characteristic cycles of perverse sheaves and milnor fibers we show that the milnor monodromy and the milnor numbers naturally appear in the characteristic cycles of irreducible perverse sheaves having the singularities of a complex hypersurface we find also a new numerical constraint on the milnor monodromy for general hypersurface singularities

kp hierarchy for the cyclic quiver we introduce a generalisation of the kp hierarchy closely related to the cyclic quiver and the cherednik algebra hk zm this hierarchy depends on m parameters one of which can be eliminated with the usual kp hierarchy corresponding to the m 1 case generalising the result of wilson invent math 133 1 1 41 1998 we show that our hierarchy admits solutions parameterised by suitable quiver varieties the pole dynamics for these solutions is shown to be governed by the classical calogero moser system for the wreath product zm sn and its new spin version these results are further extended to the case of the multi component hierarchy

on the variety of a highest weight module 1 2 let u g be the enveloping algebra of g detailed information on the primitive spectrum prim u g of u g was summarized by conjecture 7 4 of 181 here a main question was to relate prim u g with the springer correspondence parts i ii of this conjecture were established in i ii and a partial solution to iii was given in 21 sufficient e g to treat g of type a meanwhile borho and brylinski 5 have established iii for induced ideals while barbasch and vogan 1 2 have established a version of iii in which gr i i e prim u g is replaced by a certain wavefront set known to be contained in y gr 1 this last work involves some case by case analysis and gives little indication as to why the springer correspondence should arise in the study of prim u g

non existence of reflexive ideals in iwasawa algebras of chevalley type abstract let be a root system and let z p be the standard chevalley z p lie algebra associated to for any integer t 1 let g be the uniform pro p group corresponding to the powerful lie algebra p t z p and suppose that p 5 then the iwasawa algebra g has no non trivial two sided reflexive ideals this was previously proved by the authors for the root system a 1

dynamic 3d axisymmetric problems in continuously non homogeneous piezoelectric solids the meshless local petrov galerkin mlpg method is used to analyze transient dynamic problems in 3d axisymmetric piezoelectric solids with continuously inhomogeneous material properties both mechanical and thermal loads are considered here a 3d axisymmetric body is created by rotation of a cross section around an axis of symmetry axial symmetry of geometry and boundary conditions reduces the original 3d boundary value problem into a 2d problem the cross section is covered by small circular sub domains surrounding nodes randomly spread over the analyzed domain a unit step function is chosen as test function in order to derive local integral equations on the boundaries of the chosen sub domains called local boundary integral equations lbie these integral formulations are either based on the laplace transform technique or the time difference approach the local integral equations are non singular and take a very simple form despite of inhomogeneous and anisotropic material behaviour across the analyzed structure spatial variation of all physical fields or of their laplace transforms at discrete time instants are approximated on the local boundary and in the interior of the sub domain by means of the moving least squares mls method the stehfest algorithm is applied for the numerical laplace inversion in order to retrieve the time dependent solutions

characteristic varieties and vanishing cycles on presente une etude systematique des varietes caracteristiques des systemes holonomes a singularites regulieres ce sont des sous varietes lagrangiennes coniques dans le fibre cotangent t x

differential operators on homogeneous spaces iii characteristic varieties of harish chandra modules and of primitive ideals letg be a semi simple complex algebraic group with lie algebra and flag varietyx g b for each primitive idealj with trivial central character in the enveloping algebrau we define a characteristic variety in the cotangent bundle ofx which projects under the springer resolution mapt x onto the closure of a nilpotent orbit we prove that this characteristic variety is theg saturation of the characteristic variety of a highest weight module with annihilatorj we conjecture that it is irreducible forg sl n our conjecture would provide a geometrical explanation for the classification of primitive ideals in terms of weyl group representations as achieved by a joseph the presentation of these ideas here is simultaneously used to some extent as an opportunity to continue our more general systematic discussion of differential operators on a complete homogeneous space and to study more generally characteristic varieties of harish chandra modules

