calculation of the impedance matrix inner integral to prescribed precision we present a new method for evaluating the inner integral of the impedance matrix element in the traditional rao wilton glisson formulation of the method of moments for perfect conductors in this method we replace the original integrand modified by a constant phase factor by its taylor series and keep enough terms to guarantee a number of significant digits in the integration outcome we develop criteria that relate the number of taylor terms to the number of required significant digits we integrate the leading taylor terms analytically and the rest through iteration formulas we show that the iteration formulas converge for all observation points within a sphere with a radius of half a wavelength and center the triangle s centroid we compare results of our method with existing ones and find them in excellent agreement we also outline a procedure for using cubatures outside the region of convergence

efficient calculation of the green s function for multilayered planar periodic structures an efficient calculation scheme is presented for the periodic green s function in planar multilayered structures the proposed method is based on the static complex image conversion and the ewald sum technique and it converts the slowly convergent green s function into the sum of two rapidly convergent series

an efficient hybrid mlfma fft solver for the volume integral equation in case of sparse 3d inhomogeneous dielectric scatterers electromagnetic scattering problems involving inhomogeneous objects can be numerically solved by applying a method of moments discretization to the volume integral equation for electrically large problems the iterative solution of the resulting linear system is expensive both computationally and in memory use in this paper a hybrid mlfma fft method is presented which combines the fast fourier transform fft method and the high frequency multilevel fast multipole algorithm mlfma in order to reduce the cost of the matrix vector multiplications needed in the iterative solver the method represents the scatterers within a set of possibly disjoint identical cubic subdomains which are meshed using a uniform cubic grid this specific mesh allows for the application of ffts to calculate the near interactions in the mlfma and reduces the memory cost considerably since the aggregation and disaggregation matrices of the mlfma can be reused additional improvements to the general mlfma framework such as an extention of the fft interpolation scheme of sarvas et al from the scalar to the vectorial case in combination with a more economical representation of the radiation patterns on the lowest level in vector spherical harmonics are proposed and the choice of the subdomain size is discussed the hybrid method performs better in terms of speed and memory use on large sparse configurations than both the fft method and the hf mlfma separately and it has lower memory requirements on general large problems this is illustrated on a number of representative numerical test cases

accurate and efficient numerical integration of weakly singular integrals in galerkin efie solutions a galerkin descretization of the electric field integral equation for perfectly conducting surfaces using rao wilton glisson 1982 basis functions requires the numerical evaluation of integrals with singular kernels over triangular regions these singularities have been traditionally handled by utilizing a singularity extraction procedure to produce a regular integral and an analytic function to replace the original singular integral a new approach is presented here in which the four dimensional 4 d weakly singular integrals unique to the galerkin rao wilton glisson electric field integral equation solution for perfectly conducting surfaces are transformed into integrals with regular integrands the transformations allow some of the integrations to be performed analytically in some cases reducing the original 4 d integral into a 1 d numerical integration the accuracy and convergence properties of the new method are demonstrated by evaluating the scalar potential function over a unit triangle

a mesh adapted closed form regular kernel for 3d singular integral equations the green s functions employed in the method of moments mom diverge when observation and source points coincide this is at the origin of the difficulties in computing the mom matrix entries and in handling the near field interactions in fast fourier transform fft based fast methods and other sampling based methods in this paper we show that this singularity can be avoided and a modified regular green s function can be used instead this latter is obtained from the spectral representation of the usual green s function via windowing of its spectrum the width of the spectral window depends on the size of the mesh employed for discretizing the problem so that the proposed regular green s function is a mesh adapted regular kernel we address a general 3d problem we relate the mom reaction integrals to the 2d fourier spectrum of the green s function that allows to discuss the necessary spectral bandwidth for the windowed green s function we employ a tapered window and present a closed form expression for the spatial green s function numerical results are presented for 3d antenna and scattering problems discretized with rao wilton glisson rwg functions and for uniform and nonuniform meshing they show that the proposed method yields accurate solutions also for the antenna input impedance the meaning of the regularized green s function is also discussed and put in perspective

an efficient numerical evaluation of the green s function for the helmholtz operator on periodic structures abstract numerical methods which are based on boundary integral formulations require the numerical evaluation of the green s function associated with the problem in the case of periodic structures the green s function is often an infinite series this infinite series may converge slowly making numerical evaluation expensive here we present a practical computer implementation of a technique which dramatically speeds up the convergence of the infinite series green s function associated with the helmholtz operator to show the consequences of using this technique we include some numerical examples

the dade group of a p group let p be a prime number this paper solves the question of the structure of the group d p of endo permutation modules over an arbitrary finite p group p that was open after dade s original papers in 1978 19 20 and it gives a proof of the conjectures proposed in 4 and 10 this leads to a presentation of d p by explicit generators and relations generalizing the presentation obtained by dade when p is abelian

