spectral shift function for trapping energies in the semiclassical limit semiclassical asymptotics of the spectral shift function ssf for schrodinger operator is studied at trapping energies it is shown that the ssf converges to sum of a smooth function and a step function which is essentially the counting function of resonances in particular the weyl asymptotics is proved

gravity coupled with matter and the foundation of non commutative geometry we first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length elementds its unitary representations correspond to riemannian metrics and spin structure whileds is the dirac propagatords x x d 1 whered is the dirac operator we extend these simple relations to the non commutative case using tomita s involutionj we then write a spectral action the trace of a function of the length element which when applied to the non commutative geometry of the standard model will be shown cc to give the sm lagrangian coupled to gravity the internal fluctuations of the non commutative geometry are trivial in the commutative case but yield the full bosonic sector of sm with all correct quantum numbers in this slightly non commutative case the group of local gauge transformations appears spontaneously as a normal subgroup of the diffeomorphism group

quantum locally compact metric spaces abstract we introduce the notion of a quantum locally compact metric space which is the noncommutative analogue of a locally compact metric space and generalize to the non unital setting the notion of quantum metric spaces introduced by rieffel we then provide several examples of such structures including the moyal plane compact quantum metric spaces and locally compact metric spaces this paper provides an answer to the question raised in the literature about the proper notion of a quantum metric space in the non unital setup and offers important insights into noncommutative geometry for non compact quantum spaces

quantum symmetry groups of noncommutative spheres we show that the noncommutative spheres of connes and landi are quantum homogeneous spaces for certain compact quantum groups we give a general construction of homogeneous spaces which support noncommutative spin geometries

isospectral deformations of eguchi hanson spaces as nonunital spectral triples we study the isospectral deformations of the eguchi hanson spaces along a torus isometric action in the noncompact noncommutative geometry we concentrate on locality smoothness and summability conditions of the nonunital spectral triples and relate them to the geometric conditions to be noncommutative spin manifolds

analytic and gevrey hypoellipticity for a class of pseudodifferential operators in one variable abstract we study the hypoellipticity of pseudo differential operators in one variable when a positivity assumption is made on a suitable principal part we prove that the found gevrey regularity is optimal

distributed control of spatially invariant systems we consider distributed parameter systems where the underlying dynamics are spatially invariant and where the controls and measurements are spatially distributed these systems arise in many applications such as the control of vehicular platoons flow control microelectromechanical systems mems smart structures and systems described by partial differential equations with constant coefficients and distributed controls and measurements for fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator lqr h sub 2 and h sub spl infin optimal controllers can be obtained by solving a parameterized family of standard finite dimensional problems we show that optimal controllers have an inherent degree of decentralization and this provides a practical distributed controller architecture we also prove a general result that applies to partially distributed control and a variety of performance criteria stating that optimal controllers inherit the spatial invariance structure of the plant connections of this work to that on systems over rings and systems with dynamical symmetries are discussed

c completions and the dfr algebra the aim of this paper is to present the construction of a general family of c algebras which includes as a special case the quantum spacetime algebra introduced by doplicher fredenhagen and roberts it is based on an extension of the notion of c completion from algebras to bundles of algebras compatible with the usual c completion of the appropriate algebras of sections combined with a novel definition for the algebra of the canonical commutation relations using rieffel s theory of strict deformation quantization taking the c algebra of continuous sections vanishing at infinity we arrive at a functor associating a c algebra to any poisson vector bundle and recover the original dfr algebra as a particular example

dixmier traces and extrapolation description of noncommutative lorentz spaces we study the connections between dixmier traces functions and traces of heat semigroups beyond the dual of the macaev ideal and in the general context of semifinite von neumann algebras we show that the correct framework for this investigation is that of operator lorentz spaces possessing an extrapolation description we demonstrate the applicability of our results to hormander weyl pseudo differential calculus on rn in this context we prove that the dixmier trace of a pseudo differential operator coincides with the dixmier integral of its symbol

on the existence of euler lagrange orbits satisfying the conormal boundary conditions abstract let m g be a closed connected riemannian manifold l t m r be a tonelli lagrangian given two non empty closed submanifolds q 0 q 1 m and a real number k we study the existence of euler lagrange orbits with energy k connecting q 0 to q 1 and satisfying suitable boundary conditions known as conormal boundary conditions we introduce the mane critical value which is relevant for this problem and discuss existence results for supercritical and subcritical energies we also provide counterexamples showing that all the results are sharp

