loop star decomposition of basis functions in the discretization of the efie a general and readily applicable scheme is presented for the determination of the basis functions that allow the decomposition of the surface current into a solenoidal part and a nonsolenoidal remainder the proposed approach brings into correspondence these two parts with two scalar functions and generates the known loop and star basis functions the completeness of the loop star basis is discussed employing the presented scheme the issue of the irrotational property of the nonsolenoidal functions is addressed

distributive and analytic properties of lattice sums we use sums over bessel functions of the first kind to derive a convenient form of the poisson summation identity relating sums over direct lattices in two dimensions to sums over reciprocal lattices after three simple examples of the use of the identity we consider sums over complex powers of the radial distance to lattice points and also sums incorporating factors exp 4im p depending on angles of lattice points we study the distribution of zeros of lattice sums and show two which seemingly obey the riemann hypothesis and a third which does not we provide a reflection formula for angular lattice sums and a macdonald function sum for the lowest order angular lattice sum

neumann series and lattice sums we consider sums over the square lattice which depend only on radial distance and provide formulas which enable sums of functions with neumann series to be reexpressed as combinations of hypergeometric series we illustrate the procedure using trigonometric sums previously studied by borwein and borwein sums combining logarithms bessel functions j and powers of distance and sums of neumann functions we also exhibit sums which may be evaluated analytically and recurrence formulas linking sums

symmetry solutions for reaction diffusion equations with spatially dependent diffusivity nonclassical and classical symmetry techniques are employed to analyse a reaction diffusion equation with a cubic source term here the diffusivity diffusion term is assumed to be an arbitrary function of the spatial variable classification using lie point and nonclassical symmetries is performed it turns out that the diffusivity needs to be given as a quadratic function of the spatial variable for the given governing equation to admit nonclassical symmetries both nonclassical and classical symmetries are used to construct some group invariant exact solutions the results are applied to models arising in population dynamics

analysis of the annular ring loaded circular disk microstrip antenna a rigorous analysis of the natural resonance frequencies and input impedance characteristics of an annular ring loaded arl circular disk microstrip antenna is presented using vector hankel transforms the problem is formulated in terms of vector dual integral equations galerkin s method is then used to solve the equations to obtain the resonance frequencies and the current distribution on the conductive patches arising from a probe excitation due to the singular nature of the current distribution the singularity subtraction method has been used to accelerate the convergence of basis function expansions experiments for determining resonance frequencies and input impedance characteristics of an arl circular disk microstrip antenna with various substrate thicknesses have been made the theoretical results are in good agreement with the experimental data even when the thickness of the substrate is 0 1 substrate wavelength it is shown that this theory can be used to analyze some microstrip antennas with an electrically thick substrate including the analysis of mutual coupling between conductive patches or between the path and the feed of a microstrip antenna

efficient implementation of a wavelet based galerkin scheme wavelets can substantially accelerate the computation of planar circuits in method of moments mom schemes this contribution deals with the prediction of the significant system matrix entries a key to numerical efficiency further optimized grids for improved performance are defined the implementation of the method is addressed relevant practical examples such as a coupled antenna array serve to demonstrate the advantages of the proposed approach and to illustrate some of its limits

ensemble dynamics of intermittency and power law decay a spectral decomposition of the frobenius perron operator is constructed for one dimensional maps with intermittent chaos using the method of coherent states a technique using the spectral density function is applied to the the well known cusp map which generates weak type ii intermittency higher order corrections are obtained to the leading 1 t long time behavior of the x x autocorrelation

input impedance of a probe fed stacked circular microstrip antenna the input impedance of a microstrip antenna consisting of two circular microstrip disks in a stacked configuration driven by a coaxial probe is investigated a rigorous analysis is performed using a dyadic green s function formulation whereby the mixed boundary value problem is reduced to a set of coupled vector integral equations using the vector hankel transform galerkin s method is used in the spectral domain using two sets of disk current expansions one set is based on the complete set of orthogonal modes of the magnetic cavity and the other uses chebyshev polynomials with the proper edge condition for the disk currents an additional term is added to the disk current expansion to model the current properly in the vicinity of the probe disk junction the input impedance of the antenna including the probe self impedance is calculated as a function of the layered parameters and the ratio of the two disk radii disk current distributions and radiation patterns are presented the calculated results are shown to be in good agreement with experimental data

