a counterexample to the isomorphism problem for integral group rings let x be a finite group and denote its integral group ring by zx a group basis of zx is a subgroup y of the group of units of zx of augmentation 1 such that zx zy and ixi yi an example of a finite group x is given such that zx has a group basis which is not isomorphic to x a main ingredient is the existence of a subgroup g of x which possesses a non inner automorphism which becomes inner in the integral group ring zg the question whether a finite group x is determined by its integral group ring zx is known as the isomorphism problem for integral group rings it was

tensor algebras overc correspondences representations dilations andc envelopes tensor algebras overc correspondences are noncommutative generalizations of the disk algebra they contain as special cases analytic crossed products semi crossed products and popescu s noncommutative disk algebras in this paper a dilation theorem and a commutant lifting theorem for representations of tensor algebras is proved these are used to show that for certainc correspondences thec envelopes in the sense of arveson of the tensor algebras are the cuntz pimsner algebras of the correspondences

crossed products by endomorphisms of c_0 x algebras abstract in the first part of the paper we develop a theory of crossed products of a c algebra a by an arbitrary not necessarily extendible endomorphism a a we consider relative crossed products c a j where j is an ideal in a and describe up to morita rieffel equivalence all gauge invariant ideals in c a j and give six term exact sequences determining their k theory we also obtain certain criteria implying that all ideals in c a j are gauge invariant and that c a j is purely infinite in the second part we consider a situation where a is a c 0 x algebra and is such that f a f a a a f c 0 x where is an endomorphism of c 0 x pictorially speaking is a mixture of a topological dynamical system x dual to c 0 x and a continuous field of homomorphisms x between the fibers a x x x of the corresponding c bundle for systems described above we establish efficient conditions for the uniqueness property gauge invariance of all ideals and pure infiniteness of c a j we apply these results to the case when x prim a is a hausdorff space in particular if the associated c bundle is trivial we obtain formulas for k groups of all ideals in c a j in this way we constitute a large class of crossed products whose ideal structure and k theory is completely described in terms of x x x x y where y is a closed subset of x

an algorithm to construct candidates to counterexamples to the zassenhaus conjecture abstract let g be a finite group n a nilpotent normal subgroup of g and let v z g n denote the group formed by the units of the integral group ring z g of g which map to the identity under the natural homomorphism z g z g n sehgal asked whether any torsion element of v z g n is conjugate in the rational group algebra of g to an element of g this is a special case of the zassenhaus conjecture by results of cliff and weiss and hertweck sehgal s problem has a positive solution if n has at most one non cyclic sylow subgroup we present some algorithms to study sehgal s problem when n has at most one non abelian sylow subgroup they are based on the cliff weiss inequalities introduced by the authors in a previous paper with the help of these algorithms we obtain some positive answers to sehgal s problem and use them to show that for units in v z g n our method is strictly stronger than the well known help method we then present a method to use the output of one of the algorithms to construct explicit metabelian groups which are candidates to a negative solution to sehgal s problem recently eisele and margolis showed that some of the examples proposed in this paper are indeed counterexamples to the zassenhaus conjecture these are the first known counterexamples moreover we prove that every metabelian negative solution of sehgal s problem satisfying some minimal conditions is given by our construction

nica toeplitz algebras associated with product systems over right lcm semigroups abstract we prove uniqueness of representations of nica toeplitz algebras associated to product systems of c correspondences over right lcm semigroups by applying our previous abstract uniqueness results developed for c precategories our results provide an interpretation of conditions identified in work of fowler and fowler raeburn and apply also to their crossed product twisted by a product system in the new context of right lcm semigroups as well as to a new doplicher roberts type c algebra associated to the nica toeplitz algebra as a derived construction we develop nica toeplitz crossed products by actions with completely positive maps this provides a unified framework for nica toeplitz semigroup crossed products by endomorphisms and by transfer operators we illustrate these two classes of examples with semigroup c algebras of right and left semidirect products

