completely rank nonincreasing linear maps abstract we give purely algebraic characterizations of the maps that are approximate compressions or skew compressions of a unital representation of a c algebra the key techniques used also relate to closures of joint similarity orbits of matrices and elementary maps on b h

maps completely preserving commutativity and maps completely preserving jordan zero product abstract let x y be real or complex banach spaces with infinite dimension and let a b be standard operator algebras on x and y respectively in this paper we show that every map completely preserving commutativity from a onto b is a scalar multiple of either an isomorphism or in the complex case a conjugate isomorphism every map completely preserving jordan zero product from a onto b is a scalar multiple of either an isomorphism or in the complex case a conjugate isomorphism

a mass redistributed finite element method mr fem for acoustic problems using triangular mesh the accuracy of numerical results using standard finite element method fem in acoustic problems will deteriorate with increasing frequency due to the dispersion error such dispersion error depends on the balance between the stiffness and mass of discretization equation systems this paper reports an improved finite element method fem for solving acoustic problems by re distributing the mass in the mass matrix to tune the balance aiming to minimize the dispersion errors this is done by shifting the integration point locations when computing the entries of the mass matrix while ensuring the mass conservation the new method is verified through the detailed numerical error analysis and a strategy is also proposed for the best mass redistribution in terms of minimizing dispersion error the relative dispersion error of present mass redistributed finite element method mr fem is found to be much smaller than the fem solution in both theoretical prediction and numerical examination the present mr fem works well by using the linear triangular elements that can be generated automatically which enables automation in computation and saving computational cost in mesh generation numerical examples demonstrate the advantages of mr fem in comparison with the standard fem using the same triangular meshes and quadrilateral meshes

a new eighth order implicit finite difference method to solve the three dimensional helmholtz equation abstract this paper introduces a novel method for deducing high order finite difference schemes for the three dimensional helmholtz equation p 2 p f the new method can reach an eighth order of accuracy it is based on an implicit formulation by computing simultaneously the unknown variable and its corresponding derivatives the scheme is obtained from taylor series expansion and plane wave theory analysis and it is constructed from a few modifications to the standard centered finite differences a classical dispersion analysis and the error between the numerical wavenumber and the exact wavenumber is given numerical experiments are presented to verify the feasibility and accuracy of the proposed methods for a broad range of values moreover the numerical method is capable to solve with great precision the monotone and oscillatory helmholtz problem with variable values thus the proposed formulation results in an attractive method easy to implement with high order of accuracy but nearly the same computational cost as those of an explicit formulation

multiscale statistical behaviors for ising financial dynamics with continuum percolation jump abstract a financial dynamics of interaction and jump is developed and investigated by two statistical physics systems ising model and continuum percolation this proposed model aiming at understanding price fluctuations needs to define a mechanism for the formation of the price in an attempt to describe interacting micromechanism and sudden jump for stock price changes further the corresponding fluctuation behaviors and various complexity properties of logarithmic returns for the financial model are investigated by some statistical and complex analyses then p order multiscale autocorrelation function and q order multiscale entropy are also introduced to study the financial model with scaled analysis methods moreover the real stock market indexes are used to compare with the simulation returns from the financial model the empirical research shows that the simulation time series exhibits the similar fluctuation patterns with real time series

a dispersion minimizing compact finite difference scheme for the 2d helmholtz equation in this paper we present a dispersion minimizing compact finite difference scheme for solving the 2d helmholtz equation which is a fourth order scheme the error between the numerical wavenumber and the exact wavenumber is analyzed and a refined choice strategy based on minimizing the numerical dispersion is proposed for choosing weight parameters numerical results are presented to demonstrate the efficiency and accuracy of the compact finite difference scheme with refined parameters

