fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm the analysis of transient wave scattering from rigid bodies using integral equation based techniques is computationally intensive if carried out using classical schemes the evaluation of the velocity potential on the surface of a three dimensional scatterer represented in terms of ns spatial basis functions for nt time steps requires o ntns2 operations the recently developed plane wave time domain pwtd algorithm permits the rapid evaluation of transient fields that are generated by bandlimited source distributions it has been shown that incorporation of the pwtd algorithm into integral equation based solvers in a two level setting reduces the computational complexity of a transient analysis to o ntns1 5 logns in this paper it is shown that casting the pwtd scheme into a multilevel framework permits the analysis of transient acoustic surface scattering phenomena in o ntnslog2ns operations using o ntns memory numerical examples that demonstrate the efficacy of the multilevel implementation are also presented

on the implementation of discontinuous galerkin methods for volterra integral equations with highly oscillatory bessel kernels in this paper we consider implementation of discontinuous galerkin methods for weakly singular volterra integral equations of first and second kinds with highly oscillatory bessel kernels which cost the same operations independent of large values of frequencies preliminary numerical results show that the proposed method is efficient for verifying accuracy of approximate solutions

amenable and weakly amenable banach algebras with compact multiplication abstract we investigate amenable and weakly amenable banach algebras with compact multiplication any amenable banach algebra with compact multiplication is biprojective as a consequence every semisimple such algebra which has the approximation property is a topological direct sum of full matrix algebras in the radical case no such structure theorem is at hand we also investigate banach algebras which have a bounded approximate identity consisting of normalized powers of an element x any such banach algebra is either unital or radical if the algebra is also generated by x it is weakly amenable we construct a radical example with compact multiplication which moreover is an integral domain this furnishes a new example of a commutative weakly amenable non amenable radical banach algebra

theoretical aspects of the application of convolution quadrature to scattering of acoustic waves in this paper we address several theoretical questions related to the numerical approximation of the scattering of acoustic waves in two or three dimensions by penetrable non homogeneous obstacles using convolution quadrature cq techniques for the time variable and coupled boundary element method finite element method for the space variable the applicability of cq to waves requires polynomial type bounds for operators related to the operator s 2 in the right half complex plane we propose a new systematic way of dealing with this problem both at the continuous and semidiscrete in space cases we apply the technique to three different situations scattering by a group of sound soft and hard obstacles by homogeneous and non homogeneous obstacles

computing the roughening transition of ising and solid on solid models by bcsos model matching we study the roughening transition of the dual of the two dimensional 2d xy model of the discrete gaussian model of the absolute value solid on solid model and of the interface in an ising model on a three dimensional 3d simple cubic lattice the investigation relies on a renormalization group finite size scaling method that was proposed and successfully tested a few years ago the basic idea is to match the renormalization group flow of the interface observables with that of the exactly solvable body centred solid on solid bcsos model our estimates for the critical couplings are and for the xy model the discrete gaussian model and the absolute value solid on solid model respectively for the inverse roughening temperature of the ising interface we find to the best of our knowledge these are the most precise estimates for these parameters published so far

stable electric field tdie solvers via quasi exact evaluation of mot matrix elements prior theoretical studies and experience confirm that the stability of marching on in time mot solvers pertinent to the analysis of scattering from free standing three dimensional perfect electrically conducting surfaces hinges on the accurate evaluation of mot matrix elements resulting from a galerkin discretization of the underlying time domain integral equation tdie unfortunately the accurate evaluation of the four dimensional spatial integrals involved in the expressions for these matrix elements is prohibitively expensive when performed by computational means here a method that permits the quasi exact evaluation of mot matrix elements is presented specifically the proposed method permits the analytical evaluation of three out of the four spatial integrations leaving only one integral to be evaluated numerically since the latter has finite range and a piecewise smooth integrand it can be evaluated to very high accuracy using standard quadrature rules as a result the proposed method permits the fast evaluation of mot matrix elements with arbitrary user specified accuracy extensive numerical experiments show that an mot solver for the electric field tdie that uses the proposed quasi exact method is stable for a very wide range of time step sizes and yields solutions that decay exponentially after the excitation vanishes

