polar integration for exact space time quadrature in time domain integral equations a space time polar quadrature technique for numerical integration of green s function interactions in time domain integral equations is presented the method transforms 2 d surface space time integrals associated with vector and scalar potentials to a 1 d integral that is performed using gauss legendre integration the advantage of the presented technique compared to standard 2 d gaussian quadrature is that time delays between each section of the source basis function and the observation point are accounted for exactly in an analytic manner this ensures highly accurate temporal behavior of the green s function interactions thereby contributing to the stability of the overall time domain integral equations

immanants of combinatorial matrices abstract the arbitrary immanants of three matrices whose determinants are known to be generating functions for sets of combinatorial objects are examined combinatorial interpretations are given for the immanants of the matrix tree matrix and a special case of the jacobi trudi matrix these allow us to deduce immediately the nonnegativity of the coefficients in the expansion of the immanants a conjecture is made about the nonnegativity of coefficients of the expansion of the immanant of the jacobi trudi matrix in the general case this nonnegativity result is seen to fail for the hankel matrix and combinatorial reasons for this failure are given all results can be translated into statements about the nonnegativity of schur function expansions for the related symmetric functions

a linear time algorithm for obtaining the convex hull of a simple polygon in this paper a linear time algorithm is described for finding the convex hull of a simple i e non self intersecting polygon

electromagnetic scattering from 3 d curved dielectric bodies using time domain integral equations a boundary integral equation bie approach is developed to calculate transient scattering from dielectric bodies the treatment is directly in terms of the e and h fields rather than magnetic and electric currents it employs curvilinear quadratic modeling which allows accurate representation of arbitrarily shaped curved bodies the treatment is isoparametric with the same quadratic representation of the spatial field variation and with the temporal variation modeled by similar quadratic elements integration employs high order gaussian quadrature with special treatment of the singular and hypersingular integrals that arise the treatment is implicit requiring the solution of a sparse matrix equation at each timestep this adds only trivially to the cost at each timestep and by freeing the timestep from the constraint that it be smaller than the smallest nodal spacing can greatly reduce the number of timesteps that must be employed additionally it produces stable results without resort to the averaging processes proposed elsewhere example calculations of scattering from a sphere a cube and an almond are presented and compared with earlier published transient results and with results from a frequency domain treatment good agreement and improved accuracy is found

temperley lieb pfaffinants and schur q positivity conjectures we study pfaffian analogues of immanants which we call pfaffinants our main object is the tl pfaffinants which are analogues of rhoades and skandera s tl immanants we show that tl pfaffinants are positive when applied to planar networks and explain how to decompose products of complementary pfaffians in terms of tl pfaffinants we conjecture in addition that tl pfaffinants have positivity properties related to schur q functions

a novel integration method for weak singularity arising in two dimensional scattering problems in this paper we introduce a novel mechanical quadrature method for an efficient solution of weakly singular integral equations arising in two dimensional electromagnetic scattering problems this approach is based on and adapted from the recently proposed mechanical quadrature methods in extrapolation algorithms for solving mixed boundary integral equations of the helmholtz equation by mechanical quadrature methods siam j sci comput vol 31 4115 4129 2009 we report experiments for solving tm polarized induced currents and scattered fields to show its superiority to the classical method of moments when accuracy is a concern moreover additional numerical experiments made with an extrapolation algorithm suggest that the accuracy of the present method can be further improved dramatically by means of the extrapolation algorithm to some extent

inequalities and identities for generalized matrix functions abstract let be a character on the symmetric group s n and let a a ij be an n by n matrix the function d a s n n t 1 a t t is called a generalized matrix function if is an irreducible character then d is called an immanent for example if is the alternating character then d is the determinant and if 1 then d is called the permanent denoted per suppose that a is positive semidefinite hermitian we prove that the inequality 1 id d a per a holds for a variety of characters including the irreducible ones corresponding to the partitions n 1 1 and n 2 1 1 of n the main technique used to prove these inequalities is to express the immanents as sums of products of principal subpermanents these expressions for the immanents come from analogous expressions for schur polynomials by means of a correspondence of d e littlewood