component averaged row projections a robust block parallel scheme for sparse linear systems a new method for the parallel solution of large sparse linear systems is introduced it proceeds by dividing the equations into blocks and operating in block parallel iterative mode i e all the blocks are processed in parallel and the partial results are merged to form the next iterate the new scheme performs kaczmarz row projections within the blocks and merges the results by certain component averaging operations hence it is called component averaged row projections or carp the system matrix can be general nonsymmetric and ill conditioned and the division into blocks is unrestricted for partial differential equations pdes if the blocks are domain based then only variables at the boundaries between domains are averaged thereby minimizing data transfer between processors carp is very robust its application to test cases of linear systems derived from pdes shows that it converges in difficult cases where state of the art methods fail it is also very memory efficient and exhibits an almost linear speedup ratio with efficiency greater than unity in some cases a formal proof of convergence is presented it is shown that the component averaging operations are equivalent to row projections in a certain superspace so the convergence properties of carp are identical to those of kaczmarz s algorithm in the superspace carp and its convergence proof also apply to the consistent convex feasibility problem

the russo seymour welsh theorem and the equality of critical densities and the dual critical densities for continuum percolation on mathbb r 2 a russo seymour welsh rsw theorem is established for continuum percolation on mathbb r 2 the equality of various definitions of critical densities for the continuum percolation on mathbb r 2 is deduced as an application of the rsw theorem it is also shown that various notions of the size of a cluster yield the same notion of critical density

a new 9 point sixth order accurate compact finite difference method for the helmholtz equation a new 9 point sixth order accurate compact finite difference method for solving the helmholtz equation in one and two dimensions is developed and analyzed this scheme is based on sixth order approximation to the derivative calculated from the helmholtz equation a sixth order accurate symmetrical representation for the neumann boundary condition was also developed the efficiency and accuracy of the scheme is validated by its application to two test problems which have exact solutions numerical results show that this sixth order scheme has the expected accuracy and behaves robustly with respect to the wave number

arbitrary high order c0 tensor product galerkin finite element methods for the electromagnetic scattering from a large cavity the paper is concerned with the electromagnetic scattering from a large cavity embedded in an infinite ground plane the electromagnetic cavity problem is described by the helmholtz equation with a nonlocal boundary condition on the aperture of the cavity and dirichlet or neumann boundary conditions on the walls of the cavity a tensor product galerkin finite element method fem is proposed in which spaces of c 0 piecewise polynomials of degree k 1 are employed by the fast fourier transform and the toeplitz type structure of the approximation to the nonlocal operator in the nonlocal boundary condition a fast algorithm is designed for solving the linear system arising from the cavity problem with vertically layered media which requires o n 2logn operations on an nxn uniform partition numerical results for model problems illustrate the efficiency of the fast algorithm and exhibit the expected optimal global convergence rates of the finite element methods moreover our numerical results also show that the high order approximations are especially effective for problems with large wave numbers

compact finite difference schemes of sixth order for the helmholtz equation new compact finite difference schemes of sixth order are derived for the three dimensional helmholtz equation du k 2u f convergence characteristics and accuracy are compared and a truncation error analysis is presented for a broad range of k values

completely rank nonincreasing linear maps on spaces of operators we discuss some results and conjectures concerning rank nonincreasing rank preserving completely rank preserving and completely rank nonincreasing linear maps on spaces of operators we show that the main conjectures are equivalent to a statement about closures of joint similarity orbits of k tuples of matrices

additive spectrum compressors abstract additive bijections a b which compress the spectrum between two unital standard operator algebras are characterized applications to local approximate anti multiplications are also given

modeling stock price dynamics by continuum percolation system and relevant complex systems analysis abstract the continuum percolation system is developed to model a random stock price process in this work recent empirical research has demonstrated various statistical features of stock price changes the financial model aiming at understanding price fluctuations needs to define a mechanism for the formation of the price in an attempt to reproduce and explain this set of empirical facts the continuum percolation model is usually referred to as a random coverage process or a boolean model the local interaction or influence among traders is constructed by the continuum percolation and a cluster of continuum percolation is applied to define the cluster of traders sharing the same opinion about the market we investigate and analyze the statistical behaviors of normalized returns of the price model by some analysis methods including power law tail distribution analysis chaotic behavior analysis and zipf analysis moreover we consider the daily returns of shanghai stock exchange composite index from january 1997 to july 2011 and the comparisons of return behaviors between the actual data and the simulation data are exhibited

a compact difference scheme for a two dimensional nonlinear fractional klein gordon equation in polar coordinates abstract in this paper a high order finite difference scheme for a two dimensional nonlinear fractional klein gordon equation in polar coordinates is proposed the difficulty caused by the variable coefficient and the nonlinear term in the equation is carefully handled stability and convergence are analyzed using the matrix form of the scheme numerical examples are provided to demonstrate the theoretical results

