lie properties of symmetric elements in group rings abstract let be an involution of a group g extended linearly to the group algebra kg we prove that if g contains no 2 elements and k is a field of characteristic p 2 then the symmetric elements of kg are lie nilpotent lie n engel if and only if kg is lie nilpotent lie n engel

itd double edge diffraction for complex source beam illumination a new high frequency incremental theory of diffraction itd formulation for the double diffraction by metallic wedges when illuminated by complex source points csp is provided the main motivation is the extension of the class of problems that can be studied using asymptotic i e ray based and incremental methods by providing a double diffraction description for csp which are considered because they are efficient to analyze electrically large structures the new formulation provides an accurate asymptotic description of the interaction between two edges in an arbitrary configuration including slope diffraction contributions advantages of the itd formulation for csp illumination include avoiding the typical ray caustic impairments of the gtd utd ray techniques and not requiring ray tracing in complex space numerical results are presented and compared to a method of moments analysis to demonstrate the accuracy of the solution

group identities on symmetric units abstract let f be an infinite field of characteristic different from 2 g a group and an involution of g extended by linearity to an involution of the group algebra fg here we completely characterize the torsion groups g for which the symmetric units of fg satisfy a group identity when is the classical involution induced from g g 1 g g this result was obtained in a giambruno s k sehgal a valenti symmetric units and group identities manuscripta math 96 1998 443 461

direct sampling method for retrieving small perfectly conducting cracks abstract in this paper direct sampling method is considered for determining the location of a set of small linear perfectly conducting cracks from the collected far field data corresponding to an incident field to show the feasibility of the direct sampling method this study proves that the indicator function of the direct sampling method can be represented by the bessel function of order zero and the crack lengths the results of the numerical simulations are shown to support the fact that the imaging performance is highly dependent on the crack lengths to explain the fact that the imaging performance is highly dependent on the rotation of the cracks the direct sampling method is further analyzed by establishing a representation using bessel functions of orders zero and one based on the derived representation of indicator function we design improved direct sampling methods by applying incident fields with multiple directions and multiple frequencies corresponding analysis of indicator functions and simulation results are shown for demonstrating the effectiveness and improvements

a uniform double diffraction coefficient for a pair of wedges in arbitrary configuration an analytic closed form solution is presented for the double diffraction at a pair of arbitrarily placed wedges that is suitable to be used in a uniform theory of diffraction utd ray description framework here the particular assumption present in all the past literature that the two diffracting edges are coplanar is removed the doubly diffracted dd field at a pair of wedges is constructed via spectral synthesis such a procedure provides a double spectral integral representation of the dd field that is asymptotically evaluated by resorting to transition functions typical in double diffraction problems that can be expressed in terms of generalized fresnel integrals the final expression is arranged in the typical utd fashion and contains a uniform double diffraction dyadic coefficient the dd field behavior is analyzed in its transition regions to show how the dd field smoothly compensates for the total field discontinuities occurring at shadow boundaries where a singly diffracted field from a wedge is shadowed by the other wedge numerical examples are provided to verify such analysis and to test the accuracy of our utd ray description against method of moments full wave results

experimental and theoretical validation for the incremental theory of diffraction experimental and theoretical approaches to verify the validity of the incremental theory of diffraction itd are considered after providing a simple recipe for the application of the itd three geometries are examined for its validation first the itd formulation of the diffraction from a perfect electric conductor pec straight wedge is compared with the uniform theory of diffraction utd and with measurement results second the itd formulation of the diffraction from a pec disc is compared with measurement results and with the exact solution of a boundary value problem involving oblate spheroidal functions third the itd formulation of the diffraction from a hole in a pec plane is compared with the exact solution of a boundary value problem involving oblate spheroidal functions in particular this is the first time that itd results for diffraction from the disc and hole in a plane geometries are validated using exact solutions computed at a caustic in all cases examined very good agreement is found

analysis of music type imaging functional for single thin electromagnetic inhomogeneity in limited view inverse scattering problem this study analyzes the well known multiple signal classification music algorithm to identify unknown support of thin penetrable electromagnetic inhomogeneity from scattered field data collected within the so called multi static response matrix in limited view inverse scattering problems the mathematical theories of music are partially discovered e g in the full view problem for an unknown target of dielectric contrast or a perfectly conducting crack with the dirichlet boundary condition transverse magnetic tm polarization and so on hence we perform further research to analyze the music type imaging functional and to certify some well known but theoretically unexplained phenomena for this purpose we establish a relationship between the music imaging functional and an infinite series of bessel functions of integer order of the first kind this relationship is based on the rigorous asymptotic expansion formula in the existence of a thin inhomogeneity with a smooth supporting curve various results of numerical simulation are presented in order to support the identified structure of music although a priori information of the target is needed we suggest a least condition of range of incident and observation directions to apply music in the limited view problem