evaluation of 4 d reaction integrals via double application of the divergence theorem the use of the method of moments to solve surface integral equations is one of the most popular numerical techniques in electromagnetic modeling and analysis this method requires the accurate and efficient numerical evaluation of iterated surface integrals over both source and testing domains in this paper we propose a scheme for evaluating these 4 d interaction integrals between pairs of arbitrarily positioned and oriented elements the approach is based on applying the surface divergence theorem twice once on the source and once on the test domain when the integrations are reordered as two outer contour integrals plus two inner radial integrals the initial radial integrations provide significant smoothing of the underlying singular integrands the method is numerically validated for static and dynamic kernels arising in the electric field integral equation i e for kernels with 1 r singularities and linear basis functions the proposed formula to evaluate 4 d reaction integrals can be extended to different kernels and to different elements e g to curved or volumetric elements and to basis functions of higher order

tamagawa numbers for motives with noncommutative coefficients ii we provide corroborative evidence for the equivariant tamagawa number conjecture which was formulated in the first part of this article

cohomology of units and l values at zero let klk be a finite galois extension of number fields with galois group g and let s be a finite g stable set of primes of k containing all archimedean primes we denote the g module of s units of k by e es and let as be the kernel of the augmentation map zs z which sends each basis element p c s to 1 we are concerned with invariants of k k which are associated to a g homomorphism p as e inducingq0 as cq0e these invariants were defined by tate ta2 and chinburg chl when s is large i e when s contains all ramified primes of k k and the s class group cl cls of k is trivial there are two of them and each is a function of the complex characters x of g the first aw has a x equal to the tate regulator at x divided by the leading coefficient c x of the taylor expansion at s 0 of the artin l function l s x with the euler factors at primes of s omitted according to stark s conjecture st in tate s form a takes algebraic values which satisfy a o x5 a x

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

on the equivariant tamagawa number conjecture for tate motives let l be a finite abelian extension of and let k be any subfield of l for each integer r with r 0 we prove the equivariant tamagawa number conjecture for the pair h0 spec l r gal l k

endo p permutation modules this paper introduces the notion of endo p permutation kg module i give a characterization of indecomposable endo p permutation modules with vertex p via their source modules which are exactly the indecomposable endo permutation modules whose classes in the dade group d p are g stable in particular when the normalizer of p controls p fusion i give a classification of sources of endo p permutation modules using the recent classification of the dade group

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

the use of parametric elements in the moment method solution of static and dynamic volume integral equations the use of two and three dimensional parametric curved subdomains elements in the numerical solution of electromagnetic problems formulated in terms of volume integro differential equations is considered and a technique to evaluate the static and dynamic moment integrals on these domains is presented in the source region the evaluation of the moment integrals is performed by separating the integrands into a singular and a regular part the regular integrals are numerically evaluated in a parameter space where the integration domain assumes a very simple form the singular integrals are shown to be always reducible to nonsingular boundary integrals by use of a nonlinear transformation for the integration variables and an analytic integration on one variable the reduced singular integrals are then evaluated numerically in a second parameter space where the boundary of the original curved element is expressed in a simple form two simple two dimensional scattering problems in the frequency domains are considered to compare the results obtained using quadratic isoparametric curved elements against the results given by linear expansion functions on triangular elements the use of curved parametric elements permit a better geometrical description of the problem a reduced number of unknowns shorter computation times and more accurate results with respect to the usually employed linear elements

on galois structure invariants associated to tate motives we establish the equivalence of two definitions of invariants measuring the galois module structure of k groups of rings of integers in number fields due to chinburg et al on the one hand and the authors on the other we also make some remarks concerning the possibility of yet another such definition via lichtenbaum complexes

application of aim and mbpe techniques to accelerate modeling of 3 d doubly periodic structures with nonorthogonal lattices composed of bianisotropic media an efficient methodology is introduced for rapid analysis and design of three dimensional 3 d doubly periodic structures over a wide frequency range based on hybrid finite element boundary integral febi methods the 3 d doubly periodic structures can be represented as nonorthogonal lattices composed of general inhomogeneous bianisotropic media with arbitrarily shaped metallic patches based on floquet theory and periodic boundary conditions the original stated problem that involves infinite periodic structures can be converted into a single unit cell using the equivalence principle the derived bi equation formulation is applied to the top and bottom surfaces of the unit cell which results in a perfectly reflectionless boundary condition for the fe based approach then the unit cell was meshed using triangular prismatic volume elements which provide a great deal of flexibility in modeling complex planar geometries with arbitrary shapes in the transverse direction the adaptive integral method aim was employed to accelerate the calculation of the matrix vector product for the bi portion within the iterative solver furthermore a model based parameter estimation mbpe technique was proposed for the wide band interpolation of the required impedance matrix elements in the bi part for near field components that were used in the aim procedure the accuracy and efficiency of the proposed hybrid algorithms are demonstrated by the presented numerical results e g in comparison with analytical solutions several simulation results are presented to illustrate the flexibility of the proposed methods for analysis of frequency selective surfaces with arbitrarily shaped metallic patches bianisotropic materials and nonorthogonal lattice configurations