a fast high order algorithm for the solution of surface scattering problems basic implementation tests and applications we present a new algorithm for the numerical solution of problems of acoustic scattering by surfaces in three dimensional space this algorithm evaluates scattered fields through fast high order solution of the corresponding boundary integral equation the high order accuracy of our solver is achieved through use of partitions of unity together with analytical resolution of kernel singularities the acceleration in turn results from use of a novel approach which based on high order two face equivalent source approximations reduces the evaluation of far interactions to evaluation of 3 d fast fourier transforms ffts this approach is faster and substantially more accurate and it runs on dramatically smaller memories than other fft and k space methods the present algorithm computes one matrix vector multiplication in o n6 5logn to o n4 3logn operations where n is the number of surface discretization points the latter estimate applies to smooth surfaces for which our high order algorithm provides accurate solutions with small values of n the former more favorable count is valid for highly complex surfaces requiring significant amounts of subwavelength sampling further our approach exhibits super algebraic convergence it can be applied to smooth and nonsmooth scatterers and it does not suffer from accuracy breakdowns of any kind in this paper we introduce the main algorithmic components in our approach and we demonstrate its performance with a variety of numerical results in particular we show that the present algorithm can evaluate accurately in a personal computer scattering from bodies of acoustical sizes of several hundreds

convergent expansions and bounded operators in the umbral calculus on etudie des proprietes analytiques de certaines suites de fonctions speciales appelees suites de sheffer

polynomials of meixner s type in infinite dimensions jacobi fields and orthogonality measures abstract the classical polynomials of meixner s type hermite charlier laguerre meixner and meixner pollaczek polynomials are distinguished through a special form of their generating function which involves the laplace transform of their orthogonality measure in this paper we study analogs of the latter three classes of polynomials in infinite dimensions we fix as an underlying space a non compact riemannian manifold x and an intensity measure on it we consider a jacobi field in the extended fock space over l 2 x whose field operator at a point x x is of the form x x x x x x x where is a real parameter here x and x are respectively the annihilation and creation operators at the point x we then realize the field operators as multiplication operators in l 2 d where d is the dual of d c 0 x and is the spectral measure of the jacobi field we show that is a gamma measure for 2 a pascal measure for 2 and a meixner measure for is a levy noise measure the isomorphism between the extended fock space and l 2 d is carried out by infinite dimensional polynomials of meixner s type we find the generating function of these polynomials and using it we study the action of the operators x and x in the functional realization

functional calculus for infinitesimal generators of holomorphic semigroups we give a functional calculus formula for infinitesimal generators of holomorphic semigroups of operators on banach spaces which involves the bochner riesz kernels of such generators the rate of smoothness of operating functions is related to the exponent of the growth on vertical lines of the operator norm of the semigroup the strength of the formula is tested on poisson and gauss semigroups inl1 rn andl1 g for a stratified lie groupg we give also a self contained theory of smooth absolutely continuous functions on the half line 0

on the relations between poissonian white noise analysis and harmonic analysis on configuration spaces we unify techniques of poissonian white noise analysis and harmonic analysis on configuration spaces establishing relations between the main structures of both ones this leads to new results inside of infinite dimensional analysis as well as in its applications to problems of mathematical physics e g statistical mechanics of continuous systems

an analysis of time discretization in the finite element solution of hyperbolic problems abstract the problem of the time discretization of hyperbolic equations when finite elements are used to represent the spatial dependence is critically examined a modified equation analysis reveals that the classical second order accurate time stepping algorithms i e the lax wendroff leap frog and crank nicolson methods properly combine with piecewise linear finite elements in advection problems only for small values of the time step on the contrary as the courant number increases the numerical phase error does not decrease uniformly at all wavelengths so that the optimal stability limit and the unit cfl property are not achieved these fundamental numerical properties can however be recovered while still remaining in the standard galerkin finite element setting by increasing the order of accuracy of the time discretization this is accomplished by exploiting the taylor series expansion in the time increment up to the third order before performing the galerkin spatial discretization using piecewise linear interpolations as a result it appears that the proper finite element equivalents of second order finite difference schemes are implicit methods of incremental type having third and fourth order global accuracy on uniform meshes taylor galerkin methods numerical results for several linear examples are presented to illustrate the properties of the taylor galerkin schemes in one and two dimensional calculations

postmodern logarithmo technia abstract in order to solve ordinary differential equations we use an equation with the so called logarithmic derivative similar equations with a linear operator permit us to define logarithmic and antilogarithmic mappings and obtain some results unknown before for the classical derivation operator this method and its applications are exposed in detail in the author s book 1 and may be treated as an introduction into the 21 st century logarithmo technia according to the original meaning of this word in the first section there are given basic notions and facts of algebraic analysis without proofs the second section consists of the most important definitions and theorems without proofs concerning logarithms and antilogarithms the third section is concerned with properties of multiplicative true shifts in the last section is given a generalization of the binomial theorem for harmonic logarithms

on the multistep time discretization of linear initial boundary value problems and their boundary integral equations convergence estimates in terms of the data are shown for multistep methods applied to non homogeneous linear initial boundary value problems similar error bounds are derived for a new class of time discrete and fully discrete approximation schemes for boundary integral equations of such problems e g for the single layer potential equation of the wave equation in both cases the results are obtained from convergence and stability estimates for operational quadrature approximations of convolutions these estimates which are also proved here depend on bounds of the laplace transform of the distributional convolution kernel outside the stability region scaled by the time stepsize and on the smoothness of the data