compact 2d and 3d sixth order schemes for the helmholtz equation with variable wave number several studies have presented compact fourth order accurate finite difference approximation for the helmholtz equation in two or three dimensions several of these formulae allow for the wave number k to be variable other papers have extended this further to include variable coefficients within the laplacian which models non homogeneous materials in electromagnetism later papers considered more accurate compact sixth order methods but these were restricted to constant k in this paper we extend these compact sixth order schemes to variable k in both two and three dimensions results on 2d and 3d problems with known analytic solutions verify the sixth order accuracy we demonstrate that for large wave numbers the second order scheme cannot produce comparable results with reasonable grid sizes

direct implementation of high order bgt artificial boundary conditions abstract local artificial boundary conditions abcs for the numerical simulation of waves have been successfully used for decades most notably the boundary conditions due to engquist majda bayliss gunzburger turkel and higdon the basic idea behind these boundary conditions is that they cancel several leading terms in an expansion of the solution the larger the number of terms canceled the higher the order of the boundary condition and in turn the smaller the reflection error due to truncation of the original unbounded domain by an artificial outer boundary in practice however the use of local abcs has been limited to low orders first and second because higher order boundary conditions involve higher order derivatives of the solution which may harm well posedness and cause numerical instabilities they are also difficult to implement especially in finite elements a prominent exception is the development of local high order abcs based on auxiliary variables in the current paper we implement high order bayliss turkel abcs directly with no auxiliary variables yet no discrete approximation of the constituent high order derivatives either instead we represent the solution at the boundary as an expansion with respect to a continuous basis for the spherical artificial boundary the basis consists of eigenfunctions of the beltrami operator spherical harmonics which enable replacing the high order derivatives in the abcs with powers of the corresponding eigenvalues the continuous representation at the boundary is coupled to higher order compact finite differences inside the domain by the method of difference potentials mdp it maintains high order accuracy even when the boundary is not aligned with the discretization grid

additive maps on standard operator algebras preserving parts of the spectrum let a and b be standard operator algebras on infinite dimensional complex banach spaces x and y respectively and let be a unital additive surjection from a onto b we introduce thirteen parts of the spectrum for elements in a and b and prove that if preserves any one of these parts of the spectrum then it is either an isomorphism or an anti isomorphism

a numerical scheme for solving a class of logarithmic integral equations arisen from two dimensional helmholtz equations using local thin plate splines abstract this paper presents a numerical method for solving logarithmic fredholm integral equations which occur as a reformulation of two dimensional helmholtz equations over the unit circle with the robin boundary conditions the method approximates the solution utilizing the discrete collocation method based on the locally supported thin plate splines as a type of free shape parameter radial basis functions the local thin plate splines establish an efficient and stable technique to estimate an unknown function by a small set of nodes instead of all points over the solution domain to compute logarithm like singular integrals appeared in the method we use a particular nonuniform gauss legendre quadrature rule since the scheme does not require any mesh generations on the domain it can be identified as a meshless method the error estimate of the proposed method is presented numerical results are included to show the validity and efficiency of the new technique these results also confirm that the proposed method uses much less computer memory in comparison with the method established on the globally supported thin plate splines moreover it seems that the algorithm of the presented approach is attractive and easy to implement on computers

solving helmholtz equation at high wave numbers in exterior domains this paper presents effective difference schemes for solving the helmholtz equation at high wave numbers considering the problems in the polar and spherical coordinates we show that pollution free difference schemes can be constructed for annulus and hollow sphere domains but the pollution effect cannot be avoided in the neighborhood of the origin of the coordinate using the fact that the pollution effect appears in a small neighborhood of the origin of the coordinate we propose a local mesh refinement approach so that a fine grid is applied only for a small region near the origin of the coordinate and a much larger grid size is employed in the remaining domain the most attractive feature of this approach is that the computational storage can be significantly reduced while keeping almost the same numerical accuracy moreover by applying a two level local refinement technique we can further enhance the performance of the proposed scheme numerical simulations are reported to verify the effectiveness of the proposed schemes for the helmholtz problem in exterior domains

