computational modeling of uncertainty in time domain electromagnetics we discuss computationally efficient ways of accounting for the impact of uncertainty e g lack of detailed knowledge about sources materials shapes etc in computational time domain electromagnetics in contrast to classic statistical monte carlo based methods we explore a probabilistic approach based on high order accurate expansions of general stochastic processes we show this to be highly efficient and accurate on both one and two dimensional examples enabling the computation of global sensitivities of measures of interest e g radar cross sections rcs in scattering applications for a variety of types of uncertainties

extremal non compactness of composition operators with linear fractional symbol abstract we realize the norms of certain composition operators c with linear fractional symbol acting on the hardy space in terms of the roots of associated hypergeometric functions this realization leads to simple necessary and sufficient conditions on for c to exhibit extremal non compactness establishes equivalence of cohyponormality and cosubnormality of composition operators with linear fractional symbol and yields a complete classification of those linear fractional that induce composition operators whose norms are determined by the action of the adjoint c on the normalized reproducing kernels in h 2

fixed point composition and toeplitz composition c algebras abstract let be a linear fractional non automorphism self map of d that fixes t and satisfies 1 and consider the composition operator c acting on the hardy space h 2 d we determine which linear fractionally induced composition operators are contained in the unital c algebra generated by c and the ideal k of compact operators we apply these results to show that c c k and c f the unital c algebra generated by all composition operators induced by linear fractional non automorphism self maps of d that fix are each isomorphic modulo the ideal of compact operators to a unitization of a crossed product of c 0 0 1 we compute the k theory of c c k and calculate the essential spectra of a class of operators in this c algebra we also obtain a full description of the structures modulo the ideal of compact operators of the c algebras generated by the unilateral shift t z and a single linear fractionally induced composition operator

an energy conserving method for stochastic maxwell equations with multiplicative noise abstract in this paper it is shown that three dimensional stochastic maxwell equations with multiplicative noise are stochastic hamiltonian partial differential equations possessing a geometric structure i e stochastic multi symplectic conservation law and the energy of system is a conservative quantity almost surely we propose a stochastic multi symplectic energy conserving method for the equations by using the wavelet collocation method in space and stochastic symplectic method in time numerical experiments are performed to verify the excellent abilities of the proposed method in providing accurate solution and preserving energy the mean square convergence result of the method in temporal direction is tested numerically and numerical comparisons with finite difference method are also investigated

tridiagonal factorizations of fourier matrices and applications to parallel computations of discrete fourier transforms abstract let n e 2 i n and fn be the n n matrix defined by f n 1 n ij n where i and j run from 0 to n 1 two different methods are developed for factoring fn into products of tridiagonal and permutation matrices one method is based on matrix identities associated with ffts and the rader prime algorithm the other method is based on a numerical technique never before applied to fourier matrices called minimal variable oblique elimination new results established in this paper include the establishment of necessary and sufficient conditions for which minimal variable oblique elimination can be used to compute tridiagonal decompositions of arbitrary square matrices and explicit descriptions of minimal variable solutions in the case that the descriptions are satisfied proof that minimal variable oblique elimination can be applied successfully to fourier matrices of all orders and explicit descriptions of various tridiagonal decompositions of pfn for any n n permutation matrix p complexity estimates are derived for both the parallel algorithms resulting from the decompositions and computation of the decompositions and timings are estimated for processor arrays constructed using gapp chips

corrigendum to on norms of composition operators acting on bergman spaces j math anal appl 291 2004 189 202 abstract a theorem and a corollary in the paper cited in the title were stated incorrectly as was pointed out by christopher hammond we now state correctly and prove both of them these results still generalize and explain the geometric meaning of the cowen hurst norm formula we also include additional references and provide an example relevant for further study

