fast multipole method for scattering from an arbitrary pec target above or buried in a lossy half space the fast multipole method fmm was originally developed for perfect electric conductors pecs in free space through exploitation of the spectral properties of the free space green s function in the work reported here the fmm is modified for scattering from an arbitrary three dimensional 3 d pec target above or buried in a lossy half space the near terms in the fmm are handled via the original method of moments mom analysis wherein the half space green s function is evaluated efficiently and rigorously through application of the method of complex images the far fmm interactions which employ a clustering of expansion and testing functions utilize an approximation to the green s function dyadic via real image sources and far field reflection dyadics the half space fmm algorithm is validated through comparison with results computed via a rigorous mom analysis further a detailed comparison is performed on the memory and computational requirements of the mom and fmm algorithms for a target in the vicinity of a half space interface

a simple and accurate complex image interpretation of vertical antennas present in contiguous dielectric half spaces an efficient technique is developed to solve the important problem of vertical antennas located above and penetrating the interface between contiguous dielectric half spaces it begins by deriving the spectral expressions of the vector and scalar potential green functions in terms of the tm wave spectral transmission coefficient the complex image technique is used to derive simple accurate and rapidly convergent expressions of the full wave spatial green functions the spatial green functions are used in the moment method to model vertical thin wire antennas residing above the penetrating the interface separating the contiguous dielectric half spaces with and without loss

small cancellation groups and translation numbers in this paper we prove that c 4 t 4 p c 3 t 6 p and c 6 p small cancellation groups are translation discrete in the strongest possible sense and that in these groups for any g and any n there is an algorithm deciding whether or not the equation xn g has a solution there is also an algorithm for calculating for each g the maximum n such that g is an n th power of some element we also note that these groups cannot contain isomorphic copies of the group of p adic fractions and so in particular of the group of rational numbers besides we show that for c 4 t 4 and c 3 t 6 groups all translation numbers are rational and have bounded denominators

hyperbolic groups and their quotients of bounded exponents in 1987 gromov conjectured that for every non elementary hyperbolic group g there is an n n g such that the quotient group g gn is infinite the article confirms this conjecture in addition a description of finite subgroups of g gn is given it is proven that the word and conjugacy problem are solvable in g gn and that k 1g k 1 the proofs heavily depend upon prior authors results on the gromov conjecture for torsion free hyperbolic groups and on the burnside problem for periodic groups of even exponents

a method of images for a penetrable acoustic waveguide in this paper the complex image approximation to the reflection coefficient for water over a seabed half space is used to generate an image representation for a bounded acoustic waveguide with an underlying layered seabed the images are true point sources they have constant amplitudes which are raypath independent and in the case of a pekeris waveguide frequency independent this image representation is ideal for constructing the green s function kernel of the boundary integral equation method for target scattering in a waveguide the singular behavior of the green s function for an infinitesimal source receiver separation possibly with the target adjacent to one of the interfaces is modeled correctly and the image expansion has a simple analytic form which can be analytically differentiated the method is also accurate for significant source receiver separations which means that it can be used in the modeling of scattering from large sized objects and can also be used as an efficient and accurate short range propagation model for harmonic and broadband propagation in a penetrable waveguide

integral equation based domain decomposition method for solving electromagnetic wave scattering from non penetrable objects the integral equation ie method is commonly utilized to model time harmonic electromagnetic em problems one of the greatest challenges in its applications arises in the solution of the resulting ill conditioned matrix equation we introduce a new domain decomposition method ddm for the ie solution of em wave scattering from non penetrable objects the proposed method is a non overlapping non conformal ddm and it provides a computationally efficient and effective preconditioner for the ie matrix equations moreover the proposed approach is very suitable for dealing with multi scale electromagnetic problems since each sub domain has its own characteristics length and will be meshed independently furthermore for each sub domain we are free to choose the most effective ie sub domain solver based on its local geometrical features and electromagnetic characteristics additionally the multilevel fast multi pole algorithm mlfma is utilized to accelerate the computations of couplings between sub domains numerical results demonstrate that the proposed method yields rapid convergence in the outer krylov iterative solution process finally simulations of several large scale examples testify to the effectiveness and robustness of the proposed ie based ddm