on the use of cavity modes as basis functions in the full wave analysis of printed antennas magnetic wall cavity mwc modes are often employed as basis functions in the method of moments mom full wave analysis of printed antennas especially in its spectral domain version where the use of entire domain basis functions is particularly convenient but in some cases the te solenoidal modes are not included here we investigate on the effect of this exclusion explaining the nature of the te tm coupling presenting criteria to determine the necessary number of modes and giving numerical results for annular patches especially relevant in this context

all angle negative refraction and ultra refraction for liquid surface waves in 2d phononic crystals we analyse transport properties of linear liquid waves propagating within arrays of immersed rigid circular cylindrical obstacles fixed to a rough bottom a comparison between multipole and finite element methods is drawn in the case of robin boundary conditions coupled with floquet bloch boundary conditions we find that the first band is concave yet nearly flat associated waves of small negative group velocity and it displays a cut off zero frequency stop band associated with a singular perturbation thanks to this anomalous dispersion in such fluid filled structures we achieve both ultra refraction and negative refraction for waves propagating at their surface potential applications lie in a omnidirective water antenna and a convergent flat water lens the latter one is demonstrated experimentally

green s tensors and lattice sums for electrostatics and elastodynamics we present expressions for the green9s tensors in terms of lattice sums for general two dimensional arrays in both elastostatics and elastodynamics we represent the lattice sums in rapidly convergent forms by fourier transform methods we compare the static lattice sums with recently published highly accurate values for square arrays we also establish rayleigh identities for elastostatic and elastodynamic problems generalizing previous work in electrostatics and electromagnetism the rayleigh identities may be used in studies of phononic band gaps

analysis of a plane wave excited subwavelength circular aperture in a planar conducting screen illuminating a multilayer uniaxial sample a spectral domain analysis is presented of a plane wave excited subwavelength circular aperture in a planar perfectly conducting screen in close proximity to a multilayer stack which may comprise uniaxially anisotropic slices the formulation employs the bethe bouwkamp aperture model for the general case of oblique incidence and it combines the hankel transform method with a transmission line network analogue of the medium which facilitates the inclusion of any number of material layers the electromagnetic fields are expressed in terms of one dimensional 1 d hankel transform integrals which are efficiently evaluated by a numerical quadrature along a suitably selected path with convergence acceleration by extrapolation sample numerical results are presented to demonstrate the validity of the method and its utility in the modeling of multilayer near field lenses and aperture type probes of near field optical microscopy

evaluation and regularization of phase modulated eisenstein series and application to double schlomilch type sums in the study of periodic media conditionally convergent series are frequently encountered and their regularization is crucial for applications we derive an identity that regularizes two dimensional phase modulated eisenstein series for all bravais lattices yielding physically meaningful values we also obtain explicit forms for the phase modulated series in terms of holomorphic eisenstein series enabling their closed form evaluation for important high symmetry lattices results are then used to obtain representations for the related double schlomilch type sums which are also given for all bravais lattices finally we treat displaced lattices of high symmetry expressing them in terms of origin centered lattices via geometric multi set identities these identities apply to all classes of two dimensional sums allowing sums to be evaluated over each constituent of a unit cell that possesses multiple inclusions in the study of periodic media conditionally convergent series are frequently encountered and their regularization is crucial for applications we derive an identity that regularizes two dimensional phase modulated eisenstein series for all bravais lattices yielding physically meaningful values we also obtain explicit forms for the phase modulated series in terms of holomorphic eisenstein series enabling their closed form evaluation for important high symmetry lattices results are then used to obtain representations for the related double schlomilch type sums which are also given for all bravais lattices finally we treat displaced lattices of high symmetry expressing them in terms of origin centered lattices via geometric multi set identities these identities apply to all classes of two dimensional sums allowing sums to be evaluated over each constituent of a unit cell that possesses multiple inclusions

two dimensional phase modulated lattice sums with application to the helmholtz green s function a class of two dimensional phase modulated lattice sums in which the denominator is an indefinite quadratic polynomial q is expressed in terms of a single exponentially convergent series of elementary functions this expression provides an extremely efficient method for the computation of the quasi periodic green s function for the helmholtz equation that arises in a number of physical contexts when studying wave propagation through a doubly periodic medium for a class of sums in which q is positive definite our new result can be used to generate representations in terms of functions which are significant generalisations of known results