discrete product systems and twisted crossed products by semigroups a product systemeover a semigrouppis a family of hilbert spaces es s p together with multiplicationses et est we vieweas a unitary valued cocycle onp and consider twisted crossed productsa e pinvolvingeand an action ofpby endomorphisms of ac algebraa whenpis quasi lattice ordered in the sense of nica we isolate a class of covariant representations ofe and consider a twisted crossed productbp e pwhich is universal for covariant representations ofewhenehas finite dimensional fibres and in general is slightly larger in particular whenp nand dim e1 our algebrabn e n is a new infinite analogue of the toeplitz cuntz algebras ton our main theorem is a characterisation of the faithful representations ofbp e p

range profile analysis of the 2 d target above a rough surface based on the electromagnetic numerical simulation in this paper 1 d range profiles of a 2 d perfect electric conductor pec target above a 2 d pec rough surface are investigated with numerical solutions for the electric field integral equations efies of the combined scattering model the backscattering is computed accurately by the reradiation of the induced surface currents on the target and the rough surface using a stepped frequency waveform sfw 1d high resolution range profiles hrrps of the target above a rough surface are obtained by performing the inverse discrete fourier transform idft on the wideband backscattered field plots of range profiles show that the multiple interactions between the target and the bottom surface lead to a series of equivalent range profiles especially when the bottom surface is smooth range locations of the equivalent range profiles are in good agreement with the results expected from the ray theory the range profiles could be understood and analyzed based on the knowledge of the scattering mechanisms thus the connection between the numerically simulated range profiles and the scattering mechanisms is established

torsion units in integral group rings of some metabelian groups let g be an extension of an elementary abelian p group a by an abelian group x with faithful and irreducible action then any torsion unit of the integral group ring zg is rationally conjugate to a trivial unit this confirms a conjecture of zassenhaus for these groups g

lattices and cohomological mackey functors for finite cyclic p groups abstract for a finite cyclic p group g and a discrete valuation domain r of characteristic 0 with maximal ideal p r the r g permutation modules are characterized in terms of the vanishing of first degree cohomology on all subgroups cf theorem a as a consequence any r g lattice can be presented by r g permutation modules cf theorem c the proof of these results is based on a detailed analysis of the category of cohomological g mackey functors with values in the category of r modules it is shown that this category has global dimension 3 cf theorem e a crucial step in the proof of theorem e is the fact that a gentle r order category with parameter p has global dimension less than or equal to 2 cf theorem d

on unified numerical algorithm for 3 d scattering from dielectric and pec random rough surfaces we present a unified fast scattering algorithm for dielectric random rough surfaces that asymptotically reduces to the perfect electric conductor pec case when the loss tangent grows extremely large the coifman wavelets are employed to implement galerkin s procedure in the method of moments mom the coiflets based surface integral equations ies consist of both the tangential and normal components of electromagnetic fields as unknowns the inherited mathematical superiority e g local multiresolution analysis and high regularity with holder index 1 449 in smoothness allows efficiently implementing both electric field ie and magnetic field ie due to the high precision one point quadrature the coiflets yield fast evaluations of the most off diagonal entries reducing the matrix fill effort from o n2 to o n the orthogonality and riesz basis of the coiflets generate well conditioned impedance matrix with rapid convergence for the conjugate gradient solver in addition a semianalytical expression of the tapered wave carried power is derived which speeds up computations of the normalization factor of scattering coefficients numerical results demonstrate that the reduced pec model does not suffer from ill posed problems namely matrix condition numbers are kept small and solutions are stable under extremely large loss tangent where normal components of h field and tangential e field have vanished compared with the previous publications and laboratory measurements good agreement is observed

the generalized forward backward method for analyzing the scattering from targets on ocean like rough surfaces in holliday et al 1995 1996 the iterative forward backward fb method has been proposed to solve the magnetic field integral equation mfie for smooth one dimensional 1 d rough surfaces this method has proved to be very efficient converging in a very small number of iterations nevertheless this solution becomes unstable when some obstacle like a ship or a large breaking wave is included in the original problem in this paper we propose a new method the generalized forward backward gfb method to solve such kinds of complex problems the approach is formulated for the electric field integral equation efie which is solved using a hybrid combination of the conventional fb method and the method of moments mom the latter of which is only applied over a small region around the obstacle the gfb method is shown to provide accurate results while maintaining the efficiency and fast convergence of the conventional fb method some numerical results demonstrate the efficiency and accuracy of the new method even for low grazing angle scattering problems

