on the measurement of polarization suppose that a population of individuals may be grouped according to some vector of characteristics into clusters such that each cluster is very similar in terms of the attributes of its members but different clusters have members with very dissimilar attributes in that case we say that the society is polarized our purpose is to study polarization and to provide a theory of its measurement our contention is that polarization as conceptualized here is closely related to the generation of social tensions to the possibilities of revolution and revolt and to the existence of social unrest in general we take special care to distinguish our theory from the theory of inequality measurement we derive measures of polarization that are easily applicable to distributions of characteristics such as income and wealth

a fast poisson solver for complex geometries robust fast solvers for the poisson equation have generally been limited to regular geometries where direct methods based on fourier analysis or cyclic reduction and multigrid methods can be used while multigrid methods can be applied in irregular domains and to a broader class of partial differential equations they are difficult to implement in a robust fashion since they require an appropriate hierarchy of coarse grids which are not provided in many practical situations in this paper we present a new fast poisson solver based on potential theory rather than on direct discretization of the partial differential equation our method combines fast algorithms for computing volume integrals and evaluating layer potentials on a grid with a fast multipole accelerated integral equation solver the amount of work required is o m log m n where m is the number of interior grid points and n is the number of points on the boundary asymptotically the cost of our method is just twice that of a standard poisson solver on a rectangular domain in which the problem domain can be embedded independent of the complexity of the geometry

fast adaptive 2d vortex methods we present a new approach to vortex methods for the 2d euler equations we obtain long time high order accuracy at almost optimal cost by using three tools fast adaptive quadrature rules a free lagrangian formulation and a useful new analysis of the consistency error our error analysis halves the order of differentiability required of the flow and suggests an efficient new balance of smoothing parameters which works well with fast summation schemes numerical experiments with our methods confirm our theoretical predictions and display excellent long time accuracy

an improved fast multipole algorithm for potential fields a new version of the fast multipole method fmm for potential fields is presented we introduce a new representation of potentials in which most translation operators are diagonal as a result for double precision calculations in two dimensions we obtain an improvement of a factor of two to four in speed compared to previously published algorithms the improvement is expected to be much greater in three dimensions the performance of the method is illustrated with several numerical examples

solution of two dimensional vorticity equation on a lagrangian mesh anovel vorticity basedsolutionmethodologyhasbeendevelopedtocomputeunsteadye owpastbodies vorticity is evolved on a set of points and the vorticity in the remainder of the e eld is determined by linear interpolation interpolationisaccomplished bydelaunaytriangularizationofthepointsin the e eld triangulationofthevorticity e eldprovidesabasistointegratethevorticitytocomputethevelocity nodalconnectivityfromthetriangularization also provides a list of the neighboring points that are used to construct a second order least squares e t of the vorticity first and second order spatial derivatives can then be computed based on this polynomial e t surface vorticity on the body is computed to satisfy the no slip boundary condition and is introduced into the e ow via diffusion a diffusion transport velocity was derived to account for spatial movementof the vorticity dueto viscous diffusion the points are advected by the sum of the induced velocity computed from the biot savart integral and the diffusion velocity the remaining diffusion term includes a form of the laplacian and is computed directly this solution scheme was found to be stable as applied to the problem of impulsively started e ow about a circular cylinder and e at plate comparisons with experimental and the blasius boundary layer solution for a e at plate were used to demonstrate the effectiveness of this method

preference for flexibility in a savage framework we study preferences over savage acts that map states to opportunity sets and satisfy the savage axioms preferences over opportunity sets may exhibit a preference for flexibility due to an implicit uncertainty about future preferences reflecting anticipated unforeseen contingencies the main result of this paper characterizes maximization of the expected indirect utility in terms of an indirect stochastic dominance axiom that expresses a preference for more opportunities in expectation the key technical tool of the paper a version of mobius inversion has been imported from the theory of nonadditive belief functions it allows an alternative representation using choquet integration and yields a simple proof of kreps 1979 classic result

a smooth partition of unity finite element method for vortex particle regularization we present a new class of c infty smooth finite element spaces on cartesian grids based on a partition of unity approach we use these spaces to construct smooth approximations of particle fields i e finite sums of weighted dirac deltas in order to use the spaces on general domains we propose a fictitious domain formulation together with a new high order accurate stabilization stability convergence and conservation properties of the scheme are established numerical experiments confirm the analysis and show that the cartesian grid size sigma should be taken proportional to the square root of the particle spacing h resulting in significant speed ups in vortex methods

