equilibrium and stability analysis of delayed neural networks under parameter uncertainties abstract this paper proposes new results for the existence uniqueness and global asymptotic stability of the equilibrium point for neural networks with multiple time delays under parameter uncertainties by using lyapunov stability theorem and applying homeomorphism mapping theorem new delay independent stability criteria are obtained the obtained results are in terms of network parameters of the neural system only and therefore they can be easily checked we also present some illustrative numerical examples to demonstrate that our result are new and improve corresponding results derived in the previous literature

an efficient threshold dynamics method for wetting on rough surfaces the threshold dynamics method developed by merriman bence and osher mbo is an efficient method for simulating the motion by mean curvature flow when the interface is away from the solid boundary direct generalization of mbo type methods to the wetting problem with interfaces intersecting the solid boundary is not easy because solving the heat equation in a general domain with a wetting boundary condition is not as efficient as it is with the original mbo method the dynamics of the contact point also follows a different law compared with the dynamics of the interface away from the boundary in this paper we develop an efficient volume preserving threshold dynamics method for simulating wetting on rough surfaces this method is based on minimization of the weighted surface area functional over an extended domain that includes the solid phase the method is simple stable with o n log n complexity per time step and is not sensitive to the inhomogeneity or roughness of the solid boundary

an improved global asymptotic stability criterion for delayed cellular neural networks a new lyapunov krasovskii functional is constructed for delayed cellular neural networks and the s procedure is employed to handle the nonlinearities an improved global asymptotic stability criterion is also derived that is a generalization of and an improvement over previous results numerical examples demonstrate the effectiveness of the criterion

a front tracking method for multiphase free boundary problems a front tracking method for the solution of multiphase free boundary problems is presented based on the method of lines with invariant imbedding this method is sufficiently general to allow the solution of problems with three or more phases and problems in which phases appear and disappear a discussion of the method for the three phase stefan problem and for the moving contact problem as well as a proof of convergence for the latter is included in addition the method is demonstrated for a free boundary problem with a combination of stefan and ablation boundary conditions and for the two dimensional contact problem numerical results indicate that this front tracking method is fast enough to solve a wide range of problems on a personal computer

on characterizations of classical polynomials it is well known that the classical families of jacobi laguerre hermite and bessel polynomials are characterized as eigenvectors of a second order linear differential operator with polynomial coefficients rodrigues formula etc in this paper we present a unified study of the classical discrete polynomials and q polynomials of the q hahn tableau by using the difference calculus on linear type lattices we obtain in a straightforward way several characterization theorems for the classical discrete and q polynomials of the q hahn tableau finally a detailed discussion of a characterization by marcellan et al is presented

efficient algorithms for diffusion generated motion by mean curvature the problem of simulating the motion of evolving surfaces with junctions according to some curvature dependent speed arises in a number of applications by alternately diffusing and sharpening characteristic functions for each region a variety of motions have been obtained which allow for topological mergings and breakings and produce no overlapping regions or vacuums however the usual finite difference discretization of these methods is often excessively slow when accurate solutions are sought even in two dimensions we propose a new spectral discretization of these diffusion generated methods which obtains greatly improved efficiency over the usual finite difference approach these efficiency gains are obtained in part through the use of a quadrature based refinement technique by integrating fourier modes exactly and by neglecting the contributions of rapidly decaying solution transients indeed numerical studies demonstrate that the new algorithm is often more than 1000 times faster than the usual finite difference discretization our findings are demonstrated on several examples

orthogonal polynomial solutions of linear ordinary differential equations abstract this paper surveys the latest known results concerning the classification of differential equations of the form k 1 n a k x y k x y x having a sequence of polynomial eigenfunctions p n x n 0 that are orthogonal with respect to some real bilinear form since the publishing of the erice report in 1990 several new significant results and generalizations have been discovered

difference equations for the co recursive rth associated orthogonal polynomials of the dq laguerre hahn class we use some relations between the rth associated orthogonal polynomials of the dq laguerre hahn class to derive the fourth order q difference equation satisfied by the co recursive rth associated orthogonal polynomials of the dq laguerre hahn class when r 1 and for q semi classical situations this q difference equation factorizes as product of two second order q difference equations finally we study some classical situations and give some examples relative to the co recursive associated discrete q hermite ii orthogonal polynomials

