr Asc(Mid(Str, i, 1)) >= 97 And Asc(Mid(Str, i, 1)) <= 122 Then\nStr = Left(Str, i - 1) & \"'\" & Mid(Str, i, TLen)\ni = i + 1\nFor j = i To TLen\nIf Asc(Mid(Str, j, 1)) >= 48 And Asc(Mid(Str, j, 1)) <= 57 Then\nStr = Left(Str, j - 2) & \"'\" & Mid(Str, j - 1, TLen)\ni = j\nExit For\nEnd If\nNext j  End IfNext i\nIf Asc(Mid(Str, Len(Str), 1)) >= 65 And Asc(Mid(Str, Len(Str), 1)) <= 90 _\nOr Asc(Mid(Str, Len(Str), 1)) >= 97 And Asc(Mid(Str, Len(Str), 1)) <= 122 Then Str = Str & \"'\"\nIns_text_qualifiers = Str\nEnd Function\n```\n\n### Example\n\nper share amounts) 2009 2008 2007 2006 2005 2004 2008 growth rate\n\nbecomes\n\n'per share amounts) ' 2009 2008 2007 2006 2005 2004 2008 'growth rate'\n\n### The final result", null, "It is not perfect but it is a lot better.", null, "(The macro shown in the image above is not used in this article, it only shows you where to paste the code.)\n\n1. Press Alt-F11 to open the visual basic editor\n2. Press with left mouse button on Module on the Insert menu\n3. Copy and paste the above user defined function\n4. Exit visual basic editor\n5. Select a cell (B1)\n6. Type =Ins_text_qualifiers(A1) into formula bar and press ENTER\n\n### Text to columns (Excel 2007)\n\n1. Select \"Data\" tab on the ribbon\n2. Press with left mouse button on \"Text to columns\" button\n\n### Get the Excel file", null, "text-qualifier1.xls" ]

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[ "# Tolerance interval basics\n\n## What is a tolerance interval?\n\nUse tolerance intervals to compute a range of values for a product's characteristic that likely covers a specified proportion of future product output. A tolerance interval defines the upper and/or lower bounds within which a certain percent of the process output falls with a stated confidence.\n\nTo generate tolerance intervals, you must specify both a minimum percentage of the population and a confidence level. Traditionally, both values are close to 100. The percentage is the minimum percentage of the population that you want the interval to cover. The confidence level is the likelihood that an interval will actually cover the minimum percentage.\n\nFor example, a parts manufacturer wants to determine the limits that define where 99% of the parts lengths with 95% confidence will be, and compare this range to the customer specifications. Analysts randomly sample 30 parts and record the width in millimeters (mm). The tolerance interval states with 95% confidence that 99% of the population have widths that fall within the interval [5, 8]. The manufacturer is 95% confident that 99% of all parts will have widths that are between 5 and 8 mm. If this range is wider than the clients' requirements, then the process may produce excessive waste.\n###### Note\n\nMinitab uses defaults of 95% for both confidence level and minimum percentage of population in the interval.\n\n## How do tolerance intervals differ from confidence intervals and prediction intervals?\n\nConfidence intervals (CI), prediction intervals (PI) and tolerance intervals are commonly used intervals derived from sample statistics.\nConfidence interval\nA range of values that is likely to contain the value of an unknown population parameter, such as the mean, with a specified degree of confidence.\nFor example, if the 95% CI of the average fill volume of 375 ml bottles is 368–372 ml, you can be 95% confident that the true value of the process mean is within this interval.\nPrediction interval\nA range of values for a product's characteristic that represents where the value of a single new observation is likely to fall with a specified degree of confidence.\nFor example, if the 95% PI of the average fill volume of 375 ml bottles is 360–379 ml, you can be 95% confident that the next sampled bottle will have a fill volume that is within this interval.\nTolerance interval\nA range of values for a product's characteristic that likely covers where a specified proportion of the population lies with a specified degree of confidence.\nFor example, if the 95% tolerance interval for 99% of the population for the fill volume of 375 ml bottles is 358–381 ml, you can be 95% confident that 99% of the bottles to be filled in the future will have volumes that are within this interval.\n\n## Parametric and nonparametric methods\n\nMinitab can calculate tolerance intervals using a parametric method, like the method that uses the normal distribution, or a nonparametric method. Use the intervals that match your situation, as follows:\nParametric method\nIf your data follow a distribution, then a parametric method is more precise and economical than the nonparametric method. A parametric method allows you to achieve smaller margins of error with fewer observations, as long as the chosen distribution is appropriate for your data. Use the parametric method if you know from prior experience or analysis that your population follows a known distribution. A goodness-of-fit test, such as the one that Minitab includes with Stat > Quality Tools > Individual Distribution Identification, can help you decide if your data follow a distribution. Use Tolerance intervals (Normal distribution) if your data follow a normal distribution. Use Tolerance intervals (Nonnormal distribution) if your data follow one of the following distributions:\n• Lognormal\n• Gamma\n• Exponential\n• Smallest extreme value\n• Weibull\n• Largest extreme value\n• Logistic\n• Loglogistic\nMinitab includes a specific goodness-of-fit test with any tolerance interval so that you can assess the distribution.\nNonparametric method\nParametric methods are not robust to severe departures from the distribution. If you are unsure of the parent distribution, or you know that the parent distribution is not in Minitab, then use the nonparametric method. The nonparametric method requires only that the data are continuous.\nThe nonparametric method usually requires larger sample sizes than the parametric method. For example, if the minimum percentage of the population in the interval is 95%, the sample size should be approximately 90 or more for the tolerance interval to be accurate. Larger percentages of the population in the interval require larger sample sizes. For example, if the minimum percentage of the population in the interval is 99%, the sample size should be approximately 500 or more to obtain an accurate two-sided 95% tolerance interval. To have an accurate tolerance interval, the achieved confidence level must be close to your target confidence level. If your sample size is not large enough, the nonparametric interval is a non-informative interval that ranges from negative infinity to infinity. In this case, Minitab displays a finite interval based on the range of your data. As a result, the achieved confidence level is much lower than the target confidence level.\nTo determine an appropriate sample size for a tolerance interval that meets your accuracy and precision objectives, go to Stat > Power and Sample Size > Sample Size for Tolerance Intervals .\nBy using this site you agree to the use of cookies for analytics and personalized content.  Read our policy" ]

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[ "# Extrema on high degree polynomial\n\n## Homework Statement\n\nFind any extrema, points of inflection, asymptotes, and symmetry for function.\n\n## Homework Equations\n\nf(x) = (x^5-10x^3+9x) / ( x^4 - 16)\n\n## The Attempt at a Solution\n\nExtrema: I took the first derivative by using the Quotient Rule, and got\n\n(x^8 + 10x^6 - 107x^4 + 480x^2 - 144) / ( x^4 - 16)^2\n\nI know that to find an extrema, I need to determine the critical numbers. Which are when f ' is equal to 0 or is undefined. I determined that \"2\" makes f ' undefined, but it also is not defined in the original function, f(x), so that is not a critical number. But I cannot for the life of me figure out how to factor the numerator when set to 0.\n\nI tried to graph f ' , and it seems like x = 0 is a critical number, but when i plug it into the numerator it gives me -144...I feel like I am missing something, can someone please help me figure out how to determine the critical numbers please? I think I'm having more algebra issues than calculus.\n\nThen there's the possibility that I took the wrong first derivative. If someone could check me on that, I would be thankful.\n\nRelated Calculus and Beyond Homework Help News on Phys.org\nMark44\nMentor\n\n## Homework Statement\n\nFind any extrema, points of inflection, asymptotes, and symmetry for function.\n\n## Homework Equations\n\nf(x) = (x^5-10x^3+9x) / ( x^4 - 16)\n\n## The Attempt at a Solution\n\nExtrema: I took the first derivative by using the Quotient Rule, and got\n\n(x^8 + 10x^6 - 107x^4 + 480x^2 - 144) / ( x^4 - 16)^2\nYour derivative is incorrect. I get\nf'(x) = (5x^8 - 4x^7 + 10x^6 - 107x^4 + 480x^2 - 144)/(x^4 - 16)^2\n\nEdit: My mistake. My brain misfired when I added 5 and 3 and got 7. It should be\nf'(x) = (x^8 + 10x^6 - 107x^4 + 480x^2 - 144)/(x^4 - 16)^2\nI know that to find an extrema, I need to determine the critical numbers. Which are when f ' is equal to 0 or is undefined. I determined that \"2\" makes f ' undefined, but it also is not defined in the original function, f(x), so that is not a critical number. But I cannot for the life of me figure out how to factor the numerator when set to 0.\nf is undefined at x = 2 and x = -2, which you can see by factoring the denominator in f(x).\nI tried to graph f ' , and it seems like x = 0 is a critical number, but when i plug it into the numerator it gives me -144...I feel like I am missing something, can someone please help me figure out how to determine the critical numbers please? I think I'm having more algebra issues than calculus.\nIt might be helpful to sketch a graph of the function first. That way you could get an idea of approximately where the minima and maxima are. The numerator of your function factors easily, making it easy to find the five x-intercepts for the graph of the function. The denominator also factors easily. Since there are no factors in common between the numerator and denominator, there will be four vertical asymptotes.\n\nIf you divide the numerator by the denominater, you get x + a proper rational function, which means that there is a slant asymptote (i.e., the graph of the function eventually approaches the graph of y = x).\n\nTo find the zeroes of the numerator of f'(x), you'll probably need to use the rational root theorem. In a polynomial anxn + ... + a1x + a0 = 0, any rational roots p/q are such that p divides a0 and q divides an. For your problem, the polynomial you're trying to factor is 5x^8 - 4x^7 + 10x^6 - 107x^4 + 480x^2 - 144, so p has to divide 144 and q has to divide 5. Fortunutely 5 has factors only of +/-1 and +/-5. If you drew a graph of y = f(x), there will be many potential candidates that you won't need to check.\n\nThen there's the possibility that I took the wrong first derivative. If someone could check me on that, I would be thankful.\n[/quote]\n\nLast edited:\nphyzguy\nIt looks like you took the first derivative correctly. Try plotting out f and f' to identify the extrema, points of inflection, etc.\n\nExtrema: I took the first derivative by using the Quotient Rule, and got\n\n(x^8 + 10x^6 - 107x^4 + 480x^2 - 144) / ( x^4 - 16)^2\nFor what it's worth, I got the same first derivative as you did.\n\ny'=[(x^4-16)(5x^4-30x^2+9) - (x^5-10x^3+9x)(4x^3)]/(x^4-16)^2\n\n=(5x^8-30x^6-71x^4+480x^2-144-4x^8+40x^6-36x^4)/(x^4-16)^2\n\n=(x^8+10x^6-107x^4+480x^2-144)/(x^4-16)^2\n\nMark44\nMentor\nphyzguy and JOhnJDC, you are correct." ]

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[ "# 8.2: Work- The Scientific Definition\n\nLearning Objectives\n\nBy the end of this section, you will be able to:\n\n• Explain how an object must be displaced for a force on it to do work.\n• Explain how relative directions of force and displacement determine whether the work done is positive, negative, or zero.\n\n## What It Means to Do Work\n\nThe scientific definition of work differs in some ways from its everyday meaning. Certain things we think of as hard work, such as writing an exam or carrying a heavy load on level ground, are not work as defined by a scientist. The scientific definition of work reveals its relationship to energy—whenever work is done, energy is transferred. For work, in the scientific sense, to be done, a force must be exerted and there must be motion or displacement in the direction of the force.\n\nFormally, the work done on a system by a constant force is defined to be the product of the component of the force in the direction of motion times the distance through which the force acts. For one-way motion in one dimension, this is expressed in equation form as\n\n$W = |\\vec{F}| \\, \\cos \\, \\theta |\\vec{d}| \\label{eq1}$\n\nwhere $$W$$ is work, $$d$$ is the displacement of the system, and $$\\theta$$ is the angle between the force vector $$\\vec{F}$$ and the displacement vector $$\\vec{d}$$, as in Figure $$\\PageIndex{1}$$. We can also write Equation \\ref{eq1} as\n\n$W = F \\, d \\, \\cos \\, \\theta \\label{eq2}$\n\nTo find the work done on a system that undergoes motion that is not one-way or that is in two or three dimensions, we divide the motion into one-way one-dimensional segments and add up the work done over each segment.\n\nWhat is Work?\n\nThe work done on a system by a constant force is the product of the component of the force in the direction of motion times the distance through which the force acts. For one-way motion in one dimension, this is expressed in equation form as\n\n$W = F \\, d \\, \\cos \\, \\theta$\n\nwhere $$W$$ is work, $$F$$ is the magnitude of the force on the system, $$d$$ is the magnitude of the displacement of the system, and $$\\theta$$ is the angle between the force vector $$F$$ d the displacement vector $$d$$.", null, "Figure $$\\PageIndex{1}$$: Examples of work. (a) The work done by the force $$F$$ on this lawn mower is $$Fd \\, cos \\,\\theta$$. Note that $$F \\, cos \\, \\theta$$ is the component of the force in the direction of motion. (b) A person holding a briefcase does no work on it, because there is no motion. No energy is transferred to or from the briefcase. (c) The person moving the briefcase horizontally at a constant speed does no work on it, and transfers no energy to it. (d) Work is done on the briefcase by carrying it upstairs at constant speed, because there is necessarily a component of force $$F$$ in the direction of the motion. Energy is transferred to the briefcase and could in turn be used to do work. (e) When the briefcase is lowered, energy is transferred out of the briefcase and into an electric generator. Here the work done on the briefcase by the generator is negative, removing energy from the briefcase, because $$F$$ and $$d$$ are in opposite directions.\n\nTo examine what the definition of work means, let us consider the other situations shown in Figure. The person holding the briefcase in Figure $$\\PageIndex{1b}$$does no work, for example. Here $$d = 0$$, so $$W = 0$$. Why is it you get tired just holding a load? The answer is that your muscles are doing work against one another, but they are doing no work on the system of interest (the “briefcase-Earth system” - see Gravitational Potential Energy for more details). There must be motion for work to be done, and there must be a component of the force in the direction of the motion. For example, the person carrying the briefcase on level ground in Figure $$\\PageIndex{1c}$$ does no work on it, because the force is perpendicular to the motion. That is, $$\\cos \\, 90^o = 0$$, so $$W = 0$$.\n\nIn contrast, when a force exerted on the system has a component in the direction of motion, such as in Figure $$\\PageIndex{1d}$$, work is done—energy is transferred to the briefcase. Finally, in Figure $$\\PageIndex{1e}$$, energy is transferred from the briefcase to a generator. There are two good ways to interpret this energy transfer. One interpretation is that the briefcase’s weight does work on the generator, giving it energy. The other interpretation is that the generator does negative work on the briefcase, thus removing energy from it. The drawing shows the latter, with the force from the generator upward on the briefcase, and the displacement downward. This makes $$\\theta = 180^o$$, and $$\\cos \\, 180^o = -1$$, therefore $$W$$ is negative.\n\n## Calculating Work\n\nWork and energy have the same units. From the definition of work, we see that those units are force times distance. Thus, in SI units, work and energy are measured in newton-meters. A newton-meter is given the special name joule (J), and $$1 \\, J = 1 \\, N \\cdot m = 1 \\, kg \\, m^2/s^2$$. One joule is not a large amount of energy; it would lift a small 100-gram apple a distance of about 1 meter.\n\nExample $$\\PageIndex{1}$$: Calculating the Work You Do to Push a Lawn Mower Across a Large Lawn\n\nHow much work is done on the lawn mower by the person in Figure (a) if he exerts a constant force of 75.0 N at an angle $$35^o$$ below the horizontal and pushes the mower 25 m. on level ground? Convert the amount of work from joules to kilocalories and compare it with this person’s average daily intake of 10,000 kJ (about 2400 kcal) of food energy. One calorie (1 cal) of heat is the amount required to warm 1 g of water by $$1^o C$$ and is equivalent to 4,184 J, while one food calorie (1 kcal) is equivalent to 4,184 J.\n\nStrategy\n\nWe can solve this problem by substituting the given values into the definition of work done on a system, stated in the equation $$W = Fd \\, cos \\, \\theta$$. The force, angle, and displacement are given, so that only the work $$W$$ is unknown.\n\nSolution\n\nThe equation for the work is (Equation \\ref{eq2}):\n\n$W = Fd \\, \\cos \\, \\theta \\nonumber$\n\nSubstituting the known values gives\n\n\\begin{align*} W &= (75 \\, N)(25.0 \\, m)(cos \\, 35^o) \\\\[5pt] &= 1536 \\, J \\nonumber \\\\[5pt] &= 1.54 \\times 10^3 \\, J \\nonumber \\end{align*}\n\nConverting the work in joules to kilocalories yields $$W = (1536 \\, J)(1 \\, kcal/4184 \\, J) = 0.367 kcal.$$ The ratio of the work done to the daily consumption is\n\n$\\dfrac{W}{2400 \\, kcal} = 1.53 \\times 10^{-4}. \\nonumber$\n\nDiscussion\n\nThis ratio is a tiny fraction of what the person consumes, but it is typical. Very little of the energy released in the consumption of food is used to do work. Even when we “work” all day long, less than 10% of our food energy intake is used to do work and more than 90% is converted to thermal energy or stored as chemical energy in fat.\n\n## Summary\n\n• Work is the transfer of energy by a force acting on an object as it is displaced.\n• The work $$W$$ that a force $$F$$ does on an object is the product of the magnitude $$F$$ of the force, times the magnitude $$d$$ of the displacement, times the cosine of the angle $$\\theta$$ between them. In symbols, $W = Fd \\, \\cos \\, \\theta.$\n• The SI unit for work and energy is the joule (J), where $$1 \\, J = 1 \\, N \\cdot m = 1 \\, kg \\, m^2/s^2$$.\n• The work done by a force is zero if the displacement is either zero or perpendicular to the force.\n• The work done is positive if the force and displacement have the same direction, and negative if they have opposite direction.\n\n## Glossary\n\nenergy\nthe ability to do work\nwork\nthe transfer of energy by a force that causes an object to be displaced; the product of the component of the force in the direction of the displacement and the magnitude of the displacement\njoule\nSI unit of work and energy, equal to one newton-meter" ]

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", 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[ "", null, "### Get started with Spring 5 and Spring Boot 2, through the Learn Spring course:\n\n>> CHECK OUT THE COURSE\n\n## 1. Overview\n\nOne of the most welcome changes in Java 8 was the introduction of lambda expressions, as these allow us to forego anonymous classes, greatly reducing boilerplate code and improving readability.\n\nMethod references are a special type of lambda expressions. They're often used to create simple lambda expressions by referencing existing methods.\n\nThere are four kinds of method references:\n\n• Static methods\n• Instance methods of particular objects\n• Instance methods of an arbitrary object of a particular type\n• Constructor\n\nIn this tutorial, we'll explore method references in Java.\n\n## 2. Reference to a Static Method\n\nWe'll begin with a very simple example, capitalizing and printing a list of Strings:\n\n``List<String> messages = Arrays.asList(\"hello\", \"baeldung\", \"readers!\");``\n\nWe can achieve this by leveraging a simple lambda expression calling the StringUtils.capitalize() method directly:\n\n``messages.forEach(word -> StringUtils.capitalize(word));``\n\nOr, we can use a method reference to simply refer to the capitalize static method:\n\n``messages.forEach(StringUtils::capitalize);``\n\nNotice that method references always utilize the :: operator.\n\n## 3. Reference to an Instance Method of a Particular Object\n\nTo demonstrate this type of method reference, let's consider two classes:\n\n``````public class Bicycle {\n\nprivate String brand;\nprivate Integer frameSize;\n// standard constructor, getters and setters\n}\n\npublic class BicycleComparator implements Comparator {\n\n@Override\npublic int compare(Bicycle a, Bicycle b) {\nreturn a.getFrameSize().compareTo(b.getFrameSize());\n}\n\n}``````\n\nAnd, let's create a BicycleComparator object to compare bicycle frame sizes:\n\n``BicycleComparator bikeFrameSizeComparator = new BicycleComparator();``\n\nWe could use a lambda expression to sort bicycles by frame size, but we'd need to specify two bikes for comparison:\n\n``````createBicyclesList().stream()\n.sorted((a, b) -> bikeFrameSizeComparator.compare(a, b));``````\n\nInstead, we can use a method reference to have the compiler handle parameter passing for us:\n\n``````createBicyclesList().stream()\n.sorted(bikeFrameSizeComparator::compare);``````\n\nThe method reference is much cleaner and more readable, as our intention is clearly shown by the code.\n\n## 4. Reference to an Instance Method of an Arbitrary Object of a Particular Type\n\nThis type of method reference is similar to the previous example, but without having to create a custom object to perform the comparison.\n\nLet's create an Integer list that we want to sort:\n\n``List<Integer> numbers = Arrays.asList(5, 3, 50, 24, 40, 2, 9, 18);``\n\nIf we use a classic lambda expression, both parameters need to be explicitly passed, while using a method reference is much more straightforward:\n\n``````numbers.stream()\n.sorted((a, b) -> a.compareTo(b));\nnumbers.stream()\n.sorted(Integer::compareTo);``````\n\nEven though it's still a one-liner, the method reference is much easier to read and understand.\n\n## 5. Reference to a Constructor\n\nWe can reference a constructor in the same way that we referenced a static method in our first example. The only difference is that we'll use the new keyword.\n\nLet's create a Bicycle array out of a String list with different brands:\n\n``List<String> bikeBrands = Arrays.asList(\"Giant\", \"Scott\", \"Trek\", \"GT\");``\n\nFirst, we'll add a new constructor to our Bicycle class:\n\n``````public Bicycle(String brand) {\nthis.brand = brand;\nthis.frameSize = 0;\n}\n``````\n\nNext, we'll use our new constructor from a method reference and make a Bicycle array from the original String list:\n\n``````bikeBrands.stream()\n.map(Bicycle::new)\n.toArray(Bicycle[]::new);\n``````\n\nNotice how we called both Bicycle and Array constructors using a method reference, giving our code a much more concise and clear appearance.\n\n## 6. Additional Examples and Limitations\n\nAs we've seen so far, method references are a great way to make our code and intentions very clear and readable. However, we can't use them to replace all kinds of lambda expressions since they have some limitations.\n\nTheir main limitation is a result of what's also their biggest strength: the output from the previous expression needs to match the input parameters of the referenced method signature.\n\nLet's see an example of this limitation:\n\n``````createBicyclesList().forEach(b -> System.out.printf(\n\"Bike brand is '%s' and frame size is '%d'%n\",\nb.getBrand(),\nb.getFrameSize()));``````\n\nThis simple case can't be expressed with a method reference, because the printf method requires 3 parameters in our case, and using createBicyclesList().forEach() would only allow the method reference to infer one parameter (the Bicycle object).\n\nFinally, let's explore how to create a no-operation function that can be referenced from a lambda expression.\n\nIn this case, we'll want to use a lambda expression without using its parameters.\n\nFirst, let's create the doNothingAtAll method:\n\n``````private static <T> void doNothingAtAll(Object... o) {\n}``````\n\nAs it is a varargs method, it will work in any lambda expression, no matter the referenced object or number of parameters inferred.\n\nNow, let's see it in action:\n\n``````createBicyclesList()\n.forEach((o) -> MethodReferenceExamples.doNothingAtAll(o));\n``````\n\n## 7. Conclusion\n\nIn this quick tutorial, we learned what method references are in Java and how to use them to replace lambda expressions, thereby improving readability and clarifying the programmer's intent." ]