the effect of the number of processors on the convergence of the parallel block jacobi method abstract we investigate the effect on the rate of convergence of a model of the asychronized parallel iteration method of allowing the number of processors to differ from the number of splittings under certain regularization assumptions we prove that decreasing the number of processors increases the convergence rate our interpretation of this result for the model is as follows increasing the number of processors means that each processor updates the global approximation in the host node with a local iteration which is computed from older global data hence the convergence rate is reduced to prove our results we develop theorems for comparison of the spectral radii for certain nonnegative matrices which are of interest in their own right we provide numerical examples to illustrate our results

hankel transform domain analysis of open circular microstrip radiating structures a full wave analysis of a circular disk conductor printed on a dielectric substrate backed by a ground plane is presented the method is based on the galerkin s method applied in the hankel transform domain and is numerically quite efficient several numerical examples are compared with available experimental data the agreement is found to be quite good and the validity of the present method is confirmed

lattice sums for the helmholtz equation a survey of different representations for lattice sums for the helmholtz equation is made these sums arise naturally when dealing with wave scattering by periodic structures one of the main objectives is to show how the various forms depend on the dimension d of the underlying space and the lattice dimension d lambda lattice sums are related to and can be calculated from the quasi periodic green s function and this object serves as the starting point of the analysis

an annular slot antenna on a dielectric half space the radiation properties of both singly and multiply fed annular slot antennas on a dielectric air interface have been analyzed using galerkin s method applied in the hankel transform domain the validity of our method has been confirmed through comparison with both theoretical and experimental results the magic slot configuration has also been studied the polarization diversity of this radiator makes it suitable for implementing a quasioptical balanced mixer

vector hankel transform analysis of annular ring microstrip antenna a rigorous analysis of the resonant frequency characteristics of an annular ring conductor printed on a dielectric substrate backed by a ground plane is presented the problem is cast into a set of vector dual integral equations by using vector hankel transform vht galerkin s method is then applied to compute the resonant frequencies of both transverse magnetic modes tm 11 and tm 12 of the microstrip antenna the real part of the resonant frequency shift of the tm 11 mode increases with increasing dielectric thickness in contrast to the tm 12 mode while the tm 11 mode has a high q it is a poor radiating mode the tm 12 mode is more suitable for antenna applications for a probe excitation the input impedance is obtained using single mode approximation for both the tm 11 and tm 12 modes it is shown that the tm 12 mode of the annular ring has a greater bandwidth than the tm 11 mode

large mode number eigenvalues of the prolate spheroidal differential equation we show that the eigenvalues of the prolate spheroidal differential equation of zeroth order g n c where c is the so called bandwidth or ellipticity parameter are well approximated for large mode number n by a single function w in the form g n c email protected c c where c p 2 n 1 2 w is defined implicitly as the root of an algebraic equation e min 1 m 1 2 m 1 2 1 w where e is the usual incomplete integral of the second kind and email protected 2 w with c c c w has a weak singularity at c 1 proportional to c 1 log c 1 plus iterated logarithms we give chebyshev series for w accurate for email protected 0

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

on solving first kind integral equations using wavelets on a bounded interval the conventional method of moments mom when applied directly to integral equations leads to a dense matrix which often becomes computationally intractable to overcome the difficulties wavelet bases have been used previously which lead to a sparse matrix the authors refer to mom with wavelet bases as wavelet mom there have been three different ways of applying the wavelet techniques to boundary integral equations 1 wavelets on the entire real line which requires the boundary conditions to be enforced explicitly 2 wavelet bases for the bounded interval obtained by periodizing the wavelets on the real line and 3 wavelet like basis functions furthermore only orthonormal on bases have been considered the present authors propose the use of compactly supported semi orthogonal so spline wavelets specially constructed for the bounded interval in solving first kind integral equations they apply this technique to analyze a problem involving 2d em scattering from metallic cylinders it is shown that the number of unknowns in the case of wavelet mom increases by m 1 as compared to conventional mom where m is the order of the spline function results for linear m 2 and cubic m 4 splines are presented along with their comparisons to conventional mom results it is observed that the use of cubic spline wavelets almost diagonalizes the matrix while maintaining less than 1 5 of relative normed error the authors also present the explicit closed form polynomial representation of the scaling functions and wavelets

spectral method of moments for planar structures with azimuthal symmetry an efficient method of moments formulation is proposed for the analysis of planar structures in the presence of azimuthally symmetric fields boundary integral equations are derived for tm and te polarizations assuming as a reference structure a metal plate with a finite number of concentric annular slots placed above a stratified medium the equations are discretized with a galerkin testing scheme in the fourier bessel domain adopting suitable sub domain basis functions that ensure a very rapid convergence of the involved spectral integrals numerical validation is provided by comparison with state of art simulation software considering planar antennas with omnidirectional radiation patterns in order to show the accuracy of the proposed formulation