on principal blocks of p constrained groups a theorem of k w roggenkamp and l l scott shows that for a finite group g with a normal p subgroup containing its own centralizer any two group bases of the integral group ring mathbb z g are conjugate in the units of mathbb z p g though the theorem presents itself in the work of others and appears to be needed there is no published account there seems to be a flaw in the proof because a theorem appearing in the survey k w roggenkamp the isomorphism problem for integral group rings of finite groups progress in mathematics 95 birkhauser basel 1991 pp 193 220 where the main ingredients of a proof are given is false in this paper it is shown how to close this gap at least if one is only interested in the conclusion mentioned above therefore some consequences of the results of a weiss on permutation modules are stated the basic steps of which any proof should consist are discussed in some detail in doing so a complete yet short proof of the theorem is given in the case that g has a normal sylow p subgroup 2000 mathematical subject classification primary 16u60 secondary 20c05

waveguide excited microstrip patch antenna theory and experiment an arbitrarily shaped microstrip patch antenna excited through an arbitrarily shaped aperture in the mouth of a rectangular waveguide is investigated theoretically and experimentally the metallic patch resides on a dielectric substrate grounded by the waveguide flange and may be covered by a dielectric superstrate the substrate and superstrate if present consists of one or more planar homogeneous layers which may exhibit uniaxial anisotropy the analysis is based on the space domain integral equation approach more specifically the green s functions for the layered medium and the waveguide are used to formulate a coupled set of integral equations for the patch current and the aperture electric field the layered medium green s function is expressed in terms of sommerfeld type integrals and the waveguide green s function in terms of floquet series which are both accelerated to reduce the computational effort the coupled integral equations are solved by the method of moments using vector basis functions defined over triangular subdomains the dominant mode reflection coefficient in the waveguide and the far field radiation patterns are then found from the computed aperture field and patch current distributions the radar cross section rcs of a plane wave excited structure is obtained in a like manner sample numerical results are presented and are found to be in good agreement with measurements and with published data

iterative solution of high order boundary element method for acoustic impedance boundary value problems abstract a high order boundary element method for time harmonic acoustic impedance boundary value problems is presented the method is based on the galerkin type formulation of the burton miller integral equation bmie with high order polynomial basis and testing functions this formulation has several important advantages it is free of the interior resonance problem the hypersingular integral operator of the traditional bmie formulation can be avoided it leads to faster convergence in terms of the number of unknowns than the low order methods and it shows a good performance with iterative solvers to avoid the numerical difficulties associated to the implementation of the singular surface integral equations the singularity extraction technique is applied to evaluate the integrals in the singular and near singular cases the resulting matrix equation is solved iteratively with the generalized minimal residual method gmres and a simple preconditioner based on the incomplete lu factorization is applied to expedite the convergence numerical results indicate that the bmie formulation with galerkin method and high order basis functions has good convergence properties for various geometries and boundary conditions on a wide frequency range when the gmres method is applied to solve the matrix equation iteratively this in turn indicates that the formulation is well suited for an efficient application of fast solution procedures such as the fast multipole method

on equivalences between blocks of group algebras reduction to the simple components abstract a conjecture of michel broue states that if d is an abelian sylow p subgroup of a finite group g and h n g d then the principal blocks of g and h are rickard equivalent the structure of groups with abelian sylow p subgroups as determined by p fong and m e harris raises the following question assuming that broue s conjecture holds for the simple components of g under what conditions does it hold for g itself due to the structure of g this problem requires mainly the lifting of rickard complexes to p extensions of the simple components and the construction of complexes over wreath products we give here these reduction steps which may be regarded as a clifford theory of tilting complexes

volumetric testing parallel to the boundary surface for a nonconforming discretization of the electric field integral equation the volumetric monopolar rwg discretization of the electric field integral equation efie imposes no continuity constraint across edges in the surface discretization around a closed conductor the current is expanded with the monopolar rwg set and the electric field is tested over a set of tetrahedral elements attached to the boundary surface this scheme is facet oriented and therefore well suited for the scattering analysis of nonconformal meshes or composite objects the observed accuracy though is only competitive with respect to the rwg discretization for a restricted range of heights of the tetrahedral elements in this communication we introduce a novel implementation of the volumetric monopolar rwg discretization of the efie with testing over a set of wedges we show with rcs and near field results that this scheme offers improved accuracy for a wider range of heights than the approach with tetrahedral testing the application of the wedge testing to the even surface odd volumetric monopolar rwg discretization of the efie edge oriented and therefore less versatile shows similar accuracy as with tetrahedral testing which is a sign of robustness