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

[ "# What are the assumptions of negative binomial regression?\n\nI'm working with a large data set (confidential, so I can't share too much), and came to the conclusion a negative binomial regression would be necessary. I've never done a glm regression before, and I can't find any clear information about what the assumptions are. Are they the same for MLR?\n\nCan I transform the variables the same way (I've already discovered transforming the dependent variable is a bad call since it needs to be a natural number)? I already determined that the negative binomial distribution would help with the over-dispersion in my data (variance is around 2000, the mean is 48).\n\nThanks for the help!!\n\nI'm working with a large data set (confidential, so I can't share too much),\n\nIt might be possible to create a small data set that has some of the general characteristics of the real data without either the variable names nor any of the actual values.\n\nand came to the conclusion a negative binomial regression would be necessary. I've never done a glm regression before, and I can't find any clear information about what the assumptions are. Are they the same for MLR?\n\nClearly not! You already know you're assuming response is conditionally negative binomial, not conditionally normal. (Some assumptions are shared. Independence for example.)\n\nLet me talk about GLMs more generally first.\n\nGLMs include multiple regression but generalize in several ways:\n\n1) the conditional distribution of the response (dependent variable) is from the exponential family, which includes the Poisson, binomial, gamma, normal and numerous other distributions.\n\n2) the mean response is related to the predictors (independent variables) through a link function. Each family of distributions has an associated canonical link function - for example in the case of the Poisson, the canonical link is the log. The canonical links are almost always the default, but in most software you generally have several choices within each distribution choice. For the binomial the canonical link is the logit (the linear predictor is modelling $\\log(\\frac{p}{1-p})$, the log-odds of a success, or a \"1\") and for the Gamma the canonical link is the inverse - but in both cases other link functions are often used.\n\nSo if your response was $Y$ and your predictors were $X_1$ and $X_2$, with a Poisson regression with the log link you might have for your description of how the mean of $Y$ is related to the $X$'s:\n\n$\\text{E}(Y_i) = \\mu_i$\n\n$\\log\\mu_i= \\eta_i$ ($\\eta$ is called the 'linear predictor', and here the link function is $\\log$, the symbol $g$ is often used to represent the link function)\n\n$\\eta_i = \\beta_0 + \\beta_1 x_{1i} + \\beta_2 x_{2i}$\n\n3) the variance of the response is not constant, but operates through a variance-function (a function of the mean, possibly times a scaling parameter). For example, the variance of a Poisson is equal to the mean, while for a gamma it's proportional to the square of the mean. (The quasi-distributions allow some degree of decoupling of Variance function from assumed distribution)\n\n--\n\nSo what assumptions are in common with what you remember from MLR?\n\n• Independence is still there.\n\n• Homoskedasticity is no longer assumed; the variance is explicitly a function of the mean and so in general varies with the predictors (so while the model is generally heteroskedastic, the heteroskedasticity takes a specific form).\n\n• Linearity: The model is still linear in the parameters (i.e. the linear predictor is $X\\beta$), but the expected response is not linearly related to them (unless you use the identity link function!).\n\n• The distribution of the response is substantially more general\n\nThe interpretation of the output is in many ways quite similar; you can still look at estimated coefficients divided by their standard errors for example, and interpret them similarly (they're asymptotically normal - a Wald z-test - but people still seem to call them t-ratios, even when there's no theory that makes them $t$-distributed in general).\n\nComparisons between nested models (via 'anova-table' like setups) are a bit different, but similar (involving asymptotic chi-square tests). If you're comfortable with AIC and BIC these can be calculated.\n\nSimilar kinds of diagnostic displays are generally used, but can be harder to interpret.\n\nMuch of your multiple linear regression intuition will carry over if you keep the differences in mind.\n\nHere's an example of something you can do with a glm that you can't really do with linear regression (indeed, most people would use nonlinear regression for this, but GLM is easier and nicer for it) in the normal case - $Y$ is normal, modelled as a function of $x$:\n\n$\\text{E}(Y) = \\exp(\\eta) = \\exp(X\\beta) = \\exp(\\beta_0+\\beta_1 x)$ (that is, a log-link)\n\n$\\text{Var}(Y) = \\sigma^2$\n\nThat is, a least-squares fit of an exponential relationship between $Y$ and $x$.\n\nCan I transform the variables the same way (I've already discovered transforming the dependent variable is a bad call since it needs to be a natural number)?\n\nYou (usually) don't want to transform the response (DV). You sometimes may want to transform predictors (IVs) in order to achieve linearity of the linear predictor.\n\nI already determined that the negative binomial distribution would help with the over-dispersion in my data (variance is around 2000, the mean is 48).\n\nYes, it can deal with overdispersion. But take care not to confuse the conditional dispersion with the unconditional dispersion.\n\nAnother common approach - if a bit more kludgy and so somewhat less satisfying to my mind - is quasi-Poisson regression (overdispersed Poisson regression).\n\nWith the negative binomial, it's in the exponential family if you specify a particular one of its parameters (the way it's usually reparameterized for GLMS at least). Some packages will fit it if you specify the parameter, others will wrap ML estimation of that parameter (say via profile likelihood) around a GLM routine, automating the process. Some will restrict you to a smaller set of distributions; you don't say what software you might use so it's difficult to say much more there.\n\nI think usually the log-link tends to be used with negative binomial regression.\n\nThere are a number of introductory-level documents (readily found via google) that lead through some basic Poisson GLM and then negative binomial GLM analysis of data, but you may prefer to look at a book on GLMs and maybe do a little Poisson regression first just to get used to that.\n\n• +1 I agree with COOLSerdash. Lots of good information here! In addition to the recommended Google search, I'd specifically recommend a textbook called Econometrics by Example by Gujarati. Chapter 12 covers the Poisson regression model and the negative-Binomial regression model. As the title of the book suggests, there are examples. Data used in the book is available from the books companion website and so to is a summary of Chapter 12 itself. I recommend that the OP checks this out. – Graeme Walsh Jun 27 '13 at 8:00\n• I'm late to the party... but this answer helped me understand generalized linear models better than a whole stack of books at the library. – haff Sep 19 '17 at 7:48\n\nSome references I have found to be helpful in analyzing data with the negative binomial distribution specifically (including listing assumptions) and GLM/GLMMs generally are:\n\nBates, D.M., B. Machler, B. Bolker, and S. Walker. 2015. Fitting linear mixed-effects models using lme4. J. Stat. Software 67: 1-48.\n\nBolker, B.M., M.E. Brooks, C.J. Clark, S.W. Geange, J.R. Poulsen, M.H.H. Stevens, and J. White. Generalized linear mixed models: a practical guide for ecology and evolution. Trends in Ecology and Evolution 127-135.\n\nZeileis A. , C. Keleiber C, and S. Jackman 2008. Regression models for count data in R. J. Stat. Software. 27: 1-25\n\nZuur A.F., E.N. Iene , N. Walker, A.A. Saveliev, and G.M. Smith. 2009. Mixed effects models and extensions in ecology with R. Springer, NY, USA." ]

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[ "# The Euler Equation\n\nThe Euler (pronounced oiler) Equation must surely rate as one of the most elegant, beautiful and awe-inspiring formulae in maths. Its consequences are diverse and shocking when you consider its simplicity.\n\nThe Euler Equation is often given by the following:\n\nei θ = cos θ + i sin θ\n\nWhere e and i are the standard constants defined by:\n\nd/dx ex = ex\ni2 = -1\n\nAnd θ is any angle in radians.\n\n### Origins of the Euler Equation\n\nLet us consider the function:\n\ny = cos x + i sin x\n\nContinuing to treat i like any other number, we have, by differentiation:\n\ndy/dx = -sin x + i cos x = i(cos x + i sin x)\n=> dy/dx = iy\n=> i dx/dy = 1/y\n=> ix = ln y + c\n\nBut when x = 0, y = 1. So c = 0.\n\n=> ix = ln y\n=> y = eix\nSo cos x + i sin x = eix\n\nIt may be objected that we have nowhere defined the meaning of a number such as ez when z is complex; but the reader should not be deterred by such inhibitions. Indeed, the above paragraph may be regarded as providing, if not a definition, at least a reasonable exposition of the meaning of eix, making it consistent with the familiar processes of mathematics.\n\n### Consequences of the Euler Equation\n\nOne of the most fundamental consequences of the Euler Equation is shown by taking θ to equal π radians. When this is done then the equation (once rearranged slightly) gives the following:\n\neπ i + 1 = 0\n\nThis unites the five most important numbers in maths; π, i, e, 1 and 0 into one relation and so the Euler Equation is taken as one of the most important points of unification. From this equation one gains a glimmer of how the whole of maths fits together.\n\nThis glimmer is reinforced if one takes the natural log of both sides of the equation (after subtracting one from both sides). This allows us to define the natural log of the negative numbers in the complex plane as follows:\n\nln -1 = i π\n\nA far reaching result which defines a whole family of hyperbolic (or modular) forms (strongly related to hyperbolic functions) based around two mutually perpendicular complex planes (represented commonly by Argand Diagrams) sharing no axes. These were linked to another, seemingly unrelated, part of maths known as elliptic curves by the Taniyama-Shimura theorem which (as the first part of the Langland's Programme) became part of the quest for a Grand Unified Mathematics and forms the basis for some of the most important maths today. Indeed, the famed proof of Fermat's Last Theorem by Andrew Wiles was in fact also the proof of Taniyama-Shimura and so became dually celebrated as a triumph over an amateur tease-artist and as the stabilisation of an increasingly shaky foundation of an entire branch of maths.\n\nNot bad for such a simple equation." ]

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[ "# How do you find the slope of the tangent line using the formal definition of a limit?\n\nFeb 7, 2015\n\nYou would have to use the equation\n\n$f ' \\left(x\\right) = {\\lim}_{h \\to 0} \\frac{f \\left(x + h\\right) - f \\left(x\\right)}{h}$\n\nat a given point.\n\nThis derives from the average rate of change; as a line gets closer to a point on a graph, it becomes only one intersection of the line and not two (which is a secant line).\n\nHere is a link for graphical examples:\n\nhttp://facultypages.morris.umn.edu/~mcquarrb/teachingarchive/Precalculus/Lectures/AverageRateofChange.pdf\n\nThis is useful in determining the instantaneous rate of change of any curve. For example, if you have $f \\left(x\\right) = {x}^{2}$, then you can use the equation above to find the slope of the line at any x-value (by simplification and canceling the h on the denominator). Or, if they specify the value of x, then you just insert the number for x and solve for the problem.\n\nIt works for every polynomial equation, but be aware that other equations maybe complicated or may not work.\n\nLater on (if you are currently taking Calculus I), you will learn about derivatives and find ways to easily get the slope of tangent lines; for the ${x}^{2}$ part, 2x is the slope of the tangent line at any x-value. If you use the laws of derivatives and the limit definition, it turns out to be the same!\n\nOnce you understand how limits work in relation to derivatives, it becomes very interesting!" ]

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[ "# Number 333123\n\n### Properties of number 333123\n\nCross Sum:\nFactorization:\n3 * 7 * 29 * 547\nDivisors:\nCount of divisors:\nSum of divisors:\nPrime number?\nNo\nFibonacci number?\nNo\nBell Number?\nNo\nCatalan Number?\nNo\nBase 2 (Binary):\nBase 3 (Ternary):\nBase 4 (Quaternary):\nBase 5 (Quintal):\nBase 8 (Octal):\nBase 32:\na5a3\nsin(333123)\n0.88260925821365\ncos(333123)\n0.47010732531578\ntan(333123)\n1.8774633167453\nln(333123)\n12.716267070132\nlg(333123)\n5.5226046189663\nsqrt(333123)\n577.16808643583\nSquare(333123)\n\n### Number Look Up\n\nLook Up\n\n333123 which is pronounced (three hundred thirty-three thousand one hundred twenty-three) is a very unique number. The cross sum of 333123 is 15. If you factorisate the figure 333123 you will get these result 3 * 7 * 29 * 547. The figure 333123 has 16 divisors ( 1, 3, 7, 21, 29, 87, 203, 547, 609, 1641, 3829, 11487, 15863, 47589, 111041, 333123 ) whith a sum of 526080. The number 333123 is not a prime number. 333123 is not a fibonacci number. The figure 333123 is not a Bell Number. The figure 333123 is not a Catalan Number. The convertion of 333123 to base 2 (Binary) is 1010001010101000011. The convertion of 333123 to base 3 (Ternary) is 121220221220. The convertion of 333123 to base 4 (Quaternary) is 1101111003. The convertion of 333123 to base 5 (Quintal) is 41124443. The convertion of 333123 to base 8 (Octal) is 1212503. The convertion of 333123 to base 16 (Hexadecimal) is 51543. The convertion of 333123 to base 32 is a5a3. The sine of the number 333123 is 0.88260925821365. The cosine of the number 333123 is 0.47010732531578. The tangent of 333123 is 1.8774633167453. The root of 333123 is 577.16808643583.\nIf you square 333123 you will get the following result 110970933129. The natural logarithm of 333123 is 12.716267070132 and the decimal logarithm is 5.5226046189663. You should now know that 333123 is great figure!" ]

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[ "# Multidimensional result array need to merge in single with same key value using PHP\n\nI have multidimensional result of an array need to merge in single array with same key value using PHP like below desired result.\n\nResult\n\n``````Array\n(\n => Array\n(\n[POBI] => Array\n(\n[average] => 3.9885520361991\n[name] => POBI\n[year] => 2014-2015\n)\n\n[POE] => Array\n(\n[average] => 4\n[name] => POE\n[year] => 2014-2015\n)\n\n[LOS] => Array\n(\n[average] => 4\n[name] => LOS\n[year] => 2014-2015\n)\n\n[Other Cop] => Array\n(\n)\n\n)\n\n => Array\n(\n[POBI] => Array\n(\n[average] => 4\n[name] => POBI\n[year] => 2014-2015\n)\n\n[POE] => Array\n(\n[average] => 3.9\n[name] => POE\n[year] => 2014-2015\n)\n\n[LOS] => Array\n(\n[average] => 4\n[name] => LOS\n[year] => 2014-2015\n)\n\n[Other Cop] => Array\n(\n[average] => 2\n[name] => OC\n[year] => 2014-2015\n)\n\n)\n\n => Array\n(\n[POBI] => Array\n(\n[average] => 7\n[name] => POBI\n[year] => 2014-2015\n)\n\n[POE] => Array\n(\n[average] => 3.0\n[name] => POE\n[year] => 2014-2015\n)\n\n[LOS] => Array\n(\n[average] => 4\n[name] => LOS\n[year] => 2014-2015\n)\n\n[Other Cop] => Array\n(\n[average] => 1.8\n[name] => OC\n[year] => 2014-2015\n)\n)\n\n)\n``````\n\nDesired Result\n\n``````Array\n(\n[POBI] => Array\n(\n => Array\n(\n[average] => 3.9885520361991\n[name] => POBI\n[year] => 2014-2015\n)\n\n => Array\n(\n[average] => 4\n[name] => POBI\n[year] => 2014-2015\n)\n\n => Array\n(\n[average] => 7\n[name] => POBI\n[year] => 2014-2015\n)\n\n)\n\n[POE] => Array\n(\n => Array\n(\n[average] => 4\n[name] => POE\n[year] => 2014-2015\n)\n\n => Array\n(\n[average] => 3.9\n[name] => POE\n[year] => 2014-2015\n)\n\n => Array\n(\n[average] => 3.0\n[name] => POE\n[year] => 2014-2015\n)\n\n)\n\n[LOS] => Array\n(\n => Array\n(\n[average] => 4\n[name] => LOS\n[year] => 2014-2015\n)\n\n => Array\n(\n[average] => 4\n[name] => LOS\n[year] => 2014-2015\n)\n\n => Array\n(\n[average] => 4\n[name] => LOS\n[year] => 2014-2015\n)\n\n)\n\n[Other Cop] => Array\n(\n => Array\n(\n\n)\n\n => Array\n(\n[average] => 2\n[name] => OC\n[year] => 2014-2015\n)\n\n => Array\n(\n[average] => 1.8\n[name] => OC\n[year] => 2014-2015\n)\n\n)\n)\n``````\n\nMy current implementation attempts to do something like this:\n\n``````foreach(\\$data as \\$k => \\$v) {\n\\$results[\\$k] = array_column(\\$arr, \\$k);\n}\nprint_r(\\$results);\n``````\n• may be this will work: `\\$results[\\$k][] = array_column(\\$arr, \\$k);`. – Murad Hasan May 19 '16 at 14:00\n\nTry something like this:\n\n``````\\$return = [];\nforeach (\\$data as \\$key => \\$value) {\nforeach (\\$value as \\$innerKey => \\$innerValue) {\nif (!isset(\\$return[\\$innerKey])) {\n\\$return[\\$innerKey] = [];\n}\n\\$return[\\$innerKey][] = \\$innerValue;\n}\n}\n\nvar_dump(\\$return);\ndie();\n``````\n\nTry this:\n\n``````foreach (\\$yourArrayName as \\$items)\n{\nforeach (\\$items as \\$id => \\$item) {\n\\$result[\\$id][] = \\$item;\n}\n}\nprint_r(\\$result);\n``````\n\nNOTE: Your sample result data has duplicate index for 1 by the way... Should be typo I guess. Just FYI.\n\nThere is a simple solution to your problem. A one liner actually.\n\n``````\\$mergedArray = array_merge_recursive(\\$arrayOne, \\$arrayTwo);\n\n\\$merged = array_merge_recursive(\\$array, \\$array);\n``````\n\nHope this will do the trick.\n\n### Edit\n\nAs suggested by Brad Kent, if you have more than two values that need to be merged:\n\n``````\\$merged = call_use_func_array('array_merge_recursive', array_values(\\$array));\n``````\n• probably something more like `\\$merged = call_use_func_array('array_merge_recursive', array_values(\\$array));` (can't assume there are only two two \"sub-arrays\" that need merged) – Brad Kent May 19 '16 at 14:16\n• I have result set of array not individual sub arrray – Query Master May 19 '16 at 14:21\n\nyou're close. try\n\n``````\\$keys = array_keys(\\$data);\n\\$results = array();\nforeach (\\$keys as \\$key) {\n\\$results[\\$key] = array_column(\\$data, \\$key);\n}\n``````\n\nthis assumes each group has the same keys." ]

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[ "# If the length of a 37 cm spring increases to 73 cm when a 4 kg weight is hanging from it, what is the spring's constant?\n\nJul 12, 2017\n\nThe spring constant is $= 108.9 n {m}^{-} 1$\n\n#### Explanation:", null, "The mass is $= 4 k g$\n\nThe extension is $\\Delta x = 0.73 - 0.37 = 0.36 m$\n\nThe spring constant is\n\n$k = \\frac{F}{\\Delta x} = 4 \\frac{g}{0.36} = 108.9 N {m}^{-} 1$" ]

[ null, "https://useruploads.socratic.org/3ouRkVxYTNKKxn3WgD1g_hookes-law-pic1.jpg", null ]

[ "# Search Printable Skip Counting by 2 Worksheets\n\n37 filtered results\n37 filtered results\nSkip Counting by 2s\nSort by\nSkip Counting Chart\nWorksheet\nSkip Counting Chart\nUse this number chart to help your child find patterns in numbers, which will help take that first step into skip counting.\nMath\nWorksheet\nCount by Twos\nWorksheet\nCount by Twos\nKids count by twos on this first grade math worksheet. Skip counting by twos is one way children can demonstrate the meaning of addition.\nMath\nWorksheet\nSkip Counting Practice\nWorksheet\nSkip Counting Practice\nMath\nWorksheet\nMultiplication: Skip Counting to Find the Total\nWorksheet\nMultiplication: Skip Counting to Find the Total\nPractice skip counting by two, three, four, and five in this fun worksheet.\nMath\nWorksheet\nPractice Test: Number Patterns\nWorksheet\nPractice Test: Number Patterns\nReview number patterns with your second grader with this mini quiz that asks him to choose the number that comes next in each pattern.\nMath\nWorksheet\nNumber Patterns: Find the Pattern\nWorksheet\nNumber Patterns: Find the Pattern\nSharpen your first grader's number sense with an exercise in recognizing number patterns.\nMath\nWorksheet\nPractice Test: Easy Number Patterns\nWorksheet\nPractice Test: Easy Number Patterns\nReinforce math concepts with your students! Use this practice quiz to review number patterns.\nMath\nWorksheet\nDot to Dot Zoo: 5's\nWorksheet\nDot to Dot Zoo: 5's\nA giraffe dot-to-dot might be just the thing for your zoo lover. Try this giraffe dot-to-dot with your child, and be challenged with an added twist.\nMath\nWorksheet\nConnect the Dots: Practice Skip Counting by Twos\nWorksheet\nConnect the Dots: Practice Skip Counting by Twos\nChildren skip count by two to connect the dots and discover the hidden picture.\nMath\nWorksheet\nSkip Counting: Let's Practice!\nWorksheet\nSkip Counting: Let's Practice!\nPacked with skip counting practice, this sporty worksheet builds number sense and paves the way for future multiplication skills.\nMath\nWorksheet\nDot to Dot Zoo: 2's\nWorksheet\nDot to Dot Zoo: 2's\nA zebra dot-to-dot worksheet is fun from the start, and this one has a special twist. Count by twos in this zebra dot-to-dot worksheet.\nMath\nWorksheet\nEven Numbers: 90-150\nWorksheet\nEven Numbers: 90-150\nIn this 2nd grade math worksheet, your child will practice writing even numbers and counting by 2 from 90 to 150 as they write the missing numbers in the spaces.\nMath\nWorksheet\nNumber Patterns on the Beach\nWorksheet\nNumber Patterns on the Beach\nSee if your little one has the sharp eyes and math know-how to spot the patterns! Numbers jump by twos, fives, tens, and more on this math worksheet.\nMath\nWorksheet\nSkip Counting to Find the Total\nWorksheet\nSkip Counting to Find the Total\nThis vibrant worksheet teaches the simple multiplication method of skip counting.\nMath\nWorksheet\nSkip Counting by 2\nWorksheet\nSkip Counting by 2\nGet ready for multiplication by practicing skip counting by 2.\nMath\nWorksheet\nDot to Dot Constellation: Aquila\nWorksheet\nDot to Dot Constellation: Aquila\nGive your child a challenging dot-to-dot where he'll have to count by 2s. When he's done he'll see the constellation Aquila.\nMath\nWorksheet\nSkip Count by Two!\nWorksheet\nSkip Count by Two!\nCount by multiples of two at the Dot-to-Dot Zoo to complete the coloring page picture!\nMath\nWorksheet\nMissing Numbers: Counting by Twos\nWorksheet\nMissing Numbers: Counting by Twos\nDoes your child need practice with his math skills? This printable worksheet, which will help him count up to 100, will give him practice counting by 2's.\nMath\nWorksheet\nHundreds Chart: Skip Counting!\nWorksheet\nHundreds Chart: Skip Counting!\nDid you know there are patterns in numbers? Dive into skip counting with your beginning math star, a great way to prepare him for multiplication!\nMath\nWorksheet\nOdd Numbers: 101-161\nWorksheet\nOdd Numbers: 101-161\nIn this 2nd grade math worksheet, your child will practice writing odd numbers and counting by 2 from 101 to 161 as they write the missing numbers in the spaces.\nMath\nWorksheet\nWorksheet\nSearching for a worksheet that practices counting skills? This printable asks your child to determine which series of numbers is counting by twos.\nMath\nWorksheet\nSkip Counting: Count by Twos!\nWorksheet\nSkip Counting: Count by Twos!\nAs your kid counts these groups of shoes by twos, she'll get a better handle on number sequence, too.\nMath\nWorksheet\nHeart Pattern\nWorksheet\nHeart Pattern\nUse a heart pattern to practice math skills this Valentine's Day. This heart pattern worksheet gets kids to practice numeric patterns on Valentine's Day.\nMath\nWorksheet\nSkip Counting Hermit Crab\nWorksheet\nSkip Counting Hermit Crab\nThis cute little hermit crab is missing his sea shell. Connect the dots to give him a new home, and learn about odd numbers as you go!" ]

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[ "# nLab groupoid cardinality\n\nContents\n\n### Context\n\n#### Higher category theory\n\nhigher category theory\n\n# Contents\n\n## Idea\n\nThe homotopy cardinality or $\\infty$-groupoid cardinality of a (sufficiently “finite”) space or ∞-groupoid $X$ is an invariant of $X$ (a value assigned to its equivalence class) that generalizes the cardinality of a set (a 0-truncated $\\infty$-groupoid).\n\nSpecifically, whereas cardinality counts elements in a set, the homotopy cardinality counts objects up to equivalences, up to 2-equivalences, up to 3-equivalence, and so on.\n\nThis is closely related to the notion of Euler characteristic of a space or $\\infty$-groupoid. See there for more details.\n\n## Definition\n\n### Groupoid cardinality\n\nThe cardinality of a groupoid $X$ is the real number\n\n$|X| = \\sum_{[x] \\in \\pi_0(X)} \\frac{1}{|Aut(x)|} \\,,$\n\nwhere the sum is over isomorphism classes of objects of $X$ and $|Aut(x)|$ is the cardinality of the automorphism group of an object $x$ in $X$.\n\nIf this sum diverges, we say $|X| = \\infty$. If the sum converges, we say $X$ is tame. (See at homotopy type with finite homotopy groups).\n\n### $\\infty$-Groupoid cardinality\n\nThis is the special case of a more general definition:\n\nThe groupoid cardinality of an ∞-groupoid $X$ – equivalently the Euler characteristic of a topological space $X$ (that’s the same, due to the homotopy hypothesis) – is, if it converges, the alternating product of cardinalities of the (simplicial) homotopy groups\n\n$|X| := \\sum_{[x] \\in \\pi_0(X)}\\prod_{k = 1}^\\infty |\\pi_k(X,x)|^{(-1)^k} = \\sum_{[x]} \\frac{1}{|\\pi_1(X,x)|} |\\pi_2(X,x)| \\frac{1}{|\\pi_3(X,x)|} |\\pi_4(X,x)| \\cdots \\,.$\n\nThis corresponds to what is referred to as the total homotopy order of a space, which occurs notably in notes Frank Quinn in 1995 on TQFTs (see reference list), although similar ideas were explored by several researchers at that time.\n\n## Examples\n\n• Let $X$ be a discrete groupoid on a finite set $S$ with $n$ elements. Then the groupoid cardinality of $X$ is just the ordinary cardinality of the set $S$\n\n$|X| = n \\,.$\n• Let $\\mathbf{B}G$ be the delooping of a finite group $G$ with $k$ elements. Then\n\n$|\\mathbf{B}G| = \\frac{1}{k}$\n• More generally, for an action of $G$ on a set $X$, then the cardinality of the action groupoid $X//G$ is $\\frac{\\vert X\\vert} {\\vert G \\vert}$. This is traditionally sometimes called the class formula.\n\n• Let $A$ be an abelian group with $k$ elements. Then we can deloop arbitrarily often and obtain the Eilenberg-Mac Lane objects $\\mathbf{B}^n A$ for all $n \\in \\mathbb{N}$. (Under the Dold-Kan correspondence $\\mathbf{B}^n A$ is the chain complex $A[n]$ (or $A[-n]$ depending on notational convention) that is concentrated in degree $n$, where it is the group $A$). Then\n\n$|\\mathbf{B}^n A| = \\begin{cases} k & \\text{if }\\; n \\;\\text{ is even} \\\\ \\frac{1}{k} & \\text{if }\\; n \\;\\text{ is odd} \\end{cases}$\n• Let $E = core(FinSet)$ be the groupoid of finite sets and bijections – the core of FinSet. Its groupoid cardinality is the Euler number\n\n$|E| = \\sum_{n\\in \\mathbb{N}} \\frac{1}{|S_n|} = \\sum_{n\\in \\mathbb{N}} \\frac{1}{n!} = e \\,.$\n• Let $E=(E_i)$ be a finite crossed complex, (i.e., an omega-groupoid; see the work of Brown and Higgins) such that for any object $v \\in E_0$ of $E$ the cardinality of the set of $i$-cells with source $v$ is independent of the vertex $v$. Then the groupoid cardinality of $E$ can be calculated as $|E|=\\displaystyle{\\prod_{i} \\#(E_i)^{(-1)^i}}$, much like a usual Euler characteristic. For the case when $F$ is a totally free crossed complex, this gives a very neat formula for the groupoid cardinality of the internal hom $HOM(F,E)$, in the category of omega-groupoids. Therefore the groupoid cardinality of the function spaces (represented themselves by internal homs) can easily be dealt with if the underlying target space is represented by a omega-groupoid, i.e., has trivial Whitehead products. (This is explored in the papers by Faria Martins and Porter mentioned in the reference list, below.)\n\n• for $G$ a suitable algebraic group, for $\\Sigma$ a suitable algebraic curve, and for $q$ a prime number, then the groupoid cardinality of the $\\mathbb{F}_q$-points of the moduli stack of G-principal bundles over $X$, $Bun_G(X)$ is the subject of the Weil conjectures on Tamagawa numbers?." ]