application of numerical regularization options to the integral equation analysis of printed antennas in this letter a novel numerical technique is applied to the analysis of printed antennas the technique transforms the first kind electric field integral equation efie into a regularized second kind equation via extraction of two singular frequency independent operators and their numerical inversion two options are presented in which the inversion is based on the eigenfunctions of these singular operators that appear to be a generalization of the tm and te modes of a magnetic wall cavity coupled by the edge singularities the example of application shows favorable convergence properties

higher order interpolatory vector bases for computational electromagnetics low order vector basis functions compatible with the nedelec 1980 representations are widely used for electromagnetic field problems higher order functions are receiving wider application but their development is hampered by the complex procedures used to generate them and lack of a consistent notation for both elements and bases in this paper fully interpolatory higher order vector basis functions of the nedelec type are defined in a unified and consistent manner for the most common element shapes it is shown that these functions can be obtained as the product of zeroth order nedelec representations and interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties of the vector functions are discussed and expressions for the vector functions of arbitrary polynomial order are presented sample numerical results confirm the faster convergence of the higher order functions

the effect on bending waves by defects in pinned elastic plates abstract this paper presents solutions to a number of problems posed for the out of plane displacement of infinite thin elastic plates that are rigidly pinned in periodic configurations but that possess a finite number of defects we begin by considering a single one dimensional periodic array of pins we derive an analytic solution for the displacement produced by the forced oscillation of the central pin in the array and this solution is shown to be closely connected to the problem of scattering of plane waves by an array when a finite number of pins are removed attention then focuses on doubly periodic rectangular arrays of pinned points possessing defects central to approaching such problems is an understanding of bloch floquet waves in periodic arrays in the absence of defects and a simple method is described for computing the associated dispersion surfaces the solutions to three problems are then sought the trapping of localised waves by a finite number of missing pins trapping of waves by entire rows of missing pins and the wave radiation pattern due to the forcing of a single pin all problems are treated analytically using bounded green s functions for thin elastic plates a discrete fourier transform solution method and simple explicit and rapidly convergent evaluations of the one and two dimensional lattice sums that arise

source neutral green functions for periodic problems in electrostatics and their equivalents in electromagnetism we consider source neutral problems for periodic problems in electrostatics these may be used to derive an identity due to lord rayleigh entirely within the context of the unit cell and without use of reasoning based on contributions from charges at an outer boundary of the periodic system or employing conditionally convergent lattice sums we also consider the equivalent of source free green9functions for the helmholtz equation which are green9functions with their specular parts removed we show that as the wavenumber tends to zero the non specular dynamic green9functions tend with no divergences to the source neutral electrostatic green9function

analytical results for a class of sums involving bessel functions and square arrays we consider a class of sums involving bessel functions summed over the square array the sums involve the length of an arbitrary vector lying within the central unit cell we establish conditions under which the sums reduce to polynomial forms in possibly with a single logarithmic term in addition and show how these polynomials may be conveniently evaluated

static bloch sums for the square array we consider sums arising in doubly quasiperiodic green s functions for the laplace equation over the square array the sums are represented as fourier series and it is shown that the coefficients in the series can be obtained as polynomials we give expressions from which the first six array sums can be evaluated efficiently and accurate to better than one part in 107 over most of the brillouin zone

on the use of subsectional spline basis functions for efficient calculation of the rcs of a microstrip array of concentric annular rings over a wide frequency band the use of b splines in the radial direction is described for efficient calculation of the radar cross section rcs of a microstrip annular ring or array of concentric annular rings over a wide frequency band galerkin s method in the vector hankel transform vht domain is used to calculate the induced current density on the annular patches an algorithm is presented for a fast and accurate calculation of the scalar hankel transforms of b splines on an arbitrary nonuniform grid which plays an important role in the numerical calculation of the reaction integrals containing the scalar hankel transforms of b splines the accuracy and computational efficiency of the method and the convergence of the rcs results with respect to the number of segments along the radial direction are studied for some annular ring and concentric ring patches

maximal polytopic stability domains in parameter space for uncertain systems abstract some results on the stability and pole location of families of uncertain systems with characteristic polynomial coefficients affected by structured perturbations are presented the case in which the coefficients are affine in a set of system physical parameters is considered assuming that the parameters are subject to polytopic perturbations of a given structure for these cases which often arise in system stability robustness analysis as for example in the robustification of controllers for multivariable closed loop systems a procedure is given to estimate maximal stability polytopic regions in the space of parameters this result is also used to derive simple necessary and sufficient conditions for the discrete time stability of convex combinations of two polynomials