numerical solution of the wave equation with variable wave speed on nonconforming domains by high order difference potentials abstract we solve the wave equation with variable wave speed on nonconforming domains with fourth order accuracy in both space and time this is accomplished using an implicit finite difference fd scheme for the wave equation and solving an elliptic modified helmholtz equation at each time step with fourth order spatial accuracy by the method of difference potentials mdp high order mdp utilizes compact fd schemes on regular structured grids to efficiently solve problems on nonconforming domains while maintaining the design convergence rate of the underlying fd scheme asymptotically the computational complexity of high order mdp scales the same as that for fd

a fourth order optimal finite difference scheme for the helmholtz equation with pml abstract in this paper 17 point and 25 point finite difference fd schemes for the helmholtz equation with perfectly matched layer pml in the two dimensional domain are presented it is shown that the 17 point fd scheme is inconsistent in the presence of pml however the 25 point fd scheme is pointwise consistent an error analysis for the numerical approximation of the exact wavenumber is also presented we present the global and refined 25 point finite difference schemes based on minimizing the numerical dispersion numerical experiments are given to illustrate the improvement of the accuracy and the reduction of the numerical dispersion

compact high order schemes with gradient direction derivatives for absorbing boundary conditions we consider several compact high order absorbing boundary conditions abcs for the helmholtz equation in three dimensions a technique called the gradient method gm for abcs is also introduced and combined with the high order abcs gm is based on the principle of using directional derivatives in the direction of the wavefront propagation the new abcs are used together with the recently introduced compact sixth order finite difference scheme for variable wave numbers experiments on problems with known analytic solutions produced very accurate results demonstrating the efficacy of the high order schemes particularly when combined with gm the new abcs are then applied to the seg eage salt model showing the advantages of the new schemes

nonuniversality and continuity of the critical covered volume fraction in continuum percolation we establish using mathematically rigorous methods that the critical covered volume fraction cvf for a continuum percolation model with overlapping balls of random sizes is not a universal constant independent of the distribution of the size of the balls in addition we show that the critical cvf is a continuous function of the distribution of the radius random variable in the sense that if a sequence of random variables converges weakly to some random variable then the critical cvf based on these random variables converges to the critical cvf of the limiting random variable

complexity and multifractal behaviors of multiscale continuum percolation financial system for chinese stock markets abstract a new financial agent based time series model is developed and investigated by multiscale continuum percolation system which can be viewed as an extended version of continuum percolation system in this financial model for different parameters of proportion and density two poisson point processes where the radii of points represent the ability of receiving or transmitting information among investors are applied to model a random stock price process in an attempt to investigate the fluctuation dynamics of the financial market to validate its effectiveness and rationality we compare the statistical behaviors and the multifractal behaviors of the simulated data derived from the proposed model with those of the real stock markets further the multiscale sample entropy analysis is employed to study the complexity of the returns and the cross sample entropy analysis is applied to measure the degree of asynchrony of return autocorrelation time series the empirical results indicate that the proposed financial model can simulate and reproduce some significant characteristics of the real stock markets to a certain extent

optimal staggered grid finite difference schemes by combining taylor series expansion and sampling approximation for wave equation modeling high order staggered grid finite difference sfd schemes have been universally used to improve the accuracy of wave equation modeling however the high order sfd coefficients on spatial derivatives are usually determined by the taylor series expansion te method which just leads to great accuracy at small wavenumbers for wave equation modeling some conventional optimization methods can achieve high accuracy at large wavenumbers but they hardly guarantee the small numerical dispersion error at small wavenumbers in this paper we develop new optimal explicit sfd esfd and implicit sfd isfd schemes for wave equation modeling we first derive the optimal esfd and isfd coefficients for the first order spatial derivatives by applying the combination of the te and the sampling approximation to the dispersion relation and then analyze their numerical accuracy finally we perform elastic wave modeling with the esfd and isfd schemes based on the te method and the optimal method respectively when the appropriate number and interval for the sampling points are chosen these optimal schemes have extremely high accuracy at small wavenumbers and can also guarantee small numerical dispersion error at large wavenumbers numerical accuracy analyses and modeling results demonstrate the optimal esfd and isfd schemes can efficiently suppress the numerical dispersion and significantly improve the modeling accuracy compared to the te based esfd and isfd schemes