an efficient volume integral equation solution to em scattering by complex bodies with inhomogeneous bi isotropy a generalized volume integral equation method is formulated for electromagnetic scattering by arbitrarily shaped complex bodies with inhomogeneous bi isotropy based on the volume equivalence principle the integral equations are represented in terms of a pair of coupled bi isotropic polarized volume electric and magnetic flux densities reduction of the integral equations into the corresponding matrix equations is obtained using the method of moments mom combined with the tetrahedral mesh in the mom solution the three dimensional solenoidal function is incorporated as the basis function defined over each tetrahedral element and the details of implementation particularly the treatment of integral singularities will be elucidated the efficiency and accuracy of the proposed method are validated by illustratively supported examples

a common formalism for the integral formulations of the forward eeg problem the forward electroencephalography eeg problem involves finding a potential v from the poisson equation spl nabla spl middot spl sigma spl nabla v f in which f represents electrical sources in the brain and spl sigma the conductivity of the head tissues in the piecewise constant conductivity head model this can be accomplished by the boundary element method bem using a suitable integral formulation most previous work uses the same integral formulation corresponding to a double layer potential we present a conceptual framework based on a well known theorem theorem 1 that characterizes harmonic functions defined on the complement of a bounded smooth surface this theorem says that such harmonic functions are completely defined by their values and those of their normal derivatives on this surface it allows us to cast the previous bem approaches in a unified setting and to develop two new approaches corresponding to different ways of exploiting the same theorem specifically we first present a dual approach which involves a single layer potential then we propose a symmetric formulation which combines single and double layer potentials and which is new to the field of eeg although it has been applied to other problems in electromagnetism the three methods have been evaluated numerically using a spherical geometry with known analytical solution and the symmetric formulation achieves a significantly higher accuracy than the alternative methods additionally we present results with realistically shaped meshes beside providing a better understanding of the foundations of bem methods our approach appears to lead also to more efficient algorithms

hybrid fe bi modeling of 3 d doubly periodic structures utilizing triangular prismatic elements and an mpie formulation accelerated by the ewald transformation we present the formulation of a finite element boundary integral method for the analysis of three dimensional doubly periodic structures based on arbitrary nonorthogonal lattice configurations the method starts from a functional description of the field problem where only a single unit cell of the array is considered this unit cell is meshed with triangular prismatic volume elements and the electric field intensity is discretized with edge based expansion functions on the sidewalls of the unit cell phase boundary conditions are employed to relate the fields on opposing walls of the unit cell on the top and or bottom unit cell planar surfaces the mesh is terminated using a mixed potential integral equation the required space domain periodic green s function is calculated after applying the ewald 1921 transformation to convert the slowly converging series representation into two rapidly converging series the method is validated for simple slot and strip frequency selective surfaces as well as microstrip dipole arrays more complex geometries investigated are slot coupled microstrip patches photonic bandgap materials and the so called artificial puck plate frequency selective surface bandpass structure

central units in blocks and the odd zp theorem abstract we construct some units of order p in certain p adic group rings of finite groups which have relevance to the odd analogue of glauberman s z theorem but whose construction may have wider applicability and interest

mom matrix generation based on frequency and material independent reactions fmir mom a novel and efficient method of moments mom matrix generation technique called the frequency and material independent reactions for the method of moments fmir mom technique is presented this new matrix generation algorithm efficiently calculates impedance matrices while sweeping through frequency permittivity conductivity and or permeability values for frequency sweeps it has computational and memory costs comparable to those of interpolation techniques it has the advantage over interpolation techniques in that it does not divide the frequency range into segments and allows one to dynamically update the precision the technique expands the exponential of the green s function into a taylor series this allows the problem to be formulated as a summation where each term consists of a real valued matrix depending only on the geometry discretization multiplied by a scalar dependent on the propagation constant the algorithm s efficiency is obtained by calculating the geometry dependent matrices prior to sweeping through frequency or material parameters

relative partial characters and relative blocks of p solvable groups abstract suppose that g is a finite p solvable group and let n be a normal subgroup let irr n with inertial group t in g suppose extends to a subgroup r of t containing n such that r n is a sylow p subgroup of the quotient group t n we show that the set irr g of irreducible characters of g lying over can be partitioned into blocks which behave like the classical brauer p blocks we also establish a well behaved one to one correspondence between the blocks of g and certain brauer p blocks of a central extension of t n by a p subgroup

integral equation analysis of scattering from doubly periodic array of 3 d conducting objects the integral equation ie method formulated in the spatial domain is employed to calculate the scattering from the doubly periodic array of three dimensional 3 d perfect electric conductor pec objects the special testing and basis functions are proposed to handle the problem with non zero normal components of currents at the boundary of one period moreover a relationship between the scattering from the pec screen and its complementary structure is established in order to efficiently compute the matrix elements from the ie approach an acceleration technique with the exponential convergence rate is applied to evaluate the doubly periodic green s function the formulations in this technique are appropriately modified so that the new form facilitates numerical calculation for the general cases