domain decomposition method using integral equations and adaptive cross approximation ie aca ddm for studying antenna radiation and wave scattering from large metallic platforms in this paper we present a new methodology for a nonoverlapping domain decomposition method using boundary integral equations and adaptive cross approximation in the frequency domain ie aca ddm this paper proposes two main novelties first the ie ddm condition number is improved with the development of a formulation based on electric field integral equation efie implementation over the entire subdomains and on a simplification of the magnetic field integral equation mfie on the interfaces as a consequence the number of matrix vector products is significantly reduced during the iterative resolution then this paper proves that the aca can be applied and efficiently implemented in ie ddm methods moreover a hierarchical lu hlu decomposition is proposed to accelerate the aca solver the ie aca ddm is very suitable for the resolution of multiple excitations and to bypass the low frequency breakdown the flexibility accuracy and efficiency of ie aca ddm are demonstrated by comparing with reference integral equation solutions and scaled mock up measurements

comments on application of fft and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies in the original paper ibid vol ap 34 no 5 p 635 40 1986 t k sarkar et al describe how the fast fourier transform fft and the conjugate gradient method cgm can be used to efficiently make use of the convolutional form of the electric field integral equation for straight wire antennas the commentators agree that the cgm converges more rapidly than the previously used method of steepest descent and the spectral iteration technique they also point out that experience with the dyadic green s function encountered in the two dimensional transverse electric te and three dimensional equations for dielectric bodies is not so encouraging it is found that for these cases the cgm convergence can be quite slow degrading the efficiency of the algorithm in addition the solution obtained using the pulse basis point matching method to discretize the integral equation are very inaccurate for the two dimensional te and three dimensional cases a reply to these comments from the authors of the original paper is included

fast and accurate wide band analysis of antennas mounted on conducting platform using aim and asymptotic waveform evaluation technique the adaptive integral method aim in conjunction with the asymptotic waveform evaluation awe technique is presented for wide band analysis of antennas in the presence of electrically large conducting platforms in the awe technique the pade approximation solution obtained by matching the coefficients of the taylor series namely moments is utilized to achieve fast frequency sweeping besides the calculation and storage of the high order frequency derivatives of impedance matrices the awe technique requires repeatedly solving the linear system for the moments thus the aim is employed to reduce matrix storage and to accelerate all the matrix vector multiplications in both the linear system for the moments and the iterative solver furthermore a localized self box inclusion sbi preconditioner is used to accelerate the solution procedure of the linear system for the moments finally three numerical examples are given and discussed the input admittance and return loss of the antennas over a given frequency band are obtained by aim and aim awe method respectively the good agreements show that the proposed hybrid technique can greatly reduce the computation time without loss of accuracy

the equivalence of some residual properties of word hyperbolic groups abstract we show that every word hyperbolic group is residually finite if and only if every word hyperbolic group has a finite quotient

the residual finiteness of negatively curved polygons of finite groups a subgroup m g is almost malnormal provided that for each g g m the intersection m g m is finite it is proven that the free product of two virtually free groups amalgamating a finitely generated almost malnormal subgroup is residually finite a consequence of a generalization of this result is that an acute angled n gon of finite groups is residually finite if n 4 another consequence is that if g acts properly discontinuously and cocompactly on a 2 dimensional hyperbolic building whose chambers have acute angles and at least 4 sides then g is residually finite

finite grobner shirshov bases for plactic algebras and biautomatic structures for plactic monoids this paper shows that every plactic algebra of finite rank admits a finite grobner shirshov basis the result is proved by using the combinatorial properties of young tableaux to construct a finite complete rewriting system for the corresponding plactic monoid which also yields the corollaries that plactic monoids of finite rank have finite derivation type and satisfy the homological finiteness properties left and right fp fp also answering a question of zelmanov we apply this rewriting system and other techniques to show that plactic monoids of finite rank are biautomatic

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

tadpole labelled oriented graph groups and cyclically presented groups abstract we study a class of labelled oriented graph log group where the underlying graph is a tadpole graph we show that such a group is the natural hnn extension of a cyclically presented group and investigate the relationship between the log group and the cyclically presented group we relate the second homotopy groups of their presentations and show that hyperbolicity of the cyclically presented group implies solvability of the conjugacy problem for the log group in the case where the label on the tail of the log spells a positive word in the vertices in the circuit we show that the logs and groups coincide with those considered by szczepanski and vesnin we obtain new presentations for these cyclically presented groups and show that the groups of fibonacci type introduced by johnson and mawdesley are of this form these groups generalise the fibonacci groups and the sieradski groups and have been studied by various authors we continue these investigations using small cancellation and curvature methods to obtain results on hyperbolicity automaticity sq universality and solvability of decision problems

on the outer automorphism groups of finitely generated residually finite groups bumagin wise posed the question of whether every countable group can be realised as the outer automorphism group of a finitely generated residually finite group we give a partial answer to this problem for recursively presentable groups

rational subgroups of biautomatic groups centralizers of finite subsets in biautomatic groups are them selves biautomatic every polycyclic subgroup of a biautomatic group is abelian by finite