discrete dispersion relation for hp version finite element approximation at high wave number the dispersive properties of high order finite element schemes are analyzed in the setting of the helmholtz equation and an explicit form of the discrete dispersion relation is obtained for elements of arbitrary order it is shown that the numerical dispersion displays three different types of behavior depending on the size of the order of the method relative to the mesh size and the wave number quantitative estimates are obtained for the behavior and rates of decay of the dispersion error in the differing regimes all estimates are fully explicit and are shown to be sharp limits are obtained where transitions between the different regimes occur and used to provide guidelines for the selection of the mesh size and the polynomial order in terms of the wave number so that the dispersion error is controlled

maps completely preserving spectral functions abstract let x y be infinite dimensional complex banach spaces and a b be standard operator algebras on x and y respectively in this paper we show that surjective maps completely preserving certain spectral function from a to b are isomorphisms where stands for any one of 13 spectral functions l r l r p c p c p c ap s and ap s

high order finite difference methods for the helmholtz equation high order finite difference methods for solving the helmholtz equation are developed and analyzed in one and two dimensions on uniform grids the standard pointwise representation has a second order accurate local truncation error we also study two schemes which have a fourth order accurate local truncation error one of the high order schemes is based on generalizations of the pade approximation the second scheme is based on high order approximation to the derivative calculated from the helmholtz equation itself a symmetric high order representation is developed for a neumann boundary condition numerical results are presented on model problems approximated with the developed schemes

a fourth order spatial accurate and practically stable compact scheme for the cahn hilliard equation abstract we present a fourth order spatial accurate and practically stable compact difference scheme for the cahn hilliard equation the compact scheme is derived by combining a compact nine point formula and linearly stabilized splitting scheme the resulting system of discrete equations is solved by a multigrid method numerical experiments are conducted to verify the practical stability and fourth order accuracy of the proposed scheme we also demonstrate that the compact scheme is more robust and efficient than the non compact fourth order scheme by applying to parallel computing and adaptive mesh refinement

high order numerical simulation of the transmission and scattering of waves using the method of difference potentials the method of difference potentials generalizes the method of calderon s operators from pdes to arbitrary difference equations and systems it offers several key advantages such as the capability of handling boundaries interfaces that are not aligned with the discretization grid variable coefficients and nonstandard boundary conditions in doing so the complexity of the algorithm remains comparable to that of an ordinary finite difference scheme on a regular structured grid previously we have applied the method of difference potentials to solving several variable coefficient interior helmholtz problems with fourth and sixth order accuracy we have employed compact finite difference schemes as a core discretization methodology those schemes enable high order accuracy on narrow stencils and hence require only as many boundary conditions as needed for the underlying differential equation itself numerical experiments corroborate the high order accuracy of our method for variable coefficients regular grids and non conforming boundaries in the current paper we extend the previously developed methodology to exterior problems we present a complete theoretical analysis of the algorithm as well as the results of a series of numerical simulations specifically we study the scattering of time harmonic waves about smooth shapes subject to various boundary conditions we also solve the transmission scattering problems in which not only do the waves scatter off a given shape but also propagate through the interface and travel across the heterogeneous medium inside in all the cases our methodology guarantees high order accuracy for regular grids and non conforming boundaries and interfaces

on the derivation of highest order compact finite difference schemes for the one and two dimensional poisson equation with dirichlet boundary conditions the primary aim of this paper is to answer the question what are the highest order five or nine point compact finite difference schemes to answer this question we present several simple derivations of finite difference schemes for the one and two dimensional poisson equation on uniform quasi uniform and nonuniform face to face hyperrectangular grids and directly prove the existence or nonexistence of their highest order local accuracies our derivations are unique in that we do not make any initial assumptions on stencil symmetries or weights for the one dimensional problem the derivation using the three point stencil on both uniform and nonuniform grids yields a scheme with arbitrarily high order local accuracy however for the two dimensional problem the derivation using the corresponding five point stencil on uniform and quasi uniform grids yields a scheme with at most second order local accuracy and on nonuniform grids yields at most first order local accuracy when expanding the five poin