congruences between derivatives of geometric l functions we prove a natural refinement of a theorem of lichtenbaum describing the leading terms of zeta functions of curves over finite fields in terms of weil etale cohomology we then use this result to prove the validity of chinburg s 3 conjecture for all abelian extensions of global function fields to prove natural refinements and generalisations of the refined stark conjectures formulated by amongst others gross tate rubin and popescu to prove a variety of explicit restrictions on the galois module structure of unit groups and divisor class groups and to describe explicitly the fitting ideals of certain weil etale cohomology groups in an appendix coauthored with k f lai and k s tan we also show that the main conjectures of geometric iwasawa theory can be proved without using either crystalline cohomology or drinfeld modules

static and dynamic potential integrals for linearly varying source distributions in two and three dimensional problems a technique for the evaluation of static and dynamic potentials due to source distributions defined on domains with simple shape is presented the domains considered are polyhedral regions and in two dimensional problems plane polygons on which uniform or linearly varying source distributions are defined it is shown how three dimensional two dimensional potential integrals are always reducible to surface line integrals with nonsingular kernel by use of a nonlinear transformation for the integration variables that permits analytic integration in the static case the integration on the boundary is performed analytically and closed form results are given in the dynamic case the expressions of the boundary integrals are given in a form suitable for numerical integration the use of matrix notation allows for very compact expressions readily translatable into computer programs

an accurate approach for the calculation of mom matrix elements the method of moments solution on integral equations for electromagnetic scattering and radiation problems with rao wilton glisson rwg and n spl times rwg basis functions requires the calculation of singular double surface integrals over triangular subdomains in this paper an approach is presented to deal with the singularity and almost singularity in which the triangle subdomain is divided into several subtriangles and then the singular or almost singular integral is calculated over each of the subtriangles this approach is mainly based on the projection process and the local polar frame it can be used to deal with the singular double surface integrals of order 1 r and 1 r sup 2 in which vector functions may be of zeroth order and higher order numerical examples are provided to verify the validity of the method presented in this paper for dealing with the singularity and almost singularity

on the equivariant tamagawa number conjecture for tate motives and unconditional annihilation results dfg collaborative research center 701 spectral structures and topological methods in mathematics

quadrature over a pyramid or cube of integrands with a singularity at a vertex a simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex

a new acceleration technique with exponential convergence rate to evaluate periodic green functions we propose a new approach to compute the dynamic potential green function from two and three dimensional periodic arrays of point sources in a three dimensional space the method has at least exponential convergence rate in some cases it has gaussian convergence rate the convergence rate is independent of the position of the observation point in the unit cell the proposed approach can also be used to calculate the derivatives of the green function very efficiently

analysis of probe fed conformal microstrip antennas on finite grounded substrate a method based on the volume surface wire integral equation and precorrected fast fourier transform fft method is presented for accurate analysis of probe fed microstrip antennas on arbitrarily shaped finite sized ground plane and substrate the method of moments mom is used to solve the integral equation three triangular type basis functions are used to represent the unknown currents in the substrates on the conducting surfaces and probes respectively the connection of a vertical probe feed to the patch is rigorously modeled by an attachment mode at the junction the precorrected fft method is applied to reduce the memory requirement and computational cost of the traditional mom to facilitate analysis of large antenna arrays

scattering from 3 d inhomogeneous chiral bodies of arbitrary shape by the method of moments a method of moments mom solution is presented for the problem of electromagnetic scattering by a three dimensional 3d inhomogeneous chiral scatterer illuminated by an arbitrary incident field the volume equivalence principle was used to obtain coupled integral equations for equivalent volume currents these integral equations were then solved numerically using mom the volume of the scatterer was modeled by tetrahedral cells and face based expansion functions were used to approximate the equivalent currents computed results are in very good agreement with exact data or other published data

a simple transformation for near singular integrals on curvilinear elements it is difficult to evaluate the near singular four dimensional integrals in the galerkin magnetic field integral equations mfie especially for the curvilinear elements this communication presents a hyperbolic transformation to cancel the near singularities in the bf 1 bm r bf 2 kernel on curved quadrilateral elements which is addressed theoretically and numerically this method has a much simpler formula than the so called directfn method and its convergence rate may be much faster than the latter this is demonstrated by evaluating the near singular integral of a sharp edged structure composed of two curvilinear quadrilaterals

singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedra a numerical solution of integral equations typically requires calculation of integrals with singular kernels the integration of singular terms can be considered either by purely numerical techniques e g duffy s method polar co ordinate transformation or by singularity extraction in the latter method the extracted singular integral is calculated in closed form and the remaining integral is calculated numerically this method has been well established for linear and constant shape functions in this paper we extend the method for polynomial shape functions of arbitrary order we present recursive formulas by which we can extract any number of terms from the singular kernel defined by the fundamental solution of the helmholtz equation or its gradient and integrate the extracted terms times a polynomial shape function in closed form over plane triangles or tetrahedra the presented formulas generalize the singularity extraction technique for surface and volume integral equation methods with high order basis functions numerical experiments show that the developed method leads to a more accurate and robust integration scheme and in many cases also a faster method than for example duffy s transformation copyright 2003 john wiley sons ltd