the distribution and moments of the smallest eigenvalue of a random matrix of wishart type abstract given a random rectangular m n matrix with elements from a normal distribution what is the distribution of the smallest singular value to pose an equivalent question in the language of multivariate statistics what is the distribution of the smallest eigenvalue of a matrix from the central wishart distribution in the null case we give new results giving the distribution as a simple recursion this includes the more difficult case when n m is an even integer without resorting to zonal polynomials and hypergeometric functions of matrix arguments with the recursion one can obtain exact expressions for the density and the moments of the distribution in terms of functions usually no more complicated than polynomials exponentials and at worst ordinary hypergeometric functions we further elaborate on the special cases when n m 0 1 2 and 3 and give a numerical table of the expected values for 2 m 25 and 0 n m 25

on the variation of the spectra of matrices abstract several distances between the spectra of two matrices are discussed and compared optimal bounds are given which enable us to reduce certain bounds on the eigenvalue variation of matrices by a factor of about two the results of bhatia and mukherjea and of bhatia and friedland on the eigenvalue variation are derived in an elementary way using results of henrici on the spectral variation

on the use of wavelet expansions in the method of moments em scattering an approach which incorporates the theory of wavelet transforms in method of moments solutions for electromagnetic wave interaction problems is presented the unknown field or response is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function which is often referred to as the mother wavelet the wavelet expansion can adaptively fit itself to the various length scales associated with the scatterer by distributing the localized functions near the discontinuities and the more spatially diffused ones over the smooth expanses of the scatterer the approach is thus best suited for the analysis of scatterers which contain a broad spectrum of length scales ranging from a subwavelength to several wavelengths using a galerkin method and subsequently applying a threshold procedure the moment method matrix is rendered sparsely populated the structure of the matrix reveals the localized scale fitting distribution long before the matrix equation is solved the performance of the proposed discretization scheme is illustrated by a numerical study of electromagnetic coupling through a double slot aperture

the use of vector transforms in solving some electromagnetic scattering problems it is shown that there exists a class of vector transforms and vector series expansions that are independent of their scalar counterparts they can be used to simplify the solutions of a class of vector electromagnetic scattering problems the applications are shown of vector fourier hankel and mathieu transforms and series expansions to the formal solutions of scattering by rectangular circular and elliptical disks and open ended waveguides the problems solved are canonical problems however more complex problems for applications in microwaves microstrip integrated circuits geophysical probing etc can be solved in a similar fashion

combinatorial identities for binary necklaces from exact ray splitting trace formulas based on an exact trace formula for a one dimensional ray splitting system we derive novel combinatorial identities for cyclic binary sequences polya necklaces

identities and parseval type relations for the l2 transform abstract in the present paper the authors introduce identities for the l 2 transform which yield a parseval type relationship for the l 2 transform the parseval type relationship proven in this paper give rise to useful corollaries for evaluating indefinite integrals of special functions some examples are also given as illustrations of the results presented here

rigorous analysis of a circular patch antenna excited by a microstrip transmission line boundary conditions are enforced on a portion of the microstrip feed line as well as the patch antenna the integral equation for the unknown currents on the antenna and feed is solved by applying the galerkin method of moments in the fourier transform domain the validity of the solution is tested by comparison of computed results with experimental data the theoretical treatment proves to be applicable to the most common feeding arrangements namely the direct edge feed and proximity coupling excitation in the latter case two layer substrates having distinct dielectric constants are studied the purpose of the study is to deduce for a given overall substrate thickness the smallest line ground plane separation for which a match of the radiator to the feed line is still possible the advantages of such a configuration are discussed

ludwig elsner and his contributions to core applied and numerical linear algebra ludwig elsner was bona on 17 january 1939 in grog strehlitz upper silesia in germany he studied mathematics physics and astronomy at the universities of hamburg and freiburg and received his diploma in mathematics in 1963 at the university of hamburg as a member of the lively and inspiring group of lothar collatz in hamburg he worked on his ph d while holding a position at the computing center of the university of hamburg he received his ph d in 1965 and became an assistant professor at collatz institute of applied mathematics at the university of hamburg for six years during this period he spent one year 1968 1969 as senior officer at the csir in pretoria south africa in 1971 ludwig eisner became associate professor at the university of erlangen where he worked at the institute for applied mathematics until 1976 since 1976 he has been a full professor at the university of bielefeld where he has built up the numerical analysis group among many other activities in bielefeld he has twice been chairman of the department of mathematics and has planned and formed the numerical analysis group of the sonderforschungsbereich diskrete strukturen in der mathematik which since 1989 has attracted many specialists in linear algebra and numerical linear algebra to work with eisner in bielefeld numerous publications prove the success of these collaborative efforts

