continuous time additive hopfield type neural networks with impulses we investigate the global stability characteristics of a system of equations modelling the dynamics of additive hopfield type neural networks with impulses in the continuous time case

explicit terms in the small volume expansion of the shift of neumann laplacian eigenvalues due to a grounded inclusion in two dimensions abstract the first terms in the small volume asymptotic expansion of the shift of neumann laplacian eigenvalues caused by a grounded inclusion of area e 2 are derived a novel explicit formula to compute them from the capacity the eigenvalues and the eigenfunctions of the unperturbed domain the size and the position of the inclusion is given the key step in the derivation is the filtering of the spectral decomposition of the neumann function with the residue theorem as a consequence of the formula when a bifurcation of a double eigenvalue occurs as for example in the case of a generic inclusion inside a disk one eigenvalue decays like o 1 log e the other like o e 2

resonances for microstrip transmission lines in this paper we rigorously derive asymptotic formulae for resonances associated with a microstrip transmission line mounted on a planar waveguide with variable electromagnetic characteristics when the width of the line goes to zero

stability of impulsive stochastic differential delay systems and its application to impulsive stochastic neural networks this paper is concerned with the stability of n dimensional stochastic differential delay systems with nonlinear impulsive effects first the equivalent relation between the solution of the n dimensional stochastic differential delay system with nonlinear impulsive effects and that of a corresponding n dimensional stochastic differential delay system without impulsive effects is established then some stability criteria for the n dimensional stochastic differential delay systems with nonlinear impulsive effects are obtained finally the stability criteria are applied to uncertain impulsive stochastic neural networks with time varying delay the results show that this convenient and efficient method will provide a new approach to study the stability of impulsive stochastic neural networks some examples are also discussed to illustrate the effectiveness of our theoretical results

some properties of convex hulls of integer points contained in general convex sets in this paper we study properties of general closed convex sets that determine the closedness and polyhedrality of the convex hull of integer points contained in it we first present necessary and sufficient conditions for the convex hull of integer points contained in a general convex set to be closed this leads to useful results for special classes of convex sets such as pointed cones strictly convex sets and sets containing integer points in their interior we then present a sufficient condition for the convex hull of integer points in general convex sets to be a polyhedron this result generalizes the well known result due to meyer math program 7 223 225 1974 under a simple technical assumption we show that these sufficient conditions are also necessary for the convex hull of integer points contained in general convex sets to be a polyhedron

global asymptotic stability of recurrent neural networks with multiple time varying delays in this paper several sufficient conditions are established for the global asymptotic stability of recurrent neural networks with multiple time varying delays the lyapunov krasovskii stability theory for functional differential equations and the linear matrix inequality lmi approach are employed in our investigation the results are shown to be generalizations of some previously published results and are less conservative than existing results the present results are also applied to recurrent neural networks with constant time delays

linear matrix inequality representation of sets this article concerns the question which subsets of m can be represented with linear matrix inequalities lmis this gives some perspective on the scope and limitations of one of the most powerful techniques commonly used in control theory also before having much hope of representing engineering problems as lmis by automatic methods one needs a good idea of which problems can and cannot be represented by lmis little is currently known about such problems in this article we give a necessary condition that we call rigid convexity which must hold for a set m in order for to have an lmi representation rigid convexity is proved to be necessary and sufficient when m 2 this settles a question formally stated by pablo parrilo and berndt sturmfels in 15 as shown by lewis parillo and ramana 11 our main result also establishes in the case of three variables a 1958 conjecture by peter lax on hyperbolic polynomials 2006 wiley periodicals inc

boundary layer techniques for solving the helmholtz equation in the presence of small inhomogeneities we consider solutions to the helmholtz equation in two and three dimensions based on layer potential techniques we provide for such solutions a rigorous systematic derivation of complete asymptotic expansions of perturbations resulting from the presence of diametrically small inhomogeneities with constitutive parameters different from those of the background medium it is expected that our results will find important applications for developing effective algorithms for reconstructing small dielectric inhomogeneities from boundary measurements

impulsive control for a class of neural networks with bounded and unbounded delays in this paper we study the problem of global exponential stability for a class of impulsive neural networks with bounded and unbounded delays and fixed moments of impulsive effect we establish stability criteria by employing lyapunov functions and razumikhin technique an illustrative example is given to demonstrate the effectiveness of the obtained results

capacite et inegalite de faber krahn dans rn abstract in this paper we define a new capacity which allows us to control the behaviour of the dirichlet spectrum of a compact riemannian manifold with boundary with small subsets which may intersect the boundary removed this result generalises a classical result of rauch and taylor the crushed ice theorem in the second part we show that the dirichlet spectrum of a sequence of bounded euclidean domains converges to the spectrum of a ball with the same volume if the first eigenvalue of these domains converges to the first eigenvalue of a ball

exponential stability of impulsive high order hopfield type neural networks with time varying delays this paper considers the problems of global exponential stability and exponential convergence rate for impulsive high order hopfield type neural networks with time varying delays by using the method of lyapunov functions some sufficient conditions for ensuring global exponential stability of these networks are derived and the estimated exponential convergence rate is also obtained as an illustration an numerical example is worked out using the results obtained

characterizations of mixed binary convex quadratic representable sets representability results play a fundamental role in optimization since they provide characterizations of the feasible sets that arise from optimization problems in this paper we study the sets that appear in the feasibility version of mixed binary convex quadratic optimization problems we provide a complete characterization of the sets that can be obtained as the projection of such feasible regions in order to obtain this result we first provide a complete characterization of these sets in the special cases where 1 the feasible region is bounded 2 only binary extended variables are present and 3 only continuous variables are present

improved stability criteria for a class of neural networks with variable delays and impulsive perturbations this paper further investigates the problem of stability analysis for a kind of neural networks with variable delays and nonlinear impulses with the help of m matrix the homeomorphism theory some effective inequalities and analysis techniques certain novel criteria on the existence uniqueness and exponential stability of the equilibrium point have been established moreover these criteria possess adjustable real parameters which extend and improve many existing results in the literature in the end two numerical examples are provided to illustrate the validation of the theoretical results

capacitary estimates for dirichlet eigenvalues abstract lethbe the non negative definite selfadjoint operator associated to a regular irreducible dirichlet form onl2 x m assume thathhas discrete spectrum we study perturbations of this operator which arise through the imposition of dirichlet boundary conditions on a compact subset ofx the eigenvalues of the perturbed operator are of course shifted to the right under an ultracontractivity condition we show that the magnitude of this shift can be estimated by the capacity we also obtain a capacitary lower bound for the ground state shift under suitable conditions an application to the crushed ice problem is described

mixed integer quadratic programming is in np mixed integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral in this paper we prove that the decision version of mixed integer quadratic programming is in np thereby showing that it is np complete this is established by showing that if the decision version of mixed integer quadratic programming is feasible then there exists a solution of polynomial size this result generalizes and unifies classical results that quadratic programming is in np vavasis in inf process lett 36 2 73 77 17 and integer linear programming is in np borosh and treybig in proc am math soc 55 299 304 1 von zur gathen and sieveking in proc am math soc 72 155 158 18 kannan and monma in lecture notes in economics and mathematical systems vol 157 pp 161 172 springer 9 papadimitriou in j assoc comput mach 28 765 768 15

the algebraic degree of semidefinite programming given a generic semidefinite program specified by matrices with rational entries each coordinate of its optimal solution is an algebraic number we study the degree of the minimal polynomials of these algebraic numbers geometrically this degree counts the critical points attained by a linear functional on a fixed rank locus in a linear space of symmetric matrices we determine this degree using methods from complex algebraic geometry such as projective duality determinantal varieties and their chern classes

semidefinite representation of convex sets let s x in mathbb r n g 1 x geq 0 ldots g m x geq 0 be a semialgebraic set defined by multivariate polynomials g i x assume s is convex compact and has nonempty interior let s i x in mathbb r n g i x geq 0 and s resp s i be the boundary of s resp s i this paper as does the subject of semidefinite programming sdp concerns linear matrix inequalities lmis the set s is said to have an lmi representation if it equals the set of solutions to some lmi and it is known that some convex s may not be lmi representable helton and vinnikov in commun pure appl math 60 5 654 674 2007 a question arising from nesterov and nemirovski siam studies in applied mathematics society for industrial and applied mathematics siam philadelphia 1994 see helton and vinnikov in commun pure appl math 60 5 654 674 2007 and nemirovski in plenary lecture international congress of mathematicians icm madrid spain 2006 is given a subset s of mathbb r n does there exist an lmi representable set in some higher dimensional space mathbb r n n whose projection down onto mathbb r n equals s such s is called semidefinite representable or sdp representable this paper addresses the sdp representability problem the following are the main contributions of this paper i assume g i x are all concave on s if the positive definite lagrange hessian condition holds i e the hessian of the lagrange function for optimization problem of minimizing any nonzero linear function l t x on s is positive definite at the minimizer then s is sdp representable ii if each g i x is either sos concave 2 g i x w x t w x for some possibly nonsquare matrix polynomial w x or strictly quasi concave on s then s is sdp representable iii if each s i is either sos convex or poscurv convex s i is compact convex whose boundary has positive curvature and is nonsingular i e g i x 0 on s i s then s is sdp representable this also holds for s i for which s i s extends smoothly to the boundary of a poscurv convex set containing s iv we give the complexity of schmudgen and putinar s matrix positivstellensatz which are critical to the proofs of i iii

strong localized perturbations of eigenvalue problems this paper considers the effect of three types of perturbations of large magnitude but small extent on a class of linear eigenvalue problems for elliptic partial differential equations in bounded o

eigenvalue pinching and application to the stability and the almost umbilicity of hypersurfaces in this paper we give pinching theorems for the first nonzero eigenvalue of the laplacian on the compact hypersurfaces of ambient spaces with bounded sectional curvature as application we deduce rigidity results for stable constant mean curvature hypersurfaces m of these spaces n indeed we prove that if m is included in a ball of radius small enough then the hausdorff distance between m and a geodesic sphere s of n is small moreover m is diffeomorphic and quasi isometric to s as other application we give rigidity results for almost umbilic hypersurfaces

dirichlet problems on varying domains abstract the aim of the paper is to characterise sequences of domains for which solutions to an elliptic equation with dirichlet boundary conditions converge to a solution of the corresponding problem on a limit domain necessary and sufficient conditions are discussed for strong and uniform convergence for the corresponding resolvent operators examples are given to illustrate that most results are optimal

existence and exponential stability of periodic solution for impulsive cohen grossberg neural networks with time varying delays abstract this paper is concerned with the existence and global exponential stability of periodic solution for impulsive cohen grossberg neural networks with periodic coefficients and time varying delays some novel criteria on the existence and global exponential stability of periodic solution are derived by using impulsive differential inequality technique and the banach fixed point theorem the results obtained improve and extend a few of recent literature in some situations two examples with numerical simulations are given to demonstrate the efficiency of proposed methods

spectra of manifolds less a small domain soit m une variete de riemann c connexe compacte et l operateur de laplace beltrami associee on etudie le spectre pour une sous variete m compacte e 0 et b e le voisinage tubulaire de m de rayon e d operateur e

spectrum of hypersurfaces with small extrinsic radius or large λ1 in euclidean spaces abstract the reilly and hasanis koutroufiotis inequalities give sharp bounds on 1 and on the extrinsic radius of euclidean hypersurfaces in terms of the l 2 norm of their mean curvature the equality case of these inequalities characterizes the euclidean spheres in this paper we study the spectral properties of the almost extremal hypersurfaces we prove that the spectrum of the limit sphere asymptotically appears in the spectrum of almost extremal hypersurfaces for these inequalities we also construct some examples of extremizing sequences that prove that the limit spectrum can be essentially any closed subset of r that contains the spectrum of the limit sphere we also provide natural sharp condition to recover exactly the spectrum of the unit sphere

geometric lower bounds for the spectrum of elliptic pdes with dirichlet conditions in part an extension of the lower bound lemma of boggio is given for the weak forms of certain elliptic operators which are in general nonlinear and have partially dirichlet and partially neumann boundary conditions its consequences and those of an adapted hardy inequality for the location of the bottom of the spectrum are explored in corollaries wherein a variety of assumptions are placed on the shape of the dirichlet and neumann boundaries

splitting of resonant and scattering frequencies under shape deformation abstract it is well known that the main difficulty in solving eigenvalue problems under shape deformation relates to the continuation of multiple eigenvalues of the unperturbed configuration these eigenvalues may evolve under shape deformation as separated distinct eigenvalues and the splitting may only become apparent at high orders in their taylor expansion in this paper we address the splitting problem in the evaluation of resonant and scattering frequencies of the two dimensional laplacian operator under boundary variations of the domain by using surface potentials we show that the eigenvalues are the characteristic values of meromorphic operator valued functions that are of fredholm type with index 0 we then proceed from the generalized rouche s theorem to investigate the splitting problem

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

asymptotic analysis of high contrast phononic crystals and a criterion for the band gap opening we investigate the band gap structure of the frequency spectrum for elastic waves in a high contrast two component periodic elastic medium we consider two dimensional phononic crystals consisting of a background medium which is perforated by an array of holes periodic along each of the two orthogonal coordinate axes in this paper we establish a full asymptotic formula for dispersion relations of phononic band structures as the contrast of the shear modulus and that of the density become large the main ingredients are integral equation formulations of the solutions to the harmonic oscillatory linear elastic equation and several theorems concerning the characteristic values of meromorphic operator valued functions in the complex plane such as the generalized rouche s theorem we establish a connection between the band structures and the dirichlet eigenvalue problem on the elementary hole we also provide a criterion for exhibiting gaps in the band structure which shows that smaller the density of the matrix is the wider the band gap is provided that the criterion is fulfilled this phenomenon was reported by economou and sigalas j acoust soc am 95 1734 1740 1994 who observed that periodic elastic composites whose matrix has lower density and higher shear modulus compared to those of inclusions yield better open gaps our analysis in this paper agrees with this experimental finding

on global exponential stability for impulsive cellular neural networks with time varying delays in this paper the problem of global exponential stability for cellular neural networks cnns with time varying delays and fixed moments of impulsive effect is studied a new sufficient condition has been presented ensuring the global exponential stability of the equilibrium points by using piecewise continuous lyapunov functions and the razumikhin technique combined with young s inequality the results established here extend those given previously in the literature compared with the method of lyapunov functionals as in most previous studies our method is simpler and more effective for stability analysis

on the connection between schrodinger and dirichlet forms relations between schrodinger forms associated with schrodinger operators in l2 dnx rn open n 1 and the corresponding dirichlet forms are investigated various concrete examples are presented

approximation of dirichlet eigenvalues on domains with small holes abstract approximation formulas for the eigenvalues of the laplacian with dirichlet boundary conditions on domains with small holes are derived and discussed the corresponding results for the free and the supported vibrating plate follow a conceptually simple proof is given based on courant s min max principle the author s approximation for the capacity of small balls leads to a highly accurate eigenvalue approximation formula for domains with spherical holes general holes are treated by means of a harmonic correction method an isoperimetric inequality relating capacity to volume and a poincare inequality for capacity potentials in addition we provide l bounds for the eigenfunctions

layer potential techniques in spectral analysis part i complete asymptotic expansions for eigenvalues of the laplacian in domains with small inclusions we provide a rigorous derivation of new complete asymptotic expansions for eigenvalues of the laplacian in domains with small inclusions the inclusions somewhat apart from or nearly touching the boundary are of arbitrary shape and arbitrary conductivity contrast vis a vis the background domain with the limiting perfectly conducting inclusion by integral equations we reduce this problem to the study of the characteristic values of integral operators in the complex plane powerful techniques from the theory of meromorphic operator valued functions and careful asymptotic analysis of integral kernels are combined for deriving complete asymptotic expansions for eigenvalues our asymptotic formulae in this paper may be expected to lead to efficient algorithms not only for solving shape optimization problems for laplacian eigenvalues but also for determining specific internal features of an object based on scattering data measurements

artificial conditions for the linear elasticity equations in this paper we consider the equations of linear elasticity in an exterior domain we exhibit artificial boundary conditions on a circle which lead to a non coercive second order boundary value problem in the particular case of an axisymmetric geometry explicit computations can be performed in fourier series proving the well posedness except for a countable set of parameters a perturbation argument allows to consider near circular domains we complete the analysis by some numerical simulations

dynamical behavior of impulsive and periodic cohen grossberg neural networks abstract this paper investigates the existence and global stability of the periodic solution x t to cohen grossberg neural networks with periodic coefficients and impulses by using comparison results for impulsive differential equations and the method of lyapunov we describe the asymptotic behavior of all solutions in addition we give an explicit formula for the rate of exponential decay at infinity of the euclidean norm x t x t where x t is any solution of our model such a formula involves the jumps and the average of a suitable periodic function depending on the other parameters of the neural networks

level set methods for optimization problems involving geometry and constraints i frequencies of a two density inhomogeneous drum many problems in engineering design involve optimizing the geometry to maximize a certain design objective geometrical constraints are often imposed in this paper we use the level set method devised in osher and sethian j comput phys 79 12 1988 the variational level set calculus presented in zhao et al j comput phys 127 179 1996 and the projected gradient method as in rudin et al physica d 60 259 1992 to construct a simple numerical approach for problems of this type we apply this technique to a model problem involving a vibrating system whose resonant frequency or whose spectral gap is to be optimized subject to constraints on geometry our numerical results are quite promising we expect to use this approach to deal with a wide class of optimal design problems in the future

computational study of a family of mixed integer quadratic programming problems we present computational experience with a branch and cut algorithm to solve quadratic programming problems where there is an upper bound on the number of positive variables such problems arise in financial applications the algorithm solves the largest real life problems in a few minutes of run time

on global asymptotic stability of recurrent neural networks with time varying delays in this paper by constructing a new lyapunov functional and using m matrix and topological degree tool problem of the global asymptotic stability gas is discussed for a class of recurrent neural networks with time varying delays some simple and new sufficient conditions are obtained ensuring existence uniqueness of the equilibrium point and its gas of the neural networks some previous works are improved in addition this condition does not require the activation functions to be differentiable bounded and monotone nondecreasing and the weight connected matrices to be symmetric the neural network model considered in this paper include the delayed hopfield neural networks bidirectional associative memory networks and delayed cellular neural networks as its special cases

lyapunov razumikhin method for impulsive functional differential equations and applications to the population dynamics the present paper deals with the investigation of the stability of the zero solution of impulsive functional differential equations by means of piecewise continuous functions coupled with the razumikhin technique sufficient conditions for stability uniform stability and asymptotic stability of the zero solution of such equations are found

global exponential stability for impulsive cellular neural networks with time varying delays abstract in this paper we study the problem of global exponential stability for cellular neural networks cnn with time varying delays and fixed moments of impulsive effect we establish several stability criteria by employing lyapunov functions and the razumikhin technique

stability in cellular neural networks with a piecewise constant argument in this paper by using the concept of differential equations with piecewise constant arguments of generalized type 1 4 a model of cellular neural networks cnns 5 6 is developed the lyapunov razumikhin technique is applied to find sufficient conditions for the uniform asymptotic stability of equilibria global exponential stability is investigated by means of lyapunov functions an example with numerical simulations is worked out to illustrate the results

confinement of brownian motion among poissonian obstacles in ℝ d d 3 consider brownian motion among random obstacles obtained by translating a fixed compact nonpolar subset of d d 1 at the points of a poisson cloud of constant intensity v 0 assume that brownian motion is absorbed instantaneously upon entering the obstacle set in szn conf sznitman has shown that in d 2 conditionally on the event that the process does not enter the obstacle set up to time t the probability that brownian motion remains within distance t1 4 from its starting point is going to 1 as t goes to infinity we show that the same result holds true for d 3 with t1 4 replaced by t1 d 2 the proof is based on sznitmans refined method of enlargement of obstacles 10 as well as on a quantitative isoperimetric inequality due to hall 4

global attractivity of the almost periodic solution of a delay logistic population model with impulses in this paper we study the existence of almost periodic solutions of a delay logistic model with fixed moments of impulsive perturbations by using a comparison theorem and constructing a suitable lyapunov functional a set of sufficient conditions for the existence and global attractivity of a unique positive almost periodic solution is obtained as applications some special models are studied our new results improve and generalize former results

stability results for impulsive functional differential equations with infinite delays abstract this paper studies the stability problems for a class of impulsive functional differential equations with infinite delays of the form x t f t x t t x t k j k x t k k 1 2 by using the liapunov functions and razumikhin technique some new razumikhin type theorems on stability are obtained

ellipsoidal mixed integer representability representability results for mixed integer linear systems play a fundamental role in optimization since they give geometric characterizations of the feasible sets that can be formulated by mixed integer linear programming we consider a natural extension of mixed integer linear systems obtained by adding just one ellipsoidal inequality the set of points that can be described possibly using additional variables by these systems are called ellipsoidal mixed integer representable in this work we give geometric conditions that characterize ellipsoidal mixed integer representable sets

existence and stability of almost periodic solutions in impulsive neural network models abstract the existence and global exponential stability of an almost periodic solution of an impulsive neural network model with distributed delays is considered in a matrix setting the approach transforms the original network into a matrix analysis problem where a set of sufficient conditions based on spectral radius is presented a concrete hopfield model shows the advantages in comparison with a classical norm approach

fluctuations of principal eigenvalues and random scales we investigate the principal dirichlet eigenvalue of the laplacian with soft poissonian obstacles in large boxes of d 2 with the help of our recent version of the method of enlargement of obstacles 18 we derive quantitative confidence intervals for these eigenvalues we also provide less quantitative estimates which however point out the correct size of fluctuations and indicate a stiffness in their behavior in the two dimensional case we derive geometric controls which relate these eigenvalues to certain empty circular droplets our results also have natural applications to the study of the location of minima of certain intermittent random variational problems motivated by 13 17

mixed integer linear programming formulation techniques a wide range of problems can be modeled as mixed integer linear programming mip problems using standard formulation techniques however in some cases the resulting mip can be either too weak or

sums of laplace eigenvalues rotationally symmetric maximizers in the plane abstract the sum of the first n 1 eigenvalues of the laplacian is shown to be maximal among triangles for the equilateral triangle maximal among parallelograms for the square and maximal among ellipses for the disk provided the ratio area 3 moment of inertia for the domain is fixed this result holds for both dirichlet and neumann eigenvalues and similar conclusions are derived for robin boundary conditions and schrodinger eigenvalues of potentials that grow at infinity a key ingredient in the method is the tight frame property of the roots of unity for general convex plane domains the disk is conjectured to maximize sums of neumann eigenvalues

existence and stability of positive almost periodic solutions and periodic solutions for a logarithmic population model abstract by means of the cauchy matrix we give sufficient conditions for the existence and exponential stability of almost periodic solutions and periodic solutions for the delay impulsive logarithmic population

domain perturbations shift of eigenvalues and capacity abstract the notion of capacity of a subspace which was introduced in 16 is used to prove new estimates on the shift of the eigenvalues which arises if the form domain of a self adjoint and semibounded operator is restricted to a smaller subspace the upper bound on the shift of the spectral bound given in 16 is improved and another lower bound is proved which leads to a generalization of thirring s inequality if the underlying hilbert space is an l 2 space moreover we prove a similar capacitary upper bound for the second eigenvalue the results are applied to elliptic constant coefficient differential operators of arbitrary order finally it is given a capacitary characterization for the shift of the spectral bound being positive which works for operators with spectral bound of arbitrary type