measurable kac cohomology for bicrossed products we study the kac cohomology for matched pairs of locally compact groups this cohomology theory arises from the extension theory of locally compact quantum groups we prove a measurable version of the kac exact sequence and provide methods to compute the cohomology we give explicit calculations in several examples using results of moore and wigner

minimax programming under p r invexity abstract minimax programming problems involving p r invex functions with respect to are considered parametric and non parametric necessary and sufficient optimality conditions and duality results for a class of minimax programming problems are obtained under p r invexity assumption on objective and constraint functions some different types of dual problems are introduced and duality theorems is established for each dual problem

general relaxation schemes in multigrid algorithms for higher order singularity methods abstract relaxation schemes based on an approximate and incomplete factorization technique af are described these af schemes allow one to construct a fast multigrid method for solving integral equations of the second as well as of the first kind novel items are the smoothing factors found for integral equations of the first kind and the comparison with similar results for equations of the second kind application of the mg algorithm shows convergence of a second order accurate panel method to the level of the truncation error within two multigrid cycles

a multilevel formulation of the finite element method for electromagnetic scattering multigrid techniques for three dimensional 3 d electromagnetic scattering problems are presented the numerical representation of the physical problem is accomplished via a finite element discretization with nodal basis functions a total magnetic field formulation with a vector absorbing boundary condition abc is used the principal features of the multilevel technique are outlined the basic multigrid algorithms are described and estimations of their computational requirements are derived the multilevel code is tested with several scattering problems for which analytical solutions exist the obtained results clearly indicate the stability accuracy and efficiency of the multigrid method

adaptive multiscale moment method ammm for analysis of scattering from perfectly conducting plates adaptive multiscale moment method ammm is presented for the analysis of scattering from a thin perfectly conducting plate this algorithm employs the conventional moment method and a special matrix transformation which is derived from the tensor products of the two one dimensional 1 d multiscale triangular basis functions that are used for expansion and testing functions in the conventional moment method the special feature of these new basis functions introduced through this transformation is that they are orthogonal at the same scale except at the initial scale and not between scales from one scale to another scale the initial estimate for the solution can be predicted using this multiscale technique hence the compression is applied directly to the solution and the size of the linear equations to be solved is reduced thereby improving the efficiency of the conventional moment method the basic difference between this methodology and the other techniques that have been presented so far is that we apply the compression not to the impedance matrix but to the solution itself directly using an iterative solution methodology the extrapolated results at the higher scale thus provide a good initial guess for the iterative method typically when the number of unknowns exceeds a few thousand unknowns the matrix solution time exceeds generally the matrix fill time hence the goal of this method is directed in solving electrically larger problems where the matrix solution time is of concern two numerical results are presented which demonstrate that the ammm is a useful method to analyze scattering from perfectly conducting plates

free products of compact quantum groups we construct and study compact quantum groups from free products ofc algebras in this connection we discover two mysterious classes of natural compact quantum groups a u m anda o m thea u m s respectivelya o m s are non isomorphic to each other for differentm s and are not obtainable by the ordinary quantization method we also clarify some basic concepts in the theory of compact quantum groups