on the generalization of directfn for singular integrals over quadrilateral patches a set of fully numerical algorithms for evaluating the 4 d singular integrals arising from galerkin surface integral equation methods over conforming quadrilateral meshes is presented this paper is an extension of directfn which was recently developed for the case of triangular patches utilizing in the same fashion a series of coordinate transformations together with appropriate integration reorderings and is applicable to coincident edge adjacent or vertex adjacent elements the resulting formulas consist of sufficiently smooth kernels and exhibit several favorable characteristics when compared with the vast majority of the methods currently available more specifically they can be applied without modifications to the following challenging cases 1 weakly and strongly singular kernels 2 basis and testing functions of arbitrary order 3 planar and curvilinear patches 4 problem specific green functions e g expressed in spectral integral form and 5 spectral convergence to machine precision finally we show that the overall performance of the fully numerical schemes can be further improved by a judicious choice of the integration order for each dimension

kazhdan lusztig immanants and products of matrix minors abstract using the kazhdan lusztig basis c w 1 w s n for the symmetric group algebra we obtain nonnegativity properties of certain polynomials in matrix minors in particular we show that the application of these polynomials to jacobi trudi matrices yields symmetric functions which are equal to nonnegative linear combinations of schur functions

regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions the boundary integral equations bies in their original forms which govern the electromagnetic em wave scattering in three dimensional space contain at least a hypersingularity 1 r sup 3 or a cauchy singularity 1 r sup 2 usually both thus obtaining reliable numerical solutions using such equations requires considerable care especially when developing systematic numerical integration procedures for realistic problems regularized bies for the numerical computation of time harmonic em scattering fields due to arbitrarily shaped scatterers are introduced two regularization approaches utilizing an isolation method plus a mapping are presented to remove all singularities prior to numerical integration both approaches differ from all existing approaches to em scattering problems both work for integral equations initially containing either hypersingularities or cauchy singularities without the need to introduce surface divergences or other derivatives of the em fields on the boundary also neither approach is limited to flat surfaces nor flat element models of curved surfaces the muller linear combination of the electric and magnetic field integral equations efie and mfie is used to avoid the resonance difficulty that is usually associated with integral equation based formulations some preliminary numerical results for em scattering due to single and multiple dielectric spheres are presented and compared with analytical solutions

an update on minc s survey of open problems involving permanents abstract we summarise the progress which has been made since 1986 on the conjectures and open problems listed in h minc s survey articles on the theory of permanents

immanant inequalities and 0 weight spaces let n e n and let a aij be an n x n complex matrix let sn be the group of permutations of x 1 n and let w n be the set of all partitions of n as one knows to each a e n we may associate an irreducible complex representation vm sn aut ya such that using standard notation x a is the character of va generalizing the determinant and permanent of a one defines the immanants of a by putting for any a e

on the direct evaluation of weakly singular integrals in galerkin mixed potential integral equation formulations weakly singular integrals over coincident triangles arising in the galerkin discretization of mixed potential integral equation formulations are calculated using a direct evaluation method the proposed method utilizes a series of coordinate transformations together with a re ordering of the integrations in order to reduce the dimensionality of the original four dimensional 4d weakly singular integrals into 1d numerical integrations of smooth functions the final formulas can be easily evaluated with a standard gaussian quadrature rule resulting in a scheme with great accuracy and efficiency properties numerical results for the comparison of the proposed method with both singularity subtraction and singularity cancellation methods often used for the evaluation of multidimensional singular integrals are presented indicating the superior overall performance of the direct evaluation scheme

a method for direct evaluation of singular integral in direct boundary element method a new method is presented for evaluating the cauchy principal value integral and the free term in the three dimensional elastic boundary element method this method expresses the singular integral as the sum of a weakly singular integral and an integrable cauchy principal value integral the former can be computed by means of the usual standard gaussian quadrature after a transformation suggested by lachat and watson 10 who correctly limited its use only to weakly singular integral the latter can be calculated by direct integration in the cauchy principal value sense this paper also points out some limitations in the use of triangle polar co ordinate suggested by li et al 11 and later extended by zhang and xu 16 the general expression of the free term for a boundary point with arbitrary characteristic surface is also presented simple numerical examples which verify the efficiency and accuracy of the present method are given