incremental fringe formulation for a complex source point beam expansion an incremental fringe formulation iff for the scattering by large metallic objects illuminated by electromagnetic complex source points csps is presented this formulation has two main advantages first it improves the accuracy of physical optics po computations by removing spurious scattered field contributions and at the same time substituting them with more accurate incremental theory of diffraction field contributions second it reduces the complexity of po computations because it is applicable to arbitrary illuminating fields represented in terms of a csp beam expansion the advantage of using csps is mainly due to their beam like properties truncation of negligible beams lowers the computational burden in the determination of the solution explicit dyadic expressions of incremental fringe coefficients are derived for wedge shaped configurations comparisons between the proposed method po and the method of moments mom are provided

group rings whose unitary units are nilpotent abstract let f be a field of characteristic different from 2 and g a group under the classical involution on the group ring fg we show that if fg is modular then the group of unitary units of fg is nilpotent if and only if the entire unit group is nilpotent we also demonstrate that this does not necessarily hold if fg is not modular but it is still true if f is algebraically closed

a two dimensional helmhotlz equation solution for the multiple cavity scattering problem here considered is the mathematical analysis and numerical computation of the electromagnetic wave scattering by multiple cavities embedded in an infinite ground plane above the ground plane the space is filled with a homogeneous medium while the interiors of the cavities are filled with inhomogeneous media characterized by variable permittivities by introducing a new transparent boundary condition on the cavity apertures the multiple cavity scattering problem is reduced to a boundary value problem of the two dimensional helmholtz equation imposed in the separated interior domains of the cavities the existence and uniqueness of the weak solution for the model problem is achieved via a variational approach a block gauss seidel iterative method is introduced to solve the coupled system of the multiple cavity scattering problem where only a single cavity scattering problem is required to be solved at each iteration numerical examples demonstrate the efficiency and accuracy of the proposed method

direct sampling method for identifying magnetic inhomogeneities in limited aperture inverse scattering problem abstract the direct sampling method dsm in limited aperture inverse scattering problems for transverse electric te polarization is considered based on the asymptotic expansion formula in the presence of small targets we demonstrate that the indicator function of dsm can be represented by an infinite series of bessel functions of integer order and correspondingly examine various properties of dsm simulation results with noisy data are created to support theoretical results based on the identified structure of the indicator function we design a new indicator function of dsm analyze its mathematical structure and generate simulation results to demonstrate its effectiveness and improvement

imaging schemes for perfectly conducting cracks we consider the problem of locating perfectly conducting cracks and estimating their geometric features from multistatic response matrix measurements at a single or multiple frequencies a main objective is to design specific crack detection rules and to analyze their receiver operating characteristics and the associated signal to noise ratios in this paper we introduce an analytic framework that uses asymptotic expansions which are uniform with respect to the wavelength to crack size ratio in combination with a hypothesis test based formulation to construct specific procedures for detection of perfectly conducting cracks a central ingredient in our approach is the use of random matrix theory to characterize the signal space associated with the multistatic response matrix measurements we present numerical experiments to illustrate some of our main findings

symmetric units satisfying a group identity abstract let k be an infinite field of characteristic p 2 g a locally finite group and kg its group algebra let kg kg denote the k linear extension of an involution defined on g in this paper we prove under some assumptions that if the set of symmetric units of kg satisfies a group identity then kg satisfies a polynomial identity moreover in case the prime radical of kg is nilpotent we characterize the groups for which the symmetric units satisfy a group identity

a multilevel sampling method for detecting sources in a stratified ocean waveguide in the reconstruction process of sound waves in a 3d stratified waveguide a key technique is to effectively reduce the huge computational demand in this work we propose an efficient and simple multilevel reconstruction method to locate the accurate position of a point source in a stratified ocean the proposed method can be viewed as a direct sampling method since no solutions of optimizations or linear systems are involved the novel method exhibits several strengths fast convergence robustness against noise advantages in computational complexity and applicability for a very small number of receivers