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[ "arXiv Vanity renders academic papers from arXiv as responsive web pages so you don’t have to squint at a PDF. Read this paper on arXiv.org.\n\n# Dipolar Dark Matter as an Effective Field Theory\n\nLuc Blanchet Institut d’Astrophysique de Paris — UMR 7095 du CNRS,  Université Pierre & Marie Curie, 98bis boulevard Arago, 75014 Paris, France    Lavinia Heisenberg Institute for Theoretical Studies, ETH Zurich,\nClausiusstrasse 47, 8092 Zurich, Switzerland\nAugust 5, 2020August 5, 2020\nAugust 5, 2020August 5, 2020\n###### Abstract\n\nDipolar Dark Matter (DDM) is an alternative model motivated by the challenges faced by the standard cold dark matter model to describe the right phenomenology at galactic scales. A promising realisation of DDM was recently proposed in the context of massive bigravity theory. The model contains dark matter particles, as well as a vector field coupled to the effective composite metric of bigravity. This model is completely safe in the gravitational sector thanks to the underlying properties of massive bigravity. In this work we investigate the exact decoupling limit of the theory, including the contribution of the matter sector, and prove that it is free of ghosts in this limit. We conclude that the theory is acceptable as an Effective Field Theory below the strong coupling scale.\n\n###### pacs:\n95.35.+d, 04.50.Kd\n\n## I Introduction\n\nWe are witnesses of centenaries. The year 2015 marked the 100th anniversary of Albert Einstein’s elaborate theory of General Relativity (GR), while 2016 celebrated the centenary of the first paper on gravitational waves by the announcement of their experimental detection Abbott et al. (2016). GR meets the requirements of the underlying physics in a broad range of scales, from black hole to solar system size. It stood up to intense scrutiny and prevailed against all alternative competitors. It constitutes the bedrock upon which our fundamental understanding of gravity relies. However, some important questions remain.\n\nThe lack of renormalizability motivates the modifications of gravity in the ultraviolet (UV), that incorporate the quantum nature of gravity. The singularities present in the classical theory could be regularized by the new physics Beltran Jimenez et al. (2014). The UV modifications might also dictate a different scenario for the early Universe as an alternative to inflation Beltran Jimenez et al. (2015). The inflaton field in the standard picture might be just a reminiscent of the modification of gravity in the UV.\n\nFrom a more observational point of view, GR faces additional challenges on cosmological scales. In order to account for the observed amount of ingredients of the Universe, it is necessary to introduce dark matter and dark energy despite of their unclear origin. Notwithstanding of remarkable efforts, the dark matter has so far not been directly detected. Concerning the dark energy, the standard model in form of a cosmological constant accounts for most of the observations even though it faces the unnaturalness problem Weinberg (1989). Combined with the non-baryonic cold dark matter (CDM) component, the model explains remarkably well the observed fluctuations of the cosmic microwave background and the formation of large scale structures.\n\nAlbeit the many successes of the -CDM model at large scales, it has difficulties to explain the observations of dark matter at galactic scales. For instance, it is not able to account for the tight correlations between dark and luminous matter in galaxy halos Sanders and McGaugh (2002); Famaey and McGaugh (2012). In this remark, the first unsatisfactory discrepancy comes from the observed Tully-Fisher relation between the baryonic mass of spiral galaxies and their asymptotic rotation velocity. Another discrepancy, perhaps more fundamental, comes from the correlation between the presence of dark matter and the acceleration scale McGaugh et al. (2000); McGaugh (2011). The prevailing view regarding these problems is that they should be resolved once we understand the baryonic processes that affect galaxy formation and evolution Silk and Mamon (2012). However, this explanation is challenged by the fact that galactic data are in excellent agreement with the MOND (MOdified Newtonian Dynamics) empirical formula Milgrom (1983a, b, c). From a phenomenological point of view, this formula accommodates remarkably well all observations at galactic scales. Unfortunately, extrapolation of the MOND formula to the larger scale of galaxy clusters confronts an incorrect dark matter distribution Gerbal et al. (1992); Pointecouteau and Silk (2005); Clowe et al. (2006); Angus et al. (2008); Angus (2009).\n\nThe ideal scenario would be to have a hybrid model in which the properties of the -CDM model are naturally incorporated on large scales, whereas the MOND formula would take place on galactic scales. There have been many attempts to embed the physics beyond the MOND formula into an approved relativistic theory, either via invoking new propagating fields without dark matter Sanders (1997); Bekenstein (2004); Sanders (2005); Zlosnik et al. (2007); Halle et al. (2008); Milgrom (2009); Babichev et al. (2011), or by considering MOND as an emergent phenomenology Blanchet (2007); Bruneton et al. (2009); Blanchet and Le Tiec (2008, 2009); Sanders (2011); Blanchet and Marsat (2011); Bernard and Blanchet (2015); Khoury (2015); Berezhian and Khoury (2015); Verlinde (2016).\n\nHere we consider a model of the latter class, called Dipolar Dark Matter (DDM) Blanchet and Le Tiec (2008, 2009); Bernard and Blanchet (2015). The most compelling version of DDM has been recently developed, based on the formalism of massive bigravity theory Blanchet and Heisenberg (2015a, b). To describe the potential interactions between the two metrics of bigravity the model uses the effective composite metric introduced in Refs. de Rham et al. (2015, 2014); Heisenberg (2015a). Two species of dark matter particles are separately coupled to the two metrics, and an internal vector field that links the two dark matter species is coupled to the effective composite metric. The MOND formula is recovered from a mechanism of gravitational polarization in the non relativistic approximation. The model has the potential to reproduce the physics of the -CDM model at large cosmological scales.\n\nIn the present paper we address the problem of whether there are ghost instabilities in this model. The model itself Blanchet and Heisenberg (2015a, b) will be reviewed in Sec. II. The model is safe in the gravitational sector because it uses the ghost-free framework of massive bigravity. The interactions of the matter fields with the effective metric reintroduce a ghost in the matter sector beyond the strong coupling scale, as found in de Rham et al. (2015, 2014). In our model, apart from this effective coupling the different species of matter fields interact with each other via an internal vector field. This additional coupling might spoil the property of ghost freedom within the strong coupling scale. We therefore investigate, in Sec. III, the exact decoupling limit (DL) of our model, crucially including the contributions coming from the matter sector and notably from the internal vector field. The model dictates what are the relevant scalings of the matter fields in terms of the Planck mass in the DL. Using that, we shall prove that the theory is free of ghosts in the DL and conclude that it is acceptable as an Effective Field Theory below the strong coupling scale. We end the paper with a few concluding remarks in Sec. IV.\n\n## Ii Dipolar Dark Matter\n\nThe model that we would like to study in this work is the dark matter model proposed in Ref. Blanchet and Heisenberg (2015a) where the Dipolar Dark Matter (DDM) at small galactic scales is connected to bimetric gravity based on the ghost-free bimetric formulation of massive gravity de Rham et al. (2011a); Hassan and Rosen (2012). The action of a successful realisation was investigated in Blanchet and Heisenberg (2015b) and we would like to push forward the analysis performed there. The Lagrangian is the sum of a gravitational part, based on massive bigravity theory, plus a matter part: . The gravitational part reads\n\n Lgrav=M2g2√−gRg+M2f2√−fRf+m2M2eff√−g% eff, (1)\n\nwhere and denote the Ricci scalars of the two metrics and , with the corresponding Planck scales and and the interactions carrying another Planck scale , together with the graviton’s mass . In this formulation, the ghost-free potential interactions between the two metrics are defined as the square root of the determinant of the effective composite metric de Rham et al. (2015, 2014); Heisenberg (2015a)\n\n geffμν=α2gμν+2αβG% effμν+β2fμν, (2)\n\nwith the arbitrary dimensionless parameters and (typically of the order of one). Here denotes the effective metric in the previous DDM model Bernard and Blanchet (2015), given by where , or equivalently where . It is trivial to see that the square root of the determinant of this effective metric corresponds to the allowed ghost-free potential interactions de Rham et al. (2015).\n\nThe matter part of the model will consist of ordinary baryonic matter and a dark sector including dark matter particles. The crucial feature of the model is the presence of a vector field in the dark sector, that is sourced by the mass currents of dark matter particles and represents a “graviphoton” Scherk (1979). This vector field stabilizes the DDM medium and ensures a mechanism of “gravitational polarisation”. The matter action reads\n\n Lmat= −√−g(ρbar+ρg)−√−fρf +√−geff[Aμ(jμg−jμf)+λM2effW(X)]. (3)\n\nNote the presence of a non-canonical kinetic term for the vector field in form of a function of\n\n X=−FμνFμν4λ, (4)\n\nwith the field strength defined by where . The form of the function has been determined by demanding that the model reproduces the MOND phenomenology at galactic scales Bernard and Blanchet (2015); Blanchet and Heisenberg (2015b); Bernard et al. (2015). This corresponds to the limit and we have\n\n W(X)=X−23(α+β)2X3/2+O(X2), (5)\n\nso that the leading term in the action (II) is\n\n λM2effW(X)=−M2eff4FμνFμν+O(F3). (6)\n\nHence, we observe that the coupling scale of the vector field is dictated by , while the parameter enters into higher-order corrections. In order to recover the correct MOND regime for very weak accelerations of baryons in the ordinary sector, i.e. below the MOND acceleration scale , these constants have been determined as Blanchet and Heisenberg (2015b)111Recall also that the MOND acceleration is of the order of the cosmological parameters, and thus is extremely small in Planck units, .\n\n Meff=√2rgMPlandλ=a202. (7)\n\nHere represents the standard Planck constant of GR and the constant is defined below. It is worth mentioning that the standard Newtonian limit in the ordinary sector is obtained by imposing the relation\n\n M2g+α2β2M2f=M2Pl. (8)\n\nThus, in this model the three mass scales , and are of the order of the Planck mass.\n\nWe represent the scalar energy densities of the ordinary pressureless baryons, and the two species of pressureless dark matter particles by , and respectively. Such densities are conserved in the usual way with respect to their respective metrics, hence , and , with the four velocities being normalized as , and . The respective stress-energy tensors are defined as , and . The pressureless baryonic fluid obeys the geodesic law of motion , hence . On the other hand, because of their coupling to the vector field, the dark matter fluids pursue a non-geodesic motion:\n\n ∇νgTgμν =JνgFμν, (9a) ∇νfTfμν =−JνfFμν, (9b)\n\nwhere the dark matter currents and are related to those appearing in Eq. (II) by\n\n Jμg=√−geff√−gjμg% andJμf=√−geff√−fjμf. (10)\n\nIt remains to specify the link between these currents and the scalar densities and of the particles. This is provided by and , where and are two constants of the order of one, which can be interpreted as the ratios between the “charge” of the particles (with respect to the vector interaction) and their inertial mass. For correctly recovering MOND we must have  Blanchet and Heisenberg (2015b).\n\nWhereas, the stress-energy tensor of the vector field is obtained by varying (II) with respect to (holding the and metrics fixed) and corresponds to\n\n Tμνgeff=M2eff[WXFμρFννρ+λWgμνeff], (11)\n\nwhere . The evolution of the vector field is dictated by the Maxwell law\n\n (12)\n\nwhere the covariant derivative associated with is denoted by . Together with the conservation of the currents, and , the equations of motion for the vector field can also be expressed as\n\n ∇νgeffTgeffμν=−(jνg−jνf)Fμν, (13)\n\nand we can combine these equations of motion all together into a “global” conservation law\n\n √−geff∇νgeffTgeffμν+√−g∇νgTgμν+√−f∇νfTfμν=0. (14)\n\n## Iii Decoupling Limit\n\nBeing based on massive bigravity theory, the gravitational sector of the model, Eq. (1), is ghost-free up to any order in perturbation theory de Rham et al. (2011a); Hassan and Rosen (2012). In addition, the baryonic and dark matter particles can be coupled separately to either the metric or metric without changing this property de Rham et al. (2015). The case of the pure matter coupling between the vector field and the effective composite metric in Eqs. (II)–(4), is not trivial. In that case, it was shown in Ref. de Rham et al. (2015) that the coupling is ghost-free in the mini-superspace and in the decoupling limit. Furthermore it is known that such coupling to the composite metric is unique in the sense that it is the only non-minimal matter coupling that maintains ghost-freedom in the decoupling limit de Rham and Tolley (2015); Huang et al. (2015); Heisenberg (2015b).", null, "Figure 1: Schematic structure of the model. The two metrics of bigravity gμν and fμν interact through the effective composite metric geffμν, but also indirectly, via the particles ρg and ρf and the vector field Aμ.\n\nHowever, in our model the vector field is also coupled to the and particles, through the standard interaction term . This term plays a crucial role for the dark matter model to work. This coupling introduces a suplementary, indirect interaction between the two metrics of bigravity, via the and particles coupled together by the term . See Fig. 1 for a schematic illustration of the interactions in the model. As a result it was found in Ref. Blanchet and Heisenberg (2015b) that a ghost is reintroduced in the dark matter sector in the full theory. The aim of this paper is to investigate the occurence and mass of this ghost, and whether or not the decoupling limit (DL) is maintained ghost-free. If the latter is true, then the model can be used in a consistent way as an Effective Field Theory valid below the strong coupling scale.\n\nWe now detail the analysis of the DL interactions in the graviton and matter sectors. We follow the preliminary work Blanchet and Heisenberg (2015b) and investigate the scale of the reintroduced Boulware-Deser (BD) ghost Boulware and Deser (1972). We first decouple the interactions below the strong coupling scale from those entering above it, and concentrate on the pure interactions of the helicity-0 mode of the massive graviton. Using the Stückelberg trick, we restore the broken gauge invariance in the metric by replacing it by\n\n ~fμν=fab∂μϕa∂νϕb, (15)\n\nwhere and the four Stückelberg fields are decomposed into the helicity-0 mode and the helicity-1 mode ,\n\n ϕa=xa−mAaΛ33−fab∂bπΛ33. (16)\n\nHere denotes the strong coupling scale. Note, that we define it with respect to here, since the potential interactions scale with in our case.\n\nIt is well known that the would-be BD ghost in the DL, would come in the form of higher derivative interactions of the helicity-0 mode at the level of the equations of motion. Therefore we shall only follow the contributions of the helicity-0 mode and neglect the interactions of the helicity-1 mode . For simplicity we do not write the tilde symbol over the Stükelbergized version of the metric (15). Thus, considering also the helicity-2 mode in the metric, we have222If there is a BD ghost in the DL, then it will manifest itself in the higher-order equations of motion of the helicity-0 mode. For this purpose, it will be enough to follow closely the contributions of the matter couplings to the helicity-0 mode equations of motion and decouple the dynamics of the secondary helicity-2 mode in . The contributions of the latter, as derived in Fasiello and Tolley (2013), will not play any role in our analysis and will not change the final conclusions. The same is true for the contributions of the helicity-1 mode.\n\n gμν =(ημν+hμνMg)2, (17a) fμν =(ημν−ΠμνΛ33)2, (17b)\n\nwhere we introduced the notation for convenience, and raised and lowered indices with the Minkowski metric . The effective metric reads then\n\n geffμν=((α+β)ημν+Kμν)2, (18)\n\nin which we have introduced as a short-cut notation the linear combination\n\n Kμν=αMghμν−βΛ33Πμν. (19)\n\nWe will as next investigate the different contributions in the gravitational and matter sectors.\n\n### iii.1 Gravitational sector\n\nThere is no contribution of the Einstein-Hilbert term to the helicity-0 mode, since this is invariant under diffeomorphisms. On the other hand, there will be different contributions coming from the ghost-free potential interactions. The allowed potential interactions between the metrics and have been chosen in our model to be given by the square root of the determinant of the composite metric (18), which becomes in this case\n\n √−geff=4∑n=0(α+β)4−ne(n)(K), (20)\n\nwhere denote the usual symmetric polynomials associated with the matrix , and given by products of antisymmetric Levi-Cevita tensors,\n\n e(0)(K) =−124εμνρσεμνρσ, (21a) e(1)(K) =−16εμνρσεμνρλKλσ, (21b) e(2)(K) =−14εμνρσεμντλKτρKλσ, (21c) e(3)(K) =−16εμνρσεμπτλKπνKτρKλσ, (21d) e(4)(K) =−124εμνρσεϵπτλKϵμKπνKτρKλσ. (21e)\n\nIn particular, we see that .\n\nFirst of all, the pure helicity-0 mode in the ghost-free potential interactions (20) will come in the form of total derivatives de Rham and Gabadadze (2010); de Rham et al. (2011a). Indeed, as is clear from their definitions (21) in terms of antisymmetric Levi-Cevita tensors, the symmetric polynomials fully encode the total derivatives at that order, and thus will not contribute to the equation of motion of the helicity-0 mode. In fact, in Ref. de Rham and Gabadadze (2010), this very same property of total derivatives of the leading contributions at each order was used to build the ghost-free interactions away from . Secondly, there will be the pure interactions of the helicity-2 mode, obtained by setting , and these will come with the corresponding inverse powers of . Finally, there will be the mixed interactions between the helicity-2 and helicity-0 modes.\n\nWe are after the leading interactions in the DL, which correspond to sending all the Planck scales to infinity,\n\n MPl→∞,  Mg→∞,  Meff→∞,  Mf→∞, (22)\n\ntogether with the graviton’s mass , while keeping\n\n {Λ33=m2Meff,  MgMPl% ,  MeffMPl,  MfM%Pl}=const. (23)\n\nTaking into account the factor in front of the potential interactions, one immediately observes that the pure non-linear interactions of the helicity-2 modes do not contribute to the DL. As we already mentioned, the pure helicity-0 mode interactions do not contribute either. So it remains the mixed terms, for which the only surviving terms will be linear in the helicity-2 mode, and we finally obtain\n\n m2M2eff√−geff=3∑n=1anΛ3(n−1)3hμνP(n)μν(Π)+O(1Mg), (24)\n\nwhere and we posed\n\n P(n−1)μν(Π)≡∂e(n)(Π)∂Πμν. (25)\n\nIn arriving at Eq. (24) we have removed the trivial constant term in (20), and ignored the “tadpole” which is simply proportional to the trace and can be eliminated by choosing an appropriate de Sitter background (see, e.g., a discussion in Blanchet and Heisenberg (2015b)).\n\nWe can then write the total contribution of the gravitational sector in the DL, including that coming from the Einstein-Hilbert term of the metric, which enters only at the leading quadratic order in ,\n\n LDLgrav=−hμνEρσμνhρσ+3∑n=1anΛ3(n−1)3hμνP(n)μν(Π), (26)\n\nwhere is the usual Lichnerowicz operator on a flat background as defined by\n\n −2Eρσμνhρσ =□(hμν−ημνh)+∂μ∂νh −2∂(μHν)+ημν∂ρHρ, (27)\n\nwith and . The symmetric tensors are conserved, i.e. . For an easier comparison with the literature we give them as the product of two Levi-Cevita tensors appropriately contracted with the second derivative of the helicity-0 field,\n\n P(1)μν(Π) =−12εμλρσμενλρτΠτσ, (28a) P(2)μν(Π) =−12εμλρσμενλπτΠπρΠτσ, (28b) P(3)μν(Π) =−16εμλρσμενϵπτΠϵλΠπρΠτσ. (28c)\n\nThe first two interactions between the helicity-0 and helicity-2 fields in the Lagrangian (26) can be removed by the change of variable, defining\n\n ^hμν≡hμν−a12πημν+a22Λ33∂μπ∂νπ. (29)\n\nIn this way the Lagrangian of the gravitational sector in the decoupling limit becomes de Rham and Gabadadze (2010)\n\n LDLgrav= −^hμνEρσμν^hρσ+3∑n=0bnΛ3n3(∂π)2e(n)(Π) +a3Λ63^hμνP(3)μν(Π). (30)\n\nWe see in the first line the appearance of the ordinary Galileon terms up to quintic order [we denote ]. The coefficients are given by certain combinations of the ’s.333Namely, , , and . The last term of Eq. (III.1) is the remaining mixing between the helicity-0 and helicity-2 modes and is not removable by any local field redefinition like in (29).\n\nThe contribution of the gravitational sector to the equation of motion of the helicity-2 field gives\n\n δLDLgravδ^hμν=−2Eρσμν^hρσ+a3Λ63P(3)μν(Π), (31)\n\nwhile its contribution to the equation of motion of the helicity-0 field reads\n\n δLDLgravδπ=−24∑n=1nbn−1Λ3(n−1)3e(n)(Π)+a3Λ63Q(2)ρσμν(Π)∂ρ∂σ^hμν, (32)\n\nwhere we posed\n\n Q(2)ρσμν(Π)≡∂P(3)μν∂Πρσ=−12εμρϵλμενσνσπτΠπϵΠτλ. (33)\n\nThe second-order nature of the equations of motion in the gravity sector is apparent. This is the standard property of the ghost-free massive gravity interactions de Rham and Gabadadze (2010); de Rham et al. (2011b).\n\n### iii.2 Matter sector\n\nAs next, we shall control the contributions in the matter sector due to both the helicity-0 and helicity-2 fields. To this aim it is important to properly identify the matter degrees of freedom that are metric independent. These are provided by the coordinate densities defined as and , and by the ordinary (coordinate) velocities and . The associated currents and are conserved in the ordinary sense, and , and are related to the classical currents by\n\n J∗μg=√−gJμgandJ∗μf=√−fJμf. (34)\n\nWhen varying the action we must carefully impose that the independent matter degrees of freedom are the metric independent currents and . After variation we may restore the manifest covariance by going back to the classical currents using (34).\n\nNext we must specify how the matter variables will behave in the DL when we take the scaling limits (22)–(23). In the DL we want to keep intact the coupling between the helicity-2 mode and the particles living in the sector, therefore we impose\n\n Tμνbar=Mg^TμνbarandTμνg=Mg^Tμνg, (35)\n\nwith and remaining constant in the DL. As for the particles, in a similar way we demand that with being constant.\n\nThe next important point concerns the internal vector field . As we have seen this vector field is a graviphoton Scherk (1979), i.e. its scale is given by the Planck mass, witness the factor in front of the kinetic term of the vector field (6), see also the factor in front of the stress-energy tensor of the vector field, Eq. (11). For the model to work must be of the order of the Planck mass, as determined in (7). This means that we have to canonically normalize the vector field according to\n\n Aμ=^AμMeff, (36)\n\nand keep constant in the DL. Thus should be considered constant in that limit.\n\nA general variation of the matter action with respect to the two metrics reads\n\n δLmat =√−g2(Tμνbar+Tμνg)δgμν+√−f2Tμνfδfμν +√−geff2Tμνgeffδgeffμν. (37)\n\nWe insert Eqs. (17)–(18) and change the helicity-2 variable according to (29) to obtain the contribution of the matter action to the field equation for the helicity-2 field (in guise ) as\n\n δLmatδ^hμν =1Mg√−g(Tρ(μbar+Tρ(μg)(δν)ρ+hν)ρMg) +αMg√−geffTρ(μgeff((α+β)δν)ρ+Kν)ρ). (38)\n\nTaking the DL with the postulated scalings (35)–(36) we find that the helicity-2 mode of the massive graviton is just coupled in this limit to the baryons and particles,\n\n δLDLmatδ^hμν =^Tμνbar+^Tμνg, (39)\n\nwhere the (rescaled) stress-energy tensors and in the DL are computed with the Minkowski background.\n\nWe next consider the contributions of the matter sector to the equation of motion of the helicity-0 field. We find three contributions, two coming from the field redefinition (29),\n\n δLmatδπ∣∣∣(1a)=a12Mg√−g(Tμνbar+Tμνg)(ημν+hμνMg) (40a) δLmatδπ∣∣∣(1b)=αa12Mg√−geffTμνgeff((α+β)ημν+Kμν) +αa2MgΛ33∂ν[√−geffTμ(νgeff((α+β)δρ)μ+Kρ)μ)∂ρπ], (40b)\n\nand the third one being “direct”, and already investigated in Blanchet and Heisenberg (2015b) with result\n\n δLmatδπ∣∣∣(2)= −1Λ33∂μ∂ν[√−fTρμf(δνρ−ΠνρΛ33) (41) +β√−geffTρμgeff((α+β)δνρ+Kνρ)].\n\nThe latter contribution might look worrisome in the DL, but it becomes finite after using the equation of motion for the particles, Eq. (9b), and that for the vector field, Eq. (13). The calculation proceeds similarly to the one using Eqs. (3.29)–(3.32) in Ref. de Rham et al. (2015). Finally the result can be brought into the form Blanchet and Heisenberg (2015b)\n\n δLmatδπ∣∣∣(2) =1Λ33∂ν[J∗ρfFμρ(ημν−ΠμνΛ33)−1 (42) +β(J∗ρg−J∗ρf)Fμρ((α+β)ημν+Kμν)−1],\n\nwhere we describe the matter degrees of freedom by means of the coordinate currents (34).\n\nThe results (41) and (42) are general at this stage, and involve couplings between both the helicity-0 and helicity-2 modes with the matter fields — and particles, and the internal vector field . However, because of the scaling (36), which we recall is appropriate to the graviphoton whose coupling scale is given by the Planck mass, the vector field strength actually scales like in the DL limit. This fact kills all the interactions between the helicity-0 mode and the vector field in the DL, since they come with an inverse power of .444Note that if we do not impose the scaling the equation (III.2) for the helicity-2 field diverges in the DL. Similarly for Eq. (40b). Thus the direct contribution (42) is identically zero in the DL, and only the contribution (40a) is surviving, while (40b) is also zero. After further simplification with the matter equations of motion, we obtain (with and denoting the Minkowskian traces)\n\n δLDLmatδπ=a12(^Tbar+^Tg)+a2Λ33(^Tμνbar+^Tμνg)∂μ∂νπ. (43)\n\nRecapitulating, we find that the DL of the model consists of the following equation for the helicity-2 mode, i.e. or equivalently\n\n −2Eμνρσ^hρσ+a3Λ63Pμν(3)(Π)+^Tμνbar+^Tμνg=0, (44)\n\nwhich is of second-order nature. Thus, the contributions of the gravitational and matter sector to the equations of motion of the helicity-2 mode in the DL are ghost-free. Note, that the Bianchi identity of this equation (taking the divergence of it) is identically satisfied, since the particles actually follow geodesics in the DL. Indeed, using (35)–(36) together with the equations of motion [e.g. (9)], we have (the particles move on Minkowski straight lines).\n\nIn addition we have the total equation of motion of the helicity-0 mode, namely which reads\n\n −24∑n=1nbn−1Λ3(n−1)3e(n)(Π)+a3Λ63Q(2)ρσμν(Π)∂ρ∂σ^hμν (45) =−a12(^Tbar+^Tg)−a2Λ33(^Tμνbar+^Tμνg)∂μ∂νπ.\n\nSince this equation is perfectly of second-order in the derivatives of the field, we conclude our study by stating that the model is safe (ghost-free) up to the strong coupling scale. Below that scale the theory is perfectly acceptable as an Effective Field Theory, and its consequences can be worked out using perturbation theory as usual. For instance, solving at linear order the helicity-0 equation (45) we obtain the usual well-posed (hyperbolic-like) equation\n\n □π=a14b0(^Tbar+^Tg)+O(π2), (46)\n\nwhich can then be perturbatively iterated to higher order. With this we have proved, that the coupling of the dark matter particles with the internal vector field does not introduce any ghostly contribution in the DL.\n\n## Iv Conclusions\n\nThis work was dedicated to the detailed study of the decoupling limit interactions of the dark matter model proposed in Blanchet and Heisenberg (2015a, b). This model is constructed via a specific coupling of two copies of dark matter particles to two metrics in the framework of massive bigravity. Furthermore, an internal vector field links the two dark matter species. This enables us to implement a mechanism of gravitational polarization, which induces the MOND phenomenology on galactic scales (with the specific choice of parameters studied in Blanchet and Heisenberg (2015b)). Note that, since our model successfully reproduces all aspects of that phenomenology, it will be in agreement with the recent observations of the MOND mass-discrepancy-acceleration relation in McGaugh et al. (2016).\n\nSome theoretical and phenomenological consequences of this model were studied in detail in Ref. Blanchet and Heisenberg (2015b), but it was also pointed out that the decoupling limit of the theory may be problematic, with higher derivative terms occuring in the equation of motion of the helicity-0 mode of the massive graviton.\n\nIn the present work, we studied the complete DL interactions crucially including the contributions of the matter sector, and we showed that by necessary rescaling of the vector field (as appropriate for a vector field with Planckian coupling constant) the theory is free from ghosts in the DL, and hence can be used as a valid Effective Field Theory up to the strong coupling scale.\n\n###### Acknowledgements.\nWe would like to thank Claudia de Rham and Andrew Tolley for very useful and enlightening discussions. L.H. wishes to acknowledge the Institut d’Astrophysique de Paris for hospitality and support at the final stage of this work." ]