on the discretization of the integral equation describing scattering by rough conducting surfaces numerical simulations of scattering from one dimensional 1 d randomly rough surfaces with pierson moskowitz p m spectra show that if the kernel or propagator matrix with zeros on its diagonal is used in the discretized magnetic field integral equation mfie the results exhibit an excessive sensitivity to the current sampling interval especially for backscattering at low grazing angles lgas though the numerical results reported in this paper were obtained using the method of ordered multiple interactions momi a similar sampling interval sensitivity has been observed when a standard method of moments mom technique is used to solve the mfie a subsequent analysis shows that the root of the problem lies in the correct discretization of the mfie kernel we found that the inclusion of terms proportional to the surface curvature regarded by some authors as an additional correction in the diagonal of the kernel matrix virtually eliminates this sampling sensitivity effect by reviewing the discretization procedure for mfie we show that these curvature terms indeed must be included in the diagonal in order for the propagator matrix to be represented properly the recommended current sampling interval for scattering calculations with p m surfaces is also given

an efficient algorithm for electromagnetic scattering from rough surfaces using a single integral equation and multilevel sparse matrix canonical grid method an efficient algorithm for wave scattering from two dimensional lossy rough surfaces is proposed it entails the use of a single magnetic field integral equation smfie in conjunction with a multilevel sparse matrix canonical grid msmcg method the rao wilton glisson rwg triangular discretization is adopted to better model the rough surface than the pulse basis functions used in the well established smcg method using the smfie formulation only one unknown per interior edge of the triangular mesh approximating the rough surface is required and the iterative solution to the moment equation converges more rapidly than that of the conventional coupled equations for dielectric rough surfaces the msmcg method extends the applicability of the smcg method to rougher surfaces parallel implementation of the proposed method enables us to model dielectric surfaces up to a few thousand square wavelengths simulation results are presented as bistatic scattering coefficients for gaussian randomly rough surfaces

on a conjecture of zassenhaus on torsion units in integral group rings ii suppose that a group g has a normal subgroup c where c and g c are cyclic of relatively prime orders then any torsion unit in zg is rationally conjugate to a trivial unit

a counterexample to the first zassenhaus conjecture abstract hans j zassenhaus conjectured that for any unit u of finite order in the integral group ring of a finite group g there exists a unit a in the rational group algebra of g such that a 1 u a g for some g g we disprove this conjecture by first proving general results that help identify counterexamples and then providing an infinite number of examples where these results apply our smallest example is a metabelian group of order 2 7 3 2 5 7 2 19 2 whose integral group ring contains a unit of order 7 19 which in the rational group algebra is not conjugate to any element of the form g

coifman wavelets in 3 d scattering from very rough random surfaces the coifman wavelets are employed to perform galerkin s procedure in the method of moments mom the coiflets are continuous smooth overlapping yet orthogonal which permit significant reduction of the sampling rate and dramatic compression of the matrix size with respect to the pulse based mom in addition the wavelet based impedance matrix is sparse more importantly the vanishing moments of the coiflets of order l 4 provide us with high precision o h sup 5 one point quadrature which knocks down the computational effort in filling the matrix entries from o n sup 2 to o n our approach is different from the conventional wavelet technique which employs wavelets to sparsify an existing impedance matrix under similarity transformation with computational cost in o n sup 2 excellent agreement between this coifman wavelet method and the previous publications is observed