canonical representation of set functions the representation of a cooperative transferable utility game as a linear combination of unanimity games may be viewed as an isomorphism between no necessarily additive set functions on the players space and additive ones on the coalitions space or alternatively between nonadditive probability measures on a state space and additive ones on the space of events we extend the unanimity basis representation to general infinite spaces of players study spaces of games which satisfy certain properties and provide some conditions for additivity of the resulting additive set function on the space at coalitions these results also allow us to extend some representations of the choquet integral from finite to infinite spaces

regular article a fast adaptive multipole algorithm in three dimensions we present an adaptive fast multipole method for the laplace equation in three dimensions it uses both new compression techniques and diagonal forms for translation operators to achieve high accuracy at a reasonable cost

statistical inference for stochastic dominance and for the measurement of poverty and inequality we derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty welfare and inequality this includes estimators of most of the poverty indices currently in use as well as estimators of the curves used to infer stochastic dominance of any order these curves can be used to determine whether poverty inequality or social welfare is greater in one distribution than in another for general classes of indices and for ranges of possible poverty lines we also derive the sampling distribution of the maximal poverty lines up to which we may confidently assert that poverty is greater in one distribution than in another the sampling distribution of convenient dual estimators for the measurement of poverty is also established the statistical results are established for deterministic or stochastic poverty lines as well as for paired or independent samples of incomes our results are briefly illustrated using data for four countries drawn from the luxembourg income study data bases

coulomb interactions on planar structures inverting the square root of the laplacian we present an adaptive fast multipole method for inverting the square root of the laplacian in two dimensions solving this problem is the dominant computational cost in many applications arising in electrical engineering geophysical fluid dynamics and the study of thin films it corresponds to the evaluation of the field induced by a planar distribution of charge or vorticity our algorithm is direct and assumes only that the source distribution is discretized using an adaptive quad tree the amount of work grows linearly with the number of mesh points

a fast direct solver for elliptic partial differential equations on adaptively refined meshes we present a new class of fast direct solvers for elliptic partial differential equations on adaptively refined meshes these solvers rely on a combination of standard fast solvers for uniform grids and potential theory unlike standard iterative approaches they have a well defined operation count they also preserve the order of accuracy of the uniform grid solver despite the presence of coarse fine interfaces

a combined finite element stiffness equation transfer method for steady state vibration response analysis of structures an extended finite element transfer matrix method in combination with stiffness equation transfer is applied to dynamic response analysis of the structures under periodic excitations in the present method the transfer of state vectors from left to right in a combined finite element transfer matrix fe tm method is changed into the transfer of general stiffness equations of every section from left to right this method has the advantages of reducing the order of standard transfer equation systems and minimizing the propagation of round off errors occurring in recursive multiplication of transfer and point matrices furthermore the drawback that in the ordinary fe tm method the number of degrees of freedom on the left boundary be the same on the right boundary is now avoided a feset program based on this method using microcomputers is developed finally numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for steady state vibration response analysis of structures

fast triangulated vortex methods for the 2d euler equations abstract vortex methods for inviscid incompressible two dimensional fluid flow are usually based on blob approximations this paper presents a vortex method in which the vorticity is approximated by a piecewise polynomial interpolant on a delaunay triangulation of the vortices an efficient reconstruction of the delaunay triangulation at each step makes the method accurate for long times the vertices of the triangulation move with the fluid velocity which is reconstructed from the vorticity via a simplified fast multipole method for the biot savart law with a continuous source distribution the initial distribution of vortices is constructed from the initial vorticity field by an adaptive approximation method which produces good accuracy even for discontinuous initial data numerical results show that the method is highly accurate over long time intervals experiments with single and multiple circular and elliptical rotating patches of both piecewise constant and smooth vorticity indicate that the method produces much smaller errors than blob methods with the same number of degrees of freedom at little additional cost generalizations to domains with boundaries viscous flow and three space dimensions are discussed

