on the design of multifilter banks and orthonormal multiwavelet bases several forms of parametric expressions for orthogonal multifilter banks are presented the explicit expressions for a group of orthogonal multifilter banks that generate symmetric antisymmetric scaling functions and orthonormal multiwavelets are obtained based on these parametric expressions for orthogonal multifilter banks orthonormal multiwavelet pairs with good time frequency localization are constructed and examples of optimal multifilter banks are provided

vertexwise criteria for admissibility of alcoves we give a new description of the set rm adm mu of admissible alcoves as an intersection of certain obtuse cones of alcoves and we show this description may be given by imposing conditions vertexwise we use this to prove the vertexwise admissibility conjecture of pappas rapoport smithling the same idea gives simple proofs of two ingredients used in the proof of the kottwitz rapoport conjecture on existence of crystals with additional structure

multi d wavelet filter bank design using quillen suslin theorem for laurent polynomials in this paper we present a new approach for constructing the wavelet filter bank our approach enables constructing nonseparable multidimensional non redundant wavelet filter banks with fir filters using the quillen suslin theorem for laurent polynomials our construction method presents some advantages over the traditional methods of multidimensional wavelet filter bank design first it works for any spatial dimension and for any sampling matrix second it does not require the initial lowpass filters to satisfy any additional assumption such as interpolatory condition third it provides an algorithm for constructing a wavelet filter bank from a single lowpass filter so that its vanishing moments are at least as many as the accuracy number of the lowpass filter

armlets and balanced multiwavelets flipping filter construction in the scalar valued setting it is well known that the two scale sequences q sub k of daubechies orthogonal wavelets can be given explicitly by the two scale sequences p sub k of their corresponding orthogonal scaling functions such as q sub k 1 sup k p sub 1 k however due to the noncommutativity of matrix multiplication there is little such development in the multiwavelet literature to express the two scale matrix sequence q sub k of an orthogonal multiwavelet in terms of the two scale matrix sequence p sub k of its corresponding scaling function vector this paper in part is devoted to this study for the setting of orthogonal multiwavelets of dimension r 2 in particular the two lowpass filters are flipping filters whereas the two highpass filters are linear phase these results will be applied to constructing both a family of the most recently introduced notion of armlet of order n and a family of n balanced orthogonal multiwavelets

coset sum an alternative to the tensor product in wavelet construction a multivariate biorthogonal wavelet system can be obtained from a pair of multivariate biorthogonal refinement masks in multiresolution analysis setup some multivariate refinement masks may be decomposed into lower dimensional refinement masks tensor product is a popular way to construct a decomposable multivariate refinement mask from lower dimensional refinement masks we present an alternative method which we call coset sum for constructing multivariate refinement masks from univariate refinement masks the coset sum shares many essential features of the tensor product that make it attractive in practice 1 it preserves the biorthogonality of univariate refinement masks 2 it preserves the accuracy number of the univariate refinement mask and 3 the wavelet system associated with it has fast algorithms for computing and inverting the wavelet coefficients the coset sum can even provide a wavelet system with faster algorithms in certain cases than the tensor product these features of the coset sum suggest that it is worthwhile to develop and practice alternative methods to the tensor product for constructing multivariate wavelet systems some experimental results using 2 d images are presented to illustrate our findings

on factorization of m channel paraunitary filterbanks we systematically investigate the factorization of causal finite impulse response fir paraunitary filterbanks with given filter length based on the singular value decomposition of the coefficient matrices of the polyphase representation a fundamental order one factorization form is first proposed for general paraunitary systems then we develop a new structure for the design and implementation of paraunitary system based on the decomposition of hermitian unitary matrices within this framework the linear phase filterbank and pairwise mirror image symmetry filterbank are revisited their structures are special cases of the proposed general structures compared with the existing structures more efficient ones that only use approximately half the number of free parameters are derived the proposed structures are complete and minimal although the factorization theory with or without constraints is discussed in the framework of m channel filterbanks the results can be applied to wavelets and multiwavelet systems and could serve as a general theory for paraunitary systems

dimension formula for the affine deligne lusztig variety x mu b x μ b the study of certain union x mu b of affine deligne lusztig varieties in the affine flag varieties arose from the study of shimura varieties with iwahori level structure in this paper we give an explicit dimension formula for x mu b associated to sufficiently large dominant coweight mu