zariski rings and flatness of completion abstract we relate flatness and faithful flatness of the completion to the comparison and zariskian property resp of the filtration some applications have been included

cluster based color matching for image retrieval abstract color is an important attribute for image matching and retrieval we present a new method fo color matching based on a clustering algorithm in 3 d color space we define a new color feature to characterize the color information and a distance measure to compute the color similarity of images we have implemented this technique and tested it for a database of approximately 170 images the test results shoe that the efficiency of retrieval of this new method is very high

a method for the numerical inversion of laplace transforms abstract in this paper a numerical inversion method for laplace transforms based on a fourier series expansion developed by durbin 5 is presented the disadvantage of the inversion methods of that type the encountered dependence of discretization and truncation error on the free parameters is removed by the simultaneous application of a procedure for the reduction of the discretization error a method for accelerating the convergence of the fourier series and a procedure that computes approximately the best choice of the free parameters suitable for a given problem the inversion method allows the adequate application of these procedures therefore in a big range of applications a high accuracy can be achieved with only a few function evaluations of the laplace transform the inversion method is implemented as a fortran subroutine

experimental resuls of an evolution based adaptation strategy for vq image filtering abstract in this paper we propose the filtering of images based on the codebooks obtained from an evolution based adaptation strategy for vector quantization vq this evolution based vq bayesian filter vqbf is applied to noise removal and segmentation of a high resolution magnetic resonance image we compare our approach with other more conventional smoothing filters the results show that vqbf performs a smoothing that preserves region boundaries and small details it does not show the strong boundary diffusion and displacement that are common to smoothing filters border detection on the filtered images is also presented

free group algebras in division rings with valuation i abstract let r be an algebra over a commutative ring k suppose that r is endowed with a descending filtration indexed on an ordered group g such that the restriction to k is positive we show that the existence of free algebras on a certain set of generators in the induced graded ring grad r implies the existence of free group algebras in r our best results are obtained for division rings endowed with a valuation

microlocal properties of filtered rings the process of microlocalization appeared first in a strongly analytic frame in relation to systems of linear differential equations with holomorphic coefficients see e g 13 from the strictly algebraic point of view the process of microlocalization gives an answer to the following universal problem if r is a filtered ring and s c r is a multiplicatively closed subset does there exist a complete filtered ring denoted by q r with a filtered ring homomorphism 9 r q r such that the two conditions below are satisfied

completed group algebras of abelian by procyclic groups abstract let p be prime let g be a p valuable group isomorphic to z p d z p and let k be a finite field of characteristic p we will prove that all faithful prime ideals of the completed group algebra kg are controlled by z g and a complete decomposition for s p e c k g will follow the principal technique we employ will be to study the convergence of mahler expansions for inner automorphisms

rotation invariant pattern matching with color ring projection in this paper we propose a rotation invariant pattern matching scheme for detecting objects in complex color images the complexity and computational load for matching colored objects in arbitrary orientations are reduced significantly by the 1 d color ring projection representation it can rapidly select the possible locations of a reference template in the input scene by computing the normalized correlation of 1 d color ring projection patterns objects in the candidate locations are then verified by the pixel to pixel template matching to make the pixel based matching invariant to rotation a color feature is used as pixel density and the axis of least second moment is employed to estimate the rotational angle of a colored pattern the proposed method has shown promising result based on experiments on a variety of natural and industrial images

hamiltonian reduction and nearby cycles for mirabolic d modules abstract we study holonomic d modules on sl n c c n called mirabolic modules analogous to lusztig s character sheaves we describe the supports of simple mirabolic modules we show that a mirabolic module is killed by the functor of hamiltonian reduction from the category of mirabolic modules to the category of representations of the trigonometric cherednik algebra if and only if the characteristic variety of the module is contained in the unstable locus we introduce an analogue of verdier s specialization functor for representations of cherednik algebras which agrees on category o with the restriction functor of bezrukavnikov and etingof in type a we also consider a verdier specialization functor on mirabolic d modules we show that hamiltonian reduction intertwines specialization functors on mirabolic d modules with the corresponding functors on representations of the cherednik algebra this allows us to apply known hodge theoretic purity results for nearby cycles in the setting considered by bezrukavnikov and etingof