polarization concepts measurement estimation distributions can be described using density functions the main theorem uniquely characterizes a class of polarization measures that fits into what we call the identityalienation framework and simultanously satisfies a set of axioms second we provide sample estimators of population polarization indices that can be used to compare polarization across time or entities distribution free statistical inference results are also used in order to ensure that the orderings of polarization across entities are not simply due to sampling noise an illustration of the use of these tools using data from 21 countries shows that polarization and inequality orderings can often differ in practice

mathematical optimization ideas for biodiversity conservation several major environmental issues like biodiversity loss and climate change currently concern the international community these topics that are related to the development of human societies have become increasingly important since the united nations conference on environment and development unced or earth summit in rio de janeiro in 1992 in this article we are interested in the first issue we present here many examples of the help that using mathematical programming can provide to decision makers in the protection of biodiversity the examples we have chosen concern the selection of nature reserves the control of adverse effects caused by landscape fragmentation including the creation or restoration of biological corridors the ecological exploitation of forests the control of invasive species and the maintenance of genetic diversity most of the presented models are or can be approximated with linear quadratic or fractional integer formulations and emphasize spatial aspects of conservation planning many of them represent decisions taken in a static context but temporal dimension is also considered the problems presented are generally difficult combinatorial optimization problems some are well solved and others less well research is still needed to progress in solving them in order to deal with real instances satisfactorily moreover relations between researchers and practitioners have to be strengthened furthermore many recent achievements in the field of robust optimization could probably be successfully used for biodiversity protection a domain in which many data are uncertain

a triangulated vortex method for the axisymmetric euler equations a new method is presented for the prediction of unsteady axisymmetric inviscid flows by combining a triangulated vortex approach with a novel evaluation technique for the biot savart integrals a lagrangian vortex method is developed which eliminates the singularities usually present in axisymmetric methods without recourse to normalizations or other approximations furthermore the computational effort scales as the number of control points n and in the large n limit depends only on the order of quadrature employed the accuracy and computational effort are assessed by comparison with the velocity field of a gaussian core vortex ring and the use of the technique is illustrated by computation of the motion of norbury rings and of vortex ring pairing

an unsplit cell centered godunov method for ideal mhd we present a second order godunov algorithm for multidimensional ideal mhd our algorithm is based on the unsplit formulation of colella j comput phys 87 1990 with all of the primary dependent variables centered at the same location to properly represent the divergence free condition of the magnetic fields we apply a discrete projection to the intermediate values of the field at cell faces and apply a filter to the primary dependent variables at the end of each time step we test the method against a suite of linear and nonlinear tests to ascertain accuracy and stability of the scheme under a variety of conditions the test suite includes rotated planar linear waves mhd shock tube problems low beta flux tubes and a magnetized rotor problem for all of these cases we observe that the algorithm is second order accurate for smooth solutions converges to the correct weak solution for problems involving shocks and exhibits no evidence of instability or loss of accuracy due to the possible presence of non solenoidal fields

2d vortex methods and singular quadrature rules a new high order vortex method for the 2d euler equations is presented the method eliminates smoothing by constructing a singular quadrature rule for the biot savart law at each time step using quadtrees and orthogonal polynomials theory and numerical experiments show that the method is accurate and efficient yielding excellent long term accuracy in almost optimal cpu time

an adaptive fast multipole accelerated poisson solver for complex geometries abstract we present a fast direct and adaptive poisson solver for complex two dimensional geometries based on potential theory and fast multipole acceleration more precisely the solver relies on the standard decomposition of the solution as the sum of a volume integral to account for the source distribution and a layer potential to enforce the desired boundary condition the volume integral is computed by applying the fmm on a square box that encloses the domain of interest for the sake of efficiency and convergence acceleration we first extend the source distribution the right hand side in the poisson equation to the enclosing box as a c 0 function using a fast boundary integral based method we demonstrate on multiply connected domains with irregular boundaries that this continuous extension leads to high accuracy without excessive adaptive refinement near the boundary and as a result to an extremely efficient black box fast solver

a renormalization method for the evaluation of lattice sums a number of problems in solid state physics and materials science can be resolved by the evaluation of certain lattice sums sums over all sites of an infinite perfect lattice of some potential energy function one classical example the calculation of lattice sums of circular and spherical harmonics dates back to the last century to lord rayleigh s work on computing the effective conductivity of a simple composite while lord rayleigh presented an efficient asymptotic method for two dimensional problems he resorted to direct evaluation of the lattice sums in the three dimensional case more recent methods based on ewald summation have been developed by nijboer and de wette schmidt and lee and others in this article a fast method for evaluating lattice sums which is based on a new renormalization identity is described