parameterization of m band affine frames with pre assigned scaling filter affine wavelet frames related with subdivision scheme provide tools for building curves and surfaces in cagd cam at first we show that scaling filters can be parameterized by decomposed elementary matrices with the form im p pz k where k is a nonnegative integer and p is a one rank constant valued idempotent matrix p2 im theorem 2 2 then we use the method to construct m band affine wavelet frames with the given scaling filter and the dual frames general solutions for affine wavelet frames and its dual affine wavelet frames are obtained with pre assigned scaling filter theorems 3 5 and 3 6 at last a design example is given

on the μ ordinary locus of a shimura variety abstract in this paper we study the ordinary locus of a shimura variety with parahoric level structure under the axioms in 12 we show that ordinary locus is a union of certain maximal ekedahl kottwitz oort rapoport strata introduced in 12 and we give criteria on the density of the ordinary locus

the application of multiwavelet filterbanks to image processing multiwavelets are a new addition to the body of wavelet theory realizable as matrix valued filterbanks leading to wavelet bases multiwavelets offer simultaneous orthogonality symmetry and short support which is not possible with scalar two channel wavelet systems after reviewing this theory we examine the use of multiwavelets in a filterbank setting for discrete time signal and image processing multiwavelets differ from scalar wavelet systems in requiring two or more input streams to the multiwavelet filterbank we describe two methods repeated row and approximation deapproximation for obtaining such a vector input stream from a one dimensional 1 d signal algorithms for symmetric extension of signals at boundaries are then developed and naturally integrated with approximation based preprocessing we describe an additional algorithm for multiwavelet processing of two dimensional 2 d signals two rows at a time and develop a new family of multiwavelets the constrained pairs that is well suited to this approach this suite of novel techniques is then applied to two basic signal processing problems denoising via wavelet shrinkage and data compression after developing the approach via model problems in one dimension we apply multiwavelet processing to images frequently obtaining performance superior to the comparable scalar wavelet transform

on construction of multivariate parseval wavelet frames abstract a new method for the construction of compactly supported parseval wavelet frames in l 2 r d with any preassigned approximation order n for arbitrary matrix dilation m is proposed the number of wavelet functions generating a frame constructed in this way is less or equal to d 1 det m d the method is algorithmic and the algorithm is simple to use the number of generating wavelet functions can be reduced to det m for a large class of matrices m

construction of central elements in the affine hecke algebra via nearby cycles 0 1 overview let g be a connected reductive group over a finite field fq and let g k be the corresponding group over the local field k fq t let g o g k be a maximal compact subgroup of g k here o fq t and let hsph denote the hecke algebra of g k with respect to g o in other words hsph as a vector space consists of compactly supported bi g o invariant functions g k q and the product is defined by

on the flatness of local models for the symplectic group abstract we investigate the bad reduction of certain shimura varieties associated to the symplectic group more precisely we look at a model of the shimura variety at a prime p with parahoric level structure at p we show that this model is flat as conjectured by rapoport and zink ann of math stud 141 1996 and that its special fibre is reduced a crucial ingredient is faltings theorem on the normality of schubert varieties in the affine flag variety

on the coherence conjecture of pappas and rapoport we prove the generalized coherence conjecture proposed by pappas and rapoport as a corollary one of their theorems which describes the geometry of the special bers of the local models for ramied unitary groups holds unconditionally our proof is based on the study of the geometry in particular certain line bundles and adic sheaves of the global schubert varieties which are the equal characteristic counterparts of the local models

topological flatness of local models in the ramified case local models are schemes defined in terms of linear algebra which can be used to study the local structure of integral models of certain shimura varieties with parahoric level structure we investigate the local models for groups of the form open image in new window is a totally ramified extension as defined by pappas and rapoport and show that they are topologically flat in the linear case flatness can be deduced from this

the supersingular locus in siegel modular varieties with iwahori level structure we study moduli spaces of abelian varieties in positive characteristic more specifically the moduli space of principally polarized abelian varieties on the one hand and the analogous space with iwahori type level structure on the other hand we investigate the ekedahl oort stratification on the former the kottwitz rapoport stratification on the latter and their relationship in this way we obtain structural results about the supersingular locus in the case of iwahori level structure for instance a formula for its dimension in case g is even