persistence of embedded eigenvalues we consider conditions under which an embedded eigenvalue of a self adjoint operator remains embedded under small perturbations in the case of a simple eigenvalue embedded in continuous spectrum of multiplicity m infinity we show that in favorable situations the set of small perturbations of a suitable banach space which do not remove the eigenvalue form a smooth submanifold of codimension in we also have results regarding the cases when the eigenvalue is degenerate or when the multiplicity of the continuous spectrum is infinite

the noncommutative geometry of graph c algebras i the index theorem we investigate conditions on a graph c algebra for the existence of a faithful semifinite trace using such a trace and the natural gauge action of the circle on the graph algebra we construct a smooth 1 summable semi finite spectral triple the local index theorem allows us to compute the pairing with k theory this produces invariants in the k theory of the fixed point algebra and these are invariants for a finer structure than the isomorphism class of c e

dixmier measurability in marcinkiewicz spaces and applications abstract we present new results concerning the description of dixmier measurable elements in the sense of a connes in marcinkiewicz spaces and demonstrate some applications of our results in particular we complement famous connes trace theorem by describing the asymptotics of the singular function of order n classical pseudo differential operators on an n dimensional compact riemannian manifold

a hybrid evolutionary algorithm for the periodic location routing problem abstract the well known vehicle routing problem vrp has been studied in depth over the last decades nowadays generalizations of vrp have been developed for tactical or strategic decision levels of companies but not both the tactical extension or periodic vrp pvrp plans a set of trips over a multiperiod horizon subject to frequency constraints the strategic extension is motivated by interdependent depot location and routing decisions in most distribution systems low quality solutions are obtained if depots are located first regardless of the future routes in the location routing problem lrp location and routing decisions are tackled simultaneously here for the first time except for some conference papers the goal is to combine the pvrp and lrp into an even more realistic problem covering all decision levels the periodic lrp or plrp a hybrid evolutionary algorithm is proposed to solve large size instances of the plrp first an individual representing an assignment of customers to combinations of visit days is randomly generated the evolution operates through an evolutionary local search els on visit day assignments the algorithm is hybridized with a heuristic based on the randomized extended clarke and wright algorithm recwa to create feasible solutions and stops when a given number of iterations is reached the method is evaluated over three sets of instances and solutions are compared to the literature on particular cases such as one day horizon lrp or one depot pvrp this metaheuristic outperforms the previous methods for the plrp

the moyal sphere we construct a family of constant curvature metrics on the moyal plane and compute the gauss bonnet term for each of them they arise from the conformal rescaling of the metric in the orthonormal frame approach we find a particular solution which corresponds to the fubini study metric and which equips the moyal algebra with the geometry of a noncommutative sphere

noncommutative manifolds from graph and k graph c algebras in pren we constructed smooth 1 summable semifinite spectral triples for graph algebras with a faithful trace and in prs we constructed k summable semifinite spectral triples for k graph algebras in this paper we identify classes of graphs and k graphs which satisfy a version of connes conditions for noncommutative manifolds

the wave group on asymptotically hyperbolic manifolds abstract we show that the wave group on asymptotically hyperbolic manifolds belongs to an appropriate class of fourier integral operators then we use now standard techniques to analyze its regularized trace we prove that as in the case of compact manifolds without boundary the singularities of the regularized wave trace are contained in the set of periods of closed geodesics we also obtain an asymptotic expansion for the trace at zero

algebras of distributions suitable for phase space quantum mechanics ii topologies on the moyal algebra the topology of the moyal algebra may be defined in three ways the algebra may be regarded as an operator algebra over the space of smooth declining functions either on the configuration space or on the phase space itself or one may construct the algebra via a filtration of hilbert spaces or other banach spaces of distributions the equivalence of the three topologies thereby obtained is proved as a consequence by filtrating the space of tempered distributions by banach subspaces new sufficient conditions are given for a phase space function to correspond to a trace class operator via the weyl correspondence rule

spectral flow and dixmier traces abstract we obtain general theorems which enable the calculation of the dixmier trace in terms of the asymptotics of the zeta function and of the heat operator in a general semi finite von neumann algebra our results have several applications we deduce a formula for the chern character of an odd l 1 summable breuer fredholm module in terms of a hochschild 1 cycle we explain how to derive a wodzicki residue for pseudo differential operators along the orbits of an ergodic r n action on a compact space x finally we give a short proof of an index theorem of lesch for generalised toeplitz operators