d module structure of local cohomology modules of toric algebras let s be a toric algebra over a field k of characteristic 0 and let i be a monomial ideal of s we show that the local cohomology modules h i i s are of finite length over the ring of differential operators d s k generalizing the classical case of a polynomial algebra s as an application we compute the characteristic cycles of some local cohomology modules

a new algebraic approach to microlocalization of filtered rings using the construction of the rees ring associated to a filtered ring we provide a description of the microlocalization of the filtered ring by using only purely algebraic techniques the method yields an easy approach towards the study of exactness properties of the microlocalization functor every microlocalization at a regular multiplicative ore set in the associated graded ring can be obtained as the completion of a localization at an ore set of the filtered ring

on the classification of image regions by colour texture and shape abstract a unified approach to how colour texture and shape can be encoded in a single spatio chromatic feature space is developed in particular it is shown how such features can be extracted using multi scaled filtering and correlation methods which capture the variations of colour over space in ways which encode important image features not extracted by techniques which separate colour texture and shape into separate channels finally it is shown how such spatio chromatic features can be used in difficult classification problems

solvable lie algebras of dimension 4 over perfect fields abstract the solvable lie algebras of dimension not greater than four over a perfect field of reference are described in terms of their nilpotent frame counted over finite fields of q elements and classified over the real and complex number fields the number dq n of nonisomorphic solvable lie algebras of dimension n over f q roughly speaking grows as a polynomial in n with qn 2 as highest term but there are smaller additional terms depending on the residue class of q modulo n 1 if n 4

existence theorems for dualizing complexes over non commutative graded and filtered rings abstract in this note we prove existence theorems for dualizing complexes over graded and filtered rings thereby generalizing some results by zhang yekutieli and jorgensen

hypertoric category o abstract we study the representation theory of the invariant subalgebra of the weyl algebra under a torus action which we call a hypertoric enveloping algebra we define an analogue of bgg category o for this algebra and identify it with a certain category of sheaves on a hypertoric variety we prove that a regular block of this category is highest weight and koszul identify its koszul dual compute its center and study its cell structure we also consider a collection of derived auto equivalences analogous to the shuffling and twisting functors for bgg category o

degenerate whittaker functionals for real reductive groups in this paper we establish a connection between the associated variety of a representation and the existence of certain it degenerate whittaker functionals for both smooth and k finite vectors for all quasi split real reductive groups thereby generalizing results of kostant matumoto and others

a near real time evolution based adaptation strategy for dynamic color quantization of image sequences abstract color quantization of still images can be easily stated as a clustering problem color quantization of sequences of images becomes a non stationary clustering problem in this paper we propose a very simple and effective evolution based adaptive strategy to perform the adaptive computation of the color representatives for each image in the sequence salient features of the algorithm proposed here are individuals correspond to individual cluster centers to approach real time response we impose one generation adaptation for each image mutation operators are guided by the actual covariance matrices of the clusters experimental results on a sequence of indoor images are presented

lagrangian construction for representations of hecke algebras 1 let k be a non archimedean local field with the residue field consisting of q elements according to langlands philosophy irreducible complex representations of a reductive k group g should roughly speaking correspond to homomorphisms of the weil deligne group into the socalled l group let zc g be the iwahori subgroup the category of admissible gkmodules generated by z fixed vectors is known to be equivalent to the category of finite dimensional representations of the hecke algebra h z g z langlands philosophy suggests via that equivalence the following classification of irreducible hecke algebra modules stated in purely complex terms and not involving any local held