the triviality problem for profinite completions we prove that there is no algorithm that can determine whether or not a finitely presented group has a non trivial finite quotient indeed this property remains undecidable among the fundamental groups of compact non positively curved square complexes we deduce that many other properties of groups are undecidable for hyperbolic groups there cannot exist algorithms to determine largeness the existence of a linear representation with infinite image over any infinite field or the rank of the profinite completion

algorithms determining finite simple images of finitely presented groups we address the question for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection we prove both positive and negative results for a collection of finite simple groups that contains infinitely many alternating groups or contains classical groups of unbounded dimensions we prove that there is no such algorithm on the other hand for families of simple groups of lie type of bounded rank we obtain positive results for example for any fixed untwisted lie type x there is an algorithm that determines whether or not any given finitely presented group has simple images of the form x q for infinitely many q and if there are finitely many the algorithm determines them

small cancellations over relatively hyperbolic groups and embedding theorems we generalize the small cancellation theory over ordinary hyperbolic groups to relatively hyperbolic settings this generalization is then used to prove various embedding theorems for countable groups for instance we show that any countable torsion free group can be embedded into a finitely generated group with exactly two conjugacy classes in particular this gives the affirmative answer to the well known question of the existence of a finitely generated group g other than 2 such that all nontrivial elements of g are conjugate

virtual retractions conjugacy separability and omnipotence we use wreath products to provide criteria for a group to be conjugacy separable or omnipotent these criteria are in terms of virtual retractions onto cyclic subgroups we give two applications a straightforward topological proof of the theorem of stebe that infinite order elements of fuchsian groups of the first type are conjugacy distinguished and a proof that surface groups are omnipotent

a single level low rank ie qr algorithm for pec scattering problems using efie formulation this paper presents a single level matrix compression algorithm termed ie qr based on a low rank approximation to speed up the electric field integral equation efie formulation it is shown with the number of groups chosen to be proportional to n sup 1 2 where n is the number of unknowns the memory and cpu time for the resulting algorithm are both o n sup 1 5 the unique features of the algorithm are a the ie qr algorithm is based on the near rank deficiency property for well separated groups this near rank deficiency assumption holds true for many integral equation methods such as laplacian radiation and scattering problems in electromagnetics em the same algorithm can be adapted to other applications outside em with few or no modifications and b the rank estimation is achieved by a dual rank process which ranks the transmitting and receiving groups respectively thus the ie qr algorithm can achieve matrix compression without assembling the entire system matrix also a geometric neighboring preconditioner is presented in this paper this geometric neighboring preconditioner when used in conjunction with gmres is proven to be both efficient and effective for solving the compressed matrix equations

a saim faffa method for efficient computation of electromagnetic scattering problems a novel method is proposed through an effective combination of the subdomain adaptive integral method saim with the fast far field approximation faffa for efficient computation of electromagnetic scattering problems in the saim technique the whole perfectly electrically conducting structure is decomposed into subdomains and each subdomain is properly handled by the aim with its local cartesian grid individually a current continuity boundary condition is introduced on the interface between contiguous subdomains to guarantee the accuracy moreover the faffa technique is utilized to speed up the process of updating the modified excitation vectors numerical results show that the present hybrid method can not only significantly decrease the number of auxiliary grid points and the memory requirement of green s function matrix but also improve the convergence of the iterative process compared to the conventional aim

dual gpof dcim for fast computation of sommerfeld integrals and em scattering from an object partially embedded in dielectric half space a novel approach of dual gpof general pencil of functions combined with the dcim the discrete complex image method is developed to accelerate the sommerfeld integral evaluation when the mixed potential integral equation mpie is applied to numerically calculate scattering from a conductive object partially embedded in a dielectric half space where the field and source points are located in different media firstly the factors related with the field point are separated from the spectrum function and the gpof is used to find the complex image parameters at finite discrete source points secondly the gpof is used again to fit the functional relationship of each complex image parameter with the source positions to evaluate the complex image parameters for any source position in a closed functional summation comparing numerical results of dual gpof and direct numerical integration this dual gpof process is proved highly effective finally dual gpof dcim is applied to computation of electromagnetic scattering from a pec spherical object partially embedded in a dielectric half space medium and numerical scattering results upon different model parameters are presented and analyzed