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

on picard groups of blocks of finite groups we show that the subgroup of the picard group of ap block ofa finite group given by bimodules with endopermutation sources modulo theautomorphism group of a source algebra is determined locally in terms of thefusion system on a defect group we show that the picard group of a block overa complete discrete valuation ringoof characteristic zero with an algebraicclosurekoffpas residue field is a colimit of finite picard groups of blocks overp adic subrings ofo we apply the results to blocks with an abelian defectgroup and frobenius inertial quotient and specialise this further to blockswith cyclic or klein four defect groups

dilations of c correspondences and the simplicity of cuntz pimsner algebras we develop a dilation theory for c correspondences showing that every c correspondence e over a c algebra a can be universally embedded into a hilbert c bimodule xe over a c algebra ae such that the crossed product a e n is naturally isomorphic to ae xe z the cuntz pimsner algebra oe is isomorphic to ae xe z where ae and xe are quotients of ae resp xe if e is full and the left action is by generalized compact operators then xe is an equivalence bimodule or equivalently an invertible c correspondence in general xe is merely an essential hilbert c bimodule slightly extending previous results on crossed products by equivalence bimodules we apply our dilation theory to show that for full c correspondences over unital c algebras oe is simple if and only if e is minimal and nonperiodic extending and simplifying results of muhly and solel and kajiwara pinzari and watatani

zassenhaus conjecture on torsion units holds for psl 2 p with p a fermat or mersenne prime abstract h j zassenhaus conjectured that any unit of finite order in the integral group ring z g of a finite group g is conjugate in the rational group algebra q g to an element of the form g with g g this is known to be true for some series of solvable groups but recently metabelian counterexamples have been constructed the conjecture is still open for non abelian simple groups and has only been proved for thirteen such groups we prove the zassenhaus conjecture for the groups psl 2 p where p is a fermat or mersenne prime this increases the list of non abelian simple groups for which the conjecture is known by probably infinitely many but at least by 50 groups our result is an easy consequence of known results and our main theorem which states that the zassenhaus conjecture holds for a unit in z psl 2 q of order coprime with 2 q for some prime power q

bistatic scattering and emissivities of random rough dielectric lossy surfaces with the physics based two grid method in conjunction with the sparse matrix canonical grid method bistatic em wave scattering from 2 d lossy dielectric random rough surfaces 3 d scattering problem with large permittivity is studied for media with large permittivities the fields can vary rapidly on the surface thus a dense discretization of the surface is required to implement the method of moments mom for the surface integral equations such a dense discretization is also required to ensure that the emissivity can be calculated to the required accuracy of 0 01 for passive remote sensing applications we have developed a physics based two grid method pbtg that can give the accurate results of the surface fields on the dense grid and also the emissivities the pbtg consists of using two grids on the surface the coarse grid and the required dense grid the pbtg only requires moderate increase in central processing unit cpu and memory in this paper the numerical results are calculated by using the pbtg in conjunction with the sparse matrix canonical grid smcg method the computational complexity and memory requirement for the present algorithm are o n sub scg log n sub scg and o n sub scg respectively where n sub scg is the number of grid points on the coarse grid numerical simulations are illustrated for root mean square rms height of 0 3 wavelengths and correlation length of 1 0 wavelength the relative permittivity used is as high as 17 2i the numerical results are compared with that of the second order small perturbation method spm the comparisons show that a large difference in brightness temperature exists between the spm and numerical simulation results for cases with moderate rms slope

a sylow theorem for the integral group ring of psl 2 q abstract for g psl 2 p f denote by z g the integral group ring over g and by v z g the group of units of augmentation 1 in z g let r be a prime different from p using the so called help method we prove that units of r power order in v z g are rationally conjugate to elements of g as a consequence we prove that subgroups of prime power order in v z g are rationally conjugate to subgroups of g if p 2 or f 1

crossed products by endomorphisms and reduction of relations in relative cuntz pimsner algebras abstract starting from an arbitrary endomorphism of a unital c algebra a we construct a crossed product it is shown that the natural construction depends not only on the c dynamical system a but also on the choice of an ideal j orthogonal to ker the article gives an explicit description of the internal structure of this crossed product and in particular discusses the interrelation between relative cuntz pimsner algebras and partial isometric crossed products we present a canonical procedure that reduces any given c correspondence to the smallest c correspondence yielding the same relative cuntz pimsner algebra as the initial one in the context of crossed products this reduction procedure corresponds to the reduction of c dynamical systems and allows us to establish a coincidence between relative cuntz pimsner algebras and crossed products introduced