nonunital spectral triples and metric completeness in unbounded kk theory abstract we consider the general properties of bounded approximate units in non self adjoint operator algebras such algebras arise naturally from the differential structure of spectral triples and unbounded kasparov modules our results allow us to present a unified approach to characterising completeness of spectral metric spaces existence of connections on modules self adjointness and regularity of induced operators on tensor product c modules and the lifting of kasparov products to the unbounded category in particular we prove novel existence results for quasicentral approximate units in non self adjoint operator algebras allowing us to strengthen kasparov s technical theorem and extend it to this realm finally we show that given any two composable kk classes we can find unbounded representatives whose product can be constructed to yield an unbounded representative of the kasparov product

the dixmier trace and asymptotics of zeta functions abstract we obtain general theorems which enable the calculation of the dixmier trace in terms of the asymptotics of the zeta function and of the trace of the heat semigroup we prove our results in a general semi finite von neumann algebra we find for p 1 that the asymptotics of the zeta function determines an ideal strictly larger than l p on which the dixmier trace may be defined we also establish stronger versions of other results on dixmier traces and zeta functions

on asymptotic expansions of twisted products the series development of the quantum mechanical twisted product is studied the series is shown to make sense as a moment asymptotic expansion of the integral formula for the twisted product either pointwise or in the distributional sense depending on the nature of the factors a condition is given that ensures convergence and is stronger than previously known results possible applications are examined

signal matching through scale space given a collection of similar signals that have been deformed with respect to each other the general signal matching problem is to recover the deformation we formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term the minimization reduces to a dynamic system governed by a set of coupled first order differential equations the dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale among the major themes in recent work on visual signal matching have been the notions of matching as constrained optimization of variational surface reconstruction and of coarse to fine matching our solution captures these in a precise succinct and unified form results are presented for one dimensional signals a motion sequence and a stereo pair

the analysis of partial differential operators i hormander springer 1985 vol 1 391 pp vol 2 390 pp vol 3 525 pp vol 4 351 pp

the index of scattering operators of dirac equations ii abstract the index formula of scattering operators of the previous paper of the author t matsui the index of scattering operators of dirac equations commun math phys 110 1987 553 571 is shown to hold for a wider class of potentials which contains both gauge potentials with compactly supported energy and instantontype potentials

the action functional in non commutative geometry we establish the equality between the restriction of the adler manin wodzicki residue or non commutative residue to pseudodifferential operators of order n on ann dimensional compact manifoldm with the trace which j dixmier constructed on the macaev ideal we then use the latter trace to recover the yang mills interaction in the context of non commutative differential geometry

continuity statements and counterintuitive examples in connection with weyl quantization we use the properties of an integral transform relating a classical function f with the matrix elements between coherent states of its quantal counterpart q f to derive continuity properties of the weyl transform from classes of distributions to classes of quadratic forms we also give examples of pathological behavior of the weyl transform with respect to other topologies e g bounded functions leading to unbounded operators

the spectral action for moyal planes extending a result of vassilevich we obtain the asymptotic expansion for the trace of a spatially regularized heat operator l f e t where is a generalized laplacian defined with moyal products and l f is moyal left multiplication the moyal planes corresponding to any skewsymmetric matrix being spectral triples the spectral action introduced in noncommutative geometry by chamseddine and connes is computed this result generalizes the connes lott action previously computed by gayral for symplectic

global and local aspects of spectral actions the principal object in noncommutative geometry is the spectral triple consisting of an algebra a hilbert space and a dirac operator field theories are incorporated in this approach by the spectral action principle which sets the field theory action to where f is a real function such that the trace exists and is a cutoff scale in the low energy weak field limit the spectral action reproduces reasonably well the known physics including the standard model however not much is known about the spectral action beyond the low energy approximation in this paper after an extensive introduction to spectral triples and spectral actions we study various expansions of the spectral actions exemplified by the heat kernel we derive the convergence criteria for a commutative spectral triple we compute the heat kernel on the torus up to the second order in gauge connection and consider limiting cases this article is part of a special issue of journal of physics a mathematical and theoretical in honour of stuart dowker s 75th birthday devoted to applications of zeta functions and other spectral functions in mathematics and physics