accurate finite difference methods for time harmonic wave propagation finite difference methods for solving problems of time harmonic acoustics are developed and analyzed multi dimensional inhomogeneous problems with variable possibly discontinuous coefficients are considered accounting for the effects of employing non uniform grids a weighted average representation is less sensitive to transition in wave resolution due to variable wave numbers or non uniform grids than the standard pointwise representation further enhancement in method performance is obtained by basing the stencils on generalizations of pade approximation or generalized definitions of the derivative reducing spurious dispersion anisotropy and reflection and by improving the representation of source terms the resulting schemes have fourth order accurate local truncation error on uniform grids and third order in the non uniform case guidelines for discretization pertaining to grid orientation and resolution are presented

a dispersion minimizing scheme for the 3 d helmholtz equation based on ray theory we develop a new dispersion minimizing compact finite difference scheme for the helmholtz equation in 2 and 3 dimensions the scheme is based on a newly developed ray theory for difference equations a discrete helmholtz operator and a discrete operator to be applied to the source and the wavefields are constructed their coefficients are piecewise polynomial functions of hk chosen such that phase and amplitude errors are minimal the phase errors of the scheme are very small approximately as small as those of the 2 d quasi stabilized fem method and substantially smaller than those of alternatives in 3 d assuming the same number of gridpoints per wavelength is used in numerical experiments accurate solutions are obtained in constant and smoothly varying media using meshes with only five to six points per wavelength and wave propagation over hundreds of wavelengths when used as a coarse level discretization in a multigrid method the scheme can even be used with down to three points per wavelength tests on 3 d examples with up to 108 degrees of freedom show that with a recently developed hybrid solver the use of coarser meshes can lead to corresponding savings in computation time resulting in good simulation times compared to the literature

fast alternating bidirectional preconditioner for the 2d high frequency lippmann schwinger equation this paper presents a fast iterative solver for the lippmann schwinger equation for high frequency waves scattered by a smooth medium with a compactly supported inhomogeneity the solver is based on the sparsifying preconditioner l ying multiscale model simul 13 2015 pp 644 660 and a domain decomposition approach similar to the method of polarized traces l zepeda nunez and l demanet j comput phys 308 2016 pp 347 388 the iterative solver has two levels the outer level in which a sparsifying preconditioner for the lippmann schwinger equation is constructed and the inner level in which the resulting sparsified system is solved quickly using an iterative solver preconditioned with a bidirectional matrix free variant of the method of polarized traces the complexity of the construction and application of the preconditioner is cal o n and cal o n log n respectively where n is the number of degrees of freedom numerical experiments in 2 dimensions indicate that t

parallel solution of high frequency helmholtz equations using high order finite difference schemes abstract high frequency helmholtz equations pose a challenging computational task especially at high frequencies this work examines the parallel solution of such problems using 2nd 4th and 6th order finite difference schemes the examples include problems with known analytic solutions enabling error evaluation of the different schemes on various grids including problems on l shaped domains the resulting linear systems are solved with the block parallel carp cg algorithm which succeeded in lowering the relative residual indicating that it is a robust and reliable parallel solver of the resulting linear systems however lowering the error of the solution to reasonable levels with practical mesh sizes is obtained only with the higher order schemes these results corroborate the known limitations of the 2nd order scheme at modeling the helmholtz equation at high frequencies and they indicate that carp cg can also be used effectively with high order finite difference schemes furthermore the parallel scalability of carp cg improves when the wave number is increased on a fixed grid or when for a fixed wave number the grid size is decreased

a perfectly matched layer for the helmholtz equation in a semi infinite strip the perfectly matched layer pml has become a widespread technique for preventing reflections from far field boundaries for wave propagation problems in both the time dependent and frequency domains we develop a discretization to solve the helmholtz equation in an infinite two dimensional strip we solve the interior equation using high order finite differences schemes the combined helmholtz pml problem is then analyzed for the parameters that give the best performance we show that the use of local high order methods in the physical domain coupled with a specific second order approximation in the pml yields global high order accuracy in the physical domain we discuss the impact of the parameters on the effectiveness of the pml numerical results are presented to support the analysis