full wave spectral analysis and design of annular patch antenna with electromagnetically coupled microstrip feed line this paper presents a full wave analysis and the ensuing design considerations of the annular patch antenna fed by an electromagnetically coupled microstrip line the numerical analysis employs the spectral domain version of the integral equation with the method of moments formulation the basis functions on the ring patch are the eigenmodes of the corresponding magnetic wall cavity and subsectional rooftop functions are employed on the access line both tm and te modes are used along with more efficient collective solenoidal modes mode sorting criteria are given to ensure uniform convergence efficient schemes are presented for the calculation of the spectral domain reaction integrals along with criteria to avoid calculation of negligible mode to mode couplings based on the spectral analysis of the matrix condition number very good agreement is shown with measured data and design considerations are given for matching the radiator

on convexity properties of the spectral radius of nonnegative matrices abstract elementary matrix theoretic proofs are given for the following well known results r d max re an eigenvalue of a d and s d ln e d a are convex here d is diagonal a a nonnegative n n matrix and the spectral radius

lattice sums and the two dimensional periodic green s function for the helmholtz equation many algorithms that are currently used for the solution of the helmholtz equation in periodic domains require the evaluation of the green s function g x x0 the fact that the natural representat

resonant modes of a class of microstrip rings in a dielectric material a non galerkin method based on spline harmonic basis and testing functions is used to analyze the resonant characteristics resonant frequency quality factor and radiation pattern of a new class of microstrip rings our rings which we call single harmonic rings are defined by adding a perturbative single harmonic term to the constant circular ring equation in the polar coordinates this definition contains various ring shape geometries including square and triangular rings with smooth corners it is shown that the application of the spline harmonic basis and testing functions in the spectral domain leads to integrals with rapidly decaying integrands in the radial spectral direction and provides relatively smooth functions of the angular spectral variable therefore the numerical calculation of the system matrix elements can be performed easily in the polar spectral coordinate system mode families are defined based on coupled harmonics and a mode numbering scheme is introduced numerical results are produced for a range of ring parameters and variations of the resonant characteristics are investigated

an optimal bound for the spectral variation of two matrices abstract we establish a bound for the spectral variation of two complex n n matrices a b in terms of a b and a b here denotes the spectral norm it is always better than a bound previously given by bhatia and friedland and it is optimal we describe the set of pairs a b for which the bound is attained

schlomilch series and grating sums we consider sums over the set of positive integers relevant to construction of periodic green s functions for diffraction gratings and similar problems and provide a general formula for a combination of bessel functions of complex order and complex powers of distance from the origin this general formula is investigated in a number of particular cases and in particular we provide expressions which enable sums of functions with neumann series to be re expressed as combinations of hypergeometric series we also investigate sums of neumann functions of integer order using analytic continuation techniques to provide formulae for their evaluation which we demonstrate are accurate and efficient in both the high and low frequency regions we also exhibit sums which may be evaluated analytically and recurrence formulae linking sums

perturbation and interlace theorems for the unitary eigenvalue problem abstract two aspects of the perturbation problem for the eigenvalues of a unitary matrix u are treated firstly analogues of the hoffman wielandt theorem and a weyl type theorem proved by bhatia and davis are derived which are based on a different measure of the distance of spectra using a suitable parametrization of the unit circle by an angle the new results are called tangent theorems in contrast to the first mentioned well known results which are sine theorems moreover we illuminate the unknown minimizing permutations in the above weyl type theorems with respect to their angles the eigenvalues of u and the perturbed matrix are naturally ordered on the unit circle counterclockwise after a point is cut on the unit circle we prove a well known open conjecture there exists a cutting point such that the weyl type theorems both sine and tangent are true when the ordered eigenvalues of u and are paired with each other secondly the cauchy interlacing theorem for hermitian matrices is generalized it is shown that certain modified principal submatrices of u called the modified kth leading principal submatrices have the property that their eigenvalues interlace those of u finally we discuss block reflectors appearing in the description of the modified principal submatrices and generalize a result of schreiber and parlett