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[ "", null, "NumericClass - Maple Programming Help\n\n# Online Help\n\n###### All Products    Maple    MapleSim\n\nNumericClass\n\nreturn the class of x\n\n Calling Sequence NumericClass(x)\n\nParameters\n\n x - expression\n\nDescription\n\n • The NumericClass(x) function returns the class of x represented as a type. The class of x is described by a Maple type that recognizes\n - the computation environment, and\n - the numerical type of x.\n • If x is complex, then NumericClass(x) returns as narrowly constrained a type as possible to recognize x. To obtain precise information about the real and imaginary part of x separately, use NumericClass(Re(x)) and NumericClass(Im(x)).\n\nThread Safety\n\n • The NumericClass command is thread-safe as of Maple 15.\n • For more information on thread safety, see index/threadsafe.\n\nExamples\n\n > NumericClass(0);\n ${\\mathrm{rational}}{\\wedge }{\\mathrm{poszero}}$ (1)\n > NumericClass(2.3);\n ${\\mathrm{sfloat}}{\\wedge }{\\mathrm{positive}}{\\wedge }{\\mathrm{numeric}}$ (2)\n > NumericClass(infinity);\n ${\\mathrm{extended_rational}}{\\wedge }{\\mathrm{positive}}{\\wedge }{\\mathrm{\\infty }}$ (3)\n > x := 3 - 2*I;\n ${x}{≔}{3}{-}{2}{}{I}$ (4)\n > NumericClass(x);\n ${\\mathrm{nonreal}}{}\\left({\\mathrm{posint}}{\\vee }{\\mathrm{negint}}\\right)$ (5)\n > NumericClass(Re(x));\n ${\\mathrm{posint}}$ (6)\n > NumericClass(Im(x));\n ${\\mathrm{negint}}$ (7)\n > NumericClass(2*I);\n ${\\mathrm{imaginary}}{}\\left({\\mathrm{posint}}\\right)$ (8)\n > NumericClass(HFloat(-4.5));\n ${{\\mathrm{float}}}_{{8}}{\\wedge }{\\mathrm{negative}}{\\wedge }{\\mathrm{numeric}}$ (9)\n > NumericClass(HFloat(-3+5*I));\n ${\\mathrm{nonreal}}{}\\left(\\left({{\\mathrm{float}}}_{{8}}{\\wedge }{\\mathrm{negative}}{\\wedge }{\\mathrm{numeric}}\\right){\\vee }\\left({{\\mathrm{float}}}_{{8}}{\\wedge }{\\mathrm{positive}}{\\wedge }{\\mathrm{numeric}}\\right)\\right)$ (10)\n\n See Also" ]

[ null, "https://bat.bing.com/action/0", null ]

[ "# Cot Negative 30° Degrees\n\nA simple online calculator to find the cot value of negative 30° degrees / radians. Choose the degrees and radians from the select box and find the cot of negative α value. Calculate the exact value of cot negative 30° with this calculator in a simple and easy way.\n\n### Formula :\n\ncot (α)\n= 1 / tan (α)\n\nBelow listed are the other calculators to find the cos, tan, cot, csc, sec values of negative 30° degrees / radians." ]

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[ "💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!\n\nSB\n\n# Find an equation of the plane.The plane that passes through the point $(3, 1, 4)$ and contains the line of intersection of the planes $x + 2y + 3z = 1$ and $2x - y + z = -3$\n\n## $-x+2 y+z=3$\n\nVectors\n\n### Discussion\n\nYou must be signed in to discuss.\n##### Catherine R.\n\nMissouri State University\n\n##### Kristen K.\n\nUniversity of Michigan - Ann Arbor\n\n##### Michael J.\n\nIdaho State University\n\nLectures\n\nJoin Bootcamp\n\n### Video Transcript\n\nAccording to the question, we have to find the equation of the plane that passes through the .314 and contains the line of intersection of the plains. Given by the equation number one express two, Y plus trees that equal to one. And equation two is two, X minus Y plus Z is equal to minus three. So in order to find the equation of the plane according to the given equation and point given in the question. So firstly they have given a point, let's say the point is E. And the coordinates are given us 31 fools. And in order to find the question of the plane we first have to find a normal victor And using these points we can find the equation of the plane. So in order to find the normal victim to the plane we have to find another. Mhm two points in the plane using the equation one and two. Therefore if X equal to zero then Equation one and 2 becomes do Y plus tris ID Equal to one and why minus way less? That is equal to -3. And by solving the simultaneous equation continues the two variables Y and there we can find out available. So if we multiply equation do with two then It will become -2. Y Plus two, said is equal to In place of minus treat will become -6. So solving mm The equations we can get by adding distributions, we can get that pi Z is equal to minus five, therefore Z is equal to minus one and in order to find out the value of why we can put the value of set in any of these equations that is minus Y plus said equal to minus three. Immigration to if you put the value of \\$0.00 -1 then it will become Why is equal to 3 -1, that is equal to two. Therefore we got another points. Let us say it be which has coordinates zero, two and minus one. Yes. Yeah. Yeah. And in order to find another point in the plane, you have to consider the value of the Is equal to zero. Therefore equation one and 2 becomes X plus to way equal to one and two weeks -Y Equal to -3. So in order to equate this to value and catholic the values of the variables multiplying equation two by two. We get This way efficient as four. This is too And this is six. Therefore adding these two equations. We can get the value of X, that is five X equal to minus five. Therefore The value of x equal to -1. And putting the value of X. In any of the equations we can get the value of Y. That is x minus y two, X minus Y Is equal to -3. Therefore go into minus one minus white. Well to minus three and therefore the value of why is equal to minus two plus three, that is equal to one. Therefore we got the coordinates of another point. Let's suppose the point. Because they see these coordinates are minus one one and zero. Therefore The three points in the plane. Oh point E 314 point b 0 to -1 buoyancy -110. Therefore in order to find the normal vector to the plane we have to find the two lines from these points that is line A B vector is equal to 0 -3. I gap Plus 2 -1. Jacob Plus -1 -4 K Cab. This is equal to -3 icap plus Jacob -5 K cups and this is equal to victor once opposed. And another line vector that is a C vector is equal to -1 -3, icap plus 1 -1. Jacob 0 -4. Kick up this is equal to minus minus four. I grew up less zero, Jacob less mm That is -4. Kick up. And let us suppose this vector is equal to be to cap. Then in order to find the normal vector to the plane You have to find the cross product of B one. And we do this is equal to Ichabod Jacob Jacob and The values are -3, -5 And -4, 0. And minus for therefore the after calculating this cross product, the normal vector will be equal to minus four Icap. Let's eat Jacob, my bliss for kick up. So from this we can calculate the equation on the plane as follows. That is Yeah. Yeah. By the formula To find the equation of the planet is in two X minus egg zero plus being two Y minus Y zero Plus seen to that zero equal to zero, bear A. B. C. Although mhm coefficient of direction vectors for the normal victor. That is this is A. This is B. This is C. And egg zero, Y. Zero and zero. Although point in the Mhm len here this point is equal to 314 as given in the question. Okay so the aggression of the plane is equal to yeah minus four X minus three. Let's eat. Why? Minus one last four. That minus four Is equal to zero. After solving the situation, we can derive the final equation of the plane as minus X plus two. Y. Let's said equal to three. And this is the required equation under lean for the given question.\n\n#### Topics\n\nVectors\n\n##### Catherine R.\n\nMissouri State University\n\n##### Kristen K.\n\nUniversity of Michigan - Ann Arbor\n\n##### Michael J.\n\nIdaho State University\n\nLectures\n\nJoin Bootcamp" ]

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[ "Program Flow  «Prev  Next»\n Lesson 6 Nested Loops Objective Application of Nested Loops\n\n# Nested Loop\n\n### Nested loops\n\nLoops can be nested within each other. Any nested combination of the for, for-each, while, or do-while loops is permitted. This is useful for addressing a number of problems. The example that follows computes the sum of the elements of a row in a two-dimensional array. It starts by initializing each element to the sum of its indexes. The array is then displayed. This is followed by nested loops to compute and display the sum of the elements for each row:\n\n```final int numberOfRows = 2;\nfinal int numberOfColumns = 3;\nint matrix[][] = new int[numberOfRows][numberOfColumns];\nfor (int i = 0; i lt; matrix.length; i++) {\nfor (int j = 0; j < matrix[i].length; j++) {\nmatrix[i][j] = i + j;\n}\n}\nfor (int i = 0; i < matrix.length; i++) {\nfor(int element : matrix[i]) {\nSystem.out.print(element + \" \");\n}\nSystem.out.println();\n}\nfor (int i = 0; i < matrix.length; i++) {\nint sum = 0;\nfor(int element : matrix[i]) {\nsum += element;\n}\nSystem.out.println(\"Sum of row \" + i + \" is \" +sum);\n}\n```\n\nNotice the use of the length method used to control the number of times the loops are executed. This makes the code more maintainable if the size of the arrays change. When executed we get the following output:\n```0 1 2\n1 2 3\nSum of row 0 is 3\nSum of row 1 is 6\n```\n\nNotice the use of the for-each statement when the array is displayed and the sum of the rows are calculated. This simplifies the calculations. The break and continue statements can also be used within nested loops. However, they will only be used in conjunction with the current loop. That is, a break out of an inner loop will only break out of the inner loop and not the outer loop. As we will see in the next section, we can break out of the outer loop from an inner loop using labels. In the following modification of the last nested loop sequence, we break out of the inner loop when the sum exceeds 2:\n```for (int i = 0; i < matrix.length; i++) {\nint sum = 0;\nfor(int element : matrix[i]) {\nsum += element;\nif(sum > 2) {\nbreak;\n}\n}\nSystem.out.println(\"Sum of row \" + i + \" is \" +sum);\n}\n```\n\nThe execution of this nested loop will change the sum of the last row as shown below:\n```Sum of row 0 is 3\nSum of row 1 is 3\n```\n\nThe break statement took us out of the inner loop but not the outer loop. We can break out of the outer loop if there was a corresponding break statement within the immediate body of the outer loop. The continue statement behaves in a similar fashion in relation to inner and outer loops." ]

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[ "# physics\n\nA car accelerates uniformly from rest to a speed of 55 km/h (15 m/s) in 14 s. Find the distance the car travels during this time.\n\n1. 👍 0\n2. 👎 0\n3. 👁 79\n1. Multiply the average velocity, 7.64 m/s, by the time interval, 14 s.\n\nNote: 55 km/h is actually 15.28 m/s, not 15.0\n\nIf they want the answer rounded to 2 significant figures, then using 7.5 m/s for the average velocity is OK\n\n1. 👍 0\n2. 👎 0\nposted by drwls\n2. hhahaha\n\n1. 👍 0\n2. 👎 0\n3. 3.93\n\n1. 👍 0\n2. 👎 0\n\n## Similar Questions\n\n1. ### Physics\n\n1. A car starts from rest and accelerates uniformly at 3.0 m/s2. A second car starts from rest 6.0 s later at the same point and accelerates uniformly at 5.0 m/s2. How long does it take the second car to overtake the first car? 2.\n\nasked by G on February 16, 2012\n2. ### Physics\n\nTwo cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 4.8 m/s2 for 4.5 seconds. It then continues at a constant speed for 9.9\n\nasked by Jeel on January 22, 2011\n3. ### Physics\n\nTwo cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 5 m/s2 for 4.2 seconds. It then continues at a constant speed for 11.1\n\nasked by Isaiah on January 21, 2015\n4. ### Physics\n\nTwo cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 3.5 m/s2 for 3.6 seconds. It then continues at a constant speed for 10.1\n\nasked by Hayls on January 24, 2011\n5. ### physics\n\nTwo cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 4.6 m/s2 for 4.4 seconds. It then continues at a constant speed for 8.5\n\nasked by a on September 13, 2011\n6. ### physics\n\nplease somebdy help me solveing this. Two cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 4.3 m/s2 for 3.3 seconds. It then\n\nasked by atif on September 20, 2014\n7. ### physics\n\nTwo cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 5.5 m/s2 for 4.9 seconds. It then continues at a constant speed for 6.7\n\nasked by kayle on January 27, 2014\n8. ### physics with 6 questions\n\nTwo cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 3.3 m/s2 for 3.9 seconds. It then continues at a constant speed for 13.7\n\nasked by David on August 27, 2012\n9. ### physics\n\nQ: Two cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 5.7 m/s2 for 3.2 seconds. It then continues at a constant speed for 8.8\n\nasked by Alex on February 8, 2018\n10. ### physics\n\nA car starting from rest accelerates uniformly are attaing a speed of 80m/s in 30s it maintains this stedy speed for another 30s. It then slow down uniformly until it comes to rest in the next 40s" ]

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[ "Start at 1: 1×20=20, so put 1 at the start, and put its \"partner\" 20 at the other end: 1 : 20: Then try 2. factorial of n (n!) Recent advances have redefined a role for T cell factor 1 (TCF1) that goes beyond T cell development and T memory formation and encompasses new functions in the regulation of T cell biology. (2n)!! n! Definition of n!. (N factorial). Take integer variable A 2. 1.8%. Middle School Math Solutions – Equation Calculator. = 1 if n = 0 or n = 1 The factorial is normally used in Combinations and Permutations (mathematics). Algorithm: Factorial value . Factorial definition, the product of a given positive integer multiplied by all lesser positive integers: The quantity four factorial (4!) (n - 1)!! int counter = 5; long factorial = counter; while (counter > 1) factorial *= --counter; // Multiply the decremented number. For example, a \"DF\" of 100 means a 1:100 dilution. = 24 05! The factorial can be seen as the result of multiplying a sequence of descending natural numbers (such as 3 × 2 × 1). = n * (n-1)! Article continues under video . 2×10=20 works, so put in 2 and 10: 1: 2 : 10: 20: Then try 3. Solution: \"DF\" = V_f/V_i V_i = V_f/(\"DF\") =\"500 mL\"/250 = \"2.00 mL\" Pipet 2.00 mL of your stock solution into a 500 mL volumetric flask. n! Here, 4! )^2 fails to fit into a long. = 1 * 2 * 3 * 4....n The factorial of a negative number doesn't exist. Middle School Math Solutions – Polynomials Calculator, Factoring Quadratics. Factorial of a non-negative integer, is multiplication of all integers smaller than or equal to n. For example factorial of 6 is 6*5*4*3*2*1 which is 720. //n! Factorial of 1 is 1 Factorial of 2 is 2 Factorial of 3 is 12 Factorial of 4 is 288 Factorial of 5 is 34560 Which is obviously wrong. f = factorial(n) returns the product of all positive integers less than or equal to n, where n is a nonnegative integer value.If n is an array, then f contains the factorial of each value of n.The data type and size of f is the same as that of n.. I couldn’t agree more. Some identities involving double factorials are: n! Related Symbolab blog posts. For negative integers, factorials are not defined. Note: Factorial of zero = 1 . From value, A up to 1 multiply each digit and store 4. = 6 04! Welcome to our new \"Getting Started\" math solutions series. Factorial Notation. I would really like to know what is wrong with my code and how to fix it. In the above program, the function fact() is a recursive function. The factorial symbol is the exclamation mark !. 9.4%. very-5.6%. The dilution factor is often used as the denominator of a fraction. But that starts failing when (N! Factorial of number is defined as: Factorial (n) = 1*2*3 … * n. For example: Factorial of 5 = 1*2*3*4*5 = 120. Factor of 1 is 1. For the following sections on counting, we need a simple way of writing the product of all the positive whole numbers up to a given number.We use factorial notation for this.. And, the factorial of 0 is 1. 1. The official National Hockey League website including news, rosters, stats, schedules, teams, and video. The factorial of a positive number n is given by:. But there are reasons for these definitions; they are not arbitrary. So, I know I solve the problem by getting all the divisors of (N!)^2. image/svg+xml. The question is, how to solve 1/x + 1/y = 1/N! Synonyms of the month. EXAMPLE 2: How would you make 500 mL of a 1:250 dilution? One should be careful not to interpret n!! n. The product of all the positive integers from 1 to a given number: 4 factorial, usually written 4!, is equal to 24 . 2. n. The product of all the positive integers from 1 to a given number: 4 factorial, usually written 4!, is equal to 24 . We've used long instead of int to store large results of factorial. 1. 4×5=20 works, so put them in: 1: 2: 4 : 5: 10: 20: There is no whole number between 4 and 5 so you are done! = 1 for reasons that are similar to why x^0 = 1. Here, we discuss the multifaceted and context-dependent role of TCF1 in peripheral T cells, particularly during disease-induced inflammatory states such as autoimmunity, cancer, and chronic infections. that'll fit into a long). snowflake. That figure includes a brutal second half of the campaign of 11 races in 15 weeks, comprising two triple-headers and two double-headers on three different continents. = 2 n n! 104.5%. Recent Examples on the Web: Noun The exclamation point there isn’t the end of a sentence but, instead, denotes a factorial, the value obtained by multiplying the number by every number that precedes it. The factorial function is defined for non-negative integers only, that is, for the numbers $0, 1, 2, 3, \\ldots$. = 2 03! Or, you could just put the fraction into Google Calculator, which uses the gamma function to evaluate factorials of any number. factor\\:2x^5+x^4-2x-1; factor-calculator. Algorithm 1. 0.7%. Date: 03/18/98 at 16:39:40 From: Doctor Sam Subject: Re: 0 factorial = 1 Denise, You are correct that 0! The sequence of double factorials for n = 0, 1, 2,... starts. Factorial function synonyms, Factorial function pronunciation, Factorial function translation, English dictionary definition of Factorial function. 3 doesn't work (3×6=18 is too low, 3×7=21 is too high). The factorial of n is commonly written in math notation using the exclamation point character as n!.Note that n! Write a c program to check given number is Armstrong number or not. Factorial series in given range: 1 2 6 24 120 720 5040 40320 362880 3628800. = 4 ⋅ 3 ⋅ 2 ⋅ 1 = 24. = 120 06! Eukaryotic polypeptide elongation factor EF-1 is not only a major translational factor, but also one of the most important multifunctional (moonlighting) proteins. Recursive Solution: Factorial can be calculated using following recursive formula. 01! = 720 07! Factorial of 4 is 24. is pronounced as \"4 factorial\", it is also called \"4 bang\" or \"4 shriek\". Symbol:n!, where n is the given integer. = 39916800 12! See also main entry: factor See also main entry: factor Thesaurus Trending Words. Note: I don't wish to use the math.factorial function for this code. = 362880 10! en. In particular, Factorial [n] returns the factorial of a given number , which, for positive integers, is defined as .For n 1, 2, …, the first few values are therefore 1, 2, 6, 24, 120, 720, ….The special case is defined as 1, consistent with the combinatorial interpretation of there being exactly one way to arrange zero objects. 9 = 945. = n*(n-1)! cout<<\"Factorial of \"< Spicy Broth Recipe, Captain Morgan Parrot Bay Canada, Fnaf Security Breach Vanny, Canned 3 Bean Salad, Bianco Romano Granite, Best Facial Wash Philippines 2020, Ratpoison Config Reddit," ]