scattering matrix in external field problems we discuss several aspects of second quantized scattering operators s for fermions in external time dependent fields we derive our results on a general abstract level having in mind as a main application potentials of the yang mills type and in various dimensions we present a new and powerful method for proving the existence of s which is also applicable to other situations like external gravitational fields we also give two complementary derivations of the change of phase of the scattering matrix under generalized gauge transformations which can be used whenever our method of proving the existence of s applies the first is based on a causality argument i e s including phase is determined from a time evolution and the second exploits the geometry of certain infinite dimensional group extensions associated with the second quantization of one particle operators as a special case we obtain a hamiltonian derivation of the axial fermion yang mills anomaly and the schwinger terms related to it via the descent equations which is on the same footing and traces them back to a common root

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

quantum classical correspondence using projection operators classical properties associated with a large phase space domain with a smooth boundary as compared to the planck constant are shown to be expressed quantum mechanically by a family of quantum projection operators with the help of known theorems in microlocal analysis under the conditions of egorov s theorem the conservation of this correspondence under classical quantum dynamics is asserted

bayesian linearized rock physics inversion abstractthe estimation of rock and fluid properties from seismic attributes is an inverse problem rock physics modeling provides physical relations to link elastic and petrophysical variables most of these models are nonlinear therefore the inversion generally requires complex iterative optimization algorithms to estimate the reservoir model of petrophysical properties we have developed a new approach based on the linearization of the rock physics forward model using first order taylor series approximations the mathematical method adopted for the inversion is the bayesian approach previously applied successfully to amplitude variation with offset linearized inversion we developed the analytical formulation of the linearized rock physics relations for three different models empirical granular media and inclusion models and we derived the formulation of the bayesian rock physics inversion under gaussian assumptions for the prior distribution of the model the application of the inversion to real

quadratic hamiltonians in phase space quantum mechanics the dynamical evolution is described within the phase space formalism by means of the moyal propagator which is the symbol of the evolution operator quadratic hamiltonians on the phase space are distinguished in that their moyal bracket with any function equals their poisson bracket it is shown that for general time independent quadratic hamiltonians the moyal propagators transform covariantly under linear canonical transformations they are then derived and classified in a fully explicit manner using the theory of hamiltonian normal forms the authors present several tables of propagators it is proved that these propagators belong to the moyal algebra of distributions and that the spectrum of the hamiltonian may be obtained directly as the support of the fourier transform of the moyal propagator with respect to time from that the quantum mechanical problem for these hamiltonians is in principle completely solved the appropriate path integral formalism for phase space quantum mechanics leading back to the same results is outlined in an appendix

noncommutative geometry and reality we introduce the notion of real structure in our spectral geometry this notion is motivated by atiyah s kr theory and by tomita s involution j it allows us to remove two unpleasant features of the connes lott description of the standard model namely the use of bivector potentials and the asymmetry in the poincare duality and in the unimodularity condition

traces of compact operators and the noncommutative residue abstract we extend the noncommutative residue of m wodzicki on compactly supported classical pseudo differential operators of order d and generalise a connes trace theorem which states that the residue can be calculated using a singular trace on compact operators contrary to the role of the noncommutative residue for the classical pseudo differential operators a corollary is that the pseudo differential operators of order d do not have a unique trace pseudo differential operators can be non measurable in connes sense other corollaries are given clarifying the role of dixmier traces in noncommutative geometry including the definitive statement of connes original theorem

acceleration by aggregation of successive approximation methods abstract methods of successive approximation for solving linear systems or minimization problems are accelerated by aggregation disaggregation processes these processes which modify the iterates being produced are characterized by a two directional flow of information between the original higher dimensional problem and a lower dimensional aggregated version this technique is characterized by means of galerkin approximations and this in turn permits analysis of the method a deterministic as well as probabilistic analysis is given of a number of specific aggregation disaggregation examples numerical experiments have been performed and these confirm the analysis and demonstrate the acceleration

algebras of distributions suitable for phase space quantum mechanics i the twisted product of functions on r2n is extended to a algebra of tempered distributions that contains the rapidly decreasing smooth functions the distributions of compact support and all polynomials and moreover is invariant under the fourier transformation the regularity properties of the twisted product are investigated a matrix presentation of the twisted product is given with respect to an appropriate orthonormal basis which is used to construct a family of banach algebras under this product