extensions of modules over weyl algebras in this paper we calculate some ext groups of singular modules over the complex weyl algebra an in particular we determine conditions under which ext is an infinite dimensional vector space when n 2 or 3

multiplier ideals v filtrations and transversal sections we show that the restriction to a smooth transversal section commutes to the computation of multiplier ideals and v filtrations as an application we prove the constancy of the jumping numbers and the spectrum along any stratum of a whitney regular stratification

lifting ore sets of noetherian filtered rings and applications abstract let r be a filtered ring such that the rees ring r of r is left noetherian it is observed that if t is a left ore set of the associated graded ring g r consisting of homogeneous elements then the saturated set s s r s t is a left ore set of r this lifting property is used to obtain local global results on r which simplify some microlocal global results in the literature if g r is positively graded and commutative then certain structure sheaves on r are constructed

prime ideals in nilpotent iwasawa algebras let g be a nilpotent complete p valued group of finite rank and let k be a field of characteristic p we prove that every faithful prime ideal of the iwasawa algebra kg is controlled by the centre of g and use this to show that the prime spectrum of kg is a disjoint union of commutative strata we also show that every prime ideal of kg is completely prime the key ingredient in the proof is the construction of a non commutative valuation on certain filtered simple artinian rings

filtrations on simple artinian rings abstract filtrations on simple artinian rings are related to pseudo valuations by conditions on the associated graded rings

characteristic cycles of constructible sheaves in his paper k kashiwara introduced the notion of characteristic cycle for complexes of constructible sheaves on manifolds let x be a real analytic manifold and f a complex of sheaves of c vector spaces on x whose cohomology is constructible with respect to a subanalytic strati cation the characteristic cycle cc f is a subanalytic lagrangian cycle with in nite support and with values in the orientation sheaf of x in the cotangent bundle t x the de nition of cc f is morse theoretic heuristically cc f encodes the in nitesimal change of the euler characteristic of the stalks of f along the various directions in x it tends to be di cult in practice to calculate cc f explicitly for all but the simplest complexes f on the other hand the characteristic cycle construction has good functorial properties the behavior of cc f with respect to the operations of proper direct image verdier duality and non characteristic inverse image of f is well understood ks in this paper we describe the e ect of the operation of direct image by an open embedding combining our result with those that were previously known we obtain descriptions of cc rf f and cc f f analogous to those in ks for arbitrary morphisms f x y in the semi algebraic category and complexes f with semi algebraically constructible cohomology in e ect this provides an axiomatic characterization of the functor cc at least in the semi algebraic context our arguments do apply more generally in the subanalytic case but because statements become quite convoluted we shall not strive for the greatest degree of generality as a concrete application we consider the case of the ag manifold x of a complex semisimple lie algebra g here the weyl group w of g operates

chern classes for singular hypersurfaces we prove a formula expressing the chern schwartz macpherson class of a hypersurface in a nonsingular variety as a variation on another definition of the homology chern class of singular varieties introduced by w fulton and we discuss the relation between these classes and others such as mather s chern class and the l class we introduced in previous work 0 introduction there are several candidates for a notion of homology chern class of a possibly singular algebraic variety x agreeing with the class obtained as dual of the total chern class of the tangent bundle of x if x is nonsingular one such notion was introduced by r macpherson macpherson agreeing as it was later understood with a class introduced earlier by m ij schwartz and enjoying good functorial properties a different class was defined by w fulton fulton 4 2 6 in a different and somewhat more general setting the main purpose of this paper is to prove a precise relation between the schwartz macpherson and the fulton class of a hypersurface x of a nonsingular variety we denote these two classes by csm x cf x respectively a summary of the context and essential definitions is given in 1 where we present several different statements of the result the version which expresses most directly the link between the two classes mentioned above goes as follows fulton s class for a subscheme x of a nonsingular variety m is defined by cf x m c tmix n s x m that is by capping the total chern class of the ambient space against the segre class of the subscheme it is proved in fulton 4 2 6 that this definition does not depend on the choice of the ambient variety m for a hypersurface x of a nonsingular variety m let y be the singular subscheme of x locally defined by the partial derivatives of an equation of x for an integer k 0 we can consider the k th thickening x k of x along y and then consider its fulton class cf x k it is easily seen that cf x k is a polynomial in k with coefficients in the chow group a x so it can be formally evaluated at negative k s we can then define a class c x cf x 1 the main result of this paper is theorem c x is equal to the chern schwartz macpherson class of x received by the editors june 3 1997 1991 mathematics subject classification prinmary 14c17 32s60 supported in part by nsf grant dms 9500843 1999 american mathbemiatical society 3989 this content downloaded from 157 55 39 136 on thu 01 dec 2016 05 45 16 utc all use subject to http about jstor org terms