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[ "# MOSFET\n\nNote\n\nLevel 1, 2, 3 and 17 MOSFETs are described in this section. For other devices:\n\nIn this topic:\n\n## Netlist Entry\n\nMxxxx drain gate source bulk modelname [L=length] [W=width]\n+ [PD=drain_perimeter] [PS=source_perimeter]\n+ [NRD=drain_squares] [NRS=source_squares]\n+ [NRB=bulk_squares]\n+ [OFF] [IC=vds,vgs,vbs] [TEMP=local_temp] [M=area]\n drain Drain node gate Gate node source Source node bulk Bulk (substrate) node modelname Name of model. Must begin with a letter but can contain any character except whitespace and period '.'\n(The following 8 parameters are not supported by the level 17 MOSFET model)\n length Channel length (metres). width Channel width (metres). drain_area Drain area (m2). source_area Source area (m2). drain_perimeter Drain perimeter (metres). source_perimeter Source perimeter (metres). drain_squares Equivalent number of squares for drain resistance source_squares Equivalent number of squares for source resistance gate_squares Equivalent number of squares for gate resistance. Level=3 only bulk_squares Equivalent number of squares for gate resistance. Level=3 only OFF Instructs simulator to calculate operating point analysis with device initially off. This is used in latching circuits such as thyristors and bistables to induce a particular state. See .OP for more details. vds, vgs, vbs Initial condition voltages for drain-source gate-source and bulk(=substrate)-source respectively. These only have an effect if the UIC parameter is specified on the .TRAN statement. local_temp Local temperature. Overrides specification in .OPTIONS or .TEMP statements. dtemp Differential temperature. Similar to local_temp but is specified relative to circuit temperature. If both TEMP and DTEMP are specified, TEMP takes precedence. Currently implemented only for LEVEL 1,2 and 3.\n Notes SIMetrix supports four types of MOSFET model specified in the model definition. These are referred to as levels 1, 2, 3 and 7. Levels 1,2, and 3 are the same as the SPICE2 and SPICE3 equivalents. Level 17 is proprietary to SIMetrix. For further information see Level 17 MOSFET parameters below.\n\n## NMOS Model Syntax\n\n.model modelname NMOS ( level=level_number parameters )\n\n## PMOS Model Syntax\n\n.model modelname PMOS ( level=level_number parameters )\n\n## MOS Levels 1, 2 and 3: Model Parameters\n\nName Description Units Default Levels\nVTO or VT0 Threshold voltage V 0.0 all\nKP Transconductance parameter A/V2 2.0e-5 all\nGAMMA Bulk threshold parameter V 0.0 all\nPHI Surface potential V 0.6 all\nLAMBDA Channel length modulation 1/V 0.0 all\nRG Gate ohmic resistance $\\Omega$ 0.0 1,3\nRD Drain ohmic resistance $\\Omega$ 0.0 all\nRS Source ohmic resistance $\\Omega$ 0.0 all\nRB Bulk ohmic resistance $\\Omega$ 0.0 3\nRDS Drain-source shunt resistance $\\Omega$ $\\infty$ 3\nCBD B-D junction capacitance F 0.0 all\nCBS B-S junction capacitance F 0.0 all\nIS Bulk junction sat. current A 1.0e-14 all\nPB Bulk junction potential V 0.8 all\nCGSO Gate-source overlap capacitance F/m 0.0 all\nCGDO Gate-drain overlap capacitance F/m 0.0 all\nCGBO Gate-bulk overlap capacitance F/m 0.0 all\nRSH Drain and source diffusion resistance $\\Omega$/sq. 0.0 all\nCJ Zero bias bulk junction bottom capacitance/sq-metre of junction area F/m2 See note all\nMJ Bulk junction bottom grading coefficient 0.5 all\nCJSW Zero bias bulk junction sidewall capacitance F/m 0.0 all\nMJSW Bulk junction sidewall grading coefficient 0.5 1\nMJSW as above 0.33 2,3\nJS Bulk junction saturation current/sq-metre of junction area A/m2 0.0 all\nJSSW Bulk p-n saturation sidewall current/length A/m 0.0 3\nTT Bulk p-n transit time secs 0.0 3\nTOX Oxide thickness metre 1e-7 all\nNSUB Substrate doping 1/cm2 0.0 all\nNSS Surface state density 1/cm2 0.0 all\nNFS Fast surface state density 1/cm2 0.0 2,3\nTPG Type of gate material:\n +1 opposite. to substrate -1 same as substrate 0 Al gate\nall\nXJ Metallurgical junction depth metre 0.0 2,3\nLD Lateral diffusion metre 0.0 all\nUO Surface mobility cm2/Vs 600 all\nUCRIT Critical field for mobility V/cm 0.0 2\nUEXP Critical field exponent in mobility degradation 0.0 2\nUTRA Transverse field coefficient (mobility) 0.0 1,3\nVMAX Maximum drift velocity of carriers m/s 0.0 2,3\nNEFF Total channel charge (fixed and mobile) coefficient 1.0 2\nFC Forward bias depletion capacitance coefficient 0.5 all\nTNOM, T_MEASURED Reference temperature; the temperature at which the model parameters were measured $°$C 27 all\nT_ABS If specified, defines the absolute model temperature overriding the global temperature defined using .TEMP $°$C .TEMP all\nT_REL_GLOBAL Offsets global temperature defined using .TEMP. Overridden by T_ABS $°$C 0.0 all\nKF Flicker noise coefficient 0.0 all\nAF Flicker noise exponent 1.0 all\nDELTA Width effect on threshold voltage 0.0 2,3\nTHETA Mobility modulation 1/V 0.0 3\nETA Static feedback 0.0 3\nKAPPA Saturation field factor 0.2 3\nW Width metre DEFW all\nL Length metre DEFL all\nNLEV Noise model 2 all\n\n## CJ Default\n\nIf not specified CJ defaults to $\\sqrt{\\epsilon_sq\\times\\text{NSUB}\\times1\\text{e}6 / (2\\times\\text{PB})}$ where\n• $\\epsilon_s$ = 1.03594314e-10 (permittivity of silicon)\n• q = 1.6021918e-19 (electronic charge)\n• NSUB, PB model parameters\n\n## Gate Charge Model, Levels 1, 2 and 3\n\nTwo gate charge models are available for MOS Levels 1, 2 and 3 selectable by the .OPTIONS setting SPICEMOSCHARGEMODEL:\n\n.OPTIONS SPICEMOSCHARGEMODEL=0|1\nThe option value is defined as follows:\n 0 Meyer capacitance model. This is the original model used in SPICE2 and SPICE3 and derivatives. The gate charge is defined by its capacitance and does not conserve charge 1 Yang-Chatterjee charge model. This is the model used by PSpice. It is charge based and as such does correctly conserve charge\n\nMOS level 1-3 models are predominantly used as part of many manufacturer-designed power MOS and IGBT subcircuit models. In most cases the choice of gate charge model is unimportant. However, for a few models, the results vary significantly with the choice of model used. Most models are designed for PSpice and so the safest choice is the Yang-Chatterjee charge model (.OPTIONS SPICEMOSCHARGEMODEL=1). However, SIMetrix version 8.0 and earlier do not support this model so for compatibility with earlier versions the Meyer capacitance model is the default.\n\nThe setting .OPTIONS SPICECOMPATIBILITY=2 automatically enables the Yang-Chatterjee charge model as the default.\n\n## Notes for levels 1, 2 and 3:\n\nThe three levels 1 to 3 are as follows:\n\n LEVEL 1 Shichman-Hodges model. The simplest and is similar to the JFET model LEVEL 2 A complex model which models the device according to an understanding of the device physics LEVEL 3 Simpler than level 2. Uses a semi-empirical approach i.e. the device equations are partly based on observed effects rather than the theory governing its operation\nThe L and W parameters perform the same function as the L and W parameters on the device line. If omitted altogether they are set to the option values (set with .OPTIONS statement) DEFL and DEFW respectively. These values in turn default to 100 microns.\n\nThe above models differ from all other SIMetrix (and SPICE) models in that they contain many geometry relative parameters. The geometry of the device (length, width etc.) is entered on a per component basis and various electrical characteristics are calculated from parameters which are scaled according to those dimensions. This is approach is very much geared towards integrated circuit simulation and is inconvenient for discrete devices. If you are modelling a particular device by hand we recommend you use the level 17 model which is designed for discrete vertical devices.\n\n## MOS Level 17: Model Parameters\n\n Name Description Units Default VTO or VT0 Threshold voltage V 0.0 KP Transconductance parameter A/V2 2.0e-5 GAMMA Bulk threshold parameter $\\sqrt{\\text{V}}$ 0.0 PHI Surface potential V 0.6 LAMBDA Channel length modulation 1/V 0.0 RD Drain ohmic resistance $\\Omega$ 0.0 RS Source ohmic resistance $\\Omega$ 0.0 CBD B-D junction capacitance F 0.0 CBS B-S junction capacitance F 0.0 IS Bulk junction sat. current A 1.0e-14 PB Bulk junction potential V 0.8 CGSO Gate-source overlap capacitance F 0.0 CGBO Gate-bulk overlap capacitance F 0.0 CJ Zero bias bulk junction bottom capacitance F 0.0 MJ Bulk junction bottom grading coefficient 0.5 CJSW Zero bias bulk junction sidewall capacitance F 0.0 MJSW Bulk junction sidewall grading coefficient 0.5 FC Forward bias depletion capacitance coefficient 0.5 TNOM Parameter measurement temperature $°$C 27 KF Flicker noise coefficient 0.0 AF Flicker noise exponent 1.0 CGDMAX Maximum value of gate-drain capacitance F 0.0 CGDMIN Minimum value of gate-drain capacitance F 0.0 XG1CGD cgd max-min crossover gradient 1.0 XG2CGD cgd max-min crossover gradient 1.0 VTCGD cgd max-min crossover threshold voltage V 0.0 TC1RD First order temperature coefficient of RD 1/$°$C 0.0 TC2RD Second order temperature coefficient of RD 1/$°$C2 0.0\n\n## Notes for level 17\n\nIn SIMetrix version 5.2 and earlier, this model used a level parameter value of 7 instead of the current 17. The number was changed so that a PSpice compatible BSIM3 model (level=7) could be offered. In order to retain backward compatibility, any level 7 model containing the parameters cgdmax, cgdmin, xg1cgd, xg2cgd or vtcgd will automatically be switched to level=17.\n\nThe level 17 MOSFET was developed to model discrete vertical MOS transistors rather than the integrated lateral devices that levels 1 to 3 are aimed at. Level 17 is based on level 1 but has the following important additions and changes:\n\n• New parameters to model gate-drain capacitance\n• 2 new parameters to model rdson variation with temperature.\n• All parameters are absolute rather than geometry relative. (e.g. capacitance is specified in farads not farads/meter)\nAll MOSFET models supplied with SIMetrix are level 17 types. Many models supplied by manufacturers are subcircuits made up from a level 1, 2 or 3 device with additional circuitry to correctly model the gate-drain capacitance. While the latter approach can be reasonably accurate it tends to be slow because of its complexity.\n\nGate-drain capacitance equation:\n\n$\\begin{split} C_{gd} = \\left(0.5 - \\frac{1}{\\pi}\\tan^{-1}\\left(\\left(\\text{VTCGD} - v\\right) - \\text{XG1CGD}\\right)\\right)\\text{CGDMIN} \\\\ + \\left(0.5 - \\frac{1}{\\pi}\\tan^{-1}\\left(\\left(\\text{VTCGD} - v\\right)\\text{XG2CGD}\\right)\\right)\\text{CGDMAX} \\end{split}$\n\nwhere $v$ is the gate-drain voltage. This is an empirical formula devised to fit measured characteristics. Despite this it has been found to follow actual measured capacitance to remarkable accuracy.\n\nTo model gate-drain capacitance quickly and to acceptable accuracy set the five $\\text{C}_{\\text{gd}}$ parameters as follows:\n\n1. Set CGDMIN to minimum possible value of $\\text{C}_{\\text{gd}}$ i.e. when device is off and drain voltage at maximum.\n2. Set CGDMAX to maximum value of $\\text{C}_{\\text{gd}}$ i.e. when device is on with drain-source voltage low and gate-source voltage high. If this value is not known use twice the value of $\\text{C}_{\\text{gd}}$ for $\\text{V}_{\\text{gd}}=0$.\n3. Set XG2CGD to 0.5, XG1CGD to 0.1 and leave VTCGD at default of 0.\nAlthough the parasitic reverse diode is modelled, it is connected inside the terminal resistances, RD and RS which does not represent real devices very well. Further, parameters such as transit time (TT) which model the reverse recovery characteristics of the parasitic diode are not included. For this reason it is recommended that the reverse diode is modelled as an external component. Models supplied with SIMetrix are subcircuits which include this external diode." ]

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[ "# Bracket Sequence", null, "Two great friends, Eddie John and Kris Cross, are attending the Brackets Are Perfection Conference. They wholeheartedly agree with the main message of the conference and they are delighted with all the new things they learn about brackets.\n\nOne of these things is a bracket sequence. If you want to do a computation with $+$ and $\\times$, you usually write it like so:\n\n$(2 \\times (2 + 1 + 0 + 1) \\times 1) + 3 + 2.$\n\nThe brackets are only used to group multiplications and additions together. This means that you can remove all the operators, as long as you remember that addition is used for numbers outside any parentheses! A bracket sequence can then be shortened to\n\n$(\\; 2 \\; ( \\; 2 \\; 1 \\; 0 \\; 1 \\; ) \\; 1 \\; ) \\; 3 \\; 2.$\n\nThat is much better, because it saves on writing all those operators. Reading bracket sequences is easy, too. Suppose you have the following bracket sequence\n\n$5 \\; 2 \\; (\\; 3 \\; 1 \\; (\\; 2 \\; 2 \\; ) \\; ( \\; 3 \\; 3 \\; ) \\; 1 \\; ).$\n\n$5 + 2 + (\\; 3 \\; 1 \\; (\\; 2 \\; 2 \\; ) \\; ( \\; 3 \\; 3 \\; ) \\; 1 \\; ).$\n\nYou know the parentheses group a multiplication, so this is equal to\n\n$5 + 2 + (3 \\times 1 \\times (\\; 2 \\; 2 \\; ) \\times ( \\; 3 \\; 3 \\; ) \\times 1).$\n\nThen there is another level of parentheses: that groups an operation within a multiplication, so the operation must be addition.\n\n$5 + 2 + (3 \\times 1 \\times (2 + 2 ) \\times (3 + 3) \\times 1 ) = 5 + 2 + (3 \\times 1 \\times 4 \\times 6 \\times 1) = 5+2 + 72 = 79.$\n\nSince bracket sequences are so much easier than normal expressions with operators, it should be easy to evaluate some big ones. We will even allow you to write a program to do it for you.\n\nNote that $(\\; )$ is not a valid bracket sequence, nor a subsequence of any valid bracket sequence.\n\n## Input\n\n• One line containing a single integer $1\\leq n\\leq 3\\cdot 10^5$.\n\n• One line consisting of $n$ tokens, each being either (, ), or an integer $0\\leq x < 10^9+7$. It is guaranteed that the tokens form a bracket sequence.\n\n## Output\n\nOutput the value of the given bracket sequence. Since this may be very large, you should print it modulo $10^9+7$.\n\nSample Input 1 Sample Output 1\n2\n2 3\n\n5\n\nSample Input 2 Sample Output 2\n8\n( 2 ( 2 1 ) ) 3\n\n9\n\nSample Input 3 Sample Output 3\n4\n( 12 3 )\n\n36\n\nSample Input 4 Sample Output 4\n6\n( 2 ) ( 3 )\n\n5\n\nSample Input 5 Sample Output 5\n6\n( ( 2 3 ) )\n\n5\n\nSample Input 6 Sample Output 6\n11\n1 ( 0 ( 583920 ( 2839 82 ) ) )\n\n1" ]

[ null, "https://open.kattis.com/problems/bracketsequence/file/statement/en/img-0001.jpg", null ]

[ "# Zermelo-Fraenkel set theory\n\nThe Zermelo-Fraenkel set theory is a widespread axiomatic set theory that is named after Ernst Zermelo and Abraham Adolf Fraenkel . Today it is the basis of almost all branches of mathematics. The Zermelo-Fraenkel set theory without a choice axiom is abbreviated to ZF , with a choice axiom to ZFC (where the C stands for the English word choice , i.e. choice or choice).\n\n## history\n\nThe Zermelo-Fraenkel set theory is an extension of the Zermelo set theory from 1907, which is based on axioms and suggestions from Fraenkel from 1921. Fraenkel added to the replacement axiom and advocated regular sets without circular element chains and for a pure set theory whose objects are only sets. In 1930, Zermelo completed the axiom system of the Zermelo-Fraenkel set theory, which he himself referred to as the ZF system: He adopted Fraenkel's substitution axiom and added the foundation axiom to exclude circular element chains, as demanded by Fraenkel. The original ZF system is verbal and also takes into account original elements that are not quantities. Later formalized ZF systems usually do without such original elements and thus fully implement Fraenkel's ideas. Thoralf Skolem created the first precise predicate logic formalization of the pure ZF set theory in 1929 (still without a foundation axiom). This tradition has prevailed, so that today the abbreviation ZF stands for the pure Zermelo-Fraenkel set theory. The version with original elements, which is closer to the original ZF system, is still used today and is called the ZFU for clear differentiation.\n\n## meaning\n\nIt has been shown - this is an empirical finding - that almost all known mathematical statements can be formulated in such a way that provable statements can be derived from ZFC. The ZFC set theory has therefore become a tried and tested and widely accepted framework for all of mathematics. Exceptions can be found wherever you have to or want to work with real classes . Certain extensions of ZFC are then used, which provide classes or additional very large sets, for example an extension to ZFC class logic or the Neumann-Bernays-Gödel set theory or a Grothendieck universe . In any case, ZFC is now regarded as the basic system of axioms for mathematics.\n\nBecause of the fundamental importance of ZFC set theory for mathematics, a proof of freedom from contradictions for set theory was sought within the Hilbert program since 1918 . Gödel, who made important contributions to this program, was able to show in his Second Incompleteness Theorem in 1930 that such a proof of freedom from contradiction is impossible within the framework of a consistent ZFC set theory. The assumption of consistency by ZFC therefore remains a working hypothesis of mathematicians hardened by experience:\n\n\"The fact that ZFC has been studied for decades and used in mathematics without showing any contradiction, speaks for the consistency of ZFC.\"\n\n- Ebbinghaus u. a., Chapter VII, §4\n\n## The axioms of ZF and ZFC\n\nZF has an infinite number of axioms, since two axiom schemes (8th and 9th) are used, each specifying an axiom for each predicate with certain properties. The predicate logic of the first level with identity and the undefined element predicate serves as the logical basis . ${\\ displaystyle \\ in}$", null, "1. Axiom of extensionality : Sets are equal if and only if they contain the same elements.\n\n${\\ displaystyle \\ forall A, B \\ colon (A = B \\ iff \\ forall C \\ colon (C \\ in A \\ iff C \\ in B))}$", null, "The axiom implies that in ZF there are only entities with extension, which are usually called sets. All bound variables therefore automatically refer to quantities in the ZF language.\n\n2. Empty set axiom , obsolete null set axiom : There is a set without elements.\n\n${\\ displaystyle \\ exists B \\ colon \\ forall A \\ colon \\ lnot (A \\ in B)}$", null, "The uniqueness of this set immediately follows from the axiom of extensionality , which means that there is no more than such a set. This is usually referred to as a written and empty set . That means: The empty set is the only original element in ZF .${\\ displaystyle B}$", null, "${\\ displaystyle \\ emptyset}$", null, "3. Pair set axiom : For all and there is a set that has exact and as elements. ${\\ displaystyle A}$", null, "${\\ displaystyle B}$", null, "${\\ displaystyle C}$", null, "${\\ displaystyle A}$", null, "${\\ displaystyle B}$", null, "${\\ displaystyle \\ forall A, B \\ colon \\ exists C \\ colon \\ forall D \\ colon (D \\ in C \\ iff ((D = A) \\ lor (D = B)))}$", null, "Apparently this amount is also clearly determined. It is written as . The amount is usually written as.${\\ displaystyle C}$", null, "${\\ displaystyle \\ left \\ {A, B \\ right \\}}$", null, "${\\ displaystyle \\ left \\ {A, A \\ right \\}}$", null, "${\\ displaystyle \\ left \\ {A \\ right \\}}$", null, "4. Axiom of union: for every set there is a set that contains exactly the elements of the elements of as elements. ${\\ displaystyle A}$", null, "${\\ displaystyle B}$", null, "${\\ displaystyle A}$", null, "${\\ displaystyle \\ forall A \\ colon \\ exists B \\ colon \\ forall C \\ colon (C \\ in B \\ iff \\ exists D \\ colon (D \\ in A \\ land C \\ in D))}$", null, "The set is also uniquely determined and is called the union of the elements of , written as . Together with the pair amount Axiom allows the association to define.${\\ displaystyle B}$", null, "${\\ displaystyle A}$", null, "${\\ displaystyle \\ bigcup A}$", null, "${\\ displaystyle A \\ cup B: = \\ bigcup \\ {A, B \\}}$", null, "5. Axiom of infinity : There is a set that contains the empty set and with every element also the set (cf. inductive set ). ${\\ displaystyle A}$", null, "${\\ displaystyle X}$", null, "${\\ displaystyle X \\ cup \\ {X \\}}$", null, "${\\ displaystyle \\ exists A \\ colon (\\ exists X \\ in A \\ colon \\ forall Y \\ colon \\ lnot (Y \\ in X) \\ land \\ forall X \\ colon (X \\ in A \\ Rightarrow X \\ cup \\ {X \\} \\ in A))}$", null, "There are many such sets. The intersection of all these sets is the smallest set with these properties and forms the set of natural numbers ; The intersection is formed by applying the axiom of separation (see below). So the natural numbers are represented by\n${\\ displaystyle \\ mathbb {N} \\,: = \\, \\ {\\ emptyset, \\, \\ {\\ emptyset \\}, \\, \\ {\\ emptyset, \\ {\\ emptyset \\} \\}, \\, \\ {\\ emptyset , \\ {\\ emptyset \\}, \\ {\\ emptyset, \\ {\\ emptyset \\} \\} \\} \\, \\ ldots \\}}$", null, "6. Power set axiom: For every set there is a set whose elements are exactly the subsets of . ${\\ displaystyle A}$", null, "${\\ displaystyle P}$", null, "${\\ displaystyle A}$", null, "${\\ displaystyle \\ forall A \\ colon \\ exists P \\ colon \\ forall B \\ colon (B \\ in P \\ iff \\ forall C \\ colon (C \\ in B \\ Rightarrow C \\ in A))}$", null, "The amount is clearly determined. It is called the power set of and is denoted by.${\\ displaystyle P}$", null, "${\\ displaystyle A}$", null, "${\\ displaystyle {{\\ mathcal {P}} (A)}}$", null, "7. Foundation axiom or regularity axiom : Every nonempty set contains an element such that and are disjoint . ${\\ displaystyle A}$", null, "${\\ displaystyle B}$", null, "${\\ displaystyle A}$", null, "${\\ displaystyle B}$", null, "${\\ displaystyle \\ forall A \\ colon (A \\ neq \\ emptyset \\ Rightarrow \\ exists B \\ colon (B \\ in A \\ land \\ lnot \\ exists C \\ colon (C \\ in A \\ land C \\ in B)))}$", null, "The element that is too disjoint is generally not clearly determined. ${\\ displaystyle B}$", null, "${\\ displaystyle A}$", null, "The foundation axiom prevents there are infinite or cyclic sequences of sets in each of which one is included in the previous ones, because then you could a lot form that contradicts the axiom: for each is , the two sets are therefore not disjoint. This implies that a set cannot contain itself as an element.${\\ displaystyle x_ {1} \\ ni x_ {2} \\ ni x_ {3} \\ ni \\ dots}$", null, "${\\ displaystyle A = \\ {x_ {1}, x_ {2}, x_ {3}, \\ dots \\}}$", null, "${\\ displaystyle x_ {i} \\ in A}$", null, "${\\ displaystyle x_ {i + 1} \\ in x_ {i} \\ cap A}$", null, "8. Disposal axiom : This is an axiom scheme with one axiom for each predicate : For each set there is a subset of which contains exactly the elements of for which is true. ${\\ displaystyle P}$", null, "${\\ displaystyle A}$", null, "${\\ displaystyle B}$", null, "${\\ displaystyle A}$", null, "${\\ displaystyle C}$", null, "${\\ displaystyle A}$", null, "${\\ displaystyle P (C)}$", null, "For every single-digit predicate in which the variable does not appear, the following applies:${\\ displaystyle P (C)}$", null, "${\\ displaystyle B}$", null, "${\\ displaystyle \\ forall A \\ colon \\ exists B \\ colon \\ forall C \\ colon (C \\ in B \\ iff C \\ in A \\ land P (C))}$", null, "From the axiom of extensionality it immediately follows that there is exactly such a set. This is noted with .${\\ displaystyle \\ {C \\ in A | P (C) \\}}$", null, "9. Replacement axiom (Fraenkel): If a set and every element of is uniquely replaced by an arbitrary set, then it becomes a set. The replacement is made more precise by two-place predicates with similar properties to a function , namely as an axiom scheme for each such predicate: ${\\ displaystyle A}$", null, "${\\ displaystyle A}$", null, "${\\ displaystyle A}$", null, "For every predicate in which the variable does not occur:${\\ displaystyle F (X, Y)}$", null, "${\\ displaystyle B}$", null, "${\\ displaystyle \\ forall X, Y, Z \\ colon (F (X, Y) \\ land F (X, Z) \\ Rightarrow Y = Z) \\ Rightarrow \\ forall A \\ colon \\ exists B \\ colon \\ forall C \\ colon (C \\ in B \\ iff \\ exists D \\ colon (D \\ in A \\ land F (D, C)))}$", null, "The amount is clearly determined and is noted as.${\\ displaystyle \\, B}$", null, "${\\ displaystyle \\ {Y | D \\ in A \\ land F (D, Y) \\}}$", null, "In mathematics, the axiom of choice is often used, which ZF extends to ZFC:\n\n10. Axiom of choice : If there is a set of pairwise disjoint nonempty sets, then there is a set that contains exactly one element from each element of . This axiom has a complicated formula that can be simplified a bit with the uniqueness quantifier : ${\\ displaystyle A}$", null, "${\\ displaystyle A}$", null, "${\\ displaystyle \\ exists!}$", null, "${\\ displaystyle \\ forall A \\ colon {\\ Big (} ((\\ emptyset \\ not \\ in A) \\ \\ wedge \\ \\ forall X, Y, Z \\ colon ((X \\ in A \\ \\ wedge \\ Y \\ in A \\ \\ wedge \\ Z \\ in X \\ \\ wedge \\ Z \\ in Y) \\ Rightarrow (X = Y)))}$", null, "${\\ displaystyle \\ Rightarrow \\;}$", null, "${\\ displaystyle \\ exists B \\ colon \\ forall X \\ colon (X \\ in A \\ Rightarrow \\ exists! \\ Y \\ colon (Y \\ in X \\ wedge Y \\ in B)) {\\ Big)}}$", null, "Another common verbal formulation of the axiom of choice is: If a set is a non-empty set, then there is a function (of into its union) that assigns an element of to each element of (\" selects an element of \").${\\ displaystyle A}$", null, "${\\ displaystyle f}$", null, "${\\ displaystyle A}$", null, "${\\ displaystyle B}$", null, "${\\ displaystyle A}$", null, "${\\ displaystyle B}$", null, "${\\ displaystyle B}$", null, "With the ZF axioms one can derive the equivalence of the axiom of choice with the well-order theorem and the lemma of Zorn .\n\n## ZF with original elements\n\nZermelo formulated the original ZF system for quantities and primary elements. He defined sets as things containing elements or the zero set. Primordial elements are then things without elements, namely, he considered the zero set as a distinctive primitive element which, as a given constant, extends the ZF language. Quantities and primitive elements can thus be precisely defined: ${\\ displaystyle \\ emptyset}$", null, "${\\ displaystyle M {\\ text {is quantity}} \\ colon \\ iff (M = \\ emptyset) \\ lor \\ exists X \\ colon (X \\ in M)}$", null, "${\\ displaystyle U {\\ text {is the original element}} \\ colon \\ iff \\ lnot \\ exists X \\ colon (X \\ in U)}$", null, "The set theory with primitive elements is distinguished from the usual pure ZF set theory by the appended U. The axioms of ZFU and ZFCU are verbal, apart from the empty set axiom, like the axioms of ZF or ZFC, but are formalized differently because of the different framework conditions; deducible quantity conditions can be omitted.\n\n### ZFU\n\nZFU comprises the following axioms:\n\nEmpty set axiom :\n${\\ displaystyle \\ emptyset {\\ text {is the original element}}}$", null, "Axiom of determinateness (weakened axiom of extensionality):\n${\\ displaystyle A {\\ text {is quantity}} \\ land B {\\ text {is quantity}} \\ Rightarrow (A = B \\ iff \\ forall C \\ colon (C \\ in A \\ iff C \\ in B))}$", null, "Association axiom :\n${\\ displaystyle \\ forall A \\ colon \\ exists B \\ colon (B {\\ text {is quantity}} \\ land \\ forall C \\ colon (C \\ in B \\ iff \\ exists D \\ colon (D \\ in A \\ land C \\ in D)))}$", null, "Power set axiom :\n${\\ displaystyle \\ forall A \\ colon \\ exists P \\ colon \\ forall B \\ colon (B \\ in P \\ iff (B {\\ text {is quantity}} \\ land \\ forall C \\ colon (C \\ in B \\ Rightarrow C \\ in A)))}$", null, "Infinity axiom :\n${\\ displaystyle \\ exists A \\ colon (\\ exists X \\ in A \\ colon \\ forall Y \\ in A \\ colon \\ lnot (Y \\ in X) \\ land \\ forall X \\ colon (X \\ in A \\ Rightarrow X \\ cup \\ {X \\} \\ in A))}$", null, "Foundation axiom :\n${\\ displaystyle \\ exists X \\ colon (X \\ in A) \\ Rightarrow \\ exists B \\ colon (B \\ in A \\ land \\ lnot \\ exists C \\ colon (C \\ in A \\ land C \\ in B))}$", null, "Replacement axiom for two-digit predicates : ${\\ displaystyle F (X, Y)}$", null, "${\\ displaystyle \\ forall X, Y, Z \\ colon (F (X, Y) \\ land F (X, Z) \\ Rightarrow Y = Z) \\ Rightarrow \\ forall A \\ colon \\ exists B \\ colon (B {\\ text {is quantity}} \\ wedge \\ \\ forall C \\ colon (C \\ in B \\ iff \\ exists D \\ colon (D \\ in A \\ wedge \\ F (D, C))))}$", null, "The ZF axioms obviously follow from the ZFU axioms and the axiom . Because from the replacement axiom , as in ZF (see below), the pair set axiom can be derived and also the exclusion axiom , the latter here in the following form for each one-digit predicate : ${\\ displaystyle \\ forall X \\ colon X {\\ text {is quantity}}}$", null, "${\\ displaystyle P}$", null, "${\\ displaystyle \\ forall A \\ colon \\ exists B \\ colon (B {\\ text {is quantity}} \\ land \\ forall C \\ colon (C \\ in B \\ iff C \\ in A \\ land P (C)))}$", null, "### ZFCU\n\nZFCU comprises the axioms of ZFU and the following axiom of choice :\n\n${\\ displaystyle \\ forall A \\ colon ((\\ forall X \\ colon (X \\ in A \\ Rightarrow \\ exists Y \\ colon (Y \\ in X)) \\ \\ wedge \\ \\ forall X, Y, Z \\ colon ((X \\ in A \\ \\ wedge \\ Y \\ in A \\ \\ wedge \\ Z \\ in X \\ \\ wedge \\ Z \\ in Y) \\ Rightarrow (X = Y)))}$", null, "${\\ displaystyle \\ Rightarrow \\;}$", null, "${\\ displaystyle \\ exists B \\ colon \\ forall X \\ colon (X \\ in A \\ Rightarrow \\ exists! \\ Y \\ colon (Y \\ in X \\ wedge Y \\ in B))}$", null, "## Simplified ZF system (redundancy)\n\nThe ZF system is redundant, that is, it has dispensable axioms that can be derived from others. ZF or ZFU is already fully described by the axiom of extension, union, power set axiom, infinity axiom, foundation axiom and replacement axiom. This applies to the following points:\n\n• The axiom of exclusion follows from the axiom of substitution (Zermelo).\n• The void set axiom follows from the exclusion axiom and the existence of some set, which results from the infinity axiom.\n• The pair set axiom follows from the replacement axiom and the power set axiom (Zermelo).\n\nPair set axiom, union axiom and power set axiom can also be obtained from the statement that every set is an element of a level . The axiom of infinity and the axiom of substitution are equivalent to the reflection principle within the framework of the other axioms . By combining these two insights, Dana Scott reformulated ZF into the equivalent Scott system of axioms .\n\n## ZF system without equality\n\nZF and ZFU can also be based on a predicate logic without equality and define equality. The derivation of all axioms of equality only ensures the definition of identity that is customary in logic :\n\n${\\ displaystyle A = B: \\ iff \\ forall C \\ colon (A \\ in C \\ iff B \\ in C) \\ land \\ forall C \\ colon (C \\ in A \\ iff C \\ in B)}$", null, "The axiom of extensionality is not suitable for the definition! The definition of identity does not make this axiom superfluous because it cannot be derived from the definition. As an alternative, a definition of equality by extensionality would only be possible in ZF if the axiom was included, which ensures the deducibility of the above formula. This option is of course ruled out at ZFU. ${\\ displaystyle A = B: \\ iff \\ forall C \\ colon (C \\ in A \\ iff C \\ in B)}$", null, "${\\ displaystyle A = B \\ Rightarrow \\ forall C \\ colon (A \\ in C \\ iff B \\ in C)}$", null, "## Infinite axiomatizability\n\nThe substitution axiom is the only axiom scheme in ZF if one removes the redundancies of the axioms and restricts oneself to a system of independent axioms. It cannot be replaced by a finite number of individual axioms. In contrast to the theories of Neumann-Bernays-Gödel (NBG) and New Foundations (NF), ZF can not finally be axiomatized.\n\n## literature\n\n### Primary sources (chronological)\n\n• Ernst Zermelo: Investigations into the basics of set theory. 1907, In: Mathematische Annalen. 65 (1908), pp. 261-281.\n• Adolf Abraham Fraenkel: To the basics of Cantor-Zermeloschen set theory. 1921, In: Mathematische Annalen. 86: 230-237 (1922).\n• Adolf Fraenkel: Ten lectures on the foundations of set theory. 1927. Unchanged reprographic reprint Scientific Book Society Darmstadt 1972.\n• Thoralf Skolem: About some fundamental questions in mathematics. 1929, In: selected works in logic. Oslo 1970, pp. 227-273.\n• Ernst Zermelo: About limit numbers and quantity ranges. In: Fundamenta Mathematicae. 16 (1930) (PDF; 1.6 MB), pp. 29-47.\n\n### Secondary literature\n\n• Oliver Deiser: Introduction to set theory: Georg Cantor's set theory and its axiomatization by Ernst Zermelo . Springer, Berlin / Heidelberg 2004, ISBN 3-540-20401-6 .\n• Heinz-Dieter Ebbinghaus: Introduction to set theory . Spectrum Academic Publishing House, Heidelberg / Berlin 2003, ISBN 3-8274-1411-3 .\n• Adolf Fraenkel: Introduction to set theory . Springer Verlag, Berlin / Heidelberg / New York 1928. (Reprint: Dr. Martin Sendet oHG, Walluf 1972, ISBN 3-500-24960-4 ).\n• Paul R. Halmos: Naive set theory . Vandenhoeck & Ruprecht, Göttingen 1968, ISBN 3-525-40527-8 .\n• Felix Hausdorff: Fundamentals of set theory . Chelsea Publ. Co., New York 1914, 1949, 1965.\n• Arnold Oberschelp : General set theory. BI-Wissenschaft, Mannheim / Leipzig / Vienna / Zurich 1994, ISBN 3-411-17271-1 .\n\n### Individual evidence\n\n1. Ebbinghaus , chap. VII, §4\n2. David Hilbert : Axiomatic Thinking. In: Mathematical Annals. 78: 405-415 (1918). There, on page 411, the fundamental importance of the consistency of Zermelo set theory for mathematics is discussed.\n3. Verbalization based on: Fraenkel: To the basics of Cantor-Zermeloschen set theory. 1921, In: Mathematische Annalen. 86 (1922), p. 231.\n4. Ernst Zermelo : Investigations on the basics of set theory. In: Mathematical Annals. 65 (1908), p. 262, §1 (2.) Definition of quantities.\n5. Ernst Zermelo: limit numbers and quantity ranges. In: Fundamenta Mathematicae. 16 (1930), p. 30, remark in Axiom U: “Instead of the“ zero set ”there is an arbitrarily selected primordial element”.\n6. a b Ernst Zermelo: Limits and quantity ranges. In: Fundamenta Mathematicae. 16 (1930), remark p. 31.\n7. ^ Walter Felscher : Naive sets and abstract numbers I, Mannheim / Vienna / Zurich 1978, p. 62.\n8. a b\n9. ^ Walter Felscher: Naive sets and abstract numbers I. Mannheim / Vienna / Zurich 1978, p. 78f.\n10. ^ Robert Mac Naughton, A non standard truth definition , in: Proceedings of the American Mathematical Society, Vol. 5 (1954), pp. 505-509.\n11. Richard Montague, Fraenkel's addition to the axioms of Zermelo , in: Essays on the Foundation of Mathematics, pp. 91-114, Jerusalem 1961. Inadequate evidence was given in 1952 by Mostowski and Hao Wang." ]