dixmier traces on noncompact isospectral deformations abstract we extend the isospectral deformations of connes landi and dubois violette to the case of riemannian spin manifolds carrying a proper action of the noncompact abelian group r l under deformation by a torus action a standard formula relates dixmier traces of measurable operators to integrals of functions on the manifold we show that this relation persists for actions of r l under mild restrictions on the geometry of the manifold which guarantee the dixmier traceability of those operators

sequential and parallel large neighborhood search algorithms for the periodic location routing problem we propose a large neighborhood search lns algorithm to solve the periodic location routing problem plrp the plrp combines location and routing decisions over a planning horizon in which customers require visits according to a given frequency and the specific visit days can be chosen we use parallelization strategies that can exploit the availability of multiple processors the computational results show that the algorithms obtain better results than previous solution methods on a set of standard benchmark instances from the literature

a higher order nonlocal operator method for solving partial differential equations abstract a higher order nonlocal operator method for the solution of boundary value problems is developed the proposed higher order nonlocal operator brings several advantages as compared to the original nonlocal operator method ren et al 2020 which only ensures first order convergence furthermore it can be applied to directly and efficiently obtain all partial derivatives of higher orders simultaneously without the need of using shape functions only the functionals based on the nonlocal operators termed as operator functional are needed to obtain the final discrete system of equations which significantly facilitates the implementation several numerical examples are presented to show the effectiveness and accuracy of the proposed higher order nonlocal operator method including the solution of the poisson equation in 2 5 dimensional space kirchhoff and von karman plate problems incompressible elastic materials as well as phase field modeling of fracture

a variable neighborhood search heuristic for periodic routing problems the aim of this paper is to propose a new heuristic for the periodic vehicle routing problem pvrp without time windows the pvrp extends the classical vehicle routing problem vrp to a planning horizon of several days each customer requires a certain number of visits within this time horizon while there is some flexibility on the exact days of the visits hence one has to choose the visit days for each customer and to solve a vrp for each day our method is based on variable neighborhood search vns computational results are presented that show that our approach is competitive and even outperforms existing solution procedures proposed in the literature also considered is the special case of a single vehicle i e the periodic traveling salesman problem ptsp it is shown that slight changes of the proposed vns procedure is also competitive for the ptsp

integration on locally compact noncommutative spaces abstract we present an ab initio approach to integration theory for nonunital spectral triples this is done without reference to local units and in the full generality of semifinite noncommutative geometry the main result is an equality between the dixmier trace and generalised residue of the zeta function and heat kernel of suitable operators we also examine definitions for integrable bounded elements of a spectral triple based on zeta function heat kernel and dixmier trace techniques we show that zeta functions and heat kernels yield equivalent notions of integrability which imply dixmier traceability

noncommutative manifolds the instanton algebra and isospectral deformations we give new examples of noncommutative manifolds that are less standard than the nc torus or moyal deformations of n they arise naturally from basic considerations of noncommutative differential topology and have non trivial global features

a c algebraic approach to the principal symbol ii we introduce an abstract theory of the principal symbol mapping for pseudodifferential operators extending the results of sukochev and zanin j oper theory 2019 and providing a simple algebraic approach to the theory of pseudodifferential operators in settings important in noncommutative geometry we provide a variant of connes trace theorem which applies to certain noncommutative settings with a minimum of technical preliminaries our approach allows us to consider operators with non smooth symbols and we demonstrate the power of our approach by extending connes trace theorem to operators with non smooth symbols in three examples the lie group mathrm su 2 noncommutative tori and moyal planes

the quantum gromov hausdorff propinquity we introduce the quantum gromov hausdorff propinquity a new distance between quantum compact metric spaces which extends the gromovhausdorff distance to noncommutative geometry and strengthens rieffel s quantum gromov hausdorff distance and rieffel s proximity by making isomorphism a necessary condition for distance zero while being well adapted to leibniz seminorms this work offers a natural solution to the long standing problem of finding a framework for the development of a theory of leibniz lip norms over c algebras

on summability of distributions and spectral geometry modulo the moment asymptotic expansion the cesaro and parametric behaviours of distributions at infinity are equivalent on the strength of this result we construct the asymptotic analysis for spectral densities arising from elliptic pseudodifferential operators we show how cesaro developments lead to efficient calculations of the expansion coefficients of counting number functionals and green functions the bosonic action functional proposed by chamseddine and connes can more generally be validated as a cesaro asymptotic development