reflexive ideals in iwasawa algebras let g be a torsionfree compact p adic analytic group we give sufficient conditions on p and g which ensure that the iwasawa algebra og of g has no non trivial two sided reflexive ideals consequently these conditions imply that every non zero normal element in og is a unit we show that these conditions hold in the case when g is an open subgroup of and p is arbitrary using a previous result of the first author we show that there are only two prime ideals in og when g is a congruence subgroup of the zero ideal and the unique maximal ideal these statements partially answer some questions asked by the first author and brown

the dependence of the modulus of elasticity on reference temperature in generalized thermoelasticity with thermal relaxation the model of the equations of generalized thermoelasticity with thermal relaxation in an isotropic elastic medium with temperature dependent mechanical properties is established the modulus of elasticity is taken as a linear function of reference temperature the state space approach is adopted for the solution of one dimensional problems in the absence or presence of heat sources the laplace transform technique is used a numerical method is employed for the inversion of the laplace transforms numerical results for the stress distribution are given and illustrated graphically for each problem a comparison is made with results obtained in case of temperature independent modulus of elasticity

torus equivariant d modules and hypergeometric systems abstract we formalize at the level of d modules the notion that a hypergeometric systems are equivariant versions of the classical hypergeometric equations for this purpose we construct a functor b a on a suitable category of torus equivariant d modules and show that it preserves key properties such as holonomicity regularity and reducibility of monodromy representation we also examine its effect on solutions characteristic varieties and singular loci by applying b a to suitable binomial d modules we shed new light on the d module theoretic properties of systems of classical hypergeometric differential equations

color indexing using chromatic invariant abstract we present an efficient indexing matching algorithm that is independent of the changes in the illuminant color and the geometric conditions for 3 d object with multiple colors the color contents of an object can be represented by the peak coordinates in the chromaticity histogram space corresponding to the distinct colors in an image the visible color areas and their relative sizes of the histograms may change with viewing conditions but the coordinates of local maxima remain stable however a change in illumination color results in a deformation of the chromaticity distribution so as to degrade the performance of color recognition in order to discount lighting change we define a chromatic invariant that normalizes the chromaticities of the histogram peaks by the norm of each channel therefore the normalized coordinates of the peaks are stable to the changes in illumination color scaling rotation partial occlusion viewing direction and deformation test results on a database of diverse images show that the chromatic invariant yields excellent recognition rate even when the illuminant color and geometric conditions vary substantially

subspaces of non commutative spaces this paper concerns the closed points closed subspaces open subspaces weakly closed and weakly open subspaces and effective divisors on a non commutative space

donaldson thomas type invariants via microlocal geometry we prove that donaldson thomas type invariants are equal to weighted euler characteristics of their moduli spaces in particular such invariants depend only on the scheme structure of the moduli space not the symmetric obstruction theory used to define them we also introduce new invariants generalizing donaldson thomas type invariants to moduli problems with open moduli space these are useful for computing donaldson thomas type invariants over stratifications