on morita and derived equivalences for cohomological mackey algebras by results of the second author a source algebra equivalence between two p blocks of finite groups induces an equivalence between the categories of cohomological mackey functors associated with these blocks and a splendid derived equivalence between two blocks induces a derived equivalence between the corresponding categories ofcohomological mackey functors the main result of this paper proves a partial converse an equivalence resp rickard equivalence between the categories of cohomological mackey functors of two blocks of finite groups induces a permeable morita resp derived equivalence between the two block algebras

the validity of the perturbation approximation for rough surface scattering using a gaussian roughness spectrum the validity of the perturbation approximation for rough surface scattering is examined 1 by comparison with exact results obtained by solving an integral equation and 2 through comparison of low order perturbation predictions with higher order predictions the pressure release boundary condition is assumed and the field quantity calculated is the bistatic scattering cross section a gaussian roughness spectrum is used and the surfaces have height variations in only one direction it is found in general that the condition kh 1 k is the acoustic wavenumber h is the rms surface height is insufficient to guarantee the accuracy of first order or higher order perturbation theory when the surface correlation length l becomes too large or too small with h held fixed higher order perturbation terms can make larger contributions to the scattering cross section than lower order terms an explanation for this result is given the regions of validity for low order perturbation theory are also given th

3 d scattering from a pec target buried beneath a dielectric rough surface an efficient pile aca algorithm for solving a hybrid ka efie formulation an efficient hybrid ka efie formulation is deployed to analyze the electromagnetic em scattering from a 3 d perfectly electric conducting pec object buried beneath a 2 d dielectric rough surface in this approach the electric and magnetic current densities on the rough surface are analytically obtained through the current based kirchhoff approximation ka whereas the electric current density on the buried object is rigorously determined by solving the electric field integral equation efie using the galerkin s method of moments mom with rao wilton glisson rwg basis functions the ka efie matrix system is then efficiently solved by the iterative propagation inside layer expansion pile method combined with the algebraic adaptive cross approximation aca the current densities on the dielectric rough surface are thereafter used to handle the bistatic normalized radar cross section nrcs patterns the proposed hybrid approach allows a significant reduction in computation time and memory requirements compared to the rigorous poggio miller chang harrington wu pmchw efie formulation which requires solving a large mom matrix equation moreover the hybridization of the aca algorithm with the pile method improves further the computational cost thanks to the rank deficient propriety of the coupling matrices to validate the hybrid approach we compare its results with those of the rigorous pmchw efie approach

numerical analysis of scattering by dielectric random rough surfaces using modified smcg scheme and curvilinear rwg basis functions an augmented sparse matrix canonical grid smcg approach for numerical analysis of scattering by dielectric random rough surfaces is developed it is an extension of the previous modified smcg scheme for perfect electric conducting pec surfaces to dielectric cases and is enhanced by adopting curved triangulation modeling by using the curved modeling with curvilinear rao wilton glisson basis functions crwg bases the number of unknowns can be reduced substantially to extract results of the same accuracy compared with using the planar triangular discretization with planar rwg bases numerical results for gaussian and ocean like dielectric rough surfaces are provided to confirm the validity and efficacy of the proposed method

monte carlo simulations of large scale problems of random rough surface scattering and applications to grazing incidence with the bmia canonical grid method scattering of a te incident wave from a perfectly conducting one dimensional random rough surface is studied with the banded matrix iterative approach canonical grid bmia cag method the bmia cag is an improvement over the previous bmia the key idea of bmia cag is that outside the near field interaction the rest of the interactions can be translated to a canonical grid by taylor series expansion the use of a flat surface as a canonical grid for a rough surface facilitates the use of the fast fourier transform for nonnear field interaction the method can be used for monte carlo simulations of random rough surface problems with a large surface length including all the coherent wave interactions within the entire surface we illustrate results up to a surface length of 2500 wavelengths with 25000 surface unknowns the method is also applied to study scattering from random rough surfaces at near grazing incidence the numerical examples illustrate the importance of using a large surface length for some backscattering problems