short wavelets and matrix dilation equations scaling functions and orthogonal wavelets are created from the coefficients of a lowpass and highpass filter in a two band orthogonal filter bank for multifilters those coefficients are matrices this gives a new block structure for the filter bank and leads to multiple scaling functions and wavelets geronimo hardin and massopust see j approx theory vol 78 p 373 401 1994 constructed two scaling functions that have extra properties not previously achieved the functions spl phi sub 1 and spl phi sub 2 are symmetric linear phase and they have short support two intervals or less while their translates form an orthogonal family for any single function spl phi apart from haar s piecewise constants those extra properties are known to be impossible the novelty is to introduce 2 spl times 2 matrix coefficients while retaining orthogonality of the multiwavelets this note derives the properties of spl phi sub 1 and spl phi sub 2 from the matrix dilation equation that they satisfy then our main step is to construct associated wavelets two wavelets for two scaling functions the properties were derived by geronimo hardin and massopust from the iterated interpolation that led to spl phi 1 and spl phi sub 2 one pair of wavelets was found earlier by direct solution of the orthogonality conditions using mathematica our construction is in parallel with recent progress by hardin and geronimo to develop the underlying algebra from the matrix coefficients in the dilation equation in another language to build the 4 spl times 4 paraunitary polyphase matrix in the filter bank the short support opens new possibilities for applications of filters and wavelets near boundaries

symmetric orthogonal filters and wavelets with linear phase moments in this paper we study symmetric orthogonal filters with linear phase moments which are of interest in wavelet analysis and its applications we investigate relations and connections among the linear phase moments sum rules and symmetry of an orthogonal filter as one of the results we show that if a real valued orthogonal filter a is symmetric about a point then a has sum rules of order m if and only if it has linear phase moments of order 2m these connections among the linear phase moments sum rules and symmetry help us to reduce the computational complexity of constructing symmetric real valued orthogonal filters and to understand better symmetric complex valued orthogonal filters with linear phase moments to illustrate the results in the paper we provide many examples of univariate symmetric orthogonal filters with linear phase moments in particular we obtain an example of symmetric real valued 4 orthogonal filters whose associated orthogonal 4 refinable function lies in c 2 r

the lifting factorization and construction of wavelet bi frames with arbitrary generators and scaling in this paper we present the lifting factorization and construction of wavelet bi frames with arbitrary generators and scaling we show that an arbitrary polyphase matrix of a wavelet bi frame can be factorized into a series of lifting steps based on the proposed factorization we present a general construction of bi frames especially we give an explicit formula to construct the bi frames of two scaling and two generators with symmetry and one vanishing moment this paper does not involve many theories of wavelet frames in mathematics but focuses on the algebraic issues related to laurent polynomials which are efficient expressions in redundant filter banks associated with wavelet frames as an extension of the classical two channel filter bank the redundant filter bank is more complicated but also more flexible furthermore we present an algorithm to increase the number of vanishing moments to arbitrary order by lifting which is iterated and is straightforward in implementation

on compactly supported spline wavelets and a duality principle let v 1 v 0 v 1 be a multiresolution analysis of l 2 generated by the mth order b spline n m x we exhibit a compactly supported basic wavelet m x that generates the corresponding orthogonal complementary wavelet subspaces w 1 w 0 w 1 consequently the two finite sequences that describe the two scale relations of n m x and m x in terms of n m 2x j j z yield an efficient reconstruction algorithm to give an efficient wavelet decomposition algorithm based on these two finite sequences we derive a duality principle which also happens to yield the dual bases n m x j and 59 m x j relative to n m x j and m x j respectively

wavelet bases with a general integer dilation factor d 2 and better regularity properties it is well known that by adding some extra zeros to a daubechies low pass wavelet filter one gets new orthonormal wavelet basis with better regularity property in this paper we give a detailed study of this procedure in the general case of a wavelet filter associated with any integer dilation factor d 2 moreover we describe an algorithm for the construction of symmetric scaling functions with dilation factor d 4 finally we provide the reader with some numerical examples that illustrate the results of this work

wavelets in wandering subspaces mallat s construction via a multiresolution approximation of orthonormal wavelets generated by a single function is extended to wavelets generated by a finite set of functions the connection between multiresolution approximation and the concept of wandering subspaces of unitary operators in hilbert space is exploited in the general setting an example of multiresolution approximation generated by cardinal hermite b splines is constructed

uber die lokale zetafunktion von shimuravarietaten monodromiefiltration und verschwindende zyklen in ungleicher charakteristik