excision in cyclic homology and in rational algebraic k theory for a precise definition see 1 below by replacing everywhere k by k q one obtains the corresponding notion in rational algebraic k theory the above definition has an obvious counterpart for cyclic homology and algebras over a fixed field in the case of a general commutative ground ring k some restrictions on the class of allowable extensions seem inevitable due to the well known limitations of cyclic homology considered as a homology functor for algebras not flat over a ground ring an extension of k algebras will be called pure if it is pure as an extension of k modules in the sense of p m cohn 6 cf also appendix a 3 below the class of pure extensions contains e g i extensions which admit a k module splitting ii extensions a e r s with s flat over k in fact one among the several possible characterizations of purity says that an extension is pure if and only if the underlying extension of k modules is an inductive limit of split extensions see theorem a 4 of appendix a below everywhere in this paper the word excision used in the context of cyclic homology will mean excision with respect to the class of pure extensions the second purpose of the present paper is to give a complete characterization of the class of algebras possessing the excision property in cyclic homology before stating the corresponding result we need the following definition let us

the noncommutative lorentzian cylinder as an isospectral deformation we present a new example of a finite dimensional noncommutative manifold namely the noncommutative cylinder it is obtained by isospectral deformation of the canonical triple associated with the euclidean cylinder we discuss connes character formula for the cylinder in the second part we discuss noncommutative lorentzian manifolds here the definition of spectral triples involves krein spaces and operators on krein spaces a central role is played by the admissible fundamental symmetries on the krein space of square integrable sections of a spin bundle over a lorentzian manifold finally we discuss isospectral deformation of the lorentzian cylinder and determine all admissible fundamental symmetries of the noncommutative cylinder

asymptotic expansion of the trace of the heat kernel associated to the dirichlet to neumann operator abstract for a given bounded domain with smooth boundary in a smooth riemannian manifold m g by decomposing the dirichlet to neumann operator into a sum of the square root of the laplacian and a pseudodifferential operator and by applying grubb s method of symbolic calculus for the corresponding pseudodifferential heat kernel operators we establish a procedure to calculate all the coefficients of the asymptotic expansion of the trace of the heat kernel associated to dirichlet to neumann operator as t 0 in particular we explicitly give the first four coefficients of this asymptotic expansion these coefficients provide precise information regarding the area and curvatures of the boundary of the domain in terms of the spectrum of the steklov problem

constructing simple stable descriptions for image partitioning a new formulation of the image partitioning problem is presented construct a complete and stable description of an image in terms of a specified descriptive language that is simplest in the sense of being shortest we show that a descriptive language limited to a low order polynomial description of the intensity variation within each region and a chain code like description of the region boundaries yields intuitively satisfying partitions for a wide class of images the advantage of this formulation is that it can be extended to deal with subsequent steps of the image understanding problem or to deal with other attributes such as texture in a natural way by augmenting the descriptive language experiments performed on a variety of both real and synthetic images demonstrate the superior performance of this approach over partitioning techniques based on clustering vectors of local image attributes and standard edge detection techniques

gevrey regularity for a class of sums of squares of monomial vector fields abstract analytic or gevrey hypoellipticity is proved for a class of sums of squares of vector fields having a symplectic characteristic manifold of dimension 2 and arbitrary even codimension we note that this class contains examples for which the treves stratification seems to work as well as examples for which the treves stratification does not identify properly the non symplectic stratum

using greedy clustering method to solve capacitated location routing problem with fuzzy demands abstract in this paper the capacitated location routing problem with fuzzy demands clrp fd is considered in clrp fd facility location problem flp and vehicle routing problem vrp are observed simultaneously indeed the vehicles and the depots have a predefined capacity to serve the customers that have fuzzy demands to model this problem a fuzzy chance constrained programming model of that is designed based upon the fuzzy credibility theory to solve this problem a greedy clustering method gcm including the stochastic simulation is proposed to obtain the best value of the dispatcher preference index of the model and to analyze its influence on the final solution numerical experiments are carried out finally to show the performance of the greedy clustering method associated results are compared with the lower bound of the solutions

complete determination of the singularity structure of zeta functions series of extended epstein type provide examples of non trivial zeta functions with important physical applications the regular part of their analytic continuation is seen to be a convergent or an asymptotic series their singularity structure is completely determined in terms of the wodzicki residue in its generalized form which is proven to yield the residua of all the poles of the zeta function and not just that of the rightmost pole obtainable from the dixmier trace the calculation is a very down to earth application of these powerful functional analytical methods in physics