umbral calculus and special functions developpement du calcul symbolique des puissances et de la methode des coalgebres et des comodules associee application a l etude des fonctions speciales classiques hypergeometriques de laguerre sonine d hermite weber de legendre et de bessel

on the mellin transforms of hypergeometric polynomials mellin integral transform pairs for all hypergeometric orthogonal polynomials in the askey scheme ranging from the classical hermite polynomials up to the four parameter wilson polynomials are systematically discussed

analytic version of test functionals fourier transform and a characterization of measures in white noise calculus it is shown that the space j of test white noise functionals has an analytic version a which is an algebra as well as a topological linear space topologized by the projective limit of a sequence ap p n of banach spaces with respective norm given by ap supz cj p z exp 2 1 z p2 where sj p denotes the complexification of j p furthermore it is shown that the a topology and the j topology are equivalent in the course of the proof it is also shown that the space jp is isometrically isomorphic to the bargmann segal analytic functions on bj p under s transform employing this new version we are able to define the fourier transform of a generalized white noise functional as the adjoint of fourier wiener transform t1 i with parameter 1 i and moreover we show that every measure in j always satisfies a certain growth condition

cluster monte carlo algorithms abstract the swendsen wang and wolff monte carlo algorithms are described in some detail using the potts model as an example various generalizations are then reviewed and some applications are discussed two complete fortran programs for the algorithms are provided

prime like elements and semi direct products in commutative banach algebras we develop results which show that elements in the radical of a commutative banach algebra are often precluded from having prime like properties if we avoid certain exceptional situations involving torsion elements this makes the proof of the singer wermer conjecture conceptually much clearer it also motivates the definition of an element havingregular powersand allows us to strengthen our previous results concerning necessary conditions for a commutative banach algebra a to be the semidirect product of some subalgebra together with a specified principal idealsa or equivalently concerning necessary conditions for there to be an algebraicsplittingof the short exact sequence0 sa a a sa 0for some given elementsin a in particular we show that if a is aradicalbanach algebra andshas regular powers then no such splitting is possible

continuous sheffer families ii abstract continuous sheffer families have been recently introduced by the authors these are continuous versions of the sheffer sequences arising in the umbral calculus we show here that quite a number of classical special functions are examples of such families

stability and convergence of collocation schemes for retarded potential integral equations time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations solving such equations numerically is both complicated and computationally intensive and numerical methods often prove to be unstable collocation schemes are easier to implement than full finite element formulations but little appears to be known about their stability and convergence here we derive and analyze some new stable collocation schemes for the single layer equation for transient acoustic scattering and use spatial fourier and temporal laplace transform techniques to demonstrate that such stable schemes are second order convergent

numerical approximations for highly oscillatory bessel transforms and applications abstract this paper presents an efficient numerical method for approximating highly oscillatory bessel transforms based on analytic continuation we transform the integrals into the problems of integrating the forms on 0 with the integrand that does not oscillate and decays exponentially fast which can be efficiently computed by using gauss laguerre quadrature rule we then derive the error of the method depending on the frequency and the node number moreover we apply the scheme for studying the approximations of the solutions of two kinds of highly oscillatory integral equations preliminary numerical results show the efficiency and accuracy of numerical approximations

banach algebras logarithms and polynomials of convolution type abstract using elementary banach algebra techniques it is determined which elements of banach algebras like l1 b k and a have logarithms the wiener levy theorem will be used to answer the same question for more complicated banach algebras like the wiener algebra these results will be applied to polynomials of convolution type and a generalization thereof

numerical stability and convergence of approximations of retarded potential integral equations stability and convergence results for approximations of retarded potential integral equations are given such integral approximations arise in time marching schemes for direct scattering problems and are both extremely complicated and computationally intensive they are often observed to have exponentially increasing unstable solutions a stability analysis is performed which is shown to provide a way of predicting whether a given scheme is stable or not the proposed test is supported by numerical experiments and requires much less computation than the scheme itself it is also shown that if an approximation for this type of integral equation is both stable and consistent then it is convergent

hardy spaces for the strip abstract in this paper we shall study hardy spaces of analytic functions in a strip s our main result is on one hand an intrinsic characterization of the spaces and on the second that polynomials are dense we also present an orthogonal in h 2 s basis of polynomials

a general umbral calculus in infinitely many variables on etudie des suites de fonctions factorielles satisfaisant des analogues des recurrences binomiales et de sheffer et on montre comment un calcul operatoriel ressemblant au calcul umbral peut etre construit dessus