efficient solution of efie via low rank compression of multilevel predetermined interactions this paper describes the predetermined interaction list oct tree pilot algorithm and its application in expediting the solution of full wave electric field integral equation efie based scattering problems for three dimensional arbitrarily shaped conductors pilot combines features of the fast multipole method fmm and qr decomposition based matrix compression techniques to optimize setup times solve times and memory requirements the method is kernel independent and stable for electrically small structures unlike traditional fmm the novel features of the algorithm namely the mixed potential compression scheme and the hierarchical multilevel predetermined matrix structure are explained in detail a complexity estimate is presented to demonstrate the scaling in time and memory requirements examples exhibiting the accuracy and the time and memory performances are also presented finally a quantitative study is included to address the expected but gradual degradation of qr based compression techniques for electrically large structures

a dixmier douady theorem for fell algebras abstract we generalise the dixmier douady classification of continuous trace c algebras to fell algebras to do so we show that c diagonals in fell algebras are precisely abelian subalgebras with the extension property and use this to prove that every fell algebra is morita equivalent to one containing a diagonal subalgebra we then use the machinery of twisted groupoid c algebras and equivariant sheaf cohomology to define an analogue of the dixmier douady invariant for fell algebras and to prove our classification theorem

construction of units in integral group rings of finite nilpotent groups let u be the group of units of the integral group ring of a finite group g we give a set of generators of a subgroup b of u this subgroup is of finite index in u if g is an odd nilpotent group we also give an example of a 2 group such that b is of infinite index in u

numerical simulation of vector wave scattering from the target and rough surface composite model with 3 d multilevel uv method numerical simulation of vector wave scattering from three dimensional 3 d target and rough surface composite model is investigated with a 3 d multilevel uv method due to the adoption of rwg basis functions for accurate modeling of vector current the oscillation of the interaction matrix elements brings difficulty to directly apply the uv decomposition method based on the reordering of the interaction strength and the sampling according to the characteristics distribution of the interaction an em interaction based sampling algorithm is developed for the accurate reconstruction of the far interaction submatrix with uv decomposition method combined with multilevel division of the total composite model the 3 d multilevel uv method incorporating the new sampling algorithm is developed for vector wave scattering from 3 d complex target above or on a random rough surface the 3 d multilevel uv method yields a complexity of o n log n for the setup time of the impedance matrix the solve time of the matrix iterative solution and also for the memory requirements the accuracy and the efficiency of the 3 d multilevel uv method is compared and validated with the full mom method and the aca method in the tested cases finally the applications of a target above or on the rough surface for example a ship on the sea surface have been accomplished and analyzed

on the use of finite surfaces in the numerical prediction of rough surface scattering method of moments mom based monte carlo calculations are widely used in determining the average radar cross section of randomly rough surfaces it is desirable in these numerical calculations to truncate the scattering surface into as short a length as possible to minimize the solution time however truncating the surface tends to change the solution for the surface fields near the truncation points and may alter the scattered far fields in this paper these end effect errors are examined for one dimensional i e grooved or corduroy surfaces which are gaussian distributed in height and have either a gaussian or a pierson moskowitz spectra in the case of the pierson moskowitz type surface it is shown that a relatively short surface of 80 120 wavelengths can be used to obtain the average backscattered radar cross section for backscattering angles as large as 60 spl deg from normal for a comparatively smooth gaussian surface on the other hand its is shown that the truncation effects can be very significant at moderate backscattering angles also great care should be taken when examining the scattering from gaussian surfaces which are dominated by specular scattering it is shown that in this situation a very large number of calculations may be needed to obtain a good numerical average

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

a class of c algebras generalizing both graph algebras and homeomorphism c algebras i fundamental results we introduce a new class of c algebras which is a generalization of both graph algebras and homeomorphism c algebras this class is very large and also very tractable we prove the so called gauge invariant unique ness theorem and the cuntz krieger uniqueness theorem and compute the k groups of our algebras

infinitely generated pseudocompact modules for finite groups and weiss theorem abstract one of the most beautiful results in the integral representation theory of finite groups is a theorem of a weiss that detects a permutation r lattice for the finite p group g in terms of the restriction to a normal subgroup n and the n fixed points of the lattice where r is a finite extension of the p adic integers using techniques from relative homological algebra we generalize weiss theorem to the class of infinitely generated pseudocompact lattices for a finite p group allowing r to be any complete discrete valuation ring in mixed characteristic a related theorem of cliff and weiss is also generalized to this class of modules the existence of the permutation cover of a pseudocompact module is proved as a special case of a more general result the permutation cover is explicitly described