the lifting scheme for wavelet bi frames theory structure and algorithm in this paper we present the lifting scheme of wavelet bi frames along with theory analysis structure and algorithm we show how any wavelet bi frame can be decomposed into a finite sequence of simple filtering steps this decomposition corresponds to a factorization of a polyphase matrix of a wavelet bi frame based on this concept we present a new idea for constructing wavelet bi frames for the construction of symmetric bi frames we use generalized bernstein basis functions which enable us to design symmetric prediction and update filters the construction allows more efficient implementation and provides tools for custom design of wavelet bi frames by combining the different designed filters for the prediction and update steps we can devise practically unlimited forms of wavelet bi frames moreover we present an algorithm of increasing the number of vanishing moments of bi framelets to arbitrary order via the presented lifting scheme which adopts an iterative algorithm and ensures the shortest lifting scheme several construction examples are given to illustrate the results

topological flatness of orthogonal local models in the split even case i local models are schemes defined in terms of linear algebra that were introduced by rapoport and zink to study the etale local structure of integral models of certain pel shimura varieties over p adic fields a basic requirement for the integral models or equivalently for the local models is that they be flat in the case of local models for even orthogonal groups genestier observed that the original definition of the local model does not yield a flat scheme in a recent article pappas and rapoport introduced a new condition to the moduli problem defining the local model the so called spin condition and conjectured that the resulting spin local model is flat we prove a preliminary form of their conjecture in the split iwahori case namely that the spin local model is topologically flat an essential combinatorial ingredient is the equivalence of admissibility and permissibility for two minuscule cocharacters in root systems of type d

vector subdivision schemes and multiple wavelets we consider solutions of a system of refinement equations written in the form formula math where the vector of functions 1 r t is in l p r r and a is a finitely supported sequence of r r matrices called the refinement mask associated with the mask a is a linear operator q a defined on l p r r by q a f z a f 2 this paper is concerned with the convergence of the subdivision scheme associated with a i e the convergence of the sequence q a n f n 1 2 in the l p norm our main result characterizes the convergence of a subdivision scheme associated with the mask a in terms of the joint spectral radius of two finite matrices derived from the mask along the way properties of the joint spectral radius and its relation to the subdivision scheme are discussed in particular the l 2 convergence of the subdivision scheme is characterized in terms of the spectral radius of the transition operator restricted to a certain invariant subspace we analyze convergence of the subdivision scheme explicitly for several interesting classes of vector refinement equations finally the theory of vector subdivision schemes is used to characterize orthonormality of multiple refinable functions this leads us to construct a class of continuous orthogonal double wavelets with symmetry

some properties of centrosymmetric matrices in this paper some properties of centrosymmetric matrices which often appear in the construction of orthonormal wavelet basis in wavelet analysis are investigated

an arc length method including line searches and accelerations this paper describes a method for introducing line searches into the arc length solution procedure such line searches may be used at each iteration to calculate an optimum scalar step length which scales the normal iterative vector in practice a loose tolerance is provided so that on many iterations the line searches are avoided however on difficult iterations the line searches are shown to lead to a substantial improvement in the convergence characteristics a simple single parameter acceleration is also developed using line search concepts the new arc length method is applied to both the geometrically nonlinear analysis of shallow shells and the materially nonlinear analysis of reinforced concrete beams and slabs significant improvements are demonstrated in relation to the standard arc length method

formulae relating the bernstein and iwahori matsumoto presentations of an affine hecke algebra abstract we consider the anti dominant variants of the elements occurring in the bernstein presentation of an affine hecke algebra h we find explicit formulae for in terms of the iwahori matsumoto generators tw w ranging over the extended affine weyl group of the root system r in the case i r is arbitrary and is a minuscule coweight or ii r is attached to gln and mek where ek is a standard basis vector and m 1 in the above cases certain minimal expressions for play a crucial role such minimal expressions exist in fact for any coweight for gln we give a sheaf theoretic interpretation of the existence of a minimal expression for the corresponding perverse sheaf on the affine schubert variety x t is the push forward of an explicit perverse sheaf on the demazure resolution m x t x t this approach yields for a minuscule coweight of any r or for an arbitrary coweight of gln a conceptual albeit less explicit expression for the coefficient w of the basis element tw in terms of the cohomology of a fiber of the demazure resolution