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[ "# 24 Irresistible Math Exit Tickets For Teachers (w/Templates)\n\nYou’ve just taught a great math lesson and feel your students “got it”… but did they?\n\nWhat you need are a few math exit tickets to find out.\n\n## What are Math Exit Tickets?\n\nMath exit tickets are quick, informal assessments that gauge how well learners grasped the lesson.\n\nThey prompt students to synthesize concepts, reflect upon new schema, and express their level of understanding.\n\nIt’s essential to regularly assess how well students are performing in math because each new learned skill lays part of the foundation for comprehending more challenging concepts.\n\nThe following math exit ticket ideas serve to help teachers informally assess and gather valuable data about students’ math proficiency.\n\nNote: Download a set of math exit tickets towards the end of this post.\n\n## Math Exit Tickets: Examples + How to Use\n\nFollowing you will find a variety of math exit ticket ideas for classroom use.\n\n### 1. 3-2-1 Math Exit Tickets\n\nThe 3-2-1 math exit tickets are divided into three parts: students first give 3 responses to a math prompt, then 2 answers to a math prompt, and then just 1 response to a math prompt.\n\nSee math sentence stems for prompt ideas.\n\n### 2. Notecards Math Exit Tickets\n\nAt the end of a lesson, restate the learning objective, and give students a few seconds to reflect.\n\nNow ask students to write their names and one of the statements below on a notecard:\n\n• Got It.\n• I Need Some Help!\n\nBefore leaving class, direct students to deposit their math exit tickets into a folder or bucket.\n\nAfterwards, separate the responses into the three categories. Quickly analyze, and adapt future instruction based on the information.\n\n(Source: Erika Savage)\n\n### 3. Triangle-Square-Circle Math Exit Tickets\n\nUsing visual representations, Triangle-Square-Circle math exit tickets prompt learners to synthesize information, ask questions, and summarize essential points.\n\n• The triangle, with 3 points, means that students must give three key points they “took away” from the math lesson.\n• The square represents what students have “squared away”, or understood, about the math lesson.\n• The circle represents one or two lingering questions learners still have about the math lesson.\n\n### 4. Get the Gist Math Exit Ticket\n\nIn fifteen words or less, students summarize the main idea of the math lesson.\n\n### 5. Passport Out Math Exit Tickets\n\nBefore learners “take off” for the day, they write…\n\n• One thing learned in the math activity\n• One area in which they need more practice\n\n### 6. Tweet of the Lesson\n\nStudents write the most important idea or message of the day’s math activity.\n\n### 7. Emoji Math Exit Tickets\n\nUse a variety of fun emoji math exit tickets to assess students’ understanding of the math lesson.\n\nThese math exit ticket ideas ask students to respond to the following tasks:\n\n• Tell what you enjoyed about the lesson.\n• Draw an emoji that represents your understanding of today’s activity.\n• What did you learn today?\n• Which parts are still troubling?\n• What was your favorite part of the math lesson?\n• Are there any parts that you don’t quite understand?\n\n### 8. Rating Scale Self-Assessment Math Ticket\n\nGive students three emojis to choose from…\n\nThey sketch on a sticky note (or circle their choice on a template) which emoji face best reflects their understanding of the math lesson.\n\n### 9. Sticky Note Math Exit Tickets\n\nOn sticky notes, students write an important part of the math lesson, a confusing part, or a connection that was made.\n\n### 10. Simile Summary Math Exit Ticket\n\nEncourage critical thinking using a Simile Summary math exit ticket.\n\nThis math exit ticket idea focuses on vocabulary, prompting students to make deeper analysis of math terms.\n\nExample…\n\nStudents complete the statement in a few sentences.\n\n### 11. Blank Math Exit Tickets\n\nIt can be time-consuming to search high and low for that perfect math exit ticket idea that focuses specifically on your targeted learning objective.\n\nSo keep a stack of blank math exit tickets on hand.\n\nStudents respond to a variety of math exit ticket questions, prompts, and math sentence stems, recording their answers on the blank templates.\n\n### 12. Pictures, Numbers, Words Math Exit Tickets\n\nThese quick math exit tickets showcase students’ depth of number sense.\n\nHere’s how it works…\n\n• Say any number.\n• Students demonstrate that number in pictures, numbers, and/or words.\n\n### 13. Glow and Grow\n\nOn a sticky note or in math journals, students write one math area/skill in which they “glowed” – a learning objective that they understood well.\n\nAfterwards, they write one “needs improvement” statement – an area in which they still need to “grow”.\n\n### 14. Journal Entry Math Exit Ticket Ideas\n\nAt the end of math instruction, provide 5 to 10 minutes for students to jot down and/or sketch in their math journal any big ideas from the lesson.\n\nFor those students who need support, provide question prompts or statement stems.\n\nIf you can possibly carve out a bit of time during the week, respond to each student.\n\nDoing so really keeps kids engaged and excited about the topic!\n\n### 15. Exit Interview\n\nWith this math exit ticket idea, students complete an exit interview about the day’s math lesson.\n\n### 16. Tic-Tac-Toe Math Exit Tickets\n\nThe Tic-Tac-Toe math exit ticket assesses vocabulary development. It encourages students to seek connections among math concepts.\n\nHere’s how it works…\n\n• Students place key vocabulary terms from the lesson anywhere on their individual Tic-Tac-Toe exit ticket.\n• They write five meaningful sentences using the terms.\n• The sentences will include three words straight across in any row, straight down from any column, or from any diagonal.\n• As a set of 3 words is used, students cross it out.\n• Students cannot repeat the same set of 3 words, but a word may be repeated if it’s part of another set.\n\n### 17. Learning Style Math Exit Ticket Ideas\n\nBased on multiple intelligence activities for the classroom, this assessment offers students the option to choose one of several math exit tickets in order to show what they know.\n\nThis is arguably one of the most engaging math exit ticket ideas because it includes activities that cater to a variety of learning styles.\n\n### 18. T.A.G Math Exit Ticket\n\nUsing the T.A.G math exit ticket, students do the following…\n\n• T = TELL something they enjoyed about the lesson.\n• A = ASK a question that will help them to get clarity about something.\n• G = GIVE a way of how they can improve.\n\n### 19. Red, Yellow, Green Math Exit Tickets\n\nFor this math exit ticket, learners circle one of three colors to represent how well they grasped the lesson material:\n\n• Red = Stop (I’m totally lost.)\n• Yellow = I’m struggling a bit. Please go slower.\n• Green = I’m ready to move on.\n\n### 20. Story Frame Math Exit Tickets\n\nStory frames are powerful tools that help students frame the learning while synthesizing concepts.\n\nEssentially, story frames are an extension of math sentence stems and encourage students to think deeper.\n\nIn the example below, students complete the math story frame, explaining the steps used to solve a math problem.\n\n### 21. Ticket to Leave\n\nDuring those few moments right before the dismissal bell is where this no-prep math exit ticket fits best.\n\nAs students line up to be dismissed, give each a multiplication fact to solve or a quick true/false statement related to a math topic.\n\nIdeally, questions/statements should be yes/no or one-answer.\n\nMove fast so that every student has a chance to answer a question before leaving.\n\n### 22. Four-Square Math Exit Ticket\n\nThis math exit ticket reinforces vocabulary acquisition.\n\nChoose a math term to place in the center of the Four-Square math exit ticket.\n\nStudents write the definition of the term, record its characteristics, give one example, and then provide one non-example.\n\n### 24. Digital Exit Tickets for Math\n\nUse a variety of digital exit tickets to assess students’ understanding of concepts.\n\n## Wrapping Up: Math Exit Tickets\n\nMath exit tickets are quick informal assessments that provide valuable feedback to teachers so that they can modify instruction to better serve students.\n\nBe sure to include a few of these essential tools in your lesson plans this week.\n\nIf you liked these math exit ticket ideas, you might be interested inexit ticket templates." ]

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[ "How do you solve 13^ { - 9x } = 16^ { x - 2}?\n\nNov 27, 2017\n\n$x = 0.214$\n\nExplanation:\n\nTake the log of both sides and solve as you would a normal equation.\n\n13^{-9x = ${16}^{x - 2}$\n\nln ${13}^{- 9 x}$=ln ${16}^{x - 2}$\n\n$- 9 x$ ln$\\left(13\\right) = \\left(x - 2\\right)$ln16\n\n$- 9 x \\cdot 2.56 = \\left(x - 2\\right) \\cdot 2.77$\n\n$- 23.08 x = 2.77 x - 5.54$\n\n$- 25.85 x = - 5.54$\n\n$x = 0.214$ (approx when using 2 decimal places)" ]

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[ "Go Down\n\n### Topic: Frequency Counter Library (Read 137504 times)previous topic - next topic\n\n#### Yuliia_Sych", null, "#75\n##### Jan 26, 2016, 12:39 am\nCan you please explain me why preamplifier scheme has such view and why there is such transistor and what this scheme do with signal (I've make it in Workbench and the signal from generator just shifts under zero level)", null, "#76\n##### Mar 04, 2016, 03:52 pm\nIn the FrequencyCounter::start() function use 1000 instead of 100 if you want to get the exact frequency in Hz. because when you write 100 in start function, it takes it in ms in library running at the back end and will calculate frequency for 100ms which obviously will be 1/10th of original frequency in Hz. Similarly using 10 in the start function will give you the frequency 1/100th of the original frequency in Hz. Hopefully you understands it now.\n\n#### futurebird", null, "#77\n##### Apr 28, 2016, 01:56 am\nI just wanted to thank the developer for this library. It was very useful on the project I created today. I hacked a digital anemometer which produced a pulsing signal, then used it to create a formula to translate the signal into windspeed in km/h.\n\nI started to try to write something like this myself thank god I found this!\n\n#### gawnieg", null, "#78\n##### Jul 28, 2016, 12:41 pm\nHello All\n\nI am trying to use dc42's code to measure a low frequency speed from the flywheel of an internal combustion engine. The signal of interest is a 5V square wave in the order of 30 to 40Hz. However, using dc40's code there are rogue high values (50 to 60Hz) appearing which is completely throwing my speed control system.\n\nI am using a servo motor to control the throttle angle based on speed to keep the speed at a setpoint, using a PID library. Would this be throwing the ISR timer? Can the two work together? Where are these rogue values coming from? They appear randomly, with every 20 to 40 seconds of running:\n\nCode: [Select]\n`#include <PID_v1.h> //include PID library in sketch#include <Wire.h>#include <Servo.h>#define ECU2_RESET 8 //was 3#define SERVO_PIN 9 //was 5#define OVERSPEED_PIN 10 //overspeed to master#define RELAY_PIN 11 //local overspeed relayvolatile unsigned long firstPulseTime;volatile unsigned long lastPulseTime;volatile unsigned long numPulses;unsigned long over_speed_setpoint = 50; //define an over speed setpoint (i.e 3000rpm) here in correct units = 3000rpm double speed_setpoint = 41 ; // see engine calcs overview for this calc. or onenote To Do sheet. 48000=2500rpm, 50000=2400rpmunsigned int sample_time = 100;unsigned long num_iterations;/////////////////////PID SETTINGS///////////////////////////////////////double Kp = 1.0; //was o.008double Ki = 0.7; // was 0.0022double Kd=0.0;////////////////////SERVO SETTINGS//////////////////////////////////////////////////double throttle_setpoint;    // variable to store the desired throttle angle - WHAT SHOULD THIS BE INITIALISED AT?? int throttle_sig; //whats set to the servo = (90-throttle_setpoint) calculated by map() functionServo myservo; //initalising servo as servo objectdouble freq_1=0; //variable for frequency readoutboolean engine_running = false; // this is false until the engine starter motor is engagedPID myPID(&freq_1, &throttle_setpoint, &speed_setpoint, Kp, Ki, Kd, DIRECT); //PID setup using speed avg //REVERSEvoid isr(){ unsigned long now = micros(); if (numPulses == 1) {   firstPulseTime = now; } else {   lastPulseTime = now; } ++numPulses;}void setup(){Serial.begin(9600);Serial.println(\"Setup Finished\"); Serial.print(\"This  run we have :  \");Serial.print(\"Kp = \");Serial.print(Kp);Serial.print(\" Ki = \");Serial.print(Ki);Serial.print(\" Kd = \");Serial.print(Kd);Serial.print(\"Sample time = \");Serial.print(sample_time);Serial.print(\"Speed setpoint = \");Serial.println(speed_setpoint);pinMode(21, INPUT);     //input for the HES signaldigitalWrite(21,HIGH); // added to prevent floating values???pinMode(OVERSPEED_PIN, OUTPUT); //pin 4 will be HIGH when engine speed is too high and shutdown is required, LOW when ok to keep running.OVERSPEED PINpinMode(RELAY_PIN,OUTPUT); //pin 7 as local overspeed pindigitalWrite(OVERSPEED_PIN,LOW); //initailly set this to low to say that there is no overspeed on system intialisationdigitalWrite(RELAY_PIN,HIGH); //initailly set this to low to say that there is no overspeed on system intialisationmyservo.attach(SERVO_PIN);//attaching the servo to PIN 9. myservo.write(8);// setting inital value of 85 to get it started on idlemyPID.SetMode(AUTOMATIC); //this sets the PID algoithm to automatic, i.e. it will compute every loop}// Measure the frequency over the specified sample time in milliseconds, returning the frequency in Hzfloat readFrequency(unsigned int sampleTime){ numPulses = 0;                      // prime the system to start a new reading attachInterrupt(2, isr, RISING);    // enable the interrupt delay(sampleTime); detachInterrupt(2); return (numPulses < 3) ? 0 : (1000000.0 * (float)(numPulses - 2))/(float)(lastPulseTime - firstPulseTime); // if the number of pulses is less than 3, then 0, otherwise - }void loop(){  if(engine_running==true){    num_iterations++;  }  freq_1 = readFrequency(sample_time);if(freq_1 > 5 && engine_running == false && freq_1 < 1000){ //if the engine is cranking then the engine_running variable is set to on so the PID controller is activated  Serial.println(\"Engine is now running, ECU activated\");  engine_running = true;        }  if(engine_running==true ){ //if closed loop control is need then the master controller will set pin 3 to HIGH AND the engine has started and the servo should be activated    myPID.Compute();//required for PID to work   throttle_sig=(int)map(throttle_setpoint, 0, 255, 6, 87);// remapping the PID controller output (0-255), set by the PID setoutput function in the setup to 90 to 0 i.e. 90 degrees throttle_setpoint is actually 0 degrees throttle angle ---23.05.2016 was 0,255,0,90 changed to 87 as was conking on start   myservo.write(throttle_sig); // this is writing the mapped PID output to the servo//      Serial.print(\"The PID OUTPUT is: \");   Serial.print(throttle_setpoint);   Serial.print(\"\\t\");//   Serial.print(\"The servo sig is: \");   Serial.print(throttle_sig);   Serial.print(\"\\t\");//   Serial.print(\"The speed is is: \");   Serial.print(freq_1);   Serial.print(\"\\t\");   Serial.print(freq_2);   Serial.print(\"\\t\");   Serial.println(millis());  }  if(freq_1 >= over_speed_setpoint){  Serial.println(freq_1);  digitalWrite(OVERSPEED_PIN,HIGH); //sending 5v signal to master to indicate overspeed  digitalWrite(RELAY_PIN,LOW);        Serial.println(\"OVERSPEED\");    }  else {  digitalWrite(OVERSPEED_PIN,LOW);//telling master that there is no overspeed present  digitalWrite(RELAY_PIN,HIGH); //keeping local overspeed relay switched on as there is no issues  }}`\n\n#### Atmoz22", null, "#79\n##### Sep 01, 2016, 07:23 pm\nHey,\n\nI have to measure the netfrequenzy and i need a resolution of milli hertz 50.xxx Hz, is it possible to change the counter resolution that he will measure milli Hertz?\n\n#### Freezin", null, "#80\n##### Oct 05, 2016, 11:57 pm\nPost 42 has a modified library for the Leonardo. As I go through the code it says it will measure the frequency on pin 12 of the Leonardo. Is there any way to change it so the input frequency can be on D5 or D11?\n\n// hardware counter setup ( refer atmega32u4)\nTCCR1A=0;                  // reset timer/counter1 control register A\nTCCR1B=0;                    // reset timer/counter1 control register A\nTCNT1=0;                    // counter value = 0\n\n// set timer/counter1 hardware as counter , counts events on pin T1 ( arduino leonardo pin 12)\n// normal mode, wgm10 .. wgm13 = 0\n\nTCCR1B |=  (1<<CS10) ;//CLOCK ESTERNO su fronte di salita\nTCCR1B |=  (1<<CS11) ;\nTCCR1B |=  (1<<CS12) ;\n\n#### anilpandeya12", null, "#81\n##### Jan 08, 2017, 08:57 am\n#include <FreqCount.h>\n\nvoid setup() {\nSerial.begin(57600);\nFreqCount.begin(1000);\n}\n\nvoid loop() {\ntone(9,3100);    //Error in compiling when added this line in arduino Uno\nif (FreqCount.available()) {\nSerial.println(count);\n}\n}\n\n#### loic_38", null, "#82\n##### Jan 10, 2017, 11:48 am\nHi All !\n\nSince the 1.8.0 update, the fequency counter using interrupt doesn't work..\nI have an Arduino.org M0 Board. Do you have the same problem with other boards ?\n\nCode: [Select]\n`void isr(){ unsigned long now = micros(); if (numPulses == 1) {   firstPulseTime = now; } else {   lastPulseTime = now; } ++numPulses;float readFrequency(unsigned int sampleTime){ numPulses = 0;                      // prime the system to start a new reading attachInterrupt(2, isr, RISING);    // enable the interrupt delay(sampleTime); detachInterrupt(2); return (numPulses < 3) ? 0 : (1000000.0 * (float)(numPulses - 2))/(float)(lastPulseTime - firstPulseTime); // if the number of pulses is less than 3, then 0, otherwise - }`\n\n#### Luis_Barragan", null, "#83\n##### Jan 10, 2019, 12:12 am\nhola que tal...\n\nestoy empezando un proyecto, modificando el contador de frecuencias, pero no tengo idea de como empezar.\n\nles explico lo que quiero a ver si alguien me ayuda....\n\nquiero contar la frecuencia de una señal analoga, guardadrla en una variable (x) y dividirla para dos  (x/2)\n\ny reproducir el valor de la variable divida en forma de pulsos digitales\n\nen otras palabras por cada dos pulsos analogicos se emita un pulso digital\n\n#### ShantelJean", null, "#84\n##### Apr 06, 2019, 02:18 am\nTry this:\n\nCode: [Select]\n`// Frequency counter sketch, for measuring frequencies low enough to execute an interrupt for each cycle// Connect the frequency source to the INT0 pin (digital pin 2 on an Arduino Uno)volatile unsigned long firstPulseTime;volatile unsigned long lastPulseTime;volatile unsigned long numPulses;void isr(){  unsigned long now = micros();  if (numPulses == 0)  {    firstPulseTime = now;  }  else  {    lastPulseTime = now;  }  ++numPulses;}void setup(){  Serial.begin(19200);}// Measure the frequency over the specified sample time in milliseconds, returning the frequency in Hzunsigned int readFrequency(unsigned int sampleTime){  numPulses = 0;                      // prime the system to start a new reading  attachInterrupt(0, isr, RISING);    // enable the interrupt  delay(sampleTime);  detachInterrupt(0);  return (numPulses < 2) ? 0 : (1000000UL * (numPulses - 1))/(lastPulseTime - firstPulseTime);}void loop(){  unsigned int freq = readFrequency(1000);  Serial.println(freq);  delay(1000);}`\nhie dc42 how can i use this code wch incoporates interrupts to measure frequency from an astable  555 timer circuit of of up to 100khz.\n\n#### jb1055", null, "#85\n##### May 20, 2019, 03:22 pm\nHello,\nI would like to measure a frequenze from 150kHZ with my Arduino Mega2560.\nDo I Need a Spezial <FreqCounter.h> for the Adruino Mega?\nI copied the Sketch from #2 but i get a lot of Errors. I quess i have the <FreqCounter.h> for the Arduino Uno\nThank you for helping.\n\nGo Up" ]