oblique propagation of electromagnetic and elastic waves for an array of cylindrical fibres this paper presents analysis of electromagnetic and elastodynamic waves propagating through a doubly periodic array of cylindrical channels in oblique incidence a new method based on a multipole scattering approach has been proposed to reduce these spectral problems for partial differential equations to certain algebraic problems of the rayleigh type we obtain a formulation in terms of an eigenvalue problem that enables us to construct the high order dispersion curves and to study both photonic and phononic band gap structures in oblique incidence we also address the question of a singular perturbation induced by the conical incidence and discuss some effective properties for ferromagnetic photonic crystal fibres in the long wavelength limit

recursive integral time extrapolation methods for waves a comparative review abstractwe compared several families of algorithms for recursive integral time extrapolation rite algorithms for waves in isotropic and anisotropic media these methods allow simulating accurate wave extrapolation with little numerical dispersion even when using larger time steps than are usually possible for conventional finite difference methods these various rite algorithms all share the use of mixed space wavenumber domain operators derived from fourier integral solutions of single mode wave equations we evaluated a taxonomy for rite methods based on how they approximated the influence of medium heterogeneity one family of methods uses mixed domain series expansions to provide accurate approximations to heterogeneous extrapolators even for large time steps we compared several methods for deriving coefficients for such series approximations another family of methods uses interpolation between different homogeneous extrapolations to approximate heterogeneous time extrapolation such methods can b

fast solution methods in electromagnetics various methods for efficiently solving electromagnetic problems are presented electromagnetic scattering problems can be roughly classified into surface and volume problems while fast methods are either differential or integral equation based the resultant systems of linear equations are either solved directly or iteratively a review of various differential equation solvers their complexities and memory requirements is given the issues of grid dispersion and hybridization with integral equation solvers are discussed several fast integral equation solvers for surface and volume scatterers are presented these solvers have reduced computational complexities and memory requirements

vector valued wavelets with triangular support for method of moments applications for a more flexible method of moments analysis of planar circuits the theory of wavelet transforms is expanded to two dimensional vector valued functions with triangular support the elementary cells being composed of right isosceles triangles efficient scaling and matrix sparsity are demonstrated with two suitable examples

on the convergence of asynchronous paracontractions with application to tomographic reconstruction from incomplete data abstract convergence of iterative processes in c k of the form x i r i j i x 1 r i 1 1 p j i x i where j i 1 2 n i 1 2 is analyzed it is shown that if the matrices p 1 p n are paracontracting in the same smooth strictly convex norm and if the sequence j i i 1 has certain regularity properties then the above iterates converge this result implies the convergence of a parallel asynchronous implementation of the algebraic reconstruction technique art algorithm often used in tomographic reconstruction from incomplete data

the hilbert transform and hermite functions a real variable proof of the l2 isometry abstract a proof of the fact that the hilbert transform can be extended as an isometry to l 2 is obtained by real variable methods using the hermite functions

a new exact integration method for the drucker prager elastoplastic model with linear isotropic hardening abstract this paper presents the exact stress solution of the non associative drucker prager elastoplastic model governed by linear isotropic hardening rule the stress integration is performed under constant strain rate assumption and the derived formulas are valid in the setting of small strain elastoplasticity theory based on the time continuous stress solution a complete discretized stress updating algorithm is also presented providing the solutions for the special cases when the initial stress state is located in the apex and when the increment produces a stress path through the apex explicit expression for the algorithmically consistent tangent tensor is also derived in addition a fully analytical strain solution is also derived for the stress driven case using constant stress rate assumption in order to get a deeper understanding of the features of these solutions two numerical test examples are also presented

quantum tomography phase space observables and generalized markov kernels we construct a generalized markov kernel which transforms the observable associated with the homodyne tomography into a covariant phase space observable with a regular kernel state illustrative examples are given in the cases of a schrodinger cat kernel state and the cahill glauber s parametrized distributions also we consider an example of a kernel state when the generalized markov kernel cannot be constructed

nonnegative matrices zero patterns and spectral inequalities we give an inequality for the spectral radius of positive linear combinations of tuples of nonnegative matrices linked in a certain way from this several observations are deduced including the perturbation inequality a t sgn a a t sgn a in which sgn denotes the signum functions applied componentwise this was motivated in part by our work on characterizing the functions ff such that f a1 ap f a1 ap in which f is applied componentwise on the left to be published elsewhere one of our observations the question of studying the combinatorial structure of the cone algebra of nonnegative matrices with given left and right perron vectors