simple cuntz pimsner rings abstract necessary and sufficient conditions for when every non zero ideal in a relative cuntz pimsner ring contains a non zero graded ideal when a relative cuntz pimsner ring is simple and when every ideal in a relative cuntz pimsner ring is graded are given a cuntz krieger uniqueness theorem for relative cuntz pimsner rings is also given and condition l and condition k for relative cuntz pimsner rings are introduced as applications of these results a uniqueness result for the toeplitz algebra of a directed graph and characterizations of when crossed products of a ring by a single automorphism and fractional skew monoid rings of a single corner isomorphism are simple are obtained

tapered wave with dominant polarization state for all angles of incidence typical applications of the method of moments mom to rough surface three dimensional 3 d electromagnetic scattering require a truncation of the surface considered and call for a tapered incident wave it is shown how such a wave can be constructed as a superposition of plane waves avoiding problems near both normal and grazing incidence and providing clean footprints and clear polarization at all angles of incidence the proposed special choice of polarization vectors removes an irregularity at the origin of the wavenumber space and leads to a least squared error property of the wave issues in the application to 3 d scattering from an object over a rough surface are discussed approximate 3 d scalar and vector tapered waves which can be evaluated without resorting to any numerical integrations are derived and important limitations to the accuracy and applicability of these approximations are pointed out

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

scattering of electromagnetic waves from rough surfaces a boundary integral method for low grazing angles we present a boundary integral method for the numerical solution of the rigorous problem of wave scattering from rough surfaces under grazing illumination the model of a locally perturbated plane is adopted a finite patch of rough surface has its roughness flattened at the edges the boundary formulation unknowns are the tangential components of the scattered field defined as the contribution from the rough area this way the numerical domain of study is correctly bounded even with a plane wave as incident field and the sampled area is made independent of the incidence this rigorous approach called the grazing method of moments is implemented on two dimensional perfectly conducting surfaces and validated by comparison with a reference numerical solution for surfaces with gaussian correlation functions now the validity of approximate models at low grazing angles can be investigated the small perturbation method and the small slope approximation are addressed in this paper scattering diagrams show how the performances of these methods deteriorate drastically at backward scattering angles as the incidence goes to grazing

cliff weiss inequalities and the zassenhaus conjecture abstract let n be a nilpotent normal subgroup of the finite group g assume that u is a unit of finite order in the integral group ring z g of g which maps to the identity under the linear extension of the natural homomorphism g g n we show how a result of cliff and weiss can be used to derive linear inequalities on the partial augmentations of u and apply this to the study of the zassenhaus conjecture this conjecture states that any unit of finite order in z g is conjugate in the rational group algebra of g to an element in g

a domain decomposition method for boundary integral equations using a transmission condition based on the near zone couplings a domain decomposition method ddm for the solution of boundary integral equations for impenetrable objects is presented the approach uses a transmission condition which is based on the near range couplings in order to obtain close approximations of the global solution on the subdomains the comparatively strong near zone interactions are taken into account to avoid unphysical reflections from the domain interfaces the algorithm can be accelerated by fast integral solvers such as the multilevel fast multipole method mlfmm by creating local subtrees which coincide with the different computing domains this concept is embedded in an inner outer iterative solution algorithm in which the ddm acts as a preconditioner in the inner iterations by introducing small overlap regions the convergence of the iterative solver is further improved this results in a very robust ddm which can be integrated into existing codes with reasonable effort and which is suited for parallelization numerical results for various open and closed objects demonstrate the effectiveness and the excellent performance of the proposed ddm for the solution of electromagnetic radiation and scattering problems

topological aperiodicity for product systems over semigroups of ore type we prove a version of uniqueness theorem for cuntz pimsner algebras of discrete product systems over semigroups of ore type to this end we introduce doplicher roberts picture of cuntz pimsner algebras and the semigroup dual to a product system of regular c correspondences under a certain aperiodicity condition on the latter we obtain the uniqueness theorem and a simplicity criterion for the algebras in question these results generalize the corresponding ones for crossed products by discrete groups due to archbold and spielberg and for exel s crossed products due to exel and vershik they also give interesting conditions for topological higher rank graphs and p graphs and apply to the new cuntz c algebra qn arising from the ax b semigroup over n