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[ "Table 3. Recent studies on meat quality detection using hyperspectral imaging (HSI) technique\n\nCategory Measured attribute Analytical method Performance References\nChicken meat Texture ACO-BPANN and PCA-BPANN Correlation coefficient of 0.754 (Khulal et al., 2016)\nPrawn TVB-N (freshness) PLSR, LS-SVM, and BP-NN Correlation coefficient of 0.9547 (Dai et al., 2016)\nBeef Total viable count (TVC) of bacteria (freshness) PLS and LS-SVM Accuracy of 97.14% (Yang et al., 2017a)\nPork meat Protein and TVB-N content PLSR and LS-SVM Correlation coefficient of 0.861 (Yang et al., 2017b)\nFish Freshness PCA and BP-ANN Accuracy of 94.17% (Huang et al., 2017)\nPork muscles Intramuscular fat contents SVM, SG, SNV, MSC, and PLSR Correlation coefficient of 0.9635 (Ma et al., 2018)\nFrozen pork Myofibrils cold structural deformation degrees PLSR and SPA Correlation coefficient of 0.896 (Cheng et al., 2018)\nLamb, beef, and pork Adulteration SVM and CNN Accuracy of 94.4% (Al-Sarayreh et al., 2018)\nBeef Adulteration PLSR and SVM Accuracy of 95.31% (Ropodi et al., 2017)\nFish (grass carp) Textural changes (Warner-Bratzler shear force, hardness, gumminess and chewiness) PLSR Correlation coefficient of 0.7982-Correlation coefficient of 0.8774 (Ma et al., 2017)\nLamb meat Adulteration SPA and SG Correlation coefficient above 0.99 (Zheng et al., 2019)\nPork Intramuscular fat content MLR Correlation coefficient of 0.96 (Huang et al., 2017)\nPork longissimus dorsi muscles Moisture content (MC) PLSR Correlation coefficient of 0.9489 (Ma et al., 2017)\nGrass carp (Ctenopharyngodon idella) Moisture content PLSR Correlation coefficient of 0.9416 (Qu et al., 2017)\nLamb muscle Discrimination PCA, LMS, MLP-SCG, SVM, SMO, and LR Accuracy of 96.67% (Sanz et al., 2016)\nBeef Adulteration PLSR, SVM, ELM, CARS, and GA Correlation coefficient of 0.97 (Zhao et al., 2019)\nACO, ant colony optimization; PCA, principle component analysis; BPANN, back propagation artificial neural network; PLSR, partial least squares regression; LS-SVM, least square support vector machines; BP-NN, back propagation neural network; PLS, partial least squares; SG, savitzky golay; SNV, smoothing, standard normal variate; MSC, multiplicative scatter correction; SPA, successive projections algorithm; CNN, convolution neural networks; LMS, linear least mean squares; MLP-SCG, multilayer perceptron with scaled conjugate gradient; SVM, support vector machine; SMO, sequential minimal optimization; LR, logistic regression; ELM, extreme learning machine; CARS, and competitive adaptive reweighted sampling; GA, Genetic algorithm." ]

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[ "×\nGet Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.4 - Problem 31e\nGet Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.4 - Problem 31e\n\n×\n\n# Simple irreducible quadratic factors Evaluate the", null, "ISBN: 9780321570567 2\n\n## Solution for problem 31E Chapter 7.4\n\nCalculus: Early Transcendentals | 1st Edition\n\n• Textbook Solutions\n• 2901 Step-by-step solutions solved by professors and subject experts\n• Get 24/7 help from StudySoup virtual teaching assistants", null, "Calculus: Early Transcendentals | 1st Edition\n\n4 5 1 271 Reviews\n31\n0\nProblem 31E\n\nSimple irreducible quadratic factors Evaluate the following integrals.\n\nStep-by-Step Solution:\nStep 1 of 3\n\nProblem 31ESimple irreducible quadratic factors Evaluate the following integrals. AnswerTo evaluate the integral Take a partial fractionPut Factorize Multiply equation by denominatorSimpifyPlug in Therefore equation (1) becomesExpand1=Equate the coefficient of similar terms on both sides to create the list of equation …(2) ….(3) =2 ……(4) ….(5) Substitute back u=x-4 Where C is integration constantHence\n\nStep 2 of 3\n\nStep 3 of 3\n\n##### ISBN: 9780321570567\n\nUnlock Textbook Solution" ]

[ null, "https://studysoup.com/cdn/2cover_2418941", null, "https://studysoup.com/cdn/2cover_2418941", null ]

[ "# Stopping Distance and kinetic friction\n\n## Homework Statement\n\nWhile traveling on the highway with your 1000kg car, at 115.2 km/h, where you’re ABS (automatic\n\nbraking system) is disabled. This means braking is relying solely on the friction of your tires with the road when they stop spinning. A dear jumps into the road 50 meters in front of you. If the frictional force created by you slamming on your brakes is 4000N. What will your final stopping distance be? Will you\n\nhit the dear? Assume no air resistance.\n\nKinematics?\n\n## The Attempt at a Solution\n\nSum of Forces in The X direction\n(Force O' Car) - (Force O' Friction) = -ma\n\nI solved for acceleration and got -5.8 m/s^2\nplugging these into the kinematics equation I got a time... 5.52 seconds\nplugging that into the Xf = Xo + Vox t + 1/2 a t^2 I got a distance which is wrong\n\nwhat gives? what am i doing wrong?\n\nRelated Introductory Physics Homework Help News on Phys.org\nRUber\nHomework Helper\nMaybe look at the momentum of the car. Units will be N sec. What would be a reasonable way to find seconds to stop under friction force in N?\nI get something greater than 6 seconds.\n\nSteamKing\nStaff Emeritus\nHomework Helper\n\n## Homework Statement\n\nWhile traveling on the highway with your 1000kg car, at 115.2 km/h, where you’re ABS (automatic\n\nbraking system) is disabled. This means braking is relying solely on the friction of your tires with the road when they stop spinning. A dear jumps into the road 50 meters in front of you. If the frictional force created by you slamming on your brakes is 4000N. What will your final stopping distance be? Will you\n\nhit the dear? Assume no air resistance.\n\nKinematics?\n\n## The Attempt at a Solution\n\nSum of Forces in The X direction\n(Force O' Car) - (Force O' Friction) = -ma\n\nI solved for acceleration and got -5.8 m/s^2\nplugging these into the kinematics equation I got a time... 5.52 seconds\nplugging that into the Xf = Xo + Vox t + 1/2 a t^2 I got a distance which is wrong\n\nwhat gives? what am i doing wrong?\nWe have no idea; you didn't provide your complete calculations.\n\nBTW, \"you're\" = \"you are\" and shouldn't be used to mean \"your\".\n\nRUber\nHomework Helper\nBy the way...what is the acceleration caused by 4000N on a 1000kg car? If the car is starting at a constant velocity, that means acceleration of the car is zero...so what is the acceleration in the system? It is not -5.8 m/sec^2." ]

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[ "Codeforces celebrates 10 years! We are pleased to announce the crowdfunding-campaign. Congratulate us by the link https://codeforces.com/10years. ×\n\nF. Remainder Problem\ntime limit per test\n4 seconds\nmemory limit per test\n512 megabytes\ninput\nstandard input\noutput\nstandard output\n\nYou are given an array $a$ consisting of $500000$ integers (numbered from $1$ to $500000$). Initially all elements of $a$ are zero.\n\nYou have to process two types of queries to this array:\n\n• $1$ $x$ $y$ — increase $a_x$ by $y$;\n• $2$ $x$ $y$ — compute $\\sum\\limits_{i \\in R(x, y)} a_i$, where $R(x, y)$ is the set of all integers from $1$ to $500000$ which have remainder $y$ modulo $x$.\n\nCan you process all the queries?\n\nInput\n\nThe first line contains one integer $q$ ($1 \\le q \\le 500000$) — the number of queries.\n\nThen $q$ lines follow, each describing a query. The $i$-th line contains three integers $t_i$, $x_i$ and $y_i$ ($1 \\le t_i \\le 2$). If $t_i = 1$, then it is a query of the first type, $1 \\le x_i \\le 500000$, and $-1000 \\le y_i \\le 1000$. If $t_i = 2$, then it it a query of the second type, $1 \\le x_i \\le 500000$, and $0 \\le y_i < x_i$.\n\nIt is guaranteed that there will be at least one query of type $2$.\n\nOutput\n\nFor each query of type $2$ print one integer — the answer to it.\n\nExample\nInput\n5\n1 3 4\n2 3 0\n2 4 3\n1 4 -4\n2 1 0\n\nOutput\n4\n4\n0" ]

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[ "", null, "# Scaling Down Estimates from Larger Geography to Smaller Geography\n\nHello,\nI've got PUMs microdata using the tidycensus package. I'm trying to scale these estimates down to a smaller geography using this tutorial.\n\nBelow is as sparse as I can make this code, it should all be reproducible (if you have a census API key)\n\n``````library(magrittr)\nlibrary(tidycensus)\nlibrary(tigris)\nlibrary(sf)\nlibrary(ggplot2)\noptions(tigris_class = \"sf\")\noptions(tigris_use_cache = TRUE)\n\ncensus_api_key(\"MYAPIKEY\")\n}\n\n# zip map code ----\n# read in neighborhood and county map data\nmutate(area_ft_cca = as.numeric(st_area(.))))\n#ggplot(chi) + geom_sf() + geom_sf_text(aes(label = community),size=2)\n# get PUMs income data ----\npums <- get_pums( variables = c('PUMA', 'HINCP', 'ADJINC', 'NP'),\nstate = 'IL',\nsurvey = 'acs5',\nyear = 2019 )\n# https://www.census.gov/geographies/reference-maps/2010/geo/2010-pumas/illinois.html\n# chicago pums\nchi.pumas <- c( '03420', '03422', '03501', '03502', '03503',\n'03504', '03520', '03521', '03522', '03523',\n'03524', '03525', '03526', '03527', '03528',\n'03529', '03530', '03531', '03532' )\n# length(chi.pumas)\n# filter to pumas in chicago\npums %<>% filter( PUMA %in% chi.pumas )\npums %<>% distinct( PUMA, SERIALNO, WGTP, NP, HINCP, ADJINC )\n# pums %>% distinct(SERIALNO) %>% nrow()\n# create fpl threshold for each household in the sample\npums %<>%\nmutate( hhld_inc = as.numeric(HINCP)*as.numeric(ADJINC) ) %>%\nfilter( hhld_inc > 0 ) %>%\nmutate( fpl = case_when( NP == 1 ~ 12490,\nNP == 2 ~ 16910,\nNP == 3 ~ 21330,\nNP == 4 ~ 25750,\nNP == 5 ~ 30170,\nNP == 6 ~ 34590,\nNP == 7 ~ 39010,\nT ~ 43430),\nn = sum(WGTP) )\n# total N makes sense (~1m households in chicago)\n\n# calculate n_pop and n_fpl estimates for PUMA ----\npums <- pums %>%\n# in each puma\ngroup_by(PUMA) %>%\n# indicator for PUMA hhld in FPL band\nmutate(fpl_100_200 = ifelse(hhld_inc > fpl & hhld_inc < fpl * 2, 1, 0)) %>%\n# create PUMA Pop and PUMA FPL\nmutate( puma_pop = sum(WGTP) ,\npuma_fpl_100_200 = WGTP*fpl_100_200) %>%\nsummarise(puma_pop = max(puma_pop),\npuma_fpl_100_200 = sum(puma_fpl_100_200))\n\n# bring in pums map ----\nil_puma <- pumas(state = \"IL\", cb = TRUE) %>% st_transform( 4326 )\n# ggplot(il_puma) + geom_sf() + theme_void()\n# restrict to chicago pumas\nchi_puma <- il_puma %>% filter( PUMACE10 %in% chi.pumas )\n# ggplot(chi_puma) + geom_sf() + theme_void()\nchi_puma <- chi_puma %>%\nmutate(area_ft_puma = as.numeric(st_area(.))) %>%\nselect(PUMA = PUMACE10, GEOID10, NAME10, area_ft_puma, geometry)\nchi_puma_fpl <- chi_puma %>%\nleft_join(pums, \"PUMA\")\n\n# intersect the CCA shapefile with the puma shapefile\ncca_level <- st_intersection(x = chi_puma_fpl, chi) %>%\n# take the intersecting area (between puma and CCA)\nmutate(area_ft_intersect = as.numeric(st_area(.)),\n# take the puma pop estimate multiply by\n# area of the intersect (puma/CCA)\n# scaled by the area of the puma\ncca_pop = puma_pop * (as.numeric(st_area(.)) / area_ft_puma),\n# same method for FPL est\ncca_est_fpl_100_200 = puma_fpl_100_200 * (as.numeric(st_area(.)) / area_ft_puma))\n\n# use these population estimates to create a pct of fpl 100-200\ncca_fpl <- cca_level %>%\ngroup_by(community) %>%\nsummarize(\nneighdist = first(community),\nn_cca = sum(cca_pop),\nn_fpl = sum(cca_est_fpl_100_200),\npct_fpl = round(sum(cca_est_fpl_100_200) / sum(cca_pop) * 100, 1))\n\ncca_fpl %>% ggplot() +\ngeom_sf(aes(fill = pct_pov), size = .25) +\nscale_fill_viridis_c(direction = -1) +\ntheme_void()\n``````\n\nMy resulting map looks essentially like I'm just applying the PUMA FPL estimate to each CCA, when what I want is to scale the numerator (pop at FPL) and denominator (CCA Pop) by the area of the PUMA that each CCA occupies.", null, "this is a little involved but I figured this was a more appropriate place to post than SO, because it's a tidycensus and estimation problem.\nThanks!\nFrancisco\n\nThis topic was automatically closed 21 days after the last reply. New replies are no longer allowed.\n\nIf you have a query related to it or one of the replies, start a new topic and refer back with a link." ]

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[ "", null, "assigned - Maple Help\n\n# Online Help\n\n###### All Products    Maple    MapleSim\n\nassigned\n\ncheck if a name is assigned", null, "Calling Sequence assigned(n) assigned(n, val)", null, "Parameters\n\n n - name, subscripted name, or function call val - name, assignable", null, "Description\n\n • The assigned function returns true if n has a value other than its own name, and returns false otherwise.\n Note: The assigned function returns true if you have placed assumptions on n using the assume command.\n • This function is one of the exceptions to the normal evaluation rule for arguments of a function. The argument to assigned will only be evaluated as a name (see the evaln function) rather than fully evaluated.\n • The definition of assigned for array/table subscripts is\n\n$\\mathrm{assigned}\\left({A}_{i}\\right)=\\mathrm{evalb}\\left({A}_{i}\\ne \\mathrm{evaln}\\left({A}_{i}\\right)\\right)$\n\n • The definition of assigned for function calls is\n\n$\\mathrm{assigned}\\left(f\\left(x\\right)\\right)=\\mathrm{evalb}\\left(f\\left(x\\right)\\ne \\mathrm{evaln}\\left(f\\left(x\\right)\\right)\\right)$\n\n • If an optional second argument is provided, then that parameter is set to the assigned value of n.  This allows the assignment-check and fetch of the value to be done in a single command, which can be important in threaded applications with shared data, and when using weak tables.", null, "Thread Safety\n\n • The assigned command is thread-safe as of Maple 15.\n • For more information on thread safety, see index/threadsafe.", null, "Examples\n\n > $n≔4$\n ${n}{≔}{4}$ (1)\n > $\\mathrm{assigned}\\left(n\\right)$\n ${\\mathrm{true}}$ (2)\n > $\\mathrm{assigned}\\left(n,'\\mathrm{nval}'\\right)$\n ${\\mathrm{true}}$ (3)\n > $\\mathrm{nval}$\n ${4}$ (4)\n\nTable lookups can return unevaluated; using assigned or comparing against evaln of the indexed name will distinguish between a unevaluated lookup and a found value.\n\n > $a≔\\mathrm{table}\\left(\\mathrm{symmetric}\\right)$\n ${a}{≔}{table}{}\\left({\\mathrm{symmetric}}{,}\\left[\\right]\\right)$ (5)\n > $a\\left[1,2\\right]≔x$\n ${{a}}_{{1}{,}{2}}{≔}{x}$ (6)\n > $\\mathrm{assigned}\\left(a\\left[1,2\\right]\\right)$\n ${\\mathrm{true}}$ (7)\n > $\\mathrm{assigned}\\left(a\\left[2,1\\right]\\right)$\n ${\\mathrm{true}}$ (8)\n > $\\mathrm{assigned}\\left(a\\left[1,1\\right]\\right)$\n ${\\mathrm{false}}$ (9)\n > $\\mathrm{assigned}\\left(\\mathrm{abs}\\left(x\\right)\\right)$\n ${\\mathrm{false}}$ (10)\n > $\\mathrm{assigned}\\left(\\mathrm{abs}\\left(2\\right)\\right)$\n ${\\mathrm{true}}$ (11)\n\nassigned will evaluate the function to determine if it will return itself or not\n\n > f := proc(x) if(x::integer,x^2,'procname'(x)) end:\n > $\\mathrm{assigned}\\left(f\\right)$\n ${\\mathrm{true}}$ (12)\n > $\\mathrm{assigned}\\left(f\\left(x\\right)\\right)$\n ${\\mathrm{false}}$ (13)\n > $\\mathrm{assigned}\\left(f\\left(2\\right)\\right)$\n ${\\mathrm{true}}$ (14)\n\nIf you place an assumption on a name using the assume command, the assigned command returns true for that name.\n\n > $\\mathrm{assigned}\\left(b\\right)$\n ${\\mathrm{false}}$ (15)\n > $\\mathrm{assume}\\left(b,\\mathrm{positive}\\right)$\n > $\\mathrm{assigned}\\left(b\\right)$\n ${\\mathrm{true}}$ (16)\n\nNote: Evaluating an assigned call under an assumption (using the assuming command), returns true for a name only if it has a value different from its name.\n\n > $\\mathrm{assigned}\\left(c\\right)\\phantom{\\rule[-0.0ex]{0.3em}{0.0ex}}\\mathbf{assuming}\\phantom{\\rule[-0.0ex]{0.3em}{0.0ex}}c::'\\mathrm{integer}'$\n ${\\mathrm{false}}$ (17)", null, "Compatibility\n\n • The assigned command was updated in Maple 2019.\n • The val option was introduced in Maple 2019.\n • For more information on Maple 2019 changes, see Updates in Maple 2019.\n\n See Also" ]

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[ "# Inverse of $\\frac{1-e^{-x}}{x}$ on $(0,1)$\n\nI am trying to invert (or to estimate the inverse of) $$y=\\frac{1-e^{-x}}{x}$$ for $y\\in(0,1)$. The function 'looks' monotonically decreasing between $x=0$ and $x=\\infty$, but I have not been able to show this.", null, "I have been able to compute the inverse function numerically, but I am wondering if there is an analytical solution or approximation that would help speed things up.\n\nMathematica tells me that the inverse is $$x=\\frac{1+y\\cdot\\text{ProductLog}[-e^{-1/y}/y]}{y}$$ where $\\text{ProductLog}[z]$ is the solution to $z=we^w$. I have tried re-arranging the latter expression but I cannot arrive at the original function. Plotting the latter function on $y\\in(0,1)$, it looks plausible, but I don't want to use this formula without understanding where it comes from.", null, "Can anyone show me how to invert the original function or help me estimate the inverse to some degree of precision?\n\n• I don't get. You already know the inverse function depends on the Lambert function, so you just have to check Lambert function asymptotics on the related Wikipedia page. Or you may solve $y=\\frac{1-e^{-x}}{x}$ through Newton's method with starting point $x_0=-2\\log(y)$. – Jack D'Aurizio Sep 7 '15 at 17:21\n• Thanks, I did know know about the Lambert function. I will investigate it. – JS1204 Sep 7 '15 at 17:24\n• OK using the asymptotics of the Lambert function I think I can approximate Mathematica's formula for the inverse. However, I would still like to know how to arrive at Mathematica's answer for the inverse function. – JS1204 Sep 7 '15 at 17:36\n\nDerivation to obtain the Lambert $W$ function : \\begin{align} y&=\\frac{1-e^{-x}}x\\\\ x&=\\frac{1-e^{-x}}y\\\\ x\\,e^x&=\\frac{e^{x}-1}y\\\\ \\left(x-\\frac 1y\\right)\\,e^x&=-\\frac 1y\\\\ \\left(x-\\frac 1y\\right)\\,e^{\\large{x-\\frac 1y}}&=-\\frac {\\large{e^{-\\frac 1y}}}y\\\\ x-\\frac 1y&=W\\left(-\\frac {\\large{e^{-\\frac 1y}}}y\\right)\\\\ \\end{align} and the wished formula : $\\quad\\boxedx=\\frac 1y+W\\left(-\\frac {\\large{e^{-\\frac 1y}}}y\\right)$\n\nAt this point (as indicated by robjohn) we may use the fact that $\\;y\\in(0,1)\\;$ and observe that the parameter of the Lambert-$W$ function $\\,-\\dfrac 1y\\;e^{-\\large{\\frac 1y}}\\;$ will belong to $\\;\\left(-\\dfrac 1e,\\;0\\right)$.\n\nThe implications are :\n\n• for any $\\,y\\in(0,1)\\;$ we have two real solutions from the two branches of the Lambert-$W$ function (see the picture in the Wikipedia link and the discussion about the image of $W$ under or above $-1$ corresponding to the parameter $-\\dfrac 1e$) :$$x_1=\\frac 1y+W\\left(-\\frac {\\large{e^{-\\frac 1y}}}y\\right),\\;x_2=\\frac 1y+W_{-1}\\left(-\\frac {\\large{e^{-\\frac 1y}}}y\\right)$$\n• the parameter of $W$ may be written as $\\;u\\,e^u\\,$ for $u=-\\dfrac 1y\\;$ but $\\;W_{-1}(u\\,e^u)=u\\;$ in the second case so that $\\;x_2=\\dfrac 1y-\\dfrac 1y\\;$ with the solutions becoming simply : $$x_1=\\frac 1y+W\\left(-\\frac {\\large{e^{-\\frac 1y}}}y\\right),\\ x_2=0$$ ($x_2=0$ is rather a solution of $\\:x\\;y=1-e^{-x}\\;$ than of the initial equation)\n• Since the argument is negative, it should be noted that there are two branches of $\\mathrm{W}$. This is important since one value of $\\mathrm{W}\\left(-\\frac1ye^{-\\frac1y}\\right)$ is $-\\frac1y$ which gives $x=0$. – robjohn Sep 7 '15 at 22:53\n• Thanks @robjohn: (I didn't notice the bounds on $y$) I'll edit this again. Cheers, – Raymond Manzoni Sep 7 '15 at 22:58\n• Thanks! How do you get from the 4th line to the 5th line in your derivation? – JS1204 Sep 7 '15 at 22:58\n• @js86: It is a multiplication by $e^{-1/y}$ and the previous line is a subtraction of $e^x/y$. – Raymond Manzoni Sep 7 '15 at 23:00\n• of course, thanks! – JS1204 Sep 7 '15 at 23:02" ]

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[ "", null, "## Azzalini's Skew-Normal   QuickTime movie (800K)", null, "This animation shows Azzalini's", null, "varies between 0 (a standard Normal pdf) and 1 (a half-Normal pdf). Computational details are discussed on p.225 of Mathematical Statistics with Mathematica. For detail on skew densities, please see The Skew-Normal Web Site.\n\nThe following diagram plots the Azzalini skew-Normal pdf on a Pearson diagram. The diagram itself is derived as an exercise on p.185 of Mathematical Statistics with Mathematica.", null, "" ]

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[ "degrees per day to megahertz conversion\n\nConversion number between degrees per day [deg/day] and megahertz [MHz] is 3.2150205761317 × 10-14. This means, that degrees per day is smaller unit than megahertz.\n\nContents [show][hide]", null, "Switch to reverse conversion:\nfrom megahertz to degrees per day conversion\n\nEnter the number in degrees per day:\n\nDecimal Fraction Exponential Expression\n [deg/day]\neg.: 10.12345 or 1.123e5\n\nResult in megahertz\n\n?\n precision 0 1 2 3 4 5 6 7 8 9 [info] Decimal: Exponential:\n\nCalculation process of conversion value\n\n• 1 degrees per day = (exactly) ((1/31104000)) / (1000000) = 3.2150205761317 × 10-14 megahertz\n• 1 megahertz = (exactly) (1000000) / ((1/31104000)) = 31104000000000 degrees per day\n• ? degrees per day × ((1/31104000)  (\"Hz\"/\"degrees per day\")) / (1000000  (\"Hz\"/\"megahertz\")) = ? megahertz\n\nHigh precision conversion\n\nIf conversion between degrees per day to hertz and hertz to megahertz is exactly definied, high precision conversion from degrees per day to megahertz is enabled.\n\nDecimal places: (0-800)\n\ndegrees per day\nResult in megahertz:\n?\n\ndegrees per day to megahertz conversion chart\n\n Start value: [degrees per day] Step size [degrees per day] How many lines? (max 100)\n\nvisual:\ndegrees per daymegahertz\n00\n103.2150205761317 × 10-13\n206.4300411522634 × 10-13\n309.6450617283951 × 10-13\n401.2860082304527 × 10-12\n501.6075102880658 × 10-12\n601.929012345679 × 10-12\n702.2505144032922 × 10-12\n802.5720164609054 × 10-12\n902.8935185185185 × 10-12\n1003.2150205761317 × 10-12\n1103.5365226337449 × 10-12\nCopy to Excel\n\nMultiple conversion\n\nEnter numbers in degrees per day and click convert button.\nOne number per line.\n\nConverted numbers in megahertz:\nClick to select all\n\nDetails about degrees per day and megahertz units:\n\nConvert Degrees per day to other unit:\n\ndegrees per day\n\nDefinition of degrees per day unit: = 1/(360 × 86400) Hz. Degrees per day is the angular velocity where the body turn one degree in one day. Used to express very slow angular velocities.\n\nConvert Megahertz to other unit:\n\nmegahertz\n\nDefinition of megahertz unit: = 106 Hz. Millions of Hertz. How many cycles take place over one millionth of a second. Event per 0.000001 sec.", null, "" ]