duffy method for evaluation of weakly singular sie potential integrals over curved quadrilaterals with higher order basis functions a duffy method for singularity cancellation is proposed for evaluation of weakly singular potential integrals defined on generalized curved parametric quadrilateral patches with polynomial basis functions such integrals arise in evaluation of galerkin matrix elements in method of moments analysis of antennas and scatterers in cases of coincident source and test elements examples demonstrate that the proposed duffy method is more accurate more rapidly converging with the increase of orders of gauss legendre integration formulas and faster to execute than four other methods for singularity treatment considered in the study

stripline fed arbitrarily shaped printed aperture antennas a full wave analysis method is presented for modeling the radiation properties of a stripline fed planar printed aperture antenna element in this formulation both the finite length of stripline and the finite aperture may be of any arbitrary shape since their equivalent electric and magnetic currents are modeled with triangular patch basis functions galerkin s method is applied to numerically solve the coupled mixed potential integral equation mpie exact spatial domain green s functions are used to account for all radiation surface wave and mutual coupling effects interactions between the stripline feed and the radiating aperture are rigorously included numerical analysis is presented for the following nonrectangular shapes an exponentially tapered slot an annular slot an annular slot with opposing stubs and a monofilar archimedean spiral slot element results are shown for input return loss radiation patterns and axial ratio for the circularly polarized elements

integral equation analysis of scattering from multilayered periodic array using equivalence principle and connection scheme an integral equation approach is presented to analyze the two dimensional 2 d scattering from multilayered periodic array the proposed approach is capable of handling scattering from the array filled with different media in different layers combining the equivalence principle algorithm epa and connection scheme epacs it can be avoided to find and evaluate the multilayered periodic green s functions for 2n identical layers the elimination of the unknowns between top and bottom surfaces can be accelerated using the logarithm algorithm more importantly based on epacs an approach is proposed to effectively handle the semi infinitely layered case in which a unit consisting of several layers is repeated infinitely in one direction

units of p power order in principal p blocks of p constrained groups abstract let g be a finite group having a normal p subgroup n that contains its centralizer c g n and let r be a p adic ring it is shown that any finite p group of units of augmentation one in rg which normalizes n is conjugate to a subgroup of g by a unit of rg and if it centralizes n it is even contained in n

computation of stark tamagawa units let k be a totally real number field and let l denote an odd prime number we design an algorithm which computes strong numerical evidence for the validity of the equivariant tamagawa number conjecture for the q g equivariant motive h0 spec l where l k is a cyclic extension of degree l and group g this conjecture is a very deep refinement of the classical analytic class number formula in the course of the algorithm we compute a set of special units which must be considered as a generalization of the conjecturally existing stark units associated to first order vanishing dirichlet l functions

reduction of singular surface integrals to nonsingular line integrals in integral equations for planar geometries a novel procedure is presented for the evaluation of matrix elements of the tensor green function with rao wilton glisson basis functions appearing in surface integral equations in electromagnetics the procedure at this point applicable to planar geometries or geometries composed of parallel planar sheets reduces 4 d surface integrals with singular integrands to line integrals over triangle edges with regular integrands the main advantage of the derived expressions is that they offer simplicity and easily controllable accuracy achieved at a computational cost significantly lower than for previously considered techniques in particular the conventional singularity subtraction method

strong fusion control and stable equivalences abstract this article is dedicated to the proof of the following theorem let g be a finite group p be a prime number and e be a p block of g assume that the centraliser c g p of an e subpair p e p strongly controls the fusion of the block e and that a defect group of e is either abelian or for odd p has a non cyclic centre then there exists a stable equivalence of morita type between the block algebras o g e and o c g p e p where o is a complete discrete valuation ring of residual characteristic p this stable equivalence is constructed by gluing together a family of local morita equivalences which are induced by bimodules with fusion stable endo permutation sources broue had previously obtained a similar result for principal blocks in relation with the search for a modular proof of the odd z p theorem thus our theorem points towards a block theoretic analogue of the z p theorem which we state in terms of fusion control and morita equivalences

calculation of mom interaction integrals in highly conductive media the construction of the impedance matrix in the method of moments requires the calculation of interaction integrals between the expansion functions through the green s function and its derivatives the singular behavior of the green s function poses considerable problems for an accurate numerical evaluation of these integrals requiring techniques such as singularity extraction or cancellation in this contribution we will show why these methods fail when the medium is highly conductive a novel technique is proposed to handle these highly challenging integrals the complexity of the new method is independent of the conductivity

on the near interaction elements in integral equation solvers for electromagnetic scattering by three dimensional thin objects the accuracy of near interaction ni evaluation is investigated for hypersingular and strongly singular kernels in solving electromagnetic em integral equations we first define the ni between a field point and a source triangular patch using a nearness factor nf and show the accuracy of numerical integrations for the ni integrals with hypersingular or strongly singular kernels it is found that there exists a transition area or turning point before and after which the convergence behaviors of those integrations are greatly different we define the nf value at the 1 relative error as the turning point nf 0 and define nf les nf 0 as the ni range we find that nf 0 1 4 could be a bound of ni range for the triangles with a quality factor q 0 35 and analytical formulas should be used in evaluating ni elements within the bound numerical examples for em scattering by three dimensional 3d thin objects are used to demonstrate the significance of ni treatments for the accurate solutions