1d inverse problem in diffusion based optical tomography using iteratively regularized gauss newton algorithm in this paper we investigate an one dimensional inverse problem in diffusion based optical tomography using iteratively regularized gauss newton irgn algorithm for ill posed nonlinear problems we devise a stable reconstruction algorithm for the inverse problem using iterative regularization with armijo goldstein wolf agw type line search strategy we demonstrate the efficacy of the irgn combined with agw by reconstructing the scattering parameter relevant to the inverse problem in optical tomography

the groups of order 256 abstract building on earlier work a new method for generating descriptions of p groups is developed the theory and implementation of this method are described and its application in determining the 56 092 groups of order 256 is outlined

generalized foldy lax formulation we present a method for numerical wave propagation in a heterogeneous medium the medium is defined in terms of an extended scatterer or target which is surrounded by many small scatterers by extending the classic foldy lax formulation we developed an efficient algorithm for numerical wave propagation in two dimension in the method that we set forth multiple scattering among the point scatterers and the extended target is fully taken into account via a boundary integral formulation coupled with the foldy lax formulation this formulation forms the basis for our numerical procedure

the limited aperture problem of inverse acoustic scattering dirichlet boundary conditions let d be a bounded simply connected domain in the plane and let f theta k underset raise0 3em hbox smash scriptscriptstyle thicksim alpha l be the far field pattern arising from the scattering of a time harmonic acoustic plane wave u l underset raise0 3em hbox smash scriptscriptstyle thicksim x exp ik underset raise0 3em hbox smash scriptscriptstyle thicksim x cdot underset raise0 3em hbox smash scriptscriptstyle thicksim alpha l where underset raise0 3em hbox smash scriptscriptstyle thicksim alpha l is a unit vector and k is the wave number and the time harmonic factor e i omega t has been factored out it is assumed in addition that the total field satisfies homogeneous dirichlet boundary conditions on partial d in this paper a method is presented for recovering partial d given the far field patterns f theta k underset raise0 3em hbox smash scriptscriptstyle thicksim alpha l

simple components and central units in group algebras abstract let g be a finite group berman dokl akad nauk 106 1956 767 and witt j reine angew math 190 1952 231 evaluate independently the number of simple components of the group algebra fg when f is a field of characteristic 0 in this paper we extend this result to fields of arbitrary characteristic which does not divide the order of g we also compute the rank of the group of the central units of z g and obtain an alternative proof of a well known result of ritter and sehgal

multi frequency subspace migration for imaging of perfectly conducting arc like cracks in full and limited view inverse scattering problems multi frequency subspace migration imaging techniques are usually adopted for the non iterative imaging of unknown electromagnetic targets such as cracks in concrete walls or bridges and anti personnel mines in the ground in the inverse scattering problems it is confirmed that this technique is very fast effective robust and can not only be applied to full but also to limited view inverse problems if a suitable number of incidents and corresponding scattered fields are applied and collected however in many works the application of such techniques is heuristic with the motivation of such heuristic application this study analyzes the structure of the imaging functional employed in the subspace migration imaging technique in two dimensional full and limited view inverse scattering problems when the unknown targets are arbitrary shaped arc like perfectly conducting cracks located in the two dimensional homogeneous space in contrast to the statistical approach based on statistical hypothesis testing our approach is based on the fact that the subspace migration imaging functional can be expressed by a linear combination of the bessel functions of integer order of the first kind this is based on the structure of the multi static response msr matrix collected in the far field at nonzero frequency in either transverse magnetic tm mode dirichlet boundary condition or transverse electric te mode neumann boundary condition the investigation of the expression of imaging functionals gives us certain properties of subspace migration and explains why multi frequency enhances imaging resolution in particular we carefully analyze the subspace migration and confirm some properties of imaging when a small number of incident fields are applied consequently we introduce a weighted multi frequency imaging functional and confirm that it is an improved version of subspace migration in tm mode various results of numerical simulations performed on the far field data affected by large amounts of random noise are similar to the analytical results derived in this study and they provide a direction for future studies

some classes of semisimple group and loop algebras over finite fields abstract we determine the structure of the semisimple group algebra of certain groups over the rationals and over those finite fields where the wedderburn decompositions have the least number of simple components we apply our work to obtain similar information about the loop algebras of indecomposable ra loops and to produce negative answers to the isomorphism problem over various fields

an efficient algorithm for the generalized foldy lax formulation consider the scattering of a time harmonic plane wave incident on a two scale heterogeneous medium which consists of scatterers that are much smaller than the wavelength and extended scatterers that are comparable to the wavelength in this work we treat those small scatterers as isotropic point scatterers and use a generalized foldy lax formulation to model wave propagation and capture multiple scattering among point scatterers and extended scatterers our formulation is given as a coupled system which combines the original foldy lax formulation for the point scatterers and the regular boundary integral equation for the extended obstacle scatterers the existence and uniqueness of the solution for the formulation is established in terms of physical parameters such as the scattering coefficient and the separation distances computationally an efficient physically motivated gauss seidel iterative method is proposed to solve the coupled system where only a linear system of algebraic equations for point scatterers or a boundary integral equation for a single extended obstacle scatterer is required to solve at each step of iteration the convergence of the iterative method is also characterized in terms of physical parameters numerical tests for the far field patterns of scattered fields arising from uniformly or randomly distributed point scatterers and single or multiple extended obstacle scatterers are presented