hankel transform domain analysis of dual frequency stacked circular disk and annular ring microstrip antennas a theoretical and numerical analysis of the dual frequency stacked circular disk and annular ring microstrip antennas is discussed the problem is formulated in the hankel transform domain first the green s function is derived relating the transformed electric surface currents on the patches and the transformed tangential electric field components on the substrates galerkin s method is used with parseval s relation for hankel transformation to solve for the resonant frequencies and the unknown currents the far zone radiation patterns are expressed in terms of the transforms of the currents numerical results obtained for the resonant frequencies and radiation patterns are found to be in excellent agreement with the experimental data available in the literature

analysis of stacked microstrip patches with a mixed potential integral equation a method based on the mixed potential integral equation for the analysis of flat microstrip antennas in a double layer substrate is presented the method is used to compute the input impedance of a stacked patch configuration this structure permits a larger bandwidth and may also provide dual frequency operation the green s functions are discussed in detail and numerical results are obtained for the propagation constant of the dominant surface wave theoretical and experimental results are compared for a dual frequency and a broadband stacked patch antenna theoretical results for the input impedance are in good agreement with measurements the difference between theoretical and experimental results for the resonant frequency is less than 4 5 in all cases

input impedance of annular ring microstrip antennas with a dielectric cover a theoretical and numerical analysis of the annular ring microstrip antenna with a dielectric cover is performed the problem is formulated in the hankel transform domain taking a coaxial feed into consideration the integral equations for the surface current density on the patch are derived galerkin s method is used to solve for the surface current density and a stationary formula for the input impedance is obtained numerical results showing the effects of a dielectric cover on the tm sub 12 mode of the annular ring are given it is found that the dielectric cover reduces the resonant frequency decreases the resonant resistance and increases the impedance bandwidth

wavelet approximations for first kind boundary integral equations on polygons an elliptic boundary value problem in the interior or exterior of a polygon is transformed into an equivalent first kind boundary integral equation its galerkin discretization with n degrees of freedom on the boundary with spline wavelets as basis functions is analyzed a truncation strategy is presented which allows to reduce the number of nonzero elements in the stiffness matrix from o n 2 to o n log n entries the condition numbers are bounded independently of the meshwidth it is proved that the compressed scheme thus obtained yields in o n log n 2 operations approximate solutions with the same asymptotic convergence rates as the full galerkin scheme in the boundary energy norm as well as in interior points numerical examples show the asymptotic error analysis to be valid already for moderate values of n

point vortex dynamics a classical mathematics playground the idealization of a two dimensional ideal flow as a collection of point vortices embedded in otherwise irrotational flow yields a surprisingly large number of mathematical insights and connects to a large number of areas of classical mathematics several examples are given including the integrability of the three vortex problem the interplay of relative equilibria of identical vortices and the roots of certain polynomials addition formulas for the cotangent and the weierstras function projective geometry and other topics the hope and intent of the article is to garner further participation in the exploration of this intriguing dynamical system from the mathematical physics community

evaluation of phase modulated lattice sums an exact evaluation of two dimensional phase modulated lattice sums of the form exp i g x g 2 is presented in terms of the jacobian theta functions the result generalizes the identity derived by m l glasser j math phys 15 188 1974 to allow for evaluation on nonrectangular lattices the generalized identity is also applied to a problem in vortex dynamics

analysis of a circular microstrip disk antenna with a thick dielectric substrate the problem of a circular microstrip disk excited by a probe is solved using rigorous analysis the disk is assumed to have zero thickness and the current on the probe is taken to be uniform using vector hankel transforms the problem is formulated in terms of vector dual integral equations from which the unknown current can be solved for due to the singular nature of the current distribution arising from probe excitation the direct application of galerkin s basis function expansion method gives a slowly convergent result therefore the singular part of the current is removed since the singularity is known a priori the unknown current to be solved for is then regular and tenable to galerkin s method of analysis it is shown that this analysis agrees with the single mode approximation when the dielectric substrate layer is thin and that it deviates from the single mode approximation when the substrate layer is thick excellent agreement of both the computed real and imaginary parts of the input impedance with experimental data is noted the radiation patterns and the current distributions on the disk are also presented

singular values doubly stochastic matrices and applications abstract the hadamard square of any square matrix a is bounded above and below by some doubly stochastic matrices times the square of the largest and the smallest singular values of a applications to graphs permanents and eigenvalue perturbations are discussed

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed