stability analysis of markovian jump stochastic bam neural networks with impulse control and mixed time delays this paper discusses the issue of stability analysis for a class of impulsive stochastic bidirectional associative memory neural networks with both markovian jump parameters and mixed time delays the jumping parameters are modeled as a continuous time discrete state markov chain based on a novel lyapunov krasovskii functional the generalized ito s formula mathematical induction and stochastic analysis theory a linear matrix inequality approach is developed to derive some novel sufficient conditions that guarantee the exponential stability in the mean square of the equilibrium point at the same time we also investigate the robustly exponential stability in the mean square of the corresponding system with unknown parameters it should be mentioned that our stability results are delay dependent which depend on not only the upper bounds of time delays but also their lower bounds moreover the derivatives of time delays are not necessarily zero or smaller than one since several free matrices are introduced in our results consequently the results obtained in this paper are not only less conservative but also generalize and improve many earlier results finally two numerical examples and their simulations are provided to show the effectiveness of the theoretical results

the complex geometry of weak piecewise smooth solutions of integrable nonlinear pde s of shallow water and dym type an extension of the algebraic geometric method for nonlinear integrable pde s is shown to lead to new piecewise smooth weak solutions of a class of n component systems of nonlinear evolution equations this class includes among others equations from the dym and shallow water equation hierarchies the main goal of the paper is to give explicit theta functional expressions for piecewise smooth weak solutions of these nonlinear pde s which are associated to nonlinear subvarieties of hyperelliptic jacobians

exponential p convergence analysis for stochastic bam neural networks with time varying and infinite distributed delays we discuss exponential p convergence for stochastic bam neural networks the delays here are multiple time varying and infinite distributed delays we establish a new l operator delay differential integral inequality delay dependent criteria ensuring exponential p convergence are obtained giving the detail estimations of the exponential p convergence ball this paper is concerned with the problem of global exponential p convergence for stochastic bam neural networks with time varying and infinite distributed delays by constructing a new delay differential integral inequality and a novel l operator differential integral inequality and coupling with stochastic analysis techniques some delay dependent sufficient conditions are derived to guarantee exponential p convergence and the state variables of the discussed stochastic bam neural networks are globally exponentially convergent to a ball in the state space with a pre specified convergence rate meanwhile the exponential p convergent balls are also estimated here the existence and the uniqueness of the equilibrium point needs not to be considered finally two examples with numerical simulations are given to illustrate the effectiveness of the theoretical results

a small stencil and extremum preserving scheme for anisotropic diffusion problems on arbitrary 2d and 3d meshes in this paper a nonlinear extremum preserving scheme for the heterogeneous and anisotropic diffusion problems is proposed on general 2d and 3d meshes through a certain linearity preserving approach the so called harmonic averaging points located at the interface of heterogeneity are employed to define the auxiliary unknowns this new scheme is locally conservative has only cell centered unknowns and possesses a small stencil which is five point on the structured quadrilateral meshes and seven point on the structured hexahedral meshes the stability result in h 1 norm is obtained under quite general assumptions numerical results show that our scheme is robust and extremum preserving and the optimal convergence rates are verified on general distorted meshes in case that the diffusion tensor is taken to be anisotropic at times discontinuous

the geometry of the universal teichmuller space and the euler weil petersson equation on the identity component of the universal teichmuller space endowed with the takhtajan teo topology the geodesics of the weil petersson metric are shown to exist for all time this component is naturally a subgroup of the quasisymmetric homeomorphisms of the circle viewed this way the regularity of its elements is shown to be h3 2 epsilon for all epsilon 0 the evolutionary pde associated to the spatial representation of the geodesics of the weil petersson metric is derived using multiplication and composition below the critical sobolev index 3 2 geodesic completeness is used to introduce special classes of solutions of this pde analogous to peakons our setting is used to prove that there exists a unique geodesic between each two shapes in the plane in the context of the application of the weil petersson metric in imaging c 2015 elsevier inc all rights reserved

local and global well posedness of the fractional order epdiff equation on r d abstract of concern is the study of fractional order sobolev type metrics on the group of h diffeomorphism of r d and on its sobolev completions d q r d it is shown that the h s sobolev metric induces a strong and smooth riemannian metric on the banach manifolds d s r d for s 1 d 2 as a consequence a global well posedness result of the corresponding geodesic equations both on the banach manifold d s r d and on the smooth regular frechet lie group of all h diffeomorphisms is obtained in addition a local existence result for the geodesic equation for metrics of order 1 2 s 1 d 2 is derived

an integral operator induced by a zygmund function abstract we introduce a kernel function induced by a continuous function f on the unit circle and show that the corresponding integral operator on the standard bergman space is a bounded compact or hilbert schmidt operator precisely when f belongs to the big zygmund class the little zygmund class or the sobolev class h 3 2 respectively this may be considered as the infinitesimal version of the main result obtained in hu and shen 2012 9 by two of the authors

a finite volume element scheme with a monotonicity correction for anisotropic diffusion problems on general quadrilateral meshes abstract we construct a finite volume element scheme with a monotonicity correction for anisotropic diffusion problems on general quadrilateral meshes where the strict convexity restriction on the meshes is removed the main contributions of this paper include three aspects firstly the classical finite volume element c fve method is extended to severely distorted quadrilateral meshes even with concave cells by virtue of a new overlapping dual partition and a new gradient approximation in fact the choice of this dual partition and gradient approximation is also conducive to the construction of a monotone scheme secondly a new monotonicity correction is suggested based on which we obtain a monotone finite volume element m fve method the resulting m fve method still keeps the local conservation and is easy for implementation finally we analyze theoretically the truncation error and the monotonicity for this scheme besides the existence of a solution to this nonlinear scheme is proved by applying the brouwer s fixed point theorem numerical results demonstrate that the m fve method has the approximate second order accuracy and preserves well the positivity of the solution for both isotropic and anisotropic diffusion problems on severely distorted quadrilateral meshes

chord arc surfaces with small constant ii good parameterizations abstract in a companion paper we introduced a notion for hypersurfaces in r d 1 that is analogous to the chord arc condition with small constant for planar curves in this paper we address the problem of finding good parameterizations for these surfaces in particular we show that these surfaces must be homeomorphic to r d and we build parameterizations with l p bounds on the gradient and the gradient of the inverse with p as the chord arc constant goes to 0 when d 2 we use the uniformization theorem to find a quasisymmetric parameterization we do not know how to build bilipschitz parameterizations when d 2 or quasisymmetric parameterizations when d 3 the author conjectures that they do not exist in general however we can build bilipschitz reflections in all dimensions and these reflections will satisfy certain extra estimates in terms of carleson measures

diffeomorphisms groups and pattern matching in image analysis in a previous paper it was proposed to see the deformations of a common pattern as the action of an infinite dimensional group we show in this paper that this approac h can be applied numerically for pattern matching in image analysis of digital images using lie group ideas we construct a distance between deformations defined through a metric given the cost of infinitesimal deformations then we propose a numerical scheme to solve a variational problem involving this distance and leading to a sub optimal gradient pattern matching its links with fluid models are established

on h on the complement of c1 α curves abstract let be a quasiconformal mapping on the plane with complex dilatation we show that if satisfies a certain carleson measure condition then one can transfer h on the upper half plane onto the corresponding space in the complement of the quasicircle r and that this condition on characterizes c 1 curves

on douady earle extension and the contractibility of the vmo teichmuller space abstract douady earle extension provides a quasiconformal extension of a quasisymmetric homeomorphism to the unit disk and induces a continuous self map of beltrami coefficients in this note we show that is also continuous under a stronger topology on those beltrami coefficients which induce vanishing carleson measures and thus project to the vmo teichmuller space an immediate consequence is that the vmo teichmuller space is contractible

weil petersson teichmuller space revisited abstract in our previous paper 23 it was proved that a sense preserving homeomorphism g on the unit circle s 1 belongs to the weil petersson class wp s 1 namely g can be extended to a quasiconformal mapping to the unit disk whose beltrami coefficient is square integrable in the poincare metric if and only if g is absolutely continuous such that log g belongs to the sobolev class h 1 2 in this sequel to 23 we show that the smooth hilbert manifold structure on wp s 1 inherited from h 1 2 by the pullback g log g is compatible with the standard hilbert manifold structure introduced by takhtajan teo 27 this enables us to give a fast approach to some results in our previous papers 23 and 24

harmonic reflection in quasicircles and well posedness of a riemann hilbert problem on quasidisks abstract a complex harmonic function of finite dirichlet energy on a jordan domain has boundary values in a certain conformally invariant sense by a construction of h osborn we call the set of such boundary values the douglas osborn space one may then attempt to solve the dirichlet problem on the complement for these boundary values this defines a reflection of harmonic functions we show that quasicircles are precisely those jordan curves for which this reflection is defined and bounded we then use a limiting cauchy integral along level curves of green s function to show that the plemelj sokhotski jump formula holds on quasicircles with boundary data in the douglas osborn space this enables us to prove the well posedness of a riemann hilbert problem with boundary data in the douglas osborn space on quasicircles

weil petersson teichmuller space iii dependence of riemann mappings for weil petersson curves the classical riemann mapping theorem implies that there exists a so called riemann mapping which takes the upper half plane onto the left domain bounded by a jordan curve in the extended complex plane the primary purpose of the paper is to study the basic problem how does a riemann mapping depend on the corresponding jordan curve we are mainly concerned with those jordan curves in the weil petersson class namely the corresponding riemann mappings can be quasiconformally extended to the whole plane with beltrami coefficients being square integrable under the poincare metric after giving a geometric characterization of a weil petersson curve we endow the space of all normalized weil petersson curves with a new real hilbert manifold structure in a geometric manner and show that this new structure is topologically equivalent to the standard complex hilbert manifold structure which implies that an appropriately chosen riemann mapping depends continuously on a weil petersson curve and vice versa this can be considered as the first result about the continuous dependence of riemann mappings on non smooth jordan curves

the finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes we construct a new nonlinear finite volume scheme for diffusion equation on polygonal meshes and prove that the scheme satisfies the discrete extremum principle our scheme is locally conservative and has only cell centered unknowns numerical results are presented to show how our scheme works for preserving discrete extremum principle and positivity on various distorted meshes

integrable teichmuller space abstract this paper deals with the p integrable teichmuller space and gives an intrinsic characterization of a p integrable asymptotic affine homeomorphism for p 2 more precisely it is proved that a sense preserving homeomorphism h on the unit circle is p integrable asymptotic affine namely h can be extended to a quasiconformal mapping to the unit disk whose beltrami coefficient is p integrable in the poincare metric if and only if h is absolutely continuous such that log h belongs to the besov class b p s 1

chord arc curves and the beurling transform we study the relation between the geometric properties of a quasicircle gamma and the complex dilatation mu of a quasiconformal mapping that maps the real line onto gamma denoting by s the beurling transform we characterize bishop jones quasicircles in terms of the boundedness of the operator i mu s on a particular weighted l 2 space and chord arc curves in terms of its invertibility as an application we recover the l 2 boundedness of the cauchy integral on chord arc curves

anderson acceleration for fixed point iterations this paper concerns an acceleration method for fixed point iterations that originated in work of d g anderson j assoc comput mach 12 1965 pp 547 560 which we accordingly call anderson acceleration here this method has enjoyed considerable success and wide usage in electronic structure computations where it is known as anderson mixing however it seems to have been untried or underexploited in many other important applications moreover while other acceleration methods have been extensively studied by the mathematics and numerical analysis communities this method has received relatively little attention from these communities over the years a recent paper by h fang and y saad numer linear algebra appl 16 2009 pp 197 221 has clarified a remarkable relationship of anderson acceleration to quasi newton secant updating methods and extended it to define a broader anderson family of acceleration methods in this paper our goals are to shed additional light on anderson acceleration and to draw further attention to its usefulness as a general tool we first show that on linear problems anderson acceleration without truncation is essentially equivalent in a certain sense to the generalized minimal residual gmres method we also show that the type 1 variant in the fang saad anderson family is similarly essentially equivalent to the arnoldi full orthogonalization method we then discuss practical considerations for implementing anderson acceleration and illustrate its performance through numerical experiments involving a variety of applications

locally univalent functions vmoa and the dirichlet space we study geometric properties of the image of the unit circle under a bounded locally univalent function g such that log g belongs either to the dirichlet space d vmoa or the little bloch space b 0 concerning vmoa and b 0 our findings generalize the corresponding results for conformal maps shown by pommerenke in the late 1970s in the case of d we give a strictly geometric necessary condition for g to satisfy log g is an element of d and also offer two different semi geometric characterizations of when log g is an element of d

does median filtering truly preserve edges better than linear filtering image processing researchers commonly assert that median filtering is better than linear filtering for removing noise in the presence of edges using a straightforward large n decision theory framework this folk theorem is seen to be false in general we show that median filtering and linear filtering have similar asymptotic worst case mean squared error mse when the signal to noise ratio snr is of order 1 which corresponds to the case of constant per pixel noise level in a digital signal to see dramatic benefits of median smoothing in an asymptotic setting the per pixel noise level should tend to zero i e snr should grow very large we show that a two stage median filtering using two very different window widths can dramatically outperform traditional linear and median filtering in settings where the underlying object has edges in this two stage procedure the first pass at a fine scale aims at increasing the snr the second pass at a coarser scale correctly exploits the nonlinearity of the median image processing methods based on nonlinear partial differential equations pdes are often said to improve on linear filtering in the presence of edges such methods seem difficult to analyze rigorously in a decision theoretic framework a popular example is mean curvature motion mcm which is formally a kind of iterated median filtering our results on iterated median filtering suggest that some pde based methods are candidates to rigorously outperform linear filtering in an asymptotic framework

l estimates for the bar partial problem in a half planeproblem in a half plane l approche de dualite pour trouver des solutions de f est suffisante pour plusieurs problemes apparaissant en theorie h p on donne des operateurs solution qui permettent de resoudre des problemes non resolubles par la dualite

monotone finite volume schemes for diffusion equations on unstructured triangular and shape regular polygonal meshes we consider a non linear finite volume fv scheme for stationary diffusion equation we prove that the scheme is monotone i e it preserves positivity of analytical solutions on arbitrary triangular meshes for strongly anisotropic and heterogeneous full tensor coefficients the scheme is extended to regular star shaped polygonal meshes and isotropic heterogeneous coefficients

a vertex centered and positivity preserving scheme for anisotropic diffusion problems on arbitrary polygonal grids abstract we suggest a new positivity preserving finite volume scheme for anisotropic diffusion problems on arbitrary polygonal grids the scheme has vertex centered edge midpoint and cell centered unknowns the vertex centered unknowns are primary and have finite volume equations associated with them the edge midpoint and cell centered unknowns are treated as auxiliary ones and are interpolated by the primary unknowns which makes the final scheme a pure vertex centered one unlike most existing positivity preserving schemes the construction of the scheme is based on a special nonlinear two point flux approximation that has a fixed stencil and does not require the convex decomposition of the co normal in order to solve efficiently the nonlinear systems resulting from the nonlinear scheme picard method and its anderson acceleration are discussed numerical experiments demonstrate the second order accuracy and well positivity of the solution for heterogeneous and anisotropic problems on severely distorted grids the high efficiency of the anderson acceleration is also shown on reduction of the number of nonlinear iterations moreover the proposed scheme does not have the so called numerical heat barrier issue suffered by most existing cell centered and hybrid schemes however further improvements have to be made if the solution is very close to the machine precision and the mesh distortion is very severe

on the tangent space to the bmo teichmuller space abstract in a previous paper 31 we established the complex analytic manifold theory of the bmo teichmuller space in this paper we identify the function space which is the tangent space to the bmo teichmuller space

a note on the bmo teichmuller space abstract astala zinsmeister 2 introduced a new topology on the set of all strongly quasisymmetric homeomorphisms of the unit circle denoted by sqs s 1 by means of bmo norm under this new topology we prove that sqs s 1 is a partial topological group and the characteristic topological subgroup of sqs s 1 consists of strongly symmetric homeomorphisms

monotone finite volume schemes for diffusion equations on polygonal meshes we construct a nonlinear finite volume fv scheme for diffusion equation on star shaped polygonal meshes and prove that the scheme is monotone i e it preserves positivity of analytical solutions for strongly anisotropic and heterogeneous full tensor coefficients our scheme has only cell centered unknowns and it treats material discontinuities rigorously and offers an explicit expression for the normal flux numerical results are presented to show how our scheme works for preserving positivity on various distorted meshes for both smooth and non smooth highly anisotropic solutions and numerical results show that our scheme appears to be approximate second order accuracy for the solution and first order accuracy for the flux

an improved monotone finite volume scheme for diffusion equation on polygonal meshes we construct a new nonlinear monotone finite volume scheme for diffusion equation on polygonal meshes the new scheme uses the cell edge unknowns instead of cell vertex unknowns as the auxiliary unknowns in order to improve the accuracy of monotone scheme our scheme is locally conservative and has only cell centered unknowns numerical results are presented to show how our scheme works for preserving positivity on various distorted meshes specially numerical results show that the new scheme is robust and more accurate than the existing monotone scheme on some kinds of meshes

exponential stability of high order bidirectional associative memory neural networks with time delays in this paper exponential stability is studied for a class of high order bidirectional associative memory bam neural networks with time delays by employing the linear matrix inequality lmi and the lyapunov functional methods several sufficient conditions are obtained for ensuring the system to be globally exponentially stable two illustrative examples are also given in the end of this paper to show the effectiveness of our results

global exponential stability of bidirectional associative memory neural networks with distributed delays a bidirectional associative memory neural network model with distributed delays is considered by constructing a new lyapunov functional employing the homeomorphism theory m matrix theory and the inequality email protected k 1 mb k q k 0 b k 0 q k 0 with k 1 mq k r 1 and r 1 a sufficient condition is obtained to ensure the existence uniqueness and global exponential stability of the equilibrium point for the model moreover the exponential converging velocity index is estimated which depends on the delay kernel functions and the system parameters the results generalize and improve the earlier publications and remove the usual assumption that the activation functions are bounded two numerical examples are given to show the effectiveness of the obtained results

interpolation based second order monotone finite volume schemes for anisotropic diffusion equations on general grids we propose two interpolation based monotone schemes for the anisotropic diffusion problems on unstructured polygonal meshes through the linearity preserving approach the new schemes are characterized by their nonlinear two point flux approximation which is different from the existing ones and has no constraint on the associated interpolation algorithm for auxiliary unknowns thanks to the new nonlinear two point flux formulation it is no longer required that the interpolation algorithm should be a positivity preserving one the first scheme employs vertex unknowns as the auxiliary ones and a second order but not positivity preserving interpolation algorithm is utilized the second scheme uses the so called harmonic averaging points located on cell edges to define the auxiliary unknowns and a second order positivity preserving interpolation method is employed both schemes have nearly the same convergence rates as compared with their related second order linear schemes numerical results demonstrate that the new schemes are monotone and have the second order accuracy for the solution and first order for its gradient on severely distorted meshes

global asymptotic stability of bam neural networks with mixed delays and impulses in this paper bam neural networks with mixed delays and impulses are considered a new set of sufficient conditions are derived by constructing suitable lyapunov functional with matrix theory for the global asymptotic stability of bam neural networks with mixed delays and impulses moreover an example is also provided to illustrate the effectiveness of the results

diff s 1 and the teichmuller spaces precisely two of the homogeneous spaces that appear as coadjoint orbits of the group of string reparametrizations widehat diff s 1 1 carry in a natural way the structure of infinite dimensional holomorphically homogeneous complex analytic kahler manifolds these aren diff s1 rot s1 andm diff s1 mob s1 note thatn is a holomorphic disc fiber space overm now m can be naturally considered as embedded in the classical universal teichmuller spacet 1 simply by noting that a diffeomorphism ofs1 is a quasisymmetric homeomorphism t 1 is itself a homomorphically homogeneous complex banach manifold we prove in the first part of the paper that the inclusion ofm int 1 iscomplex analytic

monotonicity of control volume methods robustness of numerical methods for multiphase flow problems in porous media is important for development of methods to be used in a wide range of applications here we discuss monotonicity for a simplified problem of single phase flow but where the simulation grids and media are allowed to be general posing challenges to control volume methods we discuss discrete formulations of the maximum principle and derive sufficient criteria for discrete monotonicity for arbitrary nine point control volume discretizations for conforming quadrilateral grids in 2d these criteria are less restrictive than the m matrix property it is shown that it is impossible to construct nine point methods which unconditionally satisfy the monotonicity criteria when the discretization satisfies local conservation and exact reproduction of linear potential fields numerical examples are presented which show the validity of the criteria for monotonicity further the impact of nonmonotonicity is studied different behavior for different discretization methods is illuminated and simple ideas are presented for improvement in terms of monotonicity

anderson acceleration for nonlinear finite volume scheme for advection diffusion problems we consider the solution of systems of nonlinear algebraic equations that appear in a positivity preserving finite volume scheme for steady state advection diffusion equations we propose and analyze numerically an efficient strategy for accelerating the picard method when it is applied to these systems the strategy is based on the anderson acceleration and the adaptive inexact solution of linear systems we demonstrate its numerical robustness for three black box preconditioners

a decoupled and positivity preserving discrete duality finite volume scheme for anisotropic diffusion problems on general polygonal meshes abstract we suggest a new positivity preserving discrete duality finite volume ddfv scheme for anisotropic diffusion problems on general polygonal meshes like existing ddfv schemes this scheme is built on the primary and dual meshes and has finite volume fv equations for both vertex and cell centered unknowns the transpose of the coefficient matrix for the fv equations of the cell centered unknowns is an m matrix while that for the vertex unknowns is not an m matrix but a symmetric and positive definite matrix by employing a certain truncation technique for the vertex unknowns the positivity preserving property for both categories of unknowns is guaranteed local conservation is strictly maintained for the cell centered unknowns and conditionally maintained for the vertex unknowns since the fv equations of the vertex unknowns can be solved independently the two sets of fv equations are decoupled in contrast to existing nonlinear positivity preserving schemes the new scheme requires no nonlinear iterations for linear problems for nonlinear problems the positivity preserving mechanism of the new scheme is decoupled from its nonlinear iteration so that any nonlinear solver can be adopted moreover the positivity of the discrete solution is proved and the well posedness is analyzed rigorously for linear problems in numerical experiments the new scheme is examined extensively and compared with two positivity preserving cell centered schemes and a nonlinear ddfv scheme numerical results show that the present ddfv scheme achieves second order accuracy and preserves the positivity of the solution for heterogeneous and anisotropic problems on severely distorted grids the high efficiency of the scheme is also demonstrated by the comparison of computation time and number of nonlinear iterations

weil petersson teichmuller space ii smoothness of flow curves of h32 vector fields abstract given a continuous vector field t of sobolev class h 3 2 on the unit circle s 1 the flow maps g t of the differential equation d d t t 0 are known to be quasisymmetric homeomorphisms very recently gay balmaz ratiu 15 conjectured that the flow curve g t is in the weil petersson class wp s 1 and is continuously differentiable with respect to the hilbert manifold structure of wp s 1 introduced by takhtajan teo 40 the first assertion had already been demonstrated in our previous paper 36 in this sequel to 36 we will continue to deal with the weil petersson class wp s 1 and completely solve this conjecture in the affirmative

quasiconformal mappings and chord arc curves given a quasiconformal mapping p on the plane what conditions on its dilatation guarantee that p r is rectifiable and pir is locally abso lutely continuous we show in this paper that if satisfies certain quadratic carleson measure conditions with small norm then p r is a chord arc curve with small constant and p x p 0 g0 ea t dt for x e r with a e bmo having small norm conversely given any such map from r c we show that it has an extension to c with the right kind of dilatation similar results hold with r replaced by a chord arc curve examples are given that show that it would be hard to improve these results applications are given to conformal welding and the theorem of coifman and meyer on the real analyticity of the riemann mapping on the manifold of chord arc curves let p be a quasiconformal map of the plane onto itself thus p is a homeomorphism with locally integrable distributional derivatives and ps upz where u e l c il ul100 1 here we use the notations fz af azf 2 z id f fz 2 aa ida f this function u is called the complex dilatation of p the mapping theorem for q c maps states that for each u e l c il ul100 1 there is a q c map p on c with dilatation u and p is unique up to normalization a basic problem is to understand how geometric properties of p are reflected in u for example one would like to have natural conditions on u which imply that p r is rectifiable and p ir is absolutely continuous this question arises naturally when considering problems in conformal mappings and conformal welding in this paper we obtain such estimates for the mapping theorem and we also give some applications our results involve bmo aoo weights chord arc curves and carleson measures and so we first review the appropriate definitions a locally integrable function f on r lies in bmo if llfil sup lil if x fil dx received by the editors june 1 1986 1980 mathematics subject classification 1985 revision primary 30g60 secondary 42b20 30e20

coadjoint orbits of the virasoro group the coadjoint orbits of the virasoro group which have been investigated by lazutkin and pankratova and by segal should according to the kirillov kostant theory be related to the unitary representations of the virasoro group in this paper the classification of orbits is reconsidered with an explicit description of the possible centralizers of coadjoint orbits the possible orbits are diff s1 itself diff s1 s1 and diff s1 sl n 2 r withsl n 2 r a certain discrete series of embeddings ofsl 2 r in diff s1 and diffs1 t wheret may be any of certain rather special one parameter subgroups of diffs1 an attempt is made to clarify the relation between orbits and representations it appears that quantization of diffs1 s1 is related to unitary representations with nondegenerate kac determinant unitary verma modules while quantization of diffs1 sl n 2 r is seemingly related to unitary representations with null vectors in leveln a better understanding of how to quantize the relevant orbits might lead to a better geometrical understanding of virasoro representation theory in the process of investigating virasoro coadjoint orbits we observe the existence of left invariant symplectic structures on the virasoro group manifold as is described in an appendix these give rise to lie bialgebra structures with the virasoro algebra as the underlying lie algebra

on the classification of the coadjoint orbits of the sobolev bott virasoro group the purpose of this paper is to give the classification of the bott virasoro coadjoint orbits with nonzero central charge in the functional analytic setting of smooth hilbert manifolds the central object of the paper is thus the completion of the bott virasoro group with respect to a sobolev topology giving rise to a smooth hilbert manifold and topological group called the sobolev bott virasoro group as a consequence of this approach analytic and geometric properties of the coadjoint orbits are studied c 2008 elsevier inc all rights reserved

robust global synchronization of complex networks with neutral type delayed nodes in this paper the problems of robust global exponential synchronization for a class of complex networks with time varying delayed couplings are considered each node in the network is composed of a class of delayed neural networks described by a nonlinear delay differential equation of neutral type since model errors commonly exist in practical applications the parameter uncertainties are involved in the considered model sufficient conditions that ensure the complex networks to be robustly globally exponentially synchronized are obtained by using the lyapunov functional method and some properties of kronecker product an illustrative example is presented to show the effectiveness of the proposed approach

geometric investigations of a vorticity model equation abstract this article consists of a detailed geometric study of the one dimensional vorticity model equation t u x 2 u x 0 h u x t r x s 1 which is a particular case of the generalized constantin lax majda equation wunsch showed that this equation is the euler arnold equation on diff s 1 when the latter is endowed with the right invariant homogeneous h 1 2 metric in this article we prove that the exponential map of this riemannian metric is not fredholm and that the sectional curvature is locally unbounded furthermore we prove a beale kato majda type blow up criterion which we then use to demonstrate a link to our non fredholmness result finally we extend a blow up result of castro cordoba to the periodic case and to a much wider class of initial conditions using a new generalization of an inequality for hilbert transforms due to cordoba cordoba

estimates for 8706 μ 1 and calderon s theorem on the cauchy integral etude du caractere borne de l operateur integral de cauchy a l aide d une transformation quasi conforme

on flows of h 3 2 vector fields on the circle in this paper we study the regularity of flow maps of h 3 2 vector fields on the circle in terms of fractional sobolev spaces this problem is motivated by the understanding of the geometry of bers s universal teichmuller space

some notes on quasisymmetric flows of zygmund vector fields abstract in an important paper 24 reimann showed that the flow mappings of a continuous vector field of zygmund class are quasisymmetric homeomorphisms in this paper we will discuss the flow mappings when the vector field belongs to the smooth zygmund class or the sobolev class h 3 2

exponential stability for stochastic reaction diffusion bam neural networks with time varying and distributed delays abstract in this paper we study the stability for a class of stochastic bidirectional associative memory bam neural networks with reaction diffusion and mixed delays the mixed delays considered in this paper are time varying and distributed delays based on a new lyapunov krasovskii functional and the poincare inequality as well as stochastic analysis theory a set of novel sufficient conditions are obtained to guarantee the stochastically exponential stability of the trivial solution or zero solution the obtained results show that the reaction diffusion term does contribute to the exponentially stabilization of the considered system moreover two numerical examples are given to show the effectiveness of the theoretical results

necessary and sufficient conditions for absolute continuity of elliptic harmonic measure our purpose in this paper is to give a necessary and sufficient condition on the modulus of continuity of the coefficients of an elliptic operator in divergence form in order that the corresponding poisson kernel for the dirichlet problem exist this condition on the coefficients is global continuity together with the additional property that the modulus of continuity along some nontangential direction at each boundary point be bounded uniformly in these points and directions by a function 7 t satisfying the dini type condition

analysis on groups of diffeomorphisms of manifolds with boundary and the averaged motion of a fluid we establish the existence of three new subgroups of the group of volumepreserving diffeomorphisms of a compact n dimensional n 2 riemannian manifold which are associated with the dirichlet neumann and mixed type boundary conditions that arise in second order elliptic pdes we prove that when endowed with the hs hilbert class topologies for s n 2 1 these subgroups are c differential manifolds we consider these new diffeomorphism groups with an h1 equivalent right invariant metric and prove the existence of unique smooth geodesics t of this metric as well as existence and uniqueness of the jacobi equations associated to this metric geodesics on these subgroups are in fact the flows of a timedependent velocity vector field u t x so that t t u t t with 0 x x and remarkably the vector field u t x solves the so called lagrangian averaged euler lae equations on m these equations and their viscous counterparts the lagrangian averaged navier stokes lans equations model the motion of a fluid at scales larger than an a priori fixed parameter 0 while averaging or filtering out the small scale motion and this is achieved without the use of artificial viscosity we prove that for divergence free initial data satisfying u 0 on m the lae equations are well posed globally when n 2 we also find the boundary conditions that make the lans equations well posed globally when n 3 and prove that solutions of the lans equations converge when n 2 3 for almost all t in some fixed time interval 0 t in hs s n 2 1 3 to solutions of the lae equations thus confirming the scaling arguments of barenblatt chorin received april 26 2000 1991 mathematics subject classification 35q35 35q53 58b20 58d05

the mimetic finite difference method for elliptic and parabolic problems with a staggered discretization of diffusion coefficient numerical schemes for nonlinear parabolic equations based on the harmonic averaging of cell centered diffusion coefficients break down when some of these coefficients go to zero or their ratio grows to tackle this problem we propose new mimetic finite difference schemes that use a staggered discretization of the diffusion coefficient the primary mimetic operator approximates div k the derived dual mimetic operator approximates the new mimetic schemes preserve symmetry and positive definiteness of the continuum problem which allows us to use algebraic solvers with optimal complexity we perform detailed numerical analysis of the new schemes for linear elliptic problems and a specially designed linear parabolic problem that has solution dynamics typical for nonlinear problems we show that the new schemes are competitive with the state of the art schemes for steady state problems but provide much more accurate solution dynamics for the transient problem

stability results for impulsive functional differential equations with infinite delay abstract for a family of differential equations with infinitive delay and impulses we establish conditions for the existence of global solutions and for the global asymptotic and global exponential stabilities of an equilibrium point the results are used to give stability criteria for a very broad family of impulsive neural network models with both unbounded distributed delays and bounded time varying discrete delays most of the impulsive neural network models with delay recently studied are included in the general framework presented here

a new stability criterion for bidirectional associative memory neural networks of neutral type in the paper the global asymptotic stability of equilibrium is considered for continuous bidirectional associative memory bam neural networks of neutral type by using the lyapunov method a new stability criterion is derived in terms of linear matrix inequality lmi to ascertain the global asymptotic stability of the bam the lmi can be solved easily by various convex optimization algorithms a numerical example is illustrated to verify our result

robust stability of uncertain fuzzy bam neural networks of neutral type with markovian jumping parameters and impulses abstract in this paper the problem of neutral type impulsive bidirectional associative memory neural networks nibamnns with time delays are first established by a takagi sugeno t s fuzzy model in which the consequent parts are composed of a set of nibamnns with interval delays and markovian jumping parameters mjps sufficient conditions to check the robust exponential stability of the derived model are based on the lyapunov krasovskii functionals lkfs containing some novel triple integral terms lyapunov stability theory and employing the free weighting matrix method the delay dependent stability conditions are established in terms of linear matrix inequalities lmis which can be very efficiently solved using matlab lmi control toolbox finally numerical examples and remarks are given to illustrate the effectiveness and usefulness of the derived results

globally exponential stabilization of neural networks with mixed time delays via impulsive control the impulsive stabilization problem of neural networks with discrete time varying delays and unbounded continuously distributed delays is considered by using impulse time dependent lyapunov function based techniques to capture the hybrid structure characteristics of the considered impulsive neural networks two novel global exponential stability criteria are obtained in terms of linear matrix inequalities which are capable of dealing with the case where both the continuous and discrete dynamics are unstable when the original continuous time delayed neural networks are not stable sufficient conditions are developed for the design of exponentially stable linear impulsive state feedback controllers four numerical examples are given to illustrate the less conservatism and effectiveness of the proposed results

the weil petersson curvature operator on the universal teichmuller space the universal teichmuller space is an infinitely dimensional generalization of the classical teichmuller space of riemann surfaces it carries a natural hilbert structure on which one can define a natural riemannian metric the weil petersson metric in this paper we investigate the weil petersson riemannian curvature operator tilde q of the universal teichmuller space with the hilbert structure and prove the following i tilde q is non positive definite ii tilde q is a bounded operator iii tilde q is not compact the set of the spectra of tilde q is not discrete as an application we show that neither the quaternionic hyperbolic space nor the cayley plane can be totally geodesically immersed in the universal teichmuller space endowed with the weil petersson metric

some new function spaces and their applications to harmonic analysis abstract in this paper a family of spaces is introduced which seems well adapted for the study of a variety of questions related to harmonic analysis and its applications these spaces are the tent spaces they provide the natural setting for the study of such things as maximal functions the relevant space here is t p and also square functions where the space t2p is relevant as such these spaces lead to unifications and simplifications of some basic techniques in harmonic analysis thus they are closely related to lp and hardy spaces important parts of whose theory become corollaries of the description of tent spaces also as proc conf harmonic analysis cortona lect notes in math vol 992 springer verlag berlin new york 1983 already indicated where these spaces first appeared explicitly the tent spaces can be used to simplify some of the results related to the cauchy integral on lipschitz curves and multilinear analysis in retrospect one can recognize that various ideas important for tent spaces had been used if only implicitly for quite some time here one should mention carleson s inequality its simplifications and extensions the theory of hardy spaces and atomic decompositions

exponential stability and periodic oscillatory solution in bam networks with delays both exponential stability and periodic oscillatory solution of bidirectional associative memory bam networks with axonal signal transmission delays are considered by constructing suitable lyapunov functional and some analysis techniques some simple sufficient conditions are given ensuring the global exponential stability and the existence of periodic oscillatory solutions of bam with delays these conditions are presented in terms of system parameters and have important leading significance in the design and applications of globally exponentially stable and periodic oscillatory neural circuits for bam with delays in addition two examples are given to illustrate the results

the transport equation in the scaling invariant besov or essen janson peng xiao space abstract this paper addresses a well posedness of the weak solution to the transport equation describing how a scalar quantity is transported in a space with an initial data in the scaling invariant besov or essen janson peng xiao space via the boundedness of the left and right compositions acting on each space

existence of an exponential periodic attractor of periodic solutions for general bam neural networks with time varying delays and impulses abstract by applying inequality analysis technique constructing a suitable lyapunov functional and combing the continuation theorem due to mawhin and gaines some novel sufficient conditions are obtained to ensure the existence of an exponential periodic attractor of periodic solutions for general neural networks with time varying including bounded and unbounded delays and impulses an example is employed to illustrate our feasible results

existence of an exponential periodic attractor of a class of impulsive differential equations with time varying delays abstract by using the continuation theorem due to mawhin and gaines some analysis techniques and the lyapunov functional method the sufficient conditions ensuring the existence of an exponential periodic attractor of a class of impulsive differential equations with time varying delays are established the results are interesting and very different from previously known results xia and wong 2009 7 tan and tan 2009 19 huang et al 2005 20 liu and huang 2006 22 finally applications and an example are given to illustrate the effectiveness of the results

quasiconformal mappings and ahlfors david curves we show that if p is a quasiconformal mapping of the plane whose dilatation satisfies a certain quadratic carleson measure condition relative to an ahlfors david curve f then p is differentiable almost everywhere on f and log ip l e bmo when f is chord arc we show that its image is a bishopjones curve if the carleson norm is small then we show that p is absolutely continuous on f the image of f is an ahlfors david curve and p ea where a e bmo with a small norm