l 2 homology for von neumann algebras the aim of this paper is to introduce a notion of l homology in the context of von neumann algebras finding a suitable co homology theory for von neumann algebras has been a dream for several generations see kr71a kr71b jkr72 ss95 and references therein one s hope is to have a powerful invariant to distinguish von neumann algebras unfortunately little positive is known about the kadison ringrose cohomology h b m m except that it vanishes in many cases furthermore there does not seem to be a good connection between the bounded cohomology theory of a group and of the bounded cohomology of its von neumann algebra our interest in developing an l cohomology theory was revived by the introduction of lcohomology invariants in the field of ergodic equivalence relations in the paper of gaboriau gab02 his results in particular imply that l betti numbers 2 i of a discrete group are the same for measure equivalent groups i e for groups that can generate isomorphic ergodic measure preserving equivalence relations parallels between the worlds of von neumann algebras and measurable equivalence relations have been noted for a long time starting with the parallel between the work of murray and von neumann mvn and that of h dye dy thus there is hope that an invariant of a group that survives measure equivalence will survive also von neumann algebra equivalence i e will be an invariant of the von neumann algebra of the group the original motivation for our construction comes from the well understood analogy between the theory of ii1 factors and that of discrete groups based on the theory of correspondences con con94 this analogy has been remarkably efficient to transpose analytic properties such as amenability or property t from the group context to the factor context con80 cj and more recently in the breakthrough work of popa popa con03 we use the theory of correspondences together with the algebraic description of l betti numbers given by luck his definition involves the computation of the algebraic group homology with coefficients in the group von neumann algebra following the guiding idea that the category of bimodules over a von neumann algebra is the analogue of the category of modules over a group we are led to the following algebraic definition of l homology of a von neumann algebra m

quantum deformation of lorentz group a one parameter quantum deformations l 2 ofsl 2 is introduced and investigated an analog of the iwasawa decomposition is proved the compact part of this decomposition coincides withs u 2 whereas the solvable part is identified as a pontryagin dual ofs u 2 it shows thats l 2 is the result of the dual version of drinfeld s double group construction applied tos u 2 the same construction applied to any compact quantum groupgc is discussed in detail in particular the explicit formulae for the haar measures on the pontryagin dualgd ofgc and on the double groupg are given we show that there exists remarkable 1 1 correspondence between representations ofg and bicovariant bimodules tensor bundles overgc the theory of smooth representations ofs l 2 is the same as that ofsl 2 clebsh gordon coefficients are however modified the corresponding tame bicovariant bimodules ons u 2 are classified an application to 4d differential calculus is presented the nonsmooth case is also discussed

on multilevel iterative methods for integral equations of the second kind and related problems we describe a unifying framework for multigrid methods and projection iterative methods for integral equations of the second kind and for the iterative aggregation method for solving input output relations the methods are formulated as iterations combined with a defect correction in a subspace convergence proofs use contraction arguments and thus involve the nonlinear case automatically some new results are presented

ccap for universal discrete quantum groups we show that the discrete duals of the free orthogonal quantum groups have the haagerup property and the completely contractive approximation property analogous results hold for the free unitary quantum groups and the quantum automorphism groups of finite dimensional c algebras the proof relies on the monoidal equivalence between free orthogonal quantum groups and su q 2 quantum groups on the construction of a sufficient supply of bounded central functionals for su q 2 quantum groups and on the free product techniques of ricard and xu our results generalize previous work in the kac setting due to brannan on the haagerup property and due to the second author on the ccap

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

the boundary of universal discrete quantum groups exactness and factoriality we study the c algebras and von neumann algebras associated with the universal discrete quantum groups they give rise to full prime factors and simple exact c algebras the main tool in our work is the study of an amenable boundary action yielding the akemann ostrand property finally this boundary can be identified with the martin or the poisson boundary of a quantum random walk

multigrid adi method for two dimensional electromagnetic simulations we propose a multigrid alternating direction implicit adi method for solving two dimensional maxwell s equations this method is based on interpreting the adi method as an iterative solver for the crank nicolson cn scheme by introducing a special procedure to solve the residual equation within the adi framework multigrid methods are incorporated into the iterative adi method the accuracy and efficiency of the proposed method are further demonstrated by numerical examples

investigation of multigrid preconditioner for integral equation fast analysis of electromagnetic scattering problems this paper proposes a multigrid preconditioner for integral equation fast analysis of electromagnetic scattering problems the multigrid model is constructed by recursively dividing every triangular element on the coarse level into 4 small ones the rao wilton glisson rwg basis functions defined on the coarse level are expressed with linear combinations of those on the fine level and the expansion coefficients of which are used to construct the restriction and interpolation operator to further accelerate the convergence of iterative solution a set of solenoidal basis functions on the coarse level are constructed additionally which are also expressed with linear combinations of rwg basis functions on the fine level and adopted to construct the second restriction and interpolation operator the two sets of coarsening techniques are then combined together to remove the low frequency components of the iterative error numerical results show that the proposed method can reduce both the steps of iteration and cpu time compared with the iterative solver without preconditioning