energy conserved splitting finite difference time domain methods for maxwell s equations in three dimensions in this paper we develop and analyze efficient energy conserved splitting finite difference time domain fdtd schemes for solving three dimensional maxwell s equations in electromagnetic computations all proposed energy conserved splitting finite difference time domain ec s fdtd algorithms are strictly proved to be energy conserved and unconditionally stable and they can be computed efficiently rigorous convergence results are obtained for the schemes the ec s fdtdii schemes are proved to have second order in both time step and spatial steps while the ec s fdtdi schemes have second order in spatial steps and first order in time step the error estimates are optimal and especially the constant in the error estimates is proved to be only o t numerical experiments confirm the theoretical analysis results

the norm of a composition operator with linear symbol acting on the dirichlet space abstract we obtain a representation for the norm of a composition operator on the dirichlet space induced by a map of the form z a z b we compare this result to an upper bound for c that is valid whenever is univalent our work relies heavily on an adjoint formula recently discovered by gallardo gutierrez and montes rodriguez

conservative stochastic differential equations mathematical and numerical analysis we consider stochastic differential equations on the whole euclidean space possessing a scalar invariant along their solutions the stochastic dynamics therefore evolves on a hypersurface of the ambient space using orthogonal coordinate systems we show the existence and uniqueness of smooth solutions of the kolmogorov equation under some ellipticity conditions over the invariant hypersurfaces if we assume moreover the existence of an invariant measure we show the exponential convergence of the solution towards its average in the second part we consider numerical approximation of the stochastic differential equation and show the convergence and numerical ergodicity of a class of projected schemes in the context of molecular dynamics this yields numerical schemes that are ergodic with respect to the microcanonical measure over isoenergy surfaces

spectral theory for algebraic combinations of toeplitz and composition operators abstract we determine the essential spectra of algebraic combinations of toeplitz operators with continuous symbol and composition operators induced by a class of linear fractional non automorphisms of the unit disk the operators in question act on the hardy space h 2 on the unit disk our method is to realize the c algebra that they generate as an extension of the compact operators by a concrete c algebra whose invertible elements are easily characterized

subnormality and composition operators on h2 if is a non constant analytic function defined on the unit disk d such that d d the composition operator c is the operator on the hardy space h2 of the unit disk defined by c f f in this paper we investigate the relationship between properties of the symbol and the subnormality of the operators c and c the main theorem shows under a regularity hypothesis that c is subnormal if and only if is in a restricted class of linear fractional transformations the two previously known special cases the affine transformations associated with the cesaro operator and the automorphisms are included as the extreme examples the proof of the main theorem consists of verifying a moment condition and yields in addition the construction of a measure that exhibits cgj as multiplication by an analytic function on p2 and the identification of the minimal normal extension as a weighted sum of shifts

stochastic conformal schemes for damped stochastic klein gordon equation with additive noise abstract in this article stochastic conformal schemes of the damped stochastic klein gordon equation with additive noise are studied it is shown that this equation possesses the stochastic conformal multi symplectic conservation law under appropriate boundary conditions the global momentum evolution law and the global energy evolution law are proposed we chiefly develop the stochastic conformal preissman scheme the stochastic conformal discrete gradient scheme and the stochastic conformal euler box scheme to preserve the geometric structures of the original system specifically we make theoretical discussions on the three proposed schemes to obtain corresponding discrete conservation laws or discrete evolution laws then the damped stochastic linear klein gordon equation and the damped stochastic nonlinear klein gordon equation with cubic nonlinearity are taken as examples to demonstrate the validity of the proposed schemes through numerical experiments and comparisons the superiorities of the proposed schemes are fully shown which are consistent with our theoretical analysis moreover the mean square convergence orders of the three stochastic conformal schemes in time direction and space direction are tested numerically

winograd s fourier transform via circulants abstract for small primes the minimal multiplication algorithms of winograd can be expressed as the eigenvalue eigenvector decomposition of the associated circulant matrix but forced into the real field

bidiagonal factorization of fourier matrices and systolic algorithms for computing discrete fourier transforms an algorithm is presented for factoring fourier matrices into products of bidiagonal matrices these factorizations have the same structure for every n and make possible discrete fourier transform dft computation via a sequence of local regular computations a parallel pipeline technique for computing sequences of k point dfts for every k