an adaptive fast gauss transform in two dimensions a variety of problems in computational physics and engineering require the convolution of the heat kernel a gaussian with either discrete sources densities supported on boundaries or continuous

on the interpretation of sarin and wakker s a simple axiomatization of nonadditive expected utility in an interesting recent paper sarin and wakker 1992 henceforth s w have provided a new axiomatization of expected utility maximization with capacities ceu its simplicity is attractive in that it provides a constructive interpretation of the role of capacities and choquet integration in the main representation theorem an important issue raised by the paper is the interpretation of the key axiom p4 cumulative dominance s w suggest an appreciation of the axiom as an adaptation of stochastic dominance principles to nonadditive probability contexts most eloquently on page 1260 if viable such an interpretation would supply the ceu model with a powerful intuitive foundation that has been lacking so far this note argues that a stochastic dominance interpretation can be maintained only at the price of either an arbitrary choice of specification which undermines its intuitive force or alternatively of an unintended restriction of the class of characterized preferences two logically independent arguments are presented the first points out an arbitrariness in the definition of the more likely than relation in terms of preferences proposition 1 the second shows a similar arbitrariness in the definition of a stochastic dominance relation in terms of a more likely than relation proposition 2 in each case the invoked symmetry conditions yield a characterization of ceu preferences with symmetric capacities a nontrivial generalization of the seu model that has received little attention in the literature for notation and definitions the reader is referred to s w s paper s w s concern is to develop an intuitively convincing axiomatization of ceu representable preference relations their key axiom p4 is formulated in terms of a more likelythan relation on the algebra v of events that is defined in terms of the preference relation a on the set of acts y to facilitate the subsequent discussion their definition is introduced here formally as a condition on the pair of relations a

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

a theory of diversity how can diversity be measured what does it mean to value biodiversity can we assist noah in constructing his preferences to address these questions we propose a multi attribute approach under which the diversity of a set of species is the sum of the values of all attributes possessed by some species in the set we develop the basic intuitions and requirements for a theory of diversity and show that the multi attribute approach satisfies them in a flexible yet tractable manner a natural starting point is to think of the diversity of a set as an aggregate of the pairwise dissimilarities between its elements the multi attribute framework allows one to make this program formally precise it is shown that the program can be realized if and only if the family of relevant attributes is well ordered acyclic moreover there is a unique functional form aggregating dissimilarity into diversity the length of a minimum spanning tree examples are taxonomic hierarchies and lines representing uni dimensional qualities in multi dimensional settings pairwise dissimilarity information among elements is insufficient to determine their diversity by consequence the qualitative and quantitative behavior of diversity differs fundamentally

fast delaunay triangulation in three dimensions abstract an efficient algorithm for delaunay triangulation of a given set of points in three dimensions based on the point insertion technique is presented various steps of the triangulation algorithm are reviewed and many acceleration procedures are devised to speed up the triangulation process new features include the search of a neighbouring point by the layering scheme locating the containing tetrahedron by random walk formulas of important geometrical quantities of a new tetrahedron based on those of an existing one a novel approach in establishing the adjacency relationship the use of adjacency table and the management of memory the resulting scheme is one of the fastest triangulation algorithms known to the authors which is able to generate tetrahedra generation rate of 15 000 tetrahedra per second for randomly generated points on a hp 735 machine

a stiffness equation transfer method for transient dynamic response analysis of structures a stiffness equation transfer method is proposed for transient dynamic response analysis of structures under various excitations this method is a development and refinement of the combined finite element transfer matrix fe tm method in the present method the transfer of state vectors from left to right in the fe tm method is changed into the transfer of general stiffness equations of every section from left to right this method has the advantages of reducing the order of the ordinary transfer equation systems and minimizing the propagation of round off errors occurring in recursive multiplication of transfer and point matrices furthermore the drawback that the number of degrees of freedom on the left boundary must be the same as that on the right boundary in the ordinary fe tm method has now been avoided the newmark generalized acceleration formulation for time discretization is employed for a solution of the time problem at the end numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for transient dynamic response analysis of structures

a cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

the noah s ark problem this paper is about the economic theory of biodiversity preservation a cost effectiveness methodology is constructed which results in a particular formula that can be used as a criterion to rank projects the ranking criterion is sufficiently operational to be useful in suggesting what to look at when determining actual conservation priorities among endangered species at the same time the formula is firmly rooted in a mathematically rigorous optimization framework so that its theoretical underpinnings are clear the underlying model called the noah s ark problem is intended to be a kind of canonical form that hones down to its analytical essence the problem of best preserving diversity under a limited budget constraint

standard state space models preclude unawareness we show that a very broad class of models including possibility correspondences necessarily fail to capture very simple and intuitive implications of unawareness we explain why standard state space formulations suffer from this problem illustrating the point with an example of a nonstandard state space model which avoids the difficulty

the fast solution of poisson s and the biharmonic equations on irregular regions we present fast methods for solving laplace s and the biharmonic equations on irregular regions with smooth boundaries the methods used for solving both equations make use of fast poisson solvers on a rectangular region in which the irregular region is embedded they also both use an integral equation formulation of the problem where the integral equations are fredholm integral equations of the second kind the main idea is to use the integral equation formulation to define a discontinuous extension of the solution to the rest of the rectangular region fast solvers are then used to compute the extended solution aside from solving the equations we have also been able to compute derivatives of the solutions with little loss of accuracy when the data was sufficiently smooth

a method for determining the velocity induced by highly anisotropic vorticity blobs resolution of boundary layer flows at moderate or high reynolds numbers with the vortex blob method requires a great many isotropic elements in this paper an approximate method for determination of the induced velocity from highly anisotropic vorticity blobs is presented and issues related to use of anisotropic elements in calculations with vortex blob algorithms for high reynolds number near wall flows are examined the method presented here can be used to determine the induced velocity from smooth blob functions of arbitrary form provided that the vorticity length scale associated with the blob is much less in one direction than in orthogonal directions the ratio of these length scales is called the blob aspect ratio and is used as a small parameter to construct an asymptotic approximation to the induced velocity field this method is applied in the present paper to derive induced velocity expressions for anisotropic gaussian blob functions in both two and three dimensions it is argued using test calculations for a blasius boundary layer that although direct calculation of the induced velocity requires about an order of magnitude more cpu time for anisotropic gaussian elements than for isotropic elements this difference is more than made up for by a reduction of several orders of magnitude in the number of elements needed to resolve boundary layer flows at moderate to high reynolds numbers it is also found that the standard vortex blob representation leads to errors in the calculation of wall slip velocity and wall shear stress due to smoothing of the discontinuity between the real and image vorticity fields at the wall but that these errors can be avoided by placing doublet type elements along the wall

a direct adaptive poisson solver of arbitrary order accuracy we present a direct adaptive solver for the poisson equation which can achieve any prescribed order of accuracy it is based on a domain decomposition approach using local spectral approximation as well as potential theory and the fast multipole method in two space dimensions the algorithm requireso nk work wherenis the number of discretization points andkis the desired order of accuracy

composite overlapping meshes for the solution of partial differential equations abstract we discuss the generation of curvilinear composite overlapping grids and the numerical solution of partial differential equations on them a composite overlapping grid consists of a set of curvilinear component grids that cover a region and overlap where they meet continuity conditions interpolation are imposed at the overlapping boundaries the principal advantage of composite grids is in the generation of grids for regions with complicated geometries the grid construction program cmpgrd is used to create composite grids with any number of component grids we describe some techniques for the solution of elliptic and time dependent pdes on composite meshes applications to the solution of the compressible navier stokes equations are presented

decomposition and representation of coalitional games a coalitional game is a real valued set function defined on an algebra f of subsets of a space x such that o 0 we prove the existence of a one to one correspondence between coalitional games bounded with respect to the composition norm and countably additive measures defined on an appropriate space