a family of orthonormal wavelet bases with dilation factor 4 abstract in this paper we study a method for the construction of orthonormal wavelet bases with dilation factor 4 more precisely for any integer m 0 we construct an orthonormal scaling filter m m that generates a mother scaling function m associated with the dilation factor 4 the computation of the different coefficients of m m 2 is done by the use of a simple iterative method also this work shows how this construction method provides us with a whole family of compactly supported orthonormal wavelet bases with arbitrary high regularity a first estimate of m the asymptotic regularity of m is given by m 0 25 m examples are provided to illustrate the results of this work

a new implementation of the lanczos method in linear problems the lanczos algorithm has proved to be a powerful solution method not only for finding the eigenvalues but for solving linear systems of equations in this work a new implementation of the algorithm is presented for solving linear systems of equations with a sequence of right hand sides the versions of the method proposed in the past treat the right hand side vectors successively by keeping the tridiagonal matrix and the orthonormal basis in fast or secondary storage the new technique handles all approximations to the solution vectors simultaneously without the necessity for keeping the tridiagonal matrix or the orthonormal basis in fast or secondary storage thus when the first solution vector has converged to a required accuracy good approximations to the remaining solution vectors have simultaneously been obtained it then takes fewer iterations to reach the final accuracy by working separately on each of the remaining vectors

a survey of quasi newton methods with reduced storage a family of non linear solution methods is investigated based on limited memory quasi newton updates depending upon the number of updates and the updating formula a number of solution schemes may be constructed such as the conjugate and secant newton methods the conventional and modified newton raphson methods and a variety of quasi newton updates under the proposed implementation the preconditioned truncated lanczos method is used for the solution of the linearized problem in each non linear iteration the complete factorization of the stiffness matrix is avoided and large scale problems can be solved efficiently both in terms of computing time and storage the non linear iterative scheme is properly modified to account for loading variation inside the increment in order to be able to trace post critical equilibrium paths

orthogonal multiwavelets with optimum time frequency resolution a procedure to design orthogonal multiwavelets with good time frequency resolution is introduced formulas to compute the time durations and the frequency bandwidths of scaling functions and multiwavelets are obtained parameter expressions for the matrix coefficients of the multifilter banks that generate symmetric antisymmetric scaling functions and multiwavelets supported in o n are presented for n 2 6 orthogonal multiwavelets with optimum time frequency resolution are constructed and some optimal multifilter banks are provided

on the μ admissible set in the extended affine weyl groups of e6 and e7 giving explicit examples we show that the admissible set and the permissible set do not agree for non trivial minuscule coweights in the cases of e6 and e7

connected components of closed affine deligne lusztig varieties for split reductive algebraic groups we determine the sets of connected components of closed affine deligne lusztig varieties with parahoric level structure

a discrete newton algorithm for minimizing a function of many variables a newton like method is presented for minimizing a function ofn variables it uses only function and gradient values and is a variant of the discrete newton algorithm this variant requires fewer operations than the standard method whenn 39 and storage is proportional ton rather thann2

tight frames of compactly supported multivariate multi wavelets this paper is devoted to the study and construction of compactly supported tight frames of multivariate multi wavelets in particular a necessary condition for their existence is derived to provide some useful guide for constructing such mra tight frames by reducing the factorization task of the associated polyphase matrix valued laurent polynomial to that of certain scalar valued non negative ones we illustrate our construction method with examples of both multivariate scalar and vector valued subdivision schemes since our constructions for c 1 and c 2 piecewise cubic schemes are quite involved we also include the corresponding matlab code in the appendix

a method of construction for biorthogonal multiwavelets system with 2r multiplicity biorthogonal multiwavelets systems are consisted of a pair of biorthogonal multiscaling functions and the corresponding a pair of multiwavelets a method for constructing biorthogonal multiwavelets systems with multiplicity 2r was derived in particular hermite interpolation mask was considered as primal masks a pair of primal and dual masks with high order of sum rules should be firstly designed in order to obtain a biorthogonal multiwavelet with high vanishing moment concretely starting from a short sequence primal masks possessing hermite interpolation properties a necessary and sufficient conditions such that primal masks satisfies the preassigned order of sum rules are established then a dual masks with short support symmetry and any preassigned order of sum rules is constructed it follows that two multiscaling functions are obtained and then multiwavelets and dual multiwavelets are derived from which a general design framework is obtained for constructing biorthogonal multiwavelets system with multiplicity 2r associated with hermite interpolation functions the biorthogonal multiwavelets constructed by our design framework has desirable properties such as symmetry short support high vanishing moments and simple structures with explicit expressions finally an example is given