noncommutative finite dimensional manifolds i spherical manifolds and related examples we exhibit large classes of examples of noncommutative finite dimensional manifolds which are non formal deformations of classical manifolds the main result of this paper is a complete description of noncommutative three dimensional spherical manifolds a noncommutative version of the sphere s 3 defined by basic k theoretic equations we find a 3 parameter family of deformations of the standard 3 sphere s 3 and a corresponding 3 parameter deformation of the 4 dimensional euclidean space 4 for generic values of the deformation parameters we show that the obtained algebras of polynomials on the deformed 4 u only depend on two parameters and are isomorphic to the algebras introduced by sklyanin in connection with the yang baxter equation it follows that different can span the same this equivalence generates a foliation of the parameter space this foliation admits singular leaves reduced to a point these critical points are either isolated or fall in two 1 parameter families up to the simple operation of taking the fixed algebra by an involution these two families are identical and we concentrate here on c for the above isomorphism with the sklyanin algebra breaks down and the corresponding algebras are special cases of deformations a notion which we generalize in any dimension and various contexts and study in some detail here and this point is crucial the dimension is not an artifact i e the dimension of the classical model but is the hochschild dimension of the corresponding algebra which remains constant during the deformation besides the standard noncommutative tori examples of deformations include the recently defined noncommutative 4 sphere as well as m dimensional generalizations noncommutative versions of spaces and quantum groups which are deformations of various classical groups we develop general tools such as the twisting of the clifford algebras in order to exhibit the spherical property of the hermitian projections corresponding to the noncommutative dimensional spherical manifolds a key result is the differential self duality properties of these projections which generalize the self duality of the round instanton

connes integration formula for the noncommutative plane our aim is to prove the integration formula on the noncommutative moyal plane in terms of singular traces a la connes

moyal planes are spectral triples axioms for nonunital spectral triples extending those introduced in the unital case by connes are proposed as a guide and for the sake of their importance in noncommutative quantum field theory the spaces r2n endowed with moyal products are intensively investigated some physical applications such as the construction of noncommutative wick monomials and the computation of the connes lott functional action are given for these noncommutative hyperplanes

multiscale optimization in neural nets one way to speed up convergence in a large optimization problem is to introduce a smaller approximate version of the problem at a coarser scale and to alternate between relaxation steps for the fine scale and coarse scale problems such an optimization method for neural networks governed by quite general objective functions is presented at the coarse scale there is a smaller approximating neural net which like the original net is nonlinear and has a nonquadratic objective function the transitions and information flow from fine to coarse scale and back do not disrupt the optimization and the user need only specify a partition of the original fine scale variables thus the method can be applied easily to many problems and networks there is generally about a fivefold improvement in estimated cost under the multiscale method in the networks to which it was applied a nontrivial speedup by a constant factor of between two and five was observed independent of problem size further improvements in computational cost are very likely to be available especially for problem specific multiscale neural net methods

hierarchically structured unit simplex transformations for parallel distributed optimization problems a stable deterministic approach is presented for incorporating unit simplex constraints based on a hierarchical deformable template structure this approach i guarantees strict confinement of the search to the unit simplex constraint set without introducing unwanted constraints ii leads to a hierarchical rather than a global network interconnection structure iii allows multiresolution processing and iv allows easy closed form incorporation of certain other inherently global constraints such as general recursive symmetries selected examples are presented which illustrate and demonstrate large scale application of the template method

moyal multiplier algebras of the test function spaces of type s the gel fand shilov spaces of type s are considered as topological algebras with respect to the moyal star product and their corresponding algebras of multipliers are defined and investigated in contrast to the well studied case of schwartz s space s these multipliers are allowed to have nonpolynomial growth or infinite order singularities the moyal multiplication is thereby extended to certain classes of ultradistributions hyperfunctions and analytic functionals the main theorem of the paper characterizes those elements of the dual of a given test function space that are the moyal multipliers of this space the smallest nontrivial fourier invariant space in the scale of s type spaces is shown to play a special role because its corresponding moyal multiplier algebra contains the largest algebra of functions for which the power series defining their star products are absolutely convergent furthermore it contains analogous algebras associated with cone shaped regions which can be used to formulate