hook immanantal inequalities for laplacians of trees abstract for an irreducible character x of the symmetric group sn indexed by the partition the immanant function d acting on an n n matrix a aij is defined as d a sn x ni 1 ai i the associated normalized immanant d is defined as d d x identity where identity is the identity permutation p heyfron has shown that for the partitions k 1n k the normalized immanant d k satisfies det a d 1 a d 2 a d n a per a 1 for all positive semidefinite hermitian matrices a when a is restricted to the laplacian matrices of graphs improvements on the inequalities above may be expected indeed in a recent survey paper r merris conjectured that d n 1 a n 2 n 1 d n a 2 wherever a is the laplacian matrix of a tree in this note we establish a refinement for the family of inequalities in 1 when a is the laplacian matrix of a tree that includes 2 as a special case these inequalities are sharp and equality holds if and only if a is the laplacian matrix of the star this is proved via the inequalities d k a d k 1 a d k 1 a d k a for k 2 3 n 1 where a is the laplacian matrix of a tree

time domain integral equation analysis of scattering from composite bodies via exact evaluation of radiation fields a novel marching on in time and poggio miller chang harrington wu tsai pmchwt based time domain integral equation solver for analyzing transient scattering from composite multiregion structures comprising homogeneous penetrable volumes and perfectly conducting surfaces is presented to render the marching on in time procedure stable observer and source integrals are approximated via multipoint collocation and evaluated in closed form the proposed scheme avoids the costly evaluation of five dimensional integrals required in full space time galerkin schemes and proves to be stable for all targets investigated including coated perfect electrically conducting surfaces and multiregion penetrable volumes

description of object shapes by apparent boundary and convex hull the notions of the apparent boundary and the strict apparent boundary of an object are introduced which together with the convex hull provide an automatic approach for object shape analysis various properties of the apparent boundary and the strict apparent boundary are established which show that they are good approximations of the real object boundary applications of the apparent boundary and the convex hull to the automatic shape characterization of planktonic foraminifera are presented

inequalities for single hook immanants let dk denote the normalized generalized matrix function based upon the irreducible character of sn associated with the partition k 1 1 of n for all positive semidefinite hermitian n by n a we prove certain inequalities in the chain det a d1 a d2 a dn 1 a dn a per a conjectured for each n this work is in pursuit of the permanent on top conjecture and this conjecture is also verified for another class of immanants the methods involve several new inequalities for eigenvalues and the permanent which may be of independent interest

complete semi analytical treatment of weakly singular integrals on planar triangles via the direct evaluation method keywords galerkin inner products method of moments mixed potential integral equations weakly singular integrals linear source distributions surface integrals potential integrals electromagnetic scattering numerical evaluation greens function shape transformation quadrature equations reference lema article 2010 007doi 10 1002 nme 2877view record in web of science record created on 2010 01 20 modified on 2016 08 08

hook immanantal inequalities for trees explained abstract let d k denote the normalized hook immanant corresponding to the partition k ln k of n p heyfron proved the family of immanantal inequalities det a d 1 a d 2 a d n a per a 1 for all positive semidefinite hermitian matrices a motivated by a conjecture of r merris it was shown by the authors that 1 may be improved to d k 1 l t k 2 k 1 d k l t 2 for all 2 k n whenever l t is the laplacian matrix of a tree t the proof of 2 relied on rather involved recursive relations for weighted matchings in the tree t as well as identities of hook characters in this work we circumvent this tedium with a new proof using the notion of vertex orientations this approach makes 2 immediately apparent and more importantly provides an insight into why it holds namely the absence of certain vertex orientations for all trees as a by product we obtain an improved bound 0 1 k 1 d k l t d k l s n k 2 k 1 d k l t d k 1 l t where s n is the star with n vertices the ease with which the inequality in 2 and its improvement are derived points to the value of the concept of vertex orientation in the study of immanantal inequalities on graphs