the free entropy dimension of hyperfinite von neumann algebras suppose m is a hyperfinite von neumann algebra with a normal tracial state and 1 n is a set of selfadjoint generators for m we calculate 0 1 n the modified free entropy dimension of 1 n moreover we show that 0 1 n depends only on m and consequently 0 1 n is independent of the choice of generators for m in the course of the argument we show that if b 1 b n is a set of selfadjoint generators for a von neumann algebra r with a normal tracial state and b 1 b n has finite dimensional approximants then 0 n 0 b 1 b n for any hyperfinite von neumann subalgebra n of r combined with a result by voiculescu this implies that if r has a regular diffuse hyperfinite von neumann subalgebra then 0 b 1 b n 1

dimension theory of arbitrary modules over finite von neumann algebras and l 2 betti numbers ii applications to grothendieck groups l 2 euler characteristics and burnside groups

the connes embedding property for quantum group von neumann algebras for a compact quantum group g of kac type we study the existence of a haar trace preserving embedding of the von neumann algebra l g into an ultrapower of the hyperfinite ii 1 factor the connes embedding property for l g we establish a connection between the connes embedding property for l g and the structure of certain quantum subgroups of g and use this to prove that the ii 1 factors l o n and l u n associated to the free orthogonal and free unitary quantum groups have the connes embedding property for all n 4 as an application we deduce that the free entropy dimension of the standard generators of l o n equals 1 for all n 4 we also mention an application of our work to the problem of classifying the quantum subgroups of o n

examples of weakly amenable discrete quantum groups abstract we prove that the free orthogonal and free unitary quantum groups f o n and f u n are weakly amenable and that their cowling haagerup constant is equal to 1 this is achieved by estimating the completely bounded norm of the projections on the coefficients of irreducible representations of their compact duals an argument of monoidal equivalence then allows us to extend this result to quantum automorphism groups of finite spaces and even yields some examples of weakly amenable non unimodular discrete quantum groups with the haagerup property

a multilevel formulation of the method of moments em scattering the modeling of electromagnetic scattering and radiation problems using the method of moments mom is limited to resonant frequencies because of the extensive computational requirements of solving large matrix equations in this study a multilevel formulation of mom which allows substantial computational savings and thus extends the application of mom to higher frequencies is presented using a hierarchy of discretization levels the multilevel technique extracts different modal components of the solution by focusing on a specific portion of the spectrum of the solution at a given level the fundamental features of this process for the mom solution of the electric field integral equation efie are developed and implemented this multilevel mom allows the rapid evaluation of the current distributions on a variety of 2 d scatterers with thousands of unknowns in fewer than ten cycles and in fractions of the normal cpu times the method is stable fast suitable for multiple excitations and adaptable as a solve module for almost any mom code

the radial masa in free orthogonal quantum groups abstract we prove that the radial subalgebra in free orthogonal quantum group factors is maximal abelian and mixing and we compute the associated bimodule the proof relies on new properties of the jones wenzl projections and on an estimate of certain scalar products of coefficients of irreducible representations

on the degrees of freedom of scattered fields starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities the degrees of freedom of the scattered field are introduced and then computed the degrees of freedom are shown to be practically equal to the nyquist number appropriate to the effective spatial bandwidth of the scattered field and to the extension of the observation domain accordingly a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error it is also shown that the field representation can be made in terms of field values and simple sampling functions provided that a marginal increase in the approximation error is tolerated the results not only completely justify the use of sampling interpolation for representing scattering fields but also demonstrate that such representation is practically an optimal one an algorithm for the reconstruction of scattered fields given the maximum allowed error is then produced