nonparametric estimation and inference about the overlap of two distributions this paper develops methodology for nonparametric estimation of a measure of the overlap of two distributions based on kernel estimation techniques this quantity has been proposed as a measure of economic polarization between two groups anderson 2004 and anderson et al 2010 in ecology it has been used to measure the overlap of species we give the asymptotic distribution theory of our estimator which in some cases of practical relevance is nonstandard due to a boundary value problem we also propose a method for conducting inference based on estimation of unknown quantities in the limiting distribution and show that our method yields consistent inference in all cases we consider we investigate the finite sample properties of our methods by simulation methods we give an application to the study of polarization within china in recent years using household survey data from two provinces taken in 1987 and 2001 we find a big increase in polarization between 1987 and 2001 according to monetary outcomes but less change in terms of living space

delayed over relaxation for iterative methods we propose a variant of the relaxation step used in the most widespread iterative methods e g jacobi over relaxation successive over relaxation which combines the iteration at the predicted step namely n 1 with the iteration at step n 1 we provide a theoretical analysis of the proposed algorithm by applying such a delayed relaxation step to a generic convergent iterative scheme we prove that under proper assumptions this significantly improves the convergence rate of the initial iterative method as a relevant example we apply the proposed algorithm to the solution of the poisson equation highlighting the advantages in comparison with classical iterative models we propose a variant of the relaxation step for iterative solvers this variant improves the convergence for matrices with real eigenvalues the proposed scheme profitably applies to elliptic problems

a new fast multipole accelerated poisson solver in two dimensions we present an adaptive fast multipole method for solving the poisson equation in two dimensions the algorithm is direct assumes that the source distribution is discretized using an adaptive quad tree and allows for dirichlet neumann periodic and free space conditions to be imposed on the boundary of a square the amount of work per grid point is comparable to that of classical fast solvers even for highly nonuniform grids

toward an empirical analysis of polarization stochastic dominance conditions may be interpreted as a means of defining the degree and nature of separateness of two distributions by describing polarization states in terms of stochastic dominance conditions this paper presents a taxonomy of and tests for polarization both between and within population distributions four examples from the poverty growth and development wage distribution and assortative pairing literatures are used to illustrate how the techniques may be used in empirical applications

a simple axiomatization of nonadditive expected utility textabstractthis paper provides an extension of savage s subjective expected utility theory for decisions under uncertainty it includes in the set of events both unambiguous events for which probabilities are additive and ambiguous events for which probabilities are permitted to be nonadditive the main axiom is cumulative dominance which adapts stochastic dominance to decision making under uncertainty we derive a choquet expected utility representation and show that a modification of cumulative dominance leads to the classical expected utility representation the relationship of our approach with that of schmeidler who uses a two stage formulation to derive choquet expected utility is also explored our work may be viewed as a unification of schmeidler 1989 and gilboa 1987

computing the ground state and dynamics of the nonlinear schrodinger equation with nonlocal interactions via the nonuniform fft we present efficient and accurate numerical methods for computing the ground state and dynamics of the nonlinear schrodinger equation nlse with nonlocal interactions based on a fast and accurate evaluation of the long range interactions via the nonuniform fast fourier transform nufft we begin with a review of the fast and accurate nufft based method in 29 for nonlocal interactions where the singularity of the fourier symbol of the interaction kernel at the origin can be canceled by switching to spherical or polar coordinates we then extend the method to compute other nonlocal interactions whose fourier symbols have stronger singularity at the origin that cannot be canceled by the coordinate transform many of these interactions do not decay at infinity in the physical space which adds another layer of complexity since it is more difficult to impose the correct artificial boundary conditions for the truncated bounded computational domain the performance of our method against other existing methods is illustrated numerically with particular attention on the effect of the size of the computational domain in the physical space finally to study the ground state and dynamics of the nlse we propose efficient and accurate numerical methods by combining the nufft method for potential evaluation with the normalized gradient flow using backward euler fourier pseudospectral discretization and time splitting fourier pseudospectral method respectively extensive numerical comparisons are carried out between these methods and other existing methods for computing the ground state and dynamics of the nlse with various nonlocal interactions numerical results show that our scheme performs much better than those existing methods in terms of both accuracy and efficiency