alcoves associated to special fibers of local models the special fiber of the local model of a pel shimura variety with iwahori type level structure admits a cellular decomposition the set of strata is in a natural way a finite subset of the affine weyl group determined by the shimura data in this paper we generalize and give a new proof of a theorem of kottwitz and rapoport concerning the description of this set for the case of linear and symplectic groups for higher rank groups not of type an we produce counterexamples showing the situation is not as nice in general we also recover a theorem of deodhar characterizing the bruhat order on sn the local geometry can be approached using the rapoport zink local model m j 13 this protective op scheme is a local model for the singularities in the special fiber of sh g x9 k 9 but it is defined in terms of the pair g p using linear algebra and is somewhat easier to deal with than the shimura variety itself in this paper we address certain combinatorial questions which arise in the study of the special fiber m f of m to fix ideas consider the case where g is split it turns out that m f can be regarded as a finite dimensional union of iwahori orbits in the affine flag variety for g fp t see 5 and 8 it follows that m f has a stratification indexed by a finite set perm p of the extended affine weyl group w g for g equivalently perm p can be regarded as a finite set of alcoves in the affine coxeter complex determined by a splitting for g let wo denote the finite weyl group of g for each translation in the wo orbit

preconditioned conjugate and secant newton methods for non linear problems the preconditioned conjugate gradient cg method is becoming accepted as a powerful tool for solving the linear systems of equations resulting from the application of the finite element method applications of the non linear algorithm are mainly confined to the diagonally scaled cg in this study the coupling of preconditioning techniques with non linear versions of the conjugate gradient and quasi newton methods creates a set of conjugate and secant newton methods for the solution of non linear problems the preconditioning matrices used to improve the ellipticity of the problem and to reduce the computer storage requirements are obtained by the application of the partial preconditioning and the partial elimination techniques both techniques use a drop off parameter to control the computer storage demands of the method making it more versatile for any computer hardware environment consideration is given to the development of a highly effective stability test for the line search minimization routine which computes accurate values without much effort this results in a beneficiary effect not only on the convergence properties of the methods but on their efficiency as well

topological flatness of local models for ramified unitary groups i the odd dimensional case abstract local models are certain schemes defined in terms of linear algebraic moduli problems which give etale local neighborhoods of integral models of certain p adic pel shimura varieties defined by rapoport and zink when the group defining the shimura variety ramifies at p the local models and hence the shimura models as originally defined can fail to be flat and it becomes desirable to modify their definition so as to obtain a flat scheme in the case of unitary similitude groups whose localizations at q p are ramified quasi split gu n pappas and rapoport have added new conditions the so called wedge and spin conditions to the moduli problem defining the original local models and conjectured that their new local models are flat we prove a preliminary form of their conjecture namely that their new models are topologically flat in the case n is odd

weight elimination in serre type conjectures we prove the weight elimination direction of the serre weight conjectures as formulated by herzig for forms of u n which are compact at infinity and split at places dividing p in generic situations that is we show that all modular weights for a mod p galois representation are contained in the set predicted by herzig under some additional hypotheses we also show modularity of all the obvious weights

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

a truncated newton lanczos method for overcoming limit and bifurcation points in this study procedures for overcoming limit and bifurcation points in large scale structural analysis problems are described and evaluated the methods are based on newton s method for the outer iterations while for the linearized problem in each iteration the preconditioned truncated lanczos method is employed special care is placed upon line search routines for accelerating the convergence properties and enhancing the stability of the outer method the proposed methodology retains all characteristics of an iterative method by avoiding the factorization of the current stiffness matrix the necessary eigenvalue information is retained in the tridiagonal matrix of the lanczos approach

local models of shimura varieties and a conjecture of kottwitz we give a group theoretic definition of local models as sought after in the theory of shimura varieties these are projective schemes over the integers of a p adic local field that are expected to model the singularities of integral models of shimura varieties with parahoric level structure our local models are certain mixed characteristic degenerations of grassmannian varieties they are obtained by extending constructions of beilinson drinfeld gaitsgory and the second named author to mixed characteristics and to the case of general tamely ramified reductive groups we study the singularities of local models and hence also of the corresponding integral models of shimura varieties in particular we study the monodromy inertia action and show a commutativity property for the sheaves of nearby cycles as a result we prove a conjecture of kottwitz which asserts that the semi simple trace of frobenius on the nearby cycles gives a function which is central in the parahoric hecke algebra