residually finite quantum group algebras abstract we show that provided n 3 the involutive hopf algebra a u n coacting universally on an n dimensional hilbert space has enough finite dimensional representations in the sense that every non zero element acts non trivially in some finite dimensional representation this implies that the discrete quantum group with group algebra a u n is maximal almost periodic i e it embeds in its quantum bohr compactification answering a question posed by p soltan in 21 we also prove analogous results for the involutive hopf algebra b u n coacting universally on an n dimensional hilbert space equipped with a non degenerate bilinear form

a multilevel matrix decomposition algorithm for analyzing scattering from large structures a multilevel algorithm is presented for analyzing scattering from electrically large surfaces the algorithm accelerates the iterative solution of integral equations that arise in computational electromagnetics the algorithm permits a fast matrix vector multiplication by decomposing the traditional method of moment matrix into a large number of blocks with each describing the interaction between distant scatterers the multiplication of each block by a trial solution vector is executed using a multilevel scheme that resembles a fast fourier transform fft and that only relies on well known algebraic techniques the computational complexity and the memory requirements of the proposed algorithm are o n log sup 2 n

liberation of orthogonal lie groups abstract we show that under suitable assumptions we have a one to one correspondence between classical groups and free quantum groups in the compact orthogonal case we classify the groups under correspondence with the result that there are exactly 6 of them o n s n h n b n s n b n we investigate the representation theory aspects of the correspondence with the result that for o n s n h n b n this is compatible with the bercovici pata bijection finally we discuss some more general classification problems in the compact orthogonal case notably with the construction of a new quantum group

the fusion rules of some free wreath product quantum groups and applications abstract in this article we find the fusion rules of the free wreath product quantum groups s n for any discrete group to do this we describe the spaces of intertwiners between basic corepresentations which allows us to identify the irreducible corepresentations we then apply the knowledge of the fusion rules to prove in most cases several operator algebraic properties of the associated reduced c algebras such as simplicity and uniqueness of the trace we also prove that the associated von neumann algebra is a full type ii 1 factor and that the dual of s n has the haagerup approximation property for all finite groups

large deviation bounds for matrix brownian motion we prove large deviation bounds for the convergence of hermitian matrix valued brownian motion towards free brownian motion as a consequence we obtain upper and lower bounds on the microstates entropy introduced by voiculescu 24

the analogues of entropy and of fisher s information measure in free probability theory i analogues of the entropy and fisher information measure for random variables in the context of free probability theory are introduced monotonicity properties and an analogue of the cramer rao inequality are proved

asymptotic infinitesimal freeness with amalgamation for haar quantum unitary random matrices we consider the limiting distribution of u na nu n and bn and more general expressions where an and bn are n n matrices with entries in a unital c algebra mathcal b which have limiting mathcal b valued distributions as n and un is a n n haar distributed quantum unitary random matrix with entries independent from mathcal b under a boundedness assumption we show that u na nu n and bn are asymptotically free with amalgamation over mathcal b moreover this also holds in the stronger infinitesimal sense of belinschi shlyakhtenko

note on interpolational basis functions in the method of moments em scattering efficient basis sets for the method of moments may be obtained using quasi localized bandlimited interpolational functions that broadly speaking are defined relative to a mean sampling rate that is adjusted to curvature and proximity to edges thus reflecting the local spatial frequency bandwidth computed scattering data in a number of structures including perfectly conducting circular and elliptical two dimensional cylinders as well as a flat infinite strip indicate that reasonable accuracy can be obtained with an average rate of between 2 5 and 3 basis functions per wavelength average sampling rates need not correspond strictly to the bandwidth of the basis functions and there is considerable latitude with respect to random variation of sampling intervals although each basis function typically extends over several sample points required integrals can be obtained speedily by the use of standard sampling theoretical methods