jacobi iteration in implicit difference schemes for the wave equation it is shown how a jacobi iteration can be used to approximate the linear algebra required by a class of implicit finite difference element schemes for a linear hyperbolic pde while preserving the important properties of the implicit scheme in particular it is shown that order of accuracy stability energy conservation and isotropy of the implicit scheme are all carried over into the new scheme in general the new scheme is much more efficient than the implicit scheme it is derived from for problems in more than one space variable and can be vectorized and or parallelized quite easily furthermore it is shown that a modification of the technique can be used to improve some properties of the underlying implicit scheme at little or no extra cost

an infinite dimensional umbral calculus abstract the aim of this paper is to develop foundations of umbral calculus on the space d of distributions on r d which leads to a general theory of sheffer polynomial sequences on d we define a sequence of monic polynomials on d a polynomial sequence of binomial type and a sheffer sequence we present equivalent conditions for a sequence of monic polynomials on d to be of binomial type or a sheffer sequence respectively we also construct a lifting of a sequence of monic polynomials on r of binomial type to a polynomial sequence of binomial type on d and a lifting of a sheffer sequence on r to a sheffer sequence on d examples of lifted polynomial sequences include the falling and rising factorials on d abel hermite charlier and laguerre polynomials on d some of these polynomials have already appeared in different branches of infinite dimensional stochastic analysis and played there a fundamental role

appell polynomials as values of special functions abstract we show that there is a large class of appell sequences p n x n 0 for which there is a function f s x entire in s for fixed x with re x 0 and satisfying f n x p n x for n 0 1 2 for example in the case of bernoulli and apostol bernoulli polynomials f is essentially the hurwitz zeta function and the lerch transcendent respectively we study a subclass of these appell sequences for which the corresponding special function has a form more closely related to the classical zeta functions and give some interesting examples of these general constructions

asymptotic estimates for apostol bernoulli and apostol euler polynomials we analyze the asymptotic behavior of the apostol bernoulli polynomials bn x in detail the starting point is their fourier series on 0 1 which it is shown remains valid as an asymptotic expansion over compact subsets of the complex plane this is used to determine explicit estimates on the constants in the approximation and also to analyze oscillatory phenomena which arise in certain cases these results are transferred to the apostol euler polynomials en x via a simple relation linking them to the apostol bernoulli polynomials

an analysis of dendy s piecewise polynomial petrov galerkin method for a hyperbolic equation with stagnation points abstract a method of dendy was shown by him in the absence of stagnation points to give optimal order error for a large class of piecewise polynomial trial spaces this result is extended to the situation when stagnation points may be present the analysis contains a result of interest in connection with numerical solution of singular two point boundary value problems

sheffer homeomorphisms of spaces of entire functions in infinite dimensional analysis abstract for certain sheffer sequences s n n 0 on c grabiner 1988 proved that for each 0 1 the corresponding sheffer operator z n s n z extends to a linear self homeomorphism of e min c the frechet topological space of entire functions of order at most and minimal type when the order is equal to 0 in particular every function f e min c admits a unique decomposition f z n 0 c n s n z and the series converges in the topology of e min c within the context of a complex nuclear space and its dual space in this work we generalize grabiner s result to the case of sheffer operators corresponding to sheffer sequences on in particular for c n with n 2 we obtain the multivariate extension of grabiner s theorem furthermore for an appell sequence on a general co nuclear space we find a sufficient condition for the corresponding sheffer operator to extend to a linear self homeomorphism of e min when 1 the latter result is new even in the one dimensional case

a note on appell sequences mellin transforms and fourier series abstract a large class of appell polynomial sequences p n x n 0 are special values at the negative integers of an entire function f s x given by the mellin transform of the generating function for the sequence for the bernoulli and apostol bernoulli polynomials these are basically the hurwitz zeta function and the lerch transcendent each of these have well known fourier series which are proved in the literature using various techniques here we find the latter fourier series by directly calculating the coefficients in a straightforward manner we then show that within the context of appell sequences these are the only cases for which the polynomials have uniformly convergent fourier series in the more general context of sheffer sequences we find that there are other polynomials with uniformly convergent fourier series finally applying the same ideas to the fourier transform considered as the continuous analog of the fourier series the hermite polynomials play a role analogous to that of the bernoulli polynomials

non gaussian infinite dimensional analysis abstract we give an extension of some gaussian in particular white noise analysis objects and structures to the case of more general measures on the dual of a nuclear space

a new approach to critical exponents in phase transitions of spin systems abstract we investigate a method to obtain critical exponents using standard numerical simulation techniques for spin systems we show that by analyzing the inverse of the logarithmic derivative of the susceptibility with respect to temperature the accuracy in determining can be increased significantly the method is tested on the two and three dimensional ising models but this alternative approach is thought to be most useful for spin systems on non periodic structures like quasi crystals and fractal lattices where the finite size scaling method is difficult to apply