representing preferences with a unique subjective state space we extend kreps 1979 analysis of preference for flexibility reinterpreted by kreps 1992 as a model of unforeseen contingencies we enrich the choice set consequently obtaining uniqueness results that were not possible in kreps model we consider several representations and allow the agent to prefer commitment in some contingencies in the representations the agent acts as if she had coherent beliefs about a set of possible future ex post preferences each of which is an expected utility preference we show that this set of ex post preferences called the subjectie state space is essentially unique given the restriction that all ex post preferences are expected utility preferences and is minimal even without this restriction because the subjective state space is identified the way ex post utilities are aggregated into an ex ante ranking is also essentially unique hence when a representation that is additive across states exists the additivity is meaningful in the sense that all representations are intrinsically additive uniqueness enables us to show that the size of the subjective state space provides a measure of the agent s uncertainty about future contingencies and that the way the states are aggregated indicates whether these contingencies lead to a desire for flexibility or commitment

a simple multigrid scheme for solving the poisson equation with arbitrary domain boundaries we present a new multigrid scheme for solving the poisson equation with dirichlet boundary conditions on a cartesian grid with irregular domain boundaries this scheme was developed in the context of the adaptive mesh refinement amr schemes based on a graded octree data structure the poisson equation is solved on a level by level basis using a one way interface scheme in which boundary conditions are interpolated from the previous coarser level solution such a scheme is particularly well suited for self gravitating astrophysical flows requiring an adaptive time stepping strategy by constructing a multigrid hierarchy covering the active cells of each amr level we have designed a memory efficient algorithm that can benefit fully from the multigrid acceleration we present a simple method for capturing the boundary conditions across the multigrid hierarchy based on a second order accurate reconstruction of the boundaries of the multigrid levels in case of very complex boundaries small scale features become smaller than the discretization cell size of coarse multigrid levels and convergence problems arise we propose a simple solution to address these issues using our scheme the convergence rate usually depends on the grid size for complex grids but good linear convergence is maintained the proposed method was successfully implemented on distributed memory architectures in the ramses code for which we present and discuss convergence and accuracy properties as well as timing performances

efficient and highly accurate computation of a class of radially symmetric solutions of the navier stokes equation and the heat equation in two dimensions in this paper we test several different formulas for the computation of the exact vorticity and angular velocity in certain radially symmetric solutions of the two dimensional navier stokes equation in vorticity stream function form the class of initial conditions for the vorticity considered here has often been used by many authors in the study of vortex methods however only in the case of zero viscosity has it been possible to efficiently compute the exact vorticity and velocity at later times the expressions for the vorticity and angular velocity given in this paper enable us to compute these quantities both efficiently and highly accurately for nonzero viscosity this makes it feasible to obtain reliable error measurements in the study of vortex methods for the navier stokes equation

a stiffness equation transfer method for natural frequencies of structures abstract a stiffness equation transfer method is proposed for obtaining vibration frequencies of structures this method is an extension of the finite element transfer matrix fe tm method in the present method the transfer of state vectors from left to right in the ordinary fe tm method is changed into the transfer of stiffness equations of every section from left to right this method reduces the propagation of round off errors produced in the ordinary transfer matrix method furthermore the drawback that the number of degrees of freedom on the left boundary must be the same as that on the right boundary in the ordinary fe tm method is now avoided besides this method finds out the values of the frequency by newton raphson iteration method so no plotting of the value of the determinant versus assumed frequency is necessary an ifetm w program based on this method for use on an ibm pc586 microcomputer is developed finally numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for free vibration analysis of structures

a projection method for locally refined grids a numerical method for the solution of the two dimensional euler equatons for incompressible flow on locally refined grids is presented the method is a second order godunov projection method adapted from bell colella and glaz second order accuracy of the numerical method in time and space is established through numerical experiments the main contributions of this work concern the formulation and implementation of a projection for refined grids a discussion of the adjointness relation between gradient and divergence operators for a refined grid mac projection is presented and a refined grid approximate projection is developed an efficient multigrid method which exactly solves the projection is developed and a method for casting certain approximate projections as mac projections on refined grids is presented

the rapid evaluation of volume integrals of potential theory on general regions abstract we present a new method for the rapid high order accurate evaluation of certain volume integrals in potential theory on general irregular regions the kernels of the integrals are either a fundamental solution or a linear combination of the derivatives of a fundamental solution of a second order linear elliptic differential equation instead of using a standard quadrature formula or the exact evaluation of any integral the methods rely on rapid methods of solving the differential equation which the kernel is the solution of therefore the number of operations needed to evaluate the volume integral is essentially equal to the number of operations needed to solve the differential equation on a rectangular region with a regular grid and the method requires no evaluation of the kernel