application of multiregion model to em scattering from a dielectric rough surface with or without a target above it an efficient multiregion model is extended by the single integral equation sie method for the first time to calculate electromagnetic em scattering from a dielectric rough surface with or without a perfectly electric conducting target above it in the multiregion model the rough surface is divided into multiple regions depending on their positions along the rough surface and the energy distribution of the incident wave two intermediate regions are chosen as the dominant regions in which the method of moment is adopted if a target is located above the surface the target is also included in the dominant region hence the new model can markedly reduce the number of unknowns compared with full sie analysis mutual couplings between different regions are approximately considered based on magnetic and electric field integral equations from which closed form approximations for currents in other regions are derived

some examples of picard groups of blocks abstract we calculate examples of picard groups for 2 blocks with abelian defect groups with respect to a complete discrete valuation ring these include all blocks with abelian 2 groups of 2 rank at most three with the exception of the principal block of j 1 in particular this shows directly that all such picard groups are finite and picent the group of morita auto equivalences fixing the centre is trivial these are amongst the first calculations of this kind further we prove some general results concerning picard groups of blocks with normal defect groups as well as some other cases

on c algebras associated with c correspondences abstract we study c algebras arising from c correspondences which were introduced by the author we prove the gauge invariant uniqueness theorem and obtain conditions for our c algebras to be nuclear exact or satisfy the universal coefficient theorem we also obtain a 6 term exact sequence of k groups involving the k groups of our c algebras

monte carlo simulation of electromagnetic scattering from two dimensional random rough surfaces the fast multipole method fast fourier transform fmm fft method is developed to compute the scattering of an electromagnetic wave from a two dimensional 2 d rough surface the resulting algorithm computes a matrix vector multiply in o n log n operations this algorithm is shown to be more efficient than another o n log n algorithm the multilevel fast multipole algorithm mlfma for surfaces of small height for surfaces with larger roughness the mlfma is found to be more efficient using the mlfma monte carlo simulations are carried out to compute the statistical properties of the electromagnetic scattering from 2 d random rough surfaces using a workstation for the rougher surface backscattering enhancement is clearly observable as a pronounced peak in the backscattering direction of the computed bistatic scattering coefficient for the smoother surface the monte carlo results compare well with the results of the approximate kirchhoff theory

topological freeness for c correspondences abstract we study conditions that ensure uniqueness theorems of cuntz krieger type for relative cuntz pimsner algebras o j x associated to a c correspondence x over a c algebra a we give general sufficient conditions phrased in terms of a multivalued map x acting on the spectrum a of a when x j is of type i we construct a directed graph dual to x and prove a uniqueness theorem using this graph when x j is liminal we show that topological freeness of this graph is equivalent to the uniqueness property for o j x as well as to an algebraic condition which we call j acyclicity of x as an application we improve the fowler raeburn uniqueness theorem for the toeplitz algebra t x we give new simplicity criteria for o x we generalize and enhance uniqueness results for relative quiver c algebras of muhly and tomforde we also discuss applications to crossed products by endomorphisms

finite groups of matrices over group rings we investigate certain finite subgroups r of gln zf where ii is a finite nilpotent group such a group r gives rise to a z r x fl7 module we study the characters of these modules to limit the structure of r we also exhibit some exotic subgroups r

spectral acceleration of the generalized forward backward method the generalized forward backward gfb method was introduced as an iterative method of moments solution to compute the electromagnetic scattering from targets on ocean like rough surfaces in this paper an existing spectral acceleration algorithm is adapted to the gfb the spectral acceleration is presented for both polarizations and for perfect electrically conducting pec and non pec surfaces the accelerated scheme reduces the computational scaling cost of the gfb from o n sup 2 to o n per iteration as the length of the sea surface increases linearly with the number of unknowns n the numerical results demonstrate that the spectral acceleration introduces negligible error while greatly improving the efficiency of the gfb method