multiscale synchrony behaviors of paired financial time series by 3d multi continuum percolation abstract multiscale synchrony behaviors and nonlinear dynamics of paired financial time series are investigated in an attempt to study the cross correlation relationships between two stock markets a random stock price model is developed by a new system called three dimensional 3d multi continuum percolation system which is utilized to imitate the formation mechanism of price dynamics and explain the nonlinear behaviors found in financial time series we assume that the price fluctuations are caused by the spread of investment information the cluster of 3d multi continuum percolation represents the cluster of investors who share the same investment attitude in this paper we focus on the paired return series the paired volatility series and the paired intrinsic mode functions which are decomposed by empirical mode decomposition a new cross recurrence quantification analysis is put forward combining with multiscale cross sample entropy to investigate the multiscale synchrony of these paired series from the proposed model the corresponding research is also carried out for two china stock markets as comparison

optimal fourth order staggered grid finite difference scheme for 3d frequency domain viscoelastic wave modeling we investigate an optimal fourth order staggered grid finite difference scheme for 3d frequency domain viscoelastic wave modeling an anti lumped mass strategy is incorporated to minimize the numerical dispersion the optimal finite difference coefficients and the mass weighting coefficients are obtained by minimizing the misfit between the normalized phase velocities and the unity an iterative damped least squares method the levenberg marquardt algorithm is utilized for the optimization dispersion analysis shows that the optimal fourth order scheme presents less grid dispersion and anisotropy than the conventional fourth order scheme with respect to different poisson s ratios moreover only 3 7 grid points per minimum shear wavelength are required to keep the error of the group velocities below 1 the memory cost is then greatly reduced due to a coarser sampling a parallel iterative method named carp cg is used to solve the large ill conditioned linear system for the frequency domain modeling validations are conducted with respect to both the analytic viscoacoustic and viscoelastic solutions compared with the conventional fourth order scheme the optimal scheme generates wavefields having smaller error under the same discretization setups profiles of the wavefields are presented to confirm better agreement between the optimal results and the analytic solutions

on accuracy conditions for the numerical computation of waves abstract the helmholtz equation k 2 n 2 u f with a variable index of refraction n and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems such problems can be solved numerically by first truncating the given unbounded domain imposing a suitable outgoing radiation condition on an artificial boundary and then solving the resulting problem on the bounded domain by direct discretization for example using a finite element method in practical applications the mesh size h and the wave number k are not independent but are constrained by the accuracy of the desired computation it will be shown that the number of points per wavelength measured by kh 1 is not sufficient to determine the accuracy of a given discretization for example the quantity k 3 h 2 is shown to determine the accuracy in the l 2 norm for a second order discretization method applied to several propagation models

quenched voronoi percolation we prove that the probability of crossing a large square in quenched voronoi percolation converges to 1 2 at criticality confirming a conjecture of benjamini kalai and schramm from 1999 the main new tools are a quenched version of the box crossing property for voronoi percolation at criticality and an efron stein type bound on the variance of the probability of the crossing event in terms of the sum of the squares of the influences as a corollary of the proof we moreover obtain that the quenched crossing event at criticality is almost surely noise sensitive

sharpness of the phase transition for continuum percolation in mathbb r 2 r 2 we study the phase transition of random radii poisson boolean percolation around each point of a planar poisson point process we draw a disc of random radius independently for each point the behavior of this process is well understood when the radii are uniformly bounded from above in this article we investigate this process for unbounded and possibly heavy tailed radii distributions under mild assumptions on the radius distribution we show that both the vacant and occupied sets undergo a phase transition at the same critical parameter lambda c moreover the techniques we develop in this article can be applied to other models such as the poisson voronoi and confetti percolation