potential integrals for uniform and linear source distributions on polygonal and polyhedral domains formulas for the potentials due to uniform and linearly varying source distributions defined on simply shaped domains are systematically developed and presented domains considered are infinite planar strips infinite cylinders of polygonal cross sections planar surfaces with polygonal boundaries and volumetric regions with polyhedral boundaries the expressions obtained are compact in form and their application in the numerical solution of electromagnetics problems by the method of moments is illustrated

isomorphisms of p adic group rings a long standing problem first posed by graham higman 15 and later by brauer 4 is the isomorphism problem for integral group rings given finite groups g and h is it true that zg zh implies g 2 h many authors have worked on this question but progress has been difficult 30 perhaps the best positive result was that of whitcomb in 1968 37 who showed that the implication g h holds for g metabelian dade 9 showed there were counterexamples even in the metabelian case if z were replaced by the family of all fields some mathematicians came to believe the problem was a kind of grammatical accident that counterexamples for z were surely there if difficult to find we ourselves began this investigation looking for counterexamples but found that they were indeed very difficult to find much more difficult than we had anticipated slowly we began to believe that at least some exciting positive results were possible in this paper we answer the isomorphism problem for finite p groups over the p adic integers z zcp and in a very strong way in the normalized units augmentation 1 of z pg there is only one con gay czu ss of groups of order g 1 this answers the isomorphism problem in the affirmative for finite p groups g over z or zp and in addition computes the entire picard group 2 of the category of z g modules in terms of automorphisms of g similarly we are able to settle the isomorphism problem for finite nilpotent groups and compute the associated semilocal picard groups we also treat more general coefficient domains namely integral domains s of characteristic 0 in which no rational prime divisor of the group order is invertible for the sg isomorphism problem and treat similar semilocal dedekind domains for the picard group computations the zassenhaus conjecture concerning the rational behavior of group ring automorphisms is verified for the nilpotent case in this general setting cf corollary 3 below over z we announce a positive answer to the isomorphism

optimized numerical evaluation of singular and near singular potential integrals involving junction basis functions in analyzing conducting bodies composed of surfaces connected to wires via a method of moments discretization of the electric field integral equation junction basis functions are defined at connection points between wires and surfaces to correctly capture the physics of the current flux in the vicinity of the junction in evaluating the associated self term vector potential surface integrals two singularities are present one is related to the green s function and the other is due to the 1 behavior of the junction basis function that models the current near a junction here we present a simple and efficient numerical procedure for evaluating singular and near singular source vector potential integrals involving junction basis functions the approach is based on a double transformation that cancels both singularities and also overcomes some limitations of singularity subtraction methods the proposed scheme is then optimized to obtain at least four correct digits in the evaluation of these integrals essentially arbitrary accuracy is achievable by suitably increasing the quadrature order

galois invariants for s units let k k be a finite galois extension of number fields with galois group g and let s be a finite g stable set of primes of k containing all primes which are archimedean or ramified over k and which generates the ideal class group by theorem b the g module e of s units of k is determined up to stable isomorphism by a the inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i g lattice s which is the kernel of the augmentation inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i s inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i b the g module of roots of unity in k c a distinguished character e of h 2 g hom s and d the chinburg class m k k in the locally free class group of inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i g our method is a study of the homotopy properties of tate sequences of k k hence it is essential that our galois invariants be specified without prior knowledge of these sequences this is clear for a and b while for c it follows from theorem a which expresses e in terms of the local and global invariant maps of class field theory and for d it would follow from chinburg s conjecture that m is the root number class of k k

on derivatives of artin l series we present a universal theory of refined stark conjectures we give evidence in support of these explicit and very general conjectures including a full proof in several important cases and explain the connection to previous conjectures of bloch and kato of lichtenbaum and of serre and tate we also deduce a wide range of unconditional consequences of these results concerning the annihilation as galois modules of ideal class groups by explicit elements constructed from the values of higher order derivatives of non abelian artin l series