thick metric spaces relative hyperbolicity and quasi isometric rigidity we study the geometry of non relatively hyperbolic groups generalizing a result of schwartz any quasi isometric image of a non relatively hyperbolic space in a relatively hyperbolic space is contained in a bounded neighborhood of a single peripheral subgroup this implies that a group being relatively hyperbolic with non relatively hyperbolic peripheral subgroups is a quasi isometry invariant as an application artin groups are relatively hyperbolic if and only if freely decomposable we also introduce a new quasi isometry invariant of metric spaces called metrically thick which is sufficient for a metric space to be non hyperbolic relative to any non trivial collection of subsets thick finitely generated groups include mapping class groups of most surfaces outer automorphism groups of most free groups certain artin groups and others non uniform lattices in higher rank semisimple lie groups are thick and hence non relatively hyperbolic in contrast with rank one which provided the motivating examples of relatively hyperbolic groups mapping class groups are the first examples of non relatively hyperbolic groups having cut points in any asymptotic cone resolving several questions of drutu and sapir about the structure of relatively hyperbolic groups outside of group theory teichmuller spaces for surfaces of sufficiently large complexity are thick with respect to the weil peterson metric in contrast with brock farb s hyperbolicity result in low complexity

real axis integration of sommerfeld integrals with applications to printed circuit antennas printed circuit antennas are becoming an integral part of imaging arrays in microwave millimeter and submillimeter wave frequencies the electrical characteristics of such antennas can be analyzed by solving integral equations of the fredholm first kind the kernel involves sommerfeld integrals which are particularly difficult to solve when source and field points lie on an electrical discontinuity as it occurs in the determination of the characteristics of printed circuit antennas an analytic numeric real axis integration technique has been developed for such integrals and it is combined with piece wise sinusoidal expansions to solve the fredholm integral equation for the unknown current density

topology of finite graphs this paper derives from a course in group theory which i gave at berkeley in 1982 i wanted to prove the standard theorems on free groups and discovered that after a few preliminaries the notion of locally injective map or immersion of graphs was very useful this enables one to see in an effective easy algorithmic way just what happens with finitely generated free groups one can understand in this way 1 howson s theorem that if a and b are finitely generated subgroups of a free group then a b is finitely generated and 2 m hall s theorem that finitely generated subgroups of free groups are closed in the profinite topology during this course s m gersten came up with a simple proof of h neumann s inequality on the ranks in howson s theorem one of the ideas in gersten s proof was to use core graphs graphs with no trees hanging on subsequently i found that some consequences of a paper of greenberg s could be proved using core graphs and covering translations of immersions the most striking such result is that if a and b are finitely generated subgroups of a free group and if a c b is of finite index in both a and b then a b is of finite index in a v b the subgroup generated by a ub

on the hyperbolicity of small cancellation groups and one relator groups in the article a result relating to maps finite planar connected and simply connected 2 complexes that satisfy a c p t it is shown that a finitely generated onerelator group g whose reduced relator r is of the form r at0at1 atn 1 where the words ti are distinct and have no occurrences of the letter a 1 is not hyperbolic if and only if one has in the free group that 1 n 2 and t0t 1 1 is a proper power 2 n 3 and for some i it is true with subscripts mod 3 that tit 1 i 1tit 1 i 2 1 3 n 4 and for some i it is true with subscripts mod 4 that tit 1 i 1ti 2t 1 i 3 1

metric systolicity and two dimensional artin groups we introduce the notion of metrically systolic simplicial complexes we study geometric and large scale properties of such complexes and of groups acting on them geometrically we show that all two dimensional artin groups act geometrically on metrically systolic complexes as direct corollaries we obtain new results on two dimensional artin groups and all their finitely presented subgroups we prove that the conjugacy problem is solvable and that the dehn function is quadratic we also show several large scale features of finitely presented subgroups of two dimensional artin groups lying background for further studies concerning their quasi isometric rigidity

the equation xp yq zr and groups that act freely on l trees let g be a finitely generated group that acts freely on a lambda tree where lambda is an ordered abelian group and let x y z be elements in g we show that if x p y q z r with integers p q r geq 4 then x y and z commute

near field computation for sound propagation above ground using complex image theory in this paper a very simple method is introduced for the efficient computation of the sound field in the near region above an impedance ground or an extended reaction ground the procedure is based on complex image theory using prony s method the slowly varying factor in the integrand of the sommerfeld integral is approximated by a short series in terms of complex exponential functions the result can be exactly evaluated by the sommerfeld identity a new closed form approximate expression of the sound field is obtained which is represented as the original source its quasistatic image and several images with complex amplitudes and positions avoiding numerical evaluation of the sommerfeld integral makes these closed form expressions computationally very efficient the representation of the field with complex images makes the formula useful in measurement of ground impedance or in other cases requiring repeated mapping of the sound field numerical results show that these closed form green s functions are very accurate for the computation of the near field