wavelets of multiplicity r a multiresolution approximation km m z of l2 r is of multi plicity r 0 if there are r functions x r whose translates form a riesz basis for v in the general theory we derive necessary and sufficient conditions for the translates of x r y x y r to form a riesz basis for v the resulting reconstruction and decomposition sequences lead to the construction of dual bases for v0 and its orthogonal complement w0 in vx the general theory is applied in the construction of spline wavelets with mul tiple knots algorithms for the construction of these wavelets for some special cases are given

explicit construction of symmetric compactly supported biorthogonal multiwavelets via group transformations polyphase matrix extension of multiscaling vectors is a fundamental approach for the construction of compactly supported biorthogonal multiwavelets in this paper canonical form of polyphase matrices of multiscaling vectors and some properties of solutions satisfying the matrix equation of pr condition are studied through unimodular groups over the laurent polynomial ring under the canonical form of polyphase matrices of multiscaling vectors with the same symmetric center and different symmetric centers explicit symmetric extension formulas expressed by the polyphase matrices of multiscaling vectors can be obtained as a result a novel approach for the construction of symmetric compactly supported biorthogonal multiwavelets with multiplicity 2 is proposed finally several examples are given for verification of our proposed approach

matrix extension and biorthogonal multiwavelet construction abstract suppose that p z and p z are two r n matrices over the laurent polynomial ring r z where r p z p z i r on the unit circle t we develop an algorithm that produces two n n matrices q z and q z over r z satisfying the identity q z q z i n on t such that the submatrices formed by the first r rows of q z and q z are p z and p z respectively our algorithm is used to construct compactly supported biorthogonal multiwavelets from multiresolutions generated by univariate compactly supported biorthogonal scaling functions with an arbitrary dilation parameter m z where m 1

an algorithm for matrix extension and wavelet construction this paper gives a practical method of extending an n x r matrix p z r n with laurent polynomial entries in one complex variable z to a square matrix also with laurent polynomial entries if p z has orthonormal columns when z is restricted to the torus t it can be extended to a paraunitary matrix if p z has rank r for each z t it can be extended to a matrix with nonvanishing determinant on t the method is easily implemented in the computer it is applied to the construction of compactly supported wavelets and prewavelets from multiresolutions generated by several univariate scaling functions with an arbitrary dilation parameter

high order balanced multiwavelets theory factorization and design this paper deals with multiwavelets and the different properties of approximation and smoothness associated with them in particular we focus on the important issue of the preservation of discrete time polynomial signals by multifilterbanks we introduce and detail the property of balancing for higher degree discrete time polynomial signals and link it to a very natural factorization of the refinement mask of the lowpass synthesis multifilter this factorization turns out to be the counterpart for multiwavelets of the well known zeros at spl pi condition in the usual scalar wavelet framework the property of balancing also proves to be central to the different issues of the preservation of smooth signals by multifilterbanks the approximation power of finitely generated multiresolution analyses and the smoothness of the multiscaling functions and multiwavelets using these new results we describe the construction of a family of orthogonal multiwavelets with symmetries and compact support that is indexed by increasing order of balancing in addition we also detail for any given balancing order the orthogonal multiwavelets with minimum length multifilters

explicit construction of high pass filter sequence for orthogonal multiwavelets for the construction of multiwavelets there are no unified explicit formulas as that in the scalar case available so far in this paper by studying the relationship between length 3 and length 4 filter sequences of orthogonal multiwavelets based on the result of chui for the construction of length 3 orthogonal multiwavelets a set of explicit formulas is given for the construction of length 4 high pass filter sequence examples demonstrate that our proposed approach not only provides explicit formulas for the construction of length 4 high pass filter sequence with multiplicity r but also yields a set of new low pass and high pass filter sequences with length 3 and multiplicity 2r