a fourth order kernel free boundary integral method for implicitly defined surfaces in three space dimensions abstract the kernel free boundary integral kfbi method is a finite difference version of the traditional boundary integral method for elliptic and parabolic partial differential equations on complex domains it evaluates boundary or volume integrals involved in the solution of boundary integral equations bies by solving equivalent but simple interface problems on regular grids so that the integral kernel or green function is never needed or computed this is the essential difference of the kfbi method from the traditional ones it takes advantage of the well conditioning property of discrete bies so that the number of krylov subspace iterations is essentially independent of discretization parameter or system dimension this paper presents a fourth order kernel free boundary integral method for second order elliptic partial differential equations on complex domains in three space dimensions whose boundaries are given by implicitly defined surfaces it represents the domain boundary and discretizes data on it by intersection points of the surface with cartesian grid lines the approach has a variety of advantages the current work solves simple interface problems with corrected 27 point compact finite difference schemes and calculates the discrete equations with a fast fourier transform based elliptic solver numerical examples show that the proposed method is efficient as well as accurate

on positive linear maps preserving invertibility theorem a positive linear map 4 between two c algebras is a jordan homomorphism if d preserves invertibility and the range of is a c algebra a counterexample is given for the case that the range of q is not assumed to be a c algebra this answers a question raised by b russo proc amer math sot 17

finite clusters in high density continuous percolation compression and sphericality a percolation process inrd is considered in which the sites are a poisson process with intensity and the bond between each pair of sites is open if and only if the sites are within a fixed distancer of each other the distribution of the number of sites in the clusterc of the origin is examined and related to the geometry ofc it is shown that when andk are large there is a characteristic radius such that conditionally on c k the convex hull ofc closely approximates a ball of radius with high probability when the normal volumek thatk points would occupy is small the cluster is compressed in that the number of points per unit volume in this ball is much greater than the ambient density for larger normal volumes there is less compression this can be compared to bernoulli bond percolation on the square lattice in two dimensions where an analog of this compression is known not to occur

robust and highly scalable parallel solution of the helmholtz equation with large wave numbers numerical solution of the helmholtz equation is a challenging computational task particularly when the wave number is large for two dimensional problems direct methods provide satisfactory solutions but large three dimensional problems become unmanageable in this work the block parallel carp cg algorithm parallel computing 36 2010 is applied to the helmholtz equation with large wave numbers the effectiveness of this algorithm is shown both theoretically and practically with numerical experiments on two and three dimensional domains including heterogeneous cases and a wide range of wave numbers a second order finite difference discretization scheme is used leading to a complex nonsymmetric and indefinite linear system carp cg is both robust and efficient on the tested problems on a fixed grid its scalability improves as the wave number increases additionally when the number of grid points per wavelength is fixed the number of iterations increases linearly with the wave number convergence rates for heterogeneous cases are similar to those of homogeneous cases carp cg also outperforms at all wave numbers one of the leading methods based on the shifted laplacian preconditioner with a complex shift and solved with a multigrid

a dispersion minimizing finite difference scheme for the helmholtz equation based on point weighting abstract in this paper we develop a new dispersion minimizing finite difference scheme for the helmholtz equation with perfectly matched layer pml in two dimensional domain which is a second order 9 point scheme to discretize the second derivative operator we employ a linear combination of a point and its neighboring grid points to replace each of the five points in the traditional central difference scheme based on minimizing the numerical dispersion the combination weights are determined by minimizing the numerical dispersion with a flexible selection strategy the new scheme is simple rotation free and pointwise consistent with the equation which is different from the classical rotated 9 point difference scheme obtained by combining the cartesian coordinate system and the rotated system moreover it is a robust scheme even if the step sizes of different directions are not equal convergence analysis and dispersion analysis are given several numerical examples are presented to illustrate the numerical convergence and effectiveness of the new scheme

characterizing isomorphisms in terms of completely preserving invertibility or spectrum let a and b be standard operator algebras on complex banach spaces x and y respectively in this paper we characterize the surjective maps completely preserving the invertibility in both directions and the surjective maps completely preserving the spectrum from a to b we show that a surjective map from a to b is a ring isomorphism if and only if it is unital and completely preserves the invertibility of operators in both directions is an isomorphism if and only if it completely preserves the spectrum of operators

an optimal compact sixth order finite difference scheme for the helmholtz equation abstract in this paper we present an optimal compact finite difference scheme for solving the 2d helmholtz equation a convergence analysis is given to show that the scheme is sixth order in accuracy based on minimizing the numerical dispersion a refined optimization rule for choosing the scheme s weight parameters is proposed numerical results are presented to demonstrate the efficiency and accuracy of the compact finite difference scheme with refined parameters