characteristic cycles for the loop grassmannian and nilpotent orbits x which is a linear combination of closures of conormal bundles to submanifolds of x intuitively the microlocal multiplicities c me asurethesingularity of at in settings related to representation theory a group g acts on x is g equivariant and the microlocal multiplicities play a significant but only partially understood role in representation theory see ro sv abv and kasa e g in this paper we compute microlocal multiplicities for certain cases of interest in representation theory let g be a connected reductive group with loop group lg and let p bethesubgroup of lg consisting of loops with positive fourier coefficients then p orbits on theloop grassmannian lg p correspond to the irreducible representations l of thedual re ductivegroup g for dominant weights and of a torus of

the characteristic cycle and the singular support of a constructible sheaf we define the characteristic cycle of an etale sheaf as a cycle on the cotangent bundle of a smooth variety in positive characteristic using the singular support recently defined by beilinson we prove a formula a la milnor for the total dimension of the space of vanishing cycles and an index formula computing the euler poincare characteristic generalizing the grothendieck ogg shafarevich formula to higher dimension an essential ingredient of the construction and the proof is a partial generalization to higher dimension of the semi continuity of the swan conductor due to deligne laumon we prove the index formula by establishing certain functorial properties of characteristic cycles

multiple classifiers for color flag and trademark image retrieval a novel region based multiple classifier color image retrieval system is presented in our approach a region growing technique is first employed to cluster connected color pixels with the same color in an image to form color regions which are the primitive elements utilized in our proposed approach then three complementary region based classifiers that we developed are selected in the classifier selection stage which include color classifier shape classifier and relational classifier in each classifier a virtue probability representing the probability that an image is similar to the query image is defined thereafter a set of virtue probabilities is calculated in each classifier next the measurement dependent methods are applied to combine the virtue probabilities of classifiers in the decision combination stage the dynamic selection scheme designed in the decision combination stage can further improve the system performance dramatically experimental results reveal the feasibility and validity of our proposed approach in solving the color image retrieval problem

equivariant quantum cohomology of cotangent bundle of g p abstract let g denote a complex semisimple linear algebraic group p a parabolic subgroup of g and p g p we identify the quantum multiplication by divisors in t p in terms of stable basis which is introduced in 9 using this and the restriction formula for stable basis 17 we show that the g c equivariant quantum multiplication formula in t p is conjugate to the formula conjectured by braverman

generalized thermo piezoelectric problems with temperature dependent properties the model of the equation of generalized thermo piezoelectricity in an isotropic elastic medium with temperature dependent mechanical properties is established the modulus of elasticity is taken as a linear function of reference temperature the state space approach is adopted for the solution of one dimensional problems in the absence or presence of heat sources a numerical technique is employed to obtain the solution in the physical domain the results are given and illustrated graphically a comparison is made with results obtained in case of temperature independent modulus of elasticity

a control theorem for primitive ideals in iwasawa algebras abstract let p be a prime k q p a finite extension g a uniform pro p group we prove that all faithful primitive ideals in the iwasawa algebra kg are controlled by c g z 2 g the centraliser of the second term in the upper central series for g

a little microlocal morse theory if a complex analytic function f has a stratified isolated critical point then it is known that the cohomology of the milnor fibre of f has a direct sum decomposition in terms of the normal morse data to the strata we use microlocal morse theory to obtain the same result under the weakened hypothesis that the vanishing cycles along f have isolated support we also investigate an index theoretic proof of this fact

on irreducible representations of compact p adic analytic groups we prove that the canonical dimension of a coadmissible representation of a semisimple p adic lie group in a p adic banach space is either zero or at least half the dimension of a nonzero coadjoint orbit to do this we establish analogues for p adically completed enveloping algebras of bernstein s inequality for modules over weyl algebras the beilinson bernstein localisation theorem and quillen s lemma about the endomorphism ring of a simple module over an enveloping algebra