on a family of biorthogonal armlets with prescribed properties abstract the notion of armlets analysis ready multiwavelets was introduced and studied by jian ao lian most recently as a precise formulation of orthonormal multiwavelets that guarantee wavelet decomposition with highpass output not being effected by polynomial perturbation of the input in this paper we first extend this concept to the biorthogonal setting and then we concern ourselves about a particular construction of biorthogonal multiscaling function and multiwavelets with multiplicity r 2 in particular we consider the two pairs of lowpass filters are flipped and the two pairs of highpass filters are linearphase respectively and we also give several equivalent forms of flipping property in terms of symbols and filters associated with multiscaling functions and multiwavelets by requiring flipping property we can represent all the entries of the matrix symbols p z q z p z q z of a biorthogonal multiwavelet using p11 z and p 11 z which are the first row and first column entries of p z and p z respectively these results will lead to a procedure for the construction of biorthogonal armlets with prescribed properties consequently a family of biorthogonal multiscaling functions which are mirrored copies each other and biorthogonal multiwavelets which are armlets of higher order with symmetry and antisymmetry are constructed explicitly

some examples of square integrable representations of semisimple p adic groups we construct irreducible representations of the hecke algebra of an affine weyl group analogous to kilmoyer s reflection representation corresponding to finite weyl groups and we show that in many cases they correspond to a square integrable representation of a simple p adic group

an algorithm for constructing symmetric orthogonal multiwavelets by matrix symmetric extension symmetric extensions of paraunitary matrix is studied starting from a given m band compactly supported orthogonal multiscaling function with some symmetric property the problem to construct a corresponding m band multiwavelet which have the symmetric property can be reduced to the symmetric paraunitary extension of a given matrix it can be shown that such matrix extension is always solvable and an algorithmic approach to solve the symmetric paraunitary extension problem is presented this leads to a practical method for the construction of compactly supported symmetric orthogonal multiwavelets from a given multiscaling functions with an arbitrary integer dilation factor m 1 as an application some examples are given in particular the well known chui lian multiwavelets is recovered via the method

pro p iwahori hecke ring and supersingular representations the motivation of this paper is the search for a langlands correspondence modulo p we show that the pro p iwahori hecke ring open image in new window of a split reductive p adic group g over a local field f of finite residue field fq with q elements admits an iwahori matsumoto presentation and a bernstein z basis and we determine its centre we prove that the ring open image in new window is finitely generated as a module over its centre these results are proved in 11 only for the iwahori hecke ring let p be the prime number dividing q and let k be an algebraically closed field of characteristic p a character from the centre of open image in new window to k which is as null as possible will be called null the simple open image in new window modules with a null central character are called supersingular when g gl n we show that each simple open image in new window module of dimension n containing a character of the affine subring open image in new window is supersingular using the minimal expressions of haines generalized to open image in new window and that the number of such modules is equal to the number of irreducible k representations of the weil group wf of dimension n when the action of an uniformizer pf in the hecke algebra side and of the determinant of a frobenius frf in the galois side are fixed i e the number nn q of unitary irreducible polynomials in fq x of degree n one knows that the converse is true by explicit computations when n 2 10 and when n 3 rachel ollivier

reversing subdivision rules local linear conditions and observations on inner products abstract in a previous work samavati and bartels comput graphics forum 18 1998 97 119 we investigated how to reverse subdivision rules using global least squares fitting this led to multiresolution structures that could be viewed as semiorthogonal wavelet systems whose inner product was that for finite dimensional cartesian vector space we produced simple and sparse reconstruction filters but had to appeal to matrix factorization to obtain an efficient exact decomposition we also made some observations on how the inner product that defines the semiorthogonality influences the sparsity of the reconstruction filters in this work we carry the investigation further by studying biorthogonal systems based upon subdivision rules and local least squares fitting problems that reverse the subdivision we are able to produce multiresolution structures for some common univariate subdivision rules that have both sparse reconstruction and decomposition filters three will be presented here for quadratic and cubic b spline subdivision and for the four point interpolatory subdivision of dyn et al we observe that each biorthogonal system we produce can be interpreted as a semiorthogonal system with an inner product induced on the multiresolution that is quite different from that normally used some examples of the use of this approach on images curves and surfaces are given

balanced multiwavelets theory and design this article deals with multiwavelets which are a generalization of wavelets in the context of time varying filter banks and with their applications to signal processing and especially compression by their inherent structure multiwavelets are fit for processing multichannel signals this is the main issue in which we are interested first we review material on multiwavelets and their links with multifilter banks and especially time varying filter banks then we have a close look at the problems encountered when using multiwavelets in applications and we propose new solutions for the design of multiwavelets filter banks by introducing the so called balanced multiwavelets