music type imaging of perfectly conducting cracks in limited view inverse scattering problems abstract although standard multiple signal classification music algorithm has been considered a promising non iterative imaging technique for cracks its application is restricted to the full view inverse scattering problems many experimental results revealed that music can be applied to the imaging of perfectly conducting cracks with small length in limited view inverse scattering problem on the other hand music is not applicable for imaging of extended cracks in limited view problems but the reason behind this restricted application has not been theoretically investigated this gave an impetus for this study to attempt to identify the structure of music type algorithm that appears in the limited view inverse scattering problems by establishing a relationship between music and bessel functions of integer order of the first kind some numerical experiments are illustrated to support the identified structure of music

direct sampling method for diffusive optical tomography in this work we are concerned with the diffusive optical tomography dot problem in the case when only one or two pairs of cauchy data are available we propose a simple and efficient direct sampling method to locate inhomogeneities inside a homogeneous background and solve the dot problem in both full and limited aperture cases this new method is easy to implement and less expensive computationally numerical experiments demonstrate its effectiveness and robustness against noise in the data this provides a new promising numerical strategy for the dot problem

modified edge representation mer consisting of keller s diffraction coefficients with weighted fringe waves and its localization for evaluation of corner diffraction equivalent edge currents eecs for high frequency diffraction analysis are intermediate concepts between ray theory and wave optics physical optics po the methods of eec present some ambiguity in the definition of currents at general edge points which do not satisfy the diffraction law modified edge representation mer is a unique concept for a complete definition of eec with simple and classical keller type knife edge diffraction coefficients although singularities in the definition of eec exist the line integration of mer eec results uniform and accurate fields everywhere including geometrical boundaries except for the case of grazing incidence where reflection and incidence shadow boundaries rsb and isb are close to each other in this paper fringe wave fw part of mer eec is modified by introducing the weighting in terms of fresnel zone number fzn distance from the reflection point to improve the accuracy at and near shadow boundaries even in grazing incidence next the corner diffraction a contribution coming from edge point which does not satisfy the diffraction law is extracted in mer by introducing another weighting function using the fzn distance from scattering centers on edge its remarkable accuracy fully validates mer eecs at general edge points the dipole wave scattering from flat square and triangular plates are discussed with numerical examples

incremental diffraction coefficients for source and observation at finite distances from an edge recently an incremental theory of diffraction itd has been introduced which provides a self consistent highfrequency description of a wide class of scattering phenomena within a unified framework explicit expressions of the incremental diffracted field contributions have been obtained for a plane wave illumination of wedge shaped configurations and observation points at a finite distance from the incremental point in this paper this method is extended to treat the case when both the source and the observation point are at finite distance from the local incremental point along the edge to this end a spectral domain approach is used to derive a spectral integral representation for the incremental field contribution the latter is asymptotically evaluated to find high frequency closed form expressions which are uniformly valid at any incidence and observation aspects including caustics and shadow boundaries of the corresponding ray field description the expressions of the incremental diffraction coefficients explicitly satisfy reciprocity numerical results are presented and compared with those obtained from different techniques

incremental theory of diffraction a new improved formulation in this paper a general systematic procedure is presented for defining incremental field contributions they may provide effective tools to describe a wide class of scattering and diffraction phenomena at any aspect within a unitary self consistent framework this procedure is based on a generalization of the incremental theory of diffraction itd localization process for uniform cylindrical local canonical problems with elementary source illumination and arbitrary observation aspects in particular it is shown that the spectral integral formulation of the exact solution for the local canonical problem may also be represented as a spatial integral convolution along the longitudinal coordinates of the cylindrical configuration its integrand is then directly used to define the relevant incremental field contribution for the sake of convenience but without loss of generality this procedure is illustrated for the case of local wedge configurations also a specific suitable asymptotic analysis is developed to derive new closed form high frequency expressions from the spectral integral formulation these expressions for the incremental field contributions explicitly satisfy reciprocity and are applicable at any incidence and observation aspect this generalization of the itd localization process together with its more accurate asymptotic analysis provides a definite improvement of the method