block 2 d interpolation efficient matrix factorization and application to signal processing a block 2 d decomposition and a new block lu matrix factorization based on a newton approach are presented for solving quickly and efficiently polynomial or exponential 2 d interpolation problems the sample grids under consideration are described by the product representation x sub 0 x sub 1 x sub n x y sub 0 y sub 1 y sub m where the x grid and the y grid are not necessarily uniformly spaced the attractive features of the method are the inherent efficient parallelism the reduced computational requirements needed for the lu decomposition and the capability of implementation of 1 d fast and accurate algorithms the proposed method can be used for modeling 2 d discrete signals designing 2 d fir filters 2 d fourier matrix factorization 2 d dft etc

preservation of physical properties of stochastic maxwell equations with additive noise via stochastic multi symplectic methods stochastic maxwell equations with additive noise are a system of stochastic hamiltonian partial differential equations intrinsically possessing the stochastic multi symplectic conservation law it is shown that the averaged energy increases linearly with respect to the evolution of time and the flow of stochastic maxwell equations with additive noise preserves the divergence in the sense of expectation moreover we propose three novel stochastic multi symplectic methods to discretize stochastic maxwell equations in order to investigate the preservation of these properties numerically we make theoretical discussions and comparisons on all of the three methods to observe that all of them preserve the corresponding discrete version of the averaged divergence meanwhile we obtain the corresponding dissipative property of the discrete averaged energy satisfied by each method especially the evolution rates of the averaged energies for all of the three methods are derived which are in accordance with the continuous case numerical experiments are performed to verify our theoretical results

norms of linear fractional composition operators we obtain a representation for the norm of the composition operator c on the hardy space h 2 whenever is a linear fractional mapping of the form z b cz d the representation shows that for such mappings the norm of c always exceeds the essential norm of c moreover it shows that a formula obtained by cowen for the norms of composition operators induced by mappings of the form z sz t has no natural generalization that would yield the norms of all linear fractional composition operators for rational numbers s and t cowen s formula yields an algebraic number as the norm we show e g that the norm of c 1 2 z is a transcendental number our principal results are based on a process that allows us to associate with each non compact linear fractional composition operator c for which c c e an equation whose maximum real solution is c 2 our work answers a number of questions in the literature for example we settle an issue raised by cowen and maccluer concerning co hyponormality of a certain family of composition operators

a stochastic multi symplectic scheme for stochastic maxwell equations with additive noise abstract in this paper we investigate a stochastic multi symplectic method for stochastic maxwell equations with additive noise based on the stochastic version of variational principle we find a way to obtain the stochastic multi symplectic structure of three dimensional 3 d stochastic maxwell equations with additive noise we propose a stochastic multi symplectic scheme and show that it preserves the stochastic multi symplectic conservation law and the local and global stochastic energy dissipative properties which the equations themselves possess numerical experiments are performed to verify the numerical behaviors of the stochastic multi symplectic scheme

splitting multisymplectic integrators for maxwell s equations in the paper we describe a novel kind of multisymplectic method for three dimensional 3 d maxwell s equations splitting the 3 d maxwell s equations into three local one dimensional lod equations then applying a pair of symplectic runge kutta methods to discretize each resulting lod equation it leads to splitting multisymplectic integrators we say this kind of schemes to be lod multisymplectic scheme lod ms the discrete conservation laws convergence dispersive relation dissipation and stability are investigated for the schemes theoretical analysis shows that the schemes are unconditionally stable non dissipative and of first order accuracy in time and second order accuracy in space as a reduction we also consider the application of lod ms to 2 d maxwell s equations numerical experiments match the theoretical results well they illustrate that lod ms is not only efficient and simple in coding but also has almost all the nature of multisymplectic integrators

which linear fractional composition operators are essentially normal abstract we characterize the essentially normal composition operators induced on the hardy space h2 by linear fractional maps they are either compact normal or the nontrivial case induced by parabolic nonautomorphisms these parabolic maps induce the first known examples of nontrivially essentially normal composition operators in addition we characterize those linear fractionally induced composition operators on h2 that are essentially self adjoint and present a number of results for composition operators induced by maps that are not linear fractional

characterizations of binormal composition operators with linear fractional symbols on h2 for an analytic function d d the composition operator c is the operator on the hardy space h2 defined by c f f for all f in h2 in this paper we give necessary and sufficient conditions for the composition operator c to be binormal where the symbol is a linear fractional selfmap of d furthermore we show that c is binormal if and only if it is centered when is an automorphism of d or z sz t s t 1 we also characterize several properties of binormal composition operators with linear fractional symbols on h2

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

exponential integrators for stochastic maxwell s equations driven by ito noise abstract this article presents explicit exponential integrators for stochastic maxwell s equations driven by both multiplicative and additive noises by utilizing the regularity estimate of the mild solution we first prove that the strong order of the numerical approximation is 1 2 for general multiplicative noise combining a proper decomposition with the stochastic fubini s theorem the strong order of the proposed scheme is shown to be 1 for additive noise moreover for linear stochastic maxwell s equation with additive noise the proposed time integrator is shown to preserve exactly the symplectic structure the evolution of the energy as well as the evolution of the divergence in the sense of expectation several numerical experiments are presented in order to verify our theoretical findings

norms of composition operators with rational symbol we compute the norms of composition operators with rational symbols that satisfy certain properties extending christopher hammond s methods on operators with linear fractional symbols this leads to a host of new examples of composition operators whose norms are calculable

adjoints of rationally induced composition operators abstract we give an elementary proof of a formula recently obtained by hammond moorhouse and robbins for the adjoint of a rationally induced composition operator on the hardy space h 2 christopher hammond jennifer moorhouse marian e robbins adjoints of composition operators with rational symbol j math anal appl 341 2008 626 639 we discuss some variants and implications of this formula and use it to provide a sufficient condition for a rationally induced composition operator adjoint to be a compact perturbation of a weighted composition operator

norms and spectral radii of composition operators acting on the dirichlet space we obtain new upper bounds on the norms of univalently induced composition operators acting on the dirichlet space and compute explicitly the norms for univalent symbols whose range is the disk minus a set of measure zero as an application we show that the spectral radius of every univalently induced composition operator on the dirichlet space is equal to one

energy conserved splitting fdtd methods for maxwell s equations in this paper two new energy conserved splitting methods ec s fdtdi and ec s fdtdii for maxwell s equations in two dimensions are proposed both algorithms are energy conserved unconditionally stable and can be computed efficiently the convergence results are analyzed based on the energy method which show that the ec s fdtdi scheme is of first order in time and of second order in space and the ec s fdtdii scheme is of second order both in time and space we also obtain two identities of the discrete divergence of electric fields for these two schemes for the ec s fdtdii scheme we prove that the discrete divergence is of first order to approximate the exact divergence condition numerical dispersion analysis shows that these two schemes are non dissipative numerical experiments confirm well the theoretical analysis results

discrete gradient approach to stochastic differential equations with a conserved quantity general autonomous stochastic differential equations sdes driven by one dimensional brownian motion in the stratonovich sense with a conserved quantity i y are considered relying on this conserved quantity an equivalent skew gradient sg form of original sdes is constructed with the aim of constructing conserved numerical methods direct discrete gradient approaches which approximate directly the sg system lead to two conserved methods in indirect discrete gradient approaches we first split the sg system into subsystems which preserve the original conserved quantity then apply direct discrete gradient approaches to subsystems to produce two composition schemes the mean square convergence of order 1 for these four methods depends on the assumptions that the coefficients of sdes are lipschitz continuous with bounded second moments along the solution of sdes are twice continuous differentiable and have derivatives that are uniformly bounded three numerical experiments are presented to verify our theoretical analysis and show the advantages of these methods