amenability of hopf von neumann algebras and kac algebras abstract let m be a hopf von neumann algebra the operator predualm ofmis a completely contractive banach algebra with multiplicationm m m m we call m operator amenableif the completely contractive banach algebram isoperator amenable i e for every operatorm bimodulev every completely bounded derivation fromm into the dualm bimodulev is inner there is a weaker notion of amenability introduced by d voiculescu we say that a hopf von neumann algebra m isvoiculescu amenableif there exists a left invariant mean onm we show that if a hopf von neumann algebra m is operator amenable then it is voiculescu amenable for kac algebras there is astrong voiculescu amenability we show that for discrete kac algebras these amenabilities are all equivalent in fact if we letk m be a discrete kac algebra and letk m be its compact dual kac algebra then the following are equivalent 1 kis operator amenable 2 kis voiculescu amenable 3 the von neumann algebramis hyperfinite 4 kis strong voiculescu amenable 5 kis operator amenable 6 m has a bounded approximate identity

a multiresolution method of moments for triangular meshes this paper presents the construction use and properties of a multiresolution wavelet basis for the method of moments mom analysis of metal antennas scatterers and microwave circuits discretized by triangular meshes several application examples show fast convergence of iterative solvers and accurate solutions with highly sparse mom matrices the proposed basis is organized in hierarchical levels and keeps the different scales of the problem directly into the basis functions representation the current is divided into a solenoidal and a quasi irrotational part which allows mapping these two vector parts onto fully scalar quantities where the wavelets are defined as a byproduct this paper also presents a way to construct hierarchical sets of rao wilton glisson rwg functions on a family of meshes obtained by subsequent refinement i e with the rwg of coarser meshes expressed as linear combinations of those of finer meshes

topological generation and matrix models for quantum reflection groups abstract we prove that the von neumann algebras of quantum permutation groups and quantum reflection groups have the connes embedding property we do this by establishing several new topological generation results for the quantum permutation groups s n and the quantum reflection groups h n s we use these results to show that these quantum groups admit sufficiently many matrix models in particular all of these quantum groups have residually finite discrete duals and are in particular hyperlinear and certain flat matrix models for s n are inner faithful

multiresolution analysis of printed antennas and circuits a dual isoscalar approach a new approach is presented for the integral equation analysis of multilayer printed circuits antennas and arrays it is based on the introduction of new multiresolution vector functions with properties similar to those of the scalar wavelets and flexible enough to accommodate for general shapes the resulting method of moments mom impedance matrix shows a good conditioning that allows its safe sparsification and the efficient use of iterative methods for the solution of the linear system the results of the analysis of various real life structures show the advantage of the method

generation of excitation independent characteristic basis functions for three dimensional homogeneous dielectric bodies the aim of this paper is the development of characteristic basis functions cbfs for homogeneous dielectric bodies that are modeled with the surface equivalence principle this approach contributes to generalize the characteristic basis function method cbfm for any kind of material the foundations for the generation of these new basis functions are widely revised and the cbfm is adapted for this purpose the validity of the method is illustrated with the systematic analysis of canonical geometries as well as with the computation of the specific absorption rate inside a head like geometry in all the cases the error in the current distribution as well as in the near and far field is considered in addition a detailed comparison of the generation of the cbfs using plane waves and spherical waves is also carried out

paths in quantum cayley trees and l 2 cohomology abstract we study existence uniqueness and triviality of path cocycles in the quantum cayley graph of universal discrete quantum groups in the orthogonal case we find that the unique path cocycle is trivial in contrast with the case of free groups where it is proper in the unitary case it is neither bounded nor proper from this geometrical result we deduce the vanishing of the first l 2 betti number of a o i n

multiple grid methods for the solution of fredholm integral equations of the second kind in this paper multiple grid methods are applied for the fast solution of the large nonsparse systems of equations that arise from the discretization of fredholm integral equations of the second kind various multiple grid schemes both with nystrom and with direct interpolation are considered for these iterative methods the rates of convergence are derived using the collectively compact operator theory by anselone and atkinson estimates for the asymptotic computational complexity are given which show that the multiple grid schemes result in e n2 arithmetic operations