on multiplicative galois structure invariants introduction let n k be a finite galois extension of number fields of group g let ko z g denote the grothendieck group of finitely generated projective left 7 g modules with cl z g the subgroup of elements which have rank 0 in c1 chinburg used the four term exact sequences of prescribed extension class introduced by tate in t2 pp 56 57 to define an invariant qm n k e cl z g of the multiplicative galois structure of n the class qm n k is also often denoted q n k 3 this invariant can be described in terms of local and global weil groups and has been conjectured by chinburg to equal the cassou nogues frohlich root number class c2 there is by now a considerable amount of evidence to support this conjecture cf d 4 the conjecture is in part motivated by tate s re formulation of the stark conjecture and specifically his construction of a natural generalization of the classical dirichlet unit regulator t2 more recently frohlich has defined an integral version of the stark tate regulator and by integrally reinterpreting much of the tate approach has studied elements in natural quotients of cl z g which explicitly relate the galois structure of unit lattices and the regular part of ideal class groups cf f3 f4 d 3 in this paper we shall show that the results of fr6hlich represent approximations to the conjecture of chinburg for example we show that the fine structure results of f4 are for the special classes of abelian extensions considered there the best approximations to a proof of chinburg s conjecture which can be obtained without analysis of extension class data moreover for certain classes of field extensions the relevant cohomological questions can be resolved and so we shall obtain a full proof of the chinburg conjecture for these extensions in this way the dependence of the conjecture on the role of the canonical cohomology classes of tate in defining qm n k is made very clear also taken in conjunction with recent work of snaith sn on the additive chinburg invariant q n k 2 a special case of our results provides an infinite family of wildly ramified abelian extensions for which all of the conjectures of chinburg are now completely verified cf remark 1 11 ii

on the numerical integration of the linear shape functions times the 3 d green s function or its gradient on a plane triangle formulas for the static and dynamic potentials due to linearly varying source distributions defined on a planar triangle are presented the general linear variation of the source is represented in terms of three linear basis functions each one associated with a different vertex of the triangular domain the singular kernels considered are given by the 3 d green s function and its gradient both for the static and dynamic case in the static case the evaluation of potentials is performed analytically and compact form results are given in the dynamic case the results are given in a form suited for numerical integration

on the equivariant tamagawa number conjecture in tame cm extensions let l k be a finite galois cm extension with galois group g the equivariant tamagawa number conjecture etnc for the pair h 0 rm spec l 0 mathbb z g naturally decomposes into p parts where p runs over all rational primes if p is odd these p parts in turn decompose into a plus and a minus part let l k be tame above p we show that a certain ray class group of l defines an element in k 0 mathbb z p g mathbb q p which is determined by a corresponding stickelberger element if and only if the minus part of the etnc at p holds for this we use the lifted root number conjecture for small sets of places which is equivalent to the etnc in the number field case for abelian g we show that the minus part of the etnc at p implies the strong brumer stark conjecture at p we prove the minus part of the etnc at p for almost all primes p

explicit units and the equivariant tamagawa number conjecture let l k be a finite abelian extension of number fields of group g we study the tamagawa number t l k of h 0 spec l considered as a motive defined over k and with coefficients inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i g for a large class of extensions l k we interpret the conjectural vanishing of t l k in terms of the existence of s units in l satisfying a variety of explicit conditions these explicit conditions are in the same spirit as but are in general much finer than the conditions studied by rubin and popescu by using this approach we are able to complete the proof that t l k vanishes for all of the genus field extensions considered by frohlich in the course of proving this result we find that for certain extensions the vanishing of t l k is a refinement of the main result of solomon concerning wild euler systems

a new method to generate an almost diagonal matrix in the boundary integral equation formulation in this work a new numerical procedure is developed to generate an almost diagonal matrix for the solution of boundary integral equation formulation dealing with acoustic scattering problems the major drawback of the traditional boundary integral equation procedure resulting in a dense system matrix is eliminated in this new procedure by grouping the basis functions into a cluster the geometry of the structure is modeled by planar triangles and the basis functions are defined on the nodes by doing so one can get a benefit of a smaller size matrix to begin with furthermore by grouping these node based basis functions into a cluster an almost diagonal matrix is generated thus the solution procedure developed in this work may be utilized for very large scattering problems since the required computer resources are very low the solution procedure developed in this work is validated for the scattering cross section of the simple shapes with the closed form solutions wherever available and with the other numerical solution procedures

machine precision evaluation of singular and nearly singular potential integrals by use of gauss quadrature formulas for rational functions a new technique for machine precision evaluation of singular and nearly singular potential integrals with 1 r singularities is presented the numerical quadrature scheme is based on a new rational expression for the integrands obtained by a cancellation procedure in particular by using library routines for gauss quadrature of rational functions readily available in the literature this new expression permits the exact numerical integration of singular static potentials associated with polynomial source distributions the rules to achieve the desired numerical accuracy for singular and nearly singular static and dynamic potential integrals are presented and discussed and several numerical examples are provided

on stable equivalences with endopermutation source abstract we show that a bimodule between block algebras which has a fusion stable endopermutation module as a source and which induces morita equivalences between centralisers of nontrivial subgroups of a defect group induces a stable equivalence of morita type this is the converse to a theorem of puig the special case where the source is trivial has long been known by many authors the earliest instance of a result deducing a stable equivalence of morita type from local morita equivalences with possibly nontrivial endopermutation source is due to puig in the context of blocks with abelian defect groups with a frobenius inertial quotient the present note is motivated by an application due to biland to blocks of finite groups with structural properties known to hold for hypothetical minimal counterexamples to the z p theorem