time domain bie analysis of large three dimensional electromagnetic scattering problems a time domain boundary integral equation bie solution of the magnetic field integral equation mfie for large electromagnetic scattering problems is presented it employs isoparametric curvilinear quadratic elements to model fields geometry and time dependence eliminating staircasing problems the approach is implicit which seems to provide both stability and permits arbitrary local mesh refinement to model geometrically difficult regions without the significant cost penalty explicit methods suffer error dependence on discretization is investigated accurate results are obtained with as few as five nodes per wavelength the performance both on large scatterers and on low radar cross section rcs scatterers is demonstrated including the six wavelength nasa almond two spheres a thirteen wavelength missile and a high q cavity

a novel approach for evaluating hypersingular and strongly singular surface integrals in electromagnetics solving electromagnetic em problems by integral equation methods requires an accurate and efficient treatment for the singular integral kernels related to the green s function for surface integral equations sies there are l and k operators which include hypersingular integrals hsis and strongly singular integrals ssis respectively the hsis are generated from the double gradient of the green s function while the ssis come from the single gradient of the green s function although the hsis could be reduced to weakly singular integrals wsis in the method of moments mom implementation with divergence conforming basis function such as the rao wilton glisson rwg basis function they do appear in nystrom method nm or boundary element method bem and one has to tackle them the ssis always exist in the k operator and could also exist in the l operator when the testing function is not the rwg like basis function the treatment for the hsis and ssis is essential because they have a significant influence on the numerical solutions there have been many publications dealing with the singular integrals but they mainly focus on the wiss or ssis and the hsis were seldom addressed in this work we develop a novel approach for evaluating those hsis and ssis based on the stokes theorem the derived formulas are much simpler and more friendly in implementation since no polar coordinates or extra coordinate transformation are involved numerical experiments are presented to demonstrate the effectiveness of the approach

a linear time algorithm for computing the convex hull of an ordered crossing polygon in this paper we describe a linear time algorithm for finding the convex hull of an ordered crossing polygon and prove its correctness

an application of the boundary element method to the magnetic field integral equation a boundary element method bem for the solution of electromagnetic scattering problems using the magnetic field integral equation mfie is discussed the discretized form of the mfie is written in indicial notation with no limitations placed on the order of either the geometric or functional approximation by considering several different types of boundary elements it is determined that geometric errors can be significant and degrade the accuracy of the numerical solution it is shown that a higher order approximation for the current could significantly improve the accuracy of the numerical solution the superparametric boundary element in which the geometry was given quadratic approximation and the current was given linear approximation was more efficient than elements using lower order approximations the bem results are compared to the results obtained using the dielectric bodies of revolution dbr code

efficient evaluation of weakly singular integrals arising from electromagnetic surface integral equations solving electromagnetic em problems by integral equation methods relies on the accurate evaluation of singular integrals related to the green s function in the method of moments mom with the rao wilton glisson rwg basis function for solving surface integral equations sies the gradient operator on the scalar green s function can be moved onto the basic function and testing function resulting in a 1 r weak singularity in the integral kernel where r is the distance between an observation point and a source point the weakly singular integral can be evaluated with the well known duffy s method but it requires a two fold numerical integration in this work we develop a novel approach to evaluate the singular integral by using a local polar coordinate system the approach can automatically cancel the singularity and reduce the integral to a one fold numerical integration by deriving a closed form expression for the integral over the polar coordinate numerical examples are presented to demonstrate the effectiveness of the approach

an accurate method for the calculation of singular integrals arising in time domain integral equation analysis of electromagnetic scattering an accurate method for the evaluation of the cauchy principal value integrals arising in time domain electromagnetic wave scattering is presented this is applied to a boundary integral equation bie method employing quadratic curvilinear surface elements where such singularities do not vanish as they generally do when simpler but less accurate discretizations are employed the technique involves weakening the singularity in the original kernel to a degree where conventional integration methods may be employed and transforming the strong singularity to a line integral in a form which allows cancellation of its singular components the effectiveness of the method is demonstrated by scattering calculations on a variety of targets and the computational cost of the approach is trivial