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[ "# Difference between revisions of \"Talk:2028: Complex Numbers\"\n\nI assume this is strictly a coincidence, but in reference to the title-text, I'll just mention that Caucher Birkar [the mathematician whose Fields Medal was stolen minutes after he received it in Rio de Janeiro on Weds (1Aug2018)] received the award for work in algebraic geometry. Arcanechili (talk) 16:34, 3 August 2018 (UTC)\n\n• Perhaps it's causal not coincidental. Medal theives and perhaps Randall might read the news also. [] 162.158.79.209 00:34, 4 August 2018 (UTC)\n\nI've added a basic description of Abelian groups in the title text, and that's about as much as I know about such topics. I'm not sure what a \"meta-Abelian group\" is, is that an Abelian group of other groups? Also, could someone add basic descriptions of algebreic geometry and geometrical algebra? 172.68.94.40 18:42, 3 August 2018 (UTC)\n\nIn the title text, since groups are a concept within mathematics, it seems odd to consider mathematics as a whole forming any sort of group within itself, which I suspect is the first part of the pun. Secondly, since groups involve the commutative property, I think the last part is a pun about the order of the words algebra and geometry, as if they're commutative themselves! Ianrbibtitlht (talk) 19:19, 3 August 2018 (UTC)\n\nI meant to say 'abelian' groups involve the commutative property, and the meta prefix is referring to the fact that it's about the names rather than the mathematical details - i.e. commutative in metadata only. Ianrbibtitlht (talk) 19:24, 3 August 2018 (UTC)\nI guess the joke is that informally mathematicians form a group (a number of people classed together), what would strictly be a set in mathematics. While in mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies specific conditions. --JakubNarebski (talk) 21:18, 3 August 2018 (UTC)\n\nIt's a false dilemma. Complex numbers are vectors (", null, "$\\mathbb{C}$ is a two-dimensional", null, "$\\mathbb{R}$-vector space, and more generally every field is a vector space over any subfield), but that doesn't change anything about the fact that", null, "$i$ is by definition a square root of -1. Zmatt (talk) 20:38, 3 August 2018 (UTC)\n\nFun factoid: not only is", null, "$\\mathbb{C}$ the unique proper field extension of finite degree over", null, "$\\mathbb{R}$ (since", null, "$\\mathbb{C}$ is algebraically closed), but the converse is true as well:", null, "$\\mathbb{R}$ is the only proper subfield of finite index in", null, "$\\mathbb{C}$. They're like a weird married couple. Zmatt (talk) 20:53, 3 August 2018 (UTC)\n\nAltho there are no \"meta-abelian\" groups there are metabelian groups. If xy=yx then the commutator [x,y]=xyx^{-1}y^{-1}=1. The group generated by the commutators -- the commutator subgroup -- is thus a measure of how far a group is from being abelian. A metabelian group is a nonabelian group whose commutator subgroup is abelian. Thus a metabelian group is one made of a stack of two abelian groups. It is \"meta-abelian\" in that sense. A standard example is the group of invertible upper-trianglular matrices. The commutators all have 1s on the diagonals.\n\nOne should note that the concept of complex numbers actually is older than vector spaces. So while it is true that complex numbers are a cool variant of vectors, historically that's not true, because vectors were more or less unknown when complex numbers were used for the first time. --162.158.90.6 09:59, 4 August 2018 (UTC)\n\nShouldn't the description of a group involve two operations? There is a binary operation that gloms two things together to make a new thing, but there's also a unary operation that takes only one thing and makes a new thing -- the inverse. Without the unary operation, you only have a semigroup.108.162.215.160 09:40, 5 August 2018 (UTC)\n\nNo. The inverse operation arises as a consequence of the fact that it's a group. A group satisfies four conditions: 1. it is closed under the operation, 2. the operation is associative 3. there is an identity e such that a op e = e op a = a. 4. For every element a, there is a unique element b such that a op b = b op a = e. The inverse function falls out as a result of conditions 3 and 4 Jeremyp (talk) 10:26, 6 August 2018 (UTC)" ]

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[ "# Level of Measurement\n\nWe have seen that from theory to empirical hypothesis and from theoretically defined concepts to operational definitions, the process is by no means direct. As the example illustrates, when we operationalize a definition and derive measurement indicators, we must consider the scale of measurement. For instance, to measure the quality of software inspection we may use a five-point scale to score the inspection effectiveness or we may use percentage to indicate the inspection coverage. For some cases, more than one measurement scale is applicable ; for others, the nature of the concept and the resultant operational definition can be measured only with a certain scale. In this section, we briefly discuss the four levels of measurement: nominal scale, ordinal scale, interval scale, and ratio scale.\n\nNominal Scale\n\nThe most simple operation in science and the lowest level of measurement is classification. In classifying we attempt to sort elements into categories with respect to a certain attribute. For example, if the attribute of interest is religion, we may classify the subjects of the study into Catholics, Protestants, Jews, Buddhists, and so on. If we classify software products by the development process models through which the products were developed, then we may have categories such as waterfall development process, spiral development process, iterative development process, object-oriented programming process, and others. In a nominal scale, the two key requirements for the categories are jointly exhaustive and mutually exclusive. Mutually exclusive means a subject can be classified into one and only one category. Jointly exhaustive means that all categories together should cover all possible categories of the attribute. If the attribute has more categories than we are interested in, an \"other\" category is needed to make the categories jointly exhaustive.\n\nIn a nominal scale, the names of the categories and their sequence bear no assumptions about relationships among categories. For instance, we place the waterfall development process in front of spiral development process, but we do not imply that one is \"better than\" or \"greater than\" the other. As long as the requirements of mutually exclusive and jointly exhaustive are met, we have the minimal conditions necessary for the application of statistical analysis. For example, we may want to compare the values of interested attributes such as defect rate, cycle time, and requirements defects across the different categories of software products.\n\nOrdinal Scale\n\nOrdinal scale refers to the measurement operations through which the subjects can be compared in order. For example, we may classify families according to socio-economic status: upper class, middle class, and lower class. We may classify software development projects according to the SEI maturity levels or according to a process rigor scale: totally adheres to process, somewhat adheres to process, does not adhere to process. Our earlier example of inspection effectiveness scoring is an ordinal scale.\n\nThe ordinal measurement scale is at a higher level than the nominal scale in the measurement hierarchy. Through it we are able not only to group subjects into categories, but also to order the categories. An ordinal scale is asymmetric in the sense that if A > B is true then B > A is false. It has the transitivity property in that if A > B and B > C , then A > C .\n\nWe must recognize that an ordinal scale offers no information about the magnitude of the differences between elements. For instance, for the process rigor scale we know only that \"totally adheres to process\" is better than \"somewhat adheres to process\" in terms of the quality outcome of the software product, and \"somewhat adheres to process\" is better than \"does not adhere to process.\" However, we cannot say that the difference between the former pair of categories is the same as that between the latter pair. In customer satisfaction surveys of software products, the five-point Likert scale is often used with 1 = completely dissatisfied, 2 = somewhat dissatisfied, 3 = neutral, 4 = satisfied, and 5 = completely satisfied. We know only 5 > 4, 4 > 3, and 5 > 2, and so forth, but we cannot say how much greater 5 is than 4. Nor can we say that the difference between categories 5 and 4 is equal to that between categories 3 and 2. Indeed, to move customers from satisfied (4) to very satisfied (5) versus from dissatisfied (2) to neutral (3), may require very different actions and types of improvements.\n\nTherefore, when we translate order relations into mathematical operations, we cannot use operations such as addition, subtraction, multiplication, and division. We can use \"greater than\" and \"less than.\" However, in real-world application for some specific types of ordinal scales (such as the Likert five-point, seven-point, or ten-point scales), the assumption of equal distance is often made and operations such as averaging are applied to these scales . In such cases, we should be aware that the measurement assumption is deviated, and then use extreme caution when interpreting the results of data analysis.\n\nInterval and Ratio Scales\n\nAn interval scale indicates the exact differences between measurement points. The mathematical operations of addition and subtraction can be applied to interval scale data. For instance, assuming products A, B, and C are developed in the same language, if the defect rate of software product A is 5 defects per KLOC and product B's rate is 3.5 defects per KLOC, then we can say product A's defect level is 1.5 defects per KLOC higher than product B's defect level. An interval scale of measurement requires a well-defined unit of measurement that can be agreed on as a common standard and that is repeatable. Given a unit of measurement, it is possible to say that the difference between two scores is 15 units or that one difference is the same as a second. Assuming product C's defect rate is 2 defects per KLOC, we can thus say the difference in defect rate between products A and B is the same as that between B and C.\n\nWhen an absolute or nonarbitrary zero point can be located on an interval scale, it becomes a ratio scale. Ratio scale is the highest level of measurement and all mathematical operations can be applied to it, including division and multiplication. For example, we can say that product A's defect rate is twice as much as product C's because when the defect rate is zero, that means not a single defect exists in the product. Had the zero point been arbitrary, the statement would have been illegitimate. A good example of an interval scale with an arbitrary zero point is the traditional temperature measurement (Fahrenheit and centigrade scales). Thus we say that the difference between the average summer temperature (80 °F) and the average winter temperature (16 °F) is 64 °F, but we do not say that 80 °F is five times as hot as 16 °F. Fahrenheit and centigrade temperature scales are interval, not ratio, scales. For this reason, scientists developed the absolute temperature scale (a ratio scale) for use in scientific activities.\n\nExcept for a few notable examples, for all practical purposes almost all interval measurement scales are also ratio scales. When the size of the unit is established, it is usually possible to conceive of a zero unit.\n\nFor interval and ratio scales, the measurement can be expressed in both integer and noninteger data. Integer data are usually given in terms of frequency counts (e.g., the number of defects customers will encounter for a software product over a specified time length).\n\nWe should note that the measurement scales are hierarchical. Each higher-level scale possesses all properties of the lower ones. The higher the level of measurement, the more powerful analysis can be applied to the data. Therefore, in our operationalization process we should devise metrics that can take advantage of the highest level of measurement allowed by the nature of the concept and its definition. A higher-level measurement can always be reduced to a lower one, but not vice versa. For example, in our defect measurement we can always make various types of comparisons if the scale is in terms of actual defect rate. However, if the scale is in terms of excellent , good, average, worse than average, and poor, as compared to an industrial standard, then our ability to perform additional analysis of the data is limited.", null, "Metrics and Models in Software Quality Engineering (2nd Edition)\nISBN: 0201729156\nEAN: 2147483647\nYear: 2001\nPages: 176\n\nSimilar book on Amazon", null, "" ]

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[ "Convert 775 Centimeters to Feet and Inches\n\nHow much is 775 cm in feet and inches? Use this calculator to convert 775 centimeters to feet and inches. Change the values in the calculator below to determine a different amount. Height is commonly referred to in cm in some countries and feet and inches in others. This calculates from 775cm to feet and inches.\n\nSummary\n\nConvert from Feet and Inches\nUse this calculator to convert seven hundred and seventy-five CMs to other measuring units.\nHow big is 775 cm in feet and inches? 775 cm = 25'5.12\nHow many meters is that? How high is that? How much? How big? How far is it? How tall is 775centimeters in feet and inches? How tall am I in feet and inches?\n\nWhat is the inch to cm conversion? How many inches in a centimeter? 1 cm = .3937007874 inches" ]

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[ "# LDP LLC - MaxMax.com\n\n## Desert Study\n\nYou can jump to the Remote Sensing Section of our online store by clicking here.\n\nGoal:  Identify and quantify vegetation growing in the desert and estimate biomass.\n\nEquipment Used:  Canon550NDVI MK II vegetation stress camera\n\nSoftware Used: ImageJ with MaxMax Enhanced NDVI (ENDVI) macro\n\nNormal visual picture of area.\n\nNotice that you can see some brownish plants which are likely quite stressed as well, but it is pretty hard to see the difference between the plants and the dirt..  For this study, we want to be able to pick out vegetation.", null, "Unprocessed picture from the Canon550NDVI MK II camera.\n\nNotice that the plants now have a reddish tint.  This is because the plants reflect the near IR which is picked up by the camera in the red channel.", null, "Canon550NDVI MK II image processed with ImageJ using macro aNDVI6_MKII\n\nThe macro uses our Enhanced NDVI (ENDVI) calculation that uses all 3 bands.  This ENDVI uses\n\nENDVI = ((Red + Green ) -2*Blue) / ((Red + Green) + 2*Blue))\n\nThe logic behind this NDVI calculation is that plants will reflect both green and the near IR, which is in the red channel.  Plants absorb blue light so the blue channel is used as the visible channel and is multiplied by 2 to compensate for the 2 plant reflective channels.\n\nThe macro then further processes the data by rescaling the NDVI values to a user set maximum and minimum.  The reason for this is that if the maximum plants for this sort of picture have an NDVI of 0.50 while the rocks have a value of -0.15, most of the NDVI value in the picture will be between -0.15 and +0.50.  By rescaling the ENDVI values so that -0.15 = -1.0 and +0.50 = +1.0, then we can get a better understanding about what is in the picture.\n\nNext the macro takes the rescaled ENDVI values and maps each pixel in the picture so that the closer to +1.0, the more green the pixel and the closer to -1.0, the more blue the pixel becomes.  A new image is created where each pixel is a color representation of the rescaled NDVI values where green is mapped to the vegetation and blue is matched to stuff that isn't.\n\nNotice that now we can easily pick out the areas with plants.  We can also see that the rocks are generally blue while the dirt is generally black.\n\nDefault values for rescaling the NDVI values was minimum value of -0.15 and maximum value of +0.50.", null, "The macro measures each pixel and keeps a count of every 0.10 between -1.00 and +1.00 to summarize the picture.  You could use this to calculate the total vegetation in the picture, the stress of the vegetation, the amount of rocks and the amount of dirt.a", null, "", null, "Lastly, here is a copy of the ImageJ macro that we used:\n\n```// ENDVI 6 Macro\n// Written by Dan Llewellyn\n// www.MaxMax.com\n// For NDVI MK II Cameras```\n```// Copywrite 2011\n```\n```// This macro converts an RGB image to a Green/Blue NDVI image.\n// NDVI values > 0 are colored green with user set max value\n// NDVI values < 0 are colored blue with user set min value\n// This macro automatically rescales the image so that max value is 100% green and min value is 100% blue\n// Green shows healthy plants.\n// Blue represents negative NDVI values which are often things like dirt and rocks.```\n```\nNDVI_Plant_Max = 0.50; // Set the highest value for a NDVI plant in picture\nNDVI_Not_A_Plant = -0.15; // Set to highest value for not a plant - max negative -.15```\n`ScaledNDVI = 0; // NDVI scaled to max value`\n```///////////////////////////////////////////\n// Statistics Counters\n//////////////////////////////////////////\n// Total counters for scaled NDVI values```\n```TotalScaledNDVI_9_10 = 0; // Total scaled NDVI +0.90 to +1.00\nTotalScaledNDVI_8_9 = 0 // Total scaled NDVI +0.80 to +0.90\nTotalScaledNDVI_7_8 = 0; // Total scaled NDVI +0.70 to +0.80\nTotalScaledNDVI_6_7 = 0; // Total scaled NDVI +0.60 to +0.70\nTotalScaledNDVI_5_6 = 0; // Total scaled NDVI +0.50 to +0.60\nTotalScaledNDVI_4_5 = 0; // Total scaled NDVI +0.40 to +0.50\nTotalScaledNDVI_3_4 = 0; // Total scaled NDVI +0.30 to +0.40\nTotalScaledNDVI_2_3 = 0; // Total scaled NDVI +0.20 to +0.30\nTotalScaledNDVI_1_2 = 0; // Total scaled NDVI +0.10 to +0.20\nTotalScaledNDVI_0_1 = 0; // Total scaled NDVI +0.00 to +0.10\nTotalScaledNDVI_0_n1 = 0; // Total scaled NDVI +0.00 to -0.10\nTotalScaledNDVI_n1_n2 = 0; // Total scaled NDVI -0.10 to -0.20\nTotalScaledNDVI_n2_n3 = 0; // Total scaled NDVI -0.20 to -0.30\nTotalScaledNDVI_n3_n4 = 0; // Total scaled NDVI -0.30 to -0.40\nTotalScaledNDVI_n4_n5 = 0; // Total scaled NDVI -0.40 to -0.50\nTotalScaledNDVI_n5_n6 = 0; // Total scaled NDVI -0.50 to -0.60\nTotalScaledNDVI_n6_n7 = 0; // Total scaled NDVI -0.60 to -0.70\nTotalScaledNDVI_n7_n8 = 0; // Total scaled NDVI -0.70 to -0.80\nTotalScaledNDVI_n8_n9 = 0; // Total scaled NDVI -0.80 to -0.90\nTotalScaledNDVI_n9_n10 = 0; // Total scaled NDVI -0.90 to -1.00\n```\n`TotalScaledPixelPercent = 0; // This will be used later to calculate percent of all pixels for each Total Scaled Count`\n```MaxNDVI = 0; // Maximum NDVI\nMinNDVI = 0; // Minimum NDVI\nMaxScaledNDVI = 0; // Maximum Scaled NDVI\nMinScaledNDVI = 0; // Minimum Scaled NDVI\nTotalPixels = 0; // Total Pixels```\n```/////////////////////////////////////////////\n```\n``` requires(\"1.29m\"); // Check ImageJ version\nw = getWidth(); // Get picture width\nh = getHeight(); // Get picture height\n```\n` start = getTime(); // Get current time for progress bar`\n```\nfor (y=0; y<h; y++) // Setup nested loops to go through each x,y value in image\n{\nfor (x=0; x<w; x++)\n{\noldpixel = getPixel(x,y); // Get a pixel value\nred = (oldpixel & 0xff0000)>>16; // Extract out RGB values from packed integer with pixel value\ngreen = (oldpixel & 0x00ff00)>>8;\nblue = (oldpixel & 0x0000ff);\nNDVI = ((red+green)-(2*blue))/((red+green)+(2*blue)); // Calculate the NDVI. Will be a value between -1.0 and + 1.0\nif (NDVI < 0) // not a plant\n{\nScaledNDVI = NDVI/(-1*NDVI_Not_A_Plant); // Calc NDVI as a % of max value.\nif (ScaledNDVI < -1) ScaledNDVI = -1; // Make sure not going over limit for max. Max NDVI value is +1.0\nblue= floor(ScaledNDVI*-255); // Set red value and rescale to max 255 bit depth.\nred = 0;\ngreen = 0;\n```\n``` }\nelse // Possible plant\n{\nScaledNDVI = NDVI/NDVI_Plant_Max; // Calc NDVI as a % of max value.\nif (ScaledNDVI > 1) ScaledNDVI = 1; // Make sure not going over limit for max. Max NDVI value is +1.0\ngreen = floor(ScaledNDVI*255); // set green value and rescale to max 255 bit depth.\nblue = 0;\nred = 0;\n}\nnewpixel = ((red & 0xff)<<16)+((green & 0xff)<<8) + (blue & 0xff); // Pack new pixel integer value with new RGB data\nputPixel(x, y, newpixel); // write pixel to the screen\n```\n``` // Statistics Collection\nif (NDVI > MaxNDVI) MaxNDVI = NDVI; // Test for Max NDVI\nif (NDVI < MinNDVI) MinNDVI = NDVI; // Test for Min NDVI\nif (NDVI > MaxScaledNDVI) MaxScaledNDVI = NDVI; // Test for Max Scaled NDVI\nif (NDVI < MinScaledNDVI) MinScaledNDVI = NDVI; // Test for Min Scaled NDVI\n```\n``` if (ScaledNDVI > 0.90) // Keep track of each pixels value by binning it into correct counter\nTotalScaledNDVI_9_10 ++;\nelse if (ScaledNDVI > 0.80 && ScaledNDVI < 0.90)\nTotalScaledNDVI_8_9 ++;\nelse if (ScaledNDVI > 0.70 && ScaledNDVI < 0.80)\nTotalScaledNDVI_7_8 ++;\nelse if (ScaledNDVI > 0.60 && ScaledNDVI < 0.70)\nTotalScaledNDVI_6_7 ++;\nelse if (ScaledNDVI > 0.50 && ScaledNDVI < 0.60)\nTotalScaledNDVI_5_6 ++;\nelse if (ScaledNDVI > 0.40 && ScaledNDVI < 0.50)\nTotalScaledNDVI_4_5 ++;\nelse if (ScaledNDVI > 0.30 && ScaledNDVI < 0.40)\nTotalScaledNDVI_3_4 ++;\nelse if (ScaledNDVI > 0.20 && ScaledNDVI < 0.30)\nTotalScaledNDVI_2_3 ++;\nelse if (ScaledNDVI > 0.10 && ScaledNDVI < 0.20)\nTotalScaledNDVI_1_2 ++;\nelse if (ScaledNDVI > 0.00 && ScaledNDVI < 0.10)\nTotalScaledNDVI_0_1 ++;\nelse if (ScaledNDVI > -0.10 && ScaledNDVI < 0)\nTotalScaledNDVI_0_n1 ++;\nelse if (ScaledNDVI > -0.20 && ScaledNDVI < -0.10)\nTotalScaledNDVI_n1_n2 ++;\nelse if (ScaledNDVI > -0.30 && ScaledNDVI < -0.20)\nTotalScaledNDVI_n2_n3 ++;\nelse if (ScaledNDVI > -0.40 && ScaledNDVI < -0.30)\nTotalScaledNDVI_n3_n4 ++;\nelse if (ScaledNDVI > -0.50 && ScaledNDVI < -0.40)\nTotalScaledNDVI_n4_n5 ++;\nelse if (ScaledNDVI > -0.60 && ScaledNDVI < -0.50)\nTotalScaledNDVI_n5_n6 ++;\nelse if (ScaledNDVI > -0.70 && ScaledNDVI < -0.60)\nTotalScaledNDVI_n6_n7 ++;\nelse if (ScaledNDVI > -0.80 && ScaledNDVI < -0.70)\nTotalScaledNDVI_n7_n8 ++;\nelse if (ScaledNDVI > -0.90 && ScaledNDVI < -0.80)\nTotalScaledNDVI_n8_n9 ++;\nelse if (ScaledNDVI < -0.90)\nTotalScaledNDVI_n9_n10 ++;\n```\n``` TotalPixels ++; // Count another pixel\n```\n``` }\nif (y%10==0) showProgress(y, h-1); // show current progress\nif (y%10==0) updateDisplay();\n}\nshowStatus(round((w*h)/((getTime()-start)/1000)) + \" pixels/sec\");\nresetMinAndMax();\n```\n``` Dialog.create(\"NDVI Summary\"); // Create the pixel count dialog. Display total in counters.\nDialog.addNumber(\"Scaled NDVI Pixels 0.90 to 1.00\", TotalScaledNDVI_9_10);\nDialog.addNumber(\"Scaled NDVI Pixels 0.80 to 0.90\", TotalScaledNDVI_8_9);\nDialog.addNumber(\"Scaled NDVI Pixels 0.70 to 0.80\", TotalScaledNDVI_7_8);\nDialog.addNumber(\"Scaled NDVI Pixels 0.60 to 0.70\", TotalScaledNDVI_6_7);\nDialog.addNumber(\"Scaled NDVI Pixels 0.50 to 0.60\", TotalScaledNDVI_5_6);\nDialog.addNumber(\"Scaled NDVI Pixels 0.40 to 0.50\", TotalScaledNDVI_4_5);\nDialog.addNumber(\"Scaled NDVI Pixels 0.30 to 0.40\", TotalScaledNDVI_3_4);\nDialog.addNumber(\"Scaled NDVI Pixels 0.20 to 0.30\", TotalScaledNDVI_2_3);\nDialog.addNumber(\"Scaled NDVI Pixels 0.10 to 0.20\", TotalScaledNDVI_1_2);\nDialog.addNumber(\"Scaled NDVI Pixels 0.00 to 0.10\", TotalScaledNDVI_0_1);\nDialog.addNumber(\"Scaled NDVI Pixels -0.10 to 0.00\", TotalScaledNDVI_0_n1);\nDialog.addNumber(\"Scaled NDVI Pixels -0.20 to -0.10\", TotalScaledNDVI_n1_n2);\nDialog.addNumber(\"Scaled NDVI Pixels -0.30 to -0.20\", TotalScaledNDVI_n2_n3);\nDialog.addNumber(\"Scaled NDVI Pixels -0.40 to -0.30\", TotalScaledNDVI_n3_n4);\nDialog.addNumber(\"Scaled NDVI Pixels -0.50 to -0.40\", TotalScaledNDVI_n4_n5);\nDialog.addNumber(\"Scaled NDVI Pixels -0.60 to -0.50\", TotalScaledNDVI_n5_n6);\nDialog.addNumber(\"Scaled NDVI Pixels -0.70 to -0.60\", TotalScaledNDVI_n6_n7);\nDialog.addNumber(\"Scaled NDVI Pixels -0.80 to -0.70\", TotalScaledNDVI_n7_n8);\nDialog.addNumber(\"Scaled NDVI Pixels -0.90 to -0.80\", TotalScaledNDVI_n8_n9);\nDialog.addNumber(\"Scaled NDVI Pixels -0.10 to -0.90\", TotalScaledNDVI_n9_n10);```\n```\nDialog.addMessage(\"\\n% Count Summary\\n\"); // Create the % count summary. Calc binned pixels as % of total and display```\n```TotalScaledPixelPercent = (TotalScaledNDVI_9_10 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % 0.90 to 1.00\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_8_9 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % 0.80 to 0.90\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_7_8 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % 0.70 to 0.80\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_6_7 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % 0.60 to 0.70\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_5_6 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % 0.60 to 0.60\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_4_5 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % 0.40 to 0.50\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_3_4 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % 0.30 to 0.40\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_2_3 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % 0.20 to 0.20\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_1_2 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % 0.10 to 0.20\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_0_1 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % 0.00 to 0.10\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_0_n1 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % -0.10 to 0.00\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_n1_n2 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % -0.20 to -0.10\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_n2_n3 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % -0.30 to -0.20\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_n3_n4 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % -0.40 to -0.30\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_n4_n5 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % -0.50 to -0.40\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_n5_n6 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % -0.60 to -0.50\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_n6_n7 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % -0.70 to -0.60\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_n7_n8 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % -0.80 to -0.70\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_n8_n9 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % -0.90 to -0.80\", TotalScaledPixelPercent, 1, 5, \"%\");```\n```TotalScaledPixelPercent = (TotalScaledNDVI_n9_n10 / TotalPixels)*100;\nDialog.addNumber(\"Scaled NDVI % -1.00 to -0.90\", TotalScaledPixelPercent, 1, 5, \"%\");\n```\n` Dialog.show();`", null, "" ]

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[ "# Golang program to demonstrate the recursion\n\nHere, we are going to demonstrate the recursion in Golang (Go Language).\nSubmitted by Nidhi, on March 11, 2021 [Last updated : March 03, 2023]\n\n## Recursion Example in Golang\n\nProblem Solution:\n\nIn this program, we will create a user-defined function to print numbers from 5 to 1 using a recursive function call. A function call itself is known as a recursive function call.\n\nProgram/Source Code:\n\nThe source code to demonstrate the recursion is given below. The given program is compiled and executed successfully.\n\n## Golang code to demonstrate the example of recursion\n\n```// Golang program to demonstrate recursion\n\npackage main\n\nimport \"fmt\"\n\nfunc RecursiveFun(num int) int {\nif num == 0 {\nreturn num\n} else {\nfmt.Printf(\"%d \", num)\n}\nnum = num - 1\nreturn RecursiveFun(num)\n}\n\nfunc main() {\nRecursiveFun(5)\n}\n```\n\nOutput:\n\n```5 4 3 2 1\n```\n\nExplanation:\n\nIn the above program, we declare the package main. The main package is used to tell the Go language compiler that the package must be compiled and produced the executable file. Here, we imported the fmt package that includes the files of package fmt then we can use a function related to the fmt package.\n\n```func RecursiveFun(num int)int{\nif(num==0){\nreturn num\n}else{\nfmt.Printf(\"%d \",num)\n}\nnum=num-1\nreturn RecursiveFun(num)\n}\n```\n\nIn the above code, we implemented a recursive function RecursiveFun() that accepts an integer number as an argument and prints numbers till 1 using a recursive function call.\n\nIn the main() function, we called RecursiveFun() function to print numbers from 5 to 1 on the console screen." ]

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