generic formulas for the values at the singular points of some special monic classical hq ω orthogonal polynomials it is well known that the classical orthogonal polynomials of jacobi bessel laguerre and hermite are solutions of a sturm liouville problem of the type s x y n email protected x y n email protected ny n 0 where s and t are polynomials such that email protected 2 and email protected 1 and l n is a constant independent of x recently based on the hypergeometric character of the solutions of this differential equation w koepf and m masjed jamei a generic formula for the values at the boundary points of monic classical orthogonal polynomials j comput appl math 191 2006 98 105 found a generic formula only in terms of the coefficients of s and t for the values of the classical orthogonal polynomials at the singular points of the above differential hypergeometric equation in this paper we generalize the mentioned result giving the analogous formulas for both the classical q orthogonal polynomials of the q hahn tableau and the classical d w orthogonal polynomials both are special cases of the classical h q w orthogonal polynomials which are solutions of the hypergeometric type difference equation s x h q wh 1 q wy email protected x h q wy email protected ny n 0 where h q w is the difference operator introduced by hahn and s t and l n being as above our approach is algebraic and it does not require hypergeometric functions

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

approximation on attraction domain of cohen grossberg neural networks abstract in this paper approximations of attraction domains of the asymptotically stable equilibrium points of some typical cohen grossberg neural networks are achieved most cohen grossberg neural networks are highly nonlinear systems which makes it difficult to approximate their attraction domain under some weak assumptions we are allowed to employ the optimal lyapunov method to obtain a lyapunov function for asymptotically stable equilibrium points of a given cohen grossberg neural network with the help of this lyapunov function we approximate the corresponding attraction domain by the iterative expansion approach numerical simulations also illustrate that the approximation obtained is really part of the attraction domain

algorithms for area preserving flows we propose efficient and accurate algorithms for computing certain area preserving geometric motions of curves in the plane such as area preserving motion by curvature these schemes are based on a new class of diffusion generated motion algorithms using signed distance functions in particular they alternate two very simple and fast operations namely convolution with the gaussian kernel and construction of the distance function to generate the desired geometric flow in an unconditionally stable manner we present applications of these area preserving flows to large scale simulations of coarsening

representations for the first associated q classical orthogonal polynomials let pk x q be any system of the q classical orthogonal polynomials and let be the corresponding weight function satisfying the q difference equation dq where and are polynomials of degree at most 2 and exactly 1 respectively further let p 1 k x q be associated polynomials of the polynomials pk x q explicit forms of the coefficients bn k and cn k in the expansions p 1 n 1 x q k 0n 1bn k k x p 1 n 1 x q k 0n 1cn kpk x q are given in terms of basic hypergeometric functions here k x equals xk if 0 0 or x q k if 1 0 where x x q 1 x x the most important representatives of those two classes are the families of litte q jacobi and big q jacobi polynomials respectively writing the second order nonhomogeneous q difference equation satisfied by p 1 n 1 x q in a special form recurrence relations in k for bn k and cn k are obtained in terms of and

an augmented lkf approach involving derivative information of both state and delay an augmented lyapunov krasovskii functional lkf approach is presented to derive sufficient conditions for the existence uniqueness and globally exponential stability of the equilibrium point of a class of cellular neural networks with time varying delays by dividing the variation interval of the time delay into several subintervals with equal length a novel vector lkf is introduced and new conditions are obtained based on the homeomorphism mapping principle free weighting matrix method and linear matrix inequality techniques since the criteria are involving derivative information of both state and delay the obtained results are less conservative than some previous ones two examples are also given to show the effectiveness of the presented criteria

on askey scheme and d orthogonality i a characterization theorem this is the first in a series of papers dealing with generalized hypergeometric d orthogonal polynomials extending the polynomial families in the askey scheme in this paper we give a characterization theorem to introduce new examples of generalized hypergeometricd orthogonal polynomials to be studied in the forthcoming works for d 1 we obtain an unification of some known characterization theorems in the orthogonal polynomials theory

multistability of neural networks with time varying delays and concave convex characteristics in this paper stability of multiple equilibria of neural networks with time varying delays and concave convex characteristics is formulated and studied some sufficient conditions are obtained to ensure that an n neuron neural network with concave convex characteristics can have a fixed point located in the appointed region by means of an appropriate partition of the n dimensional state space when nonlinear activation functions of an n neuron neural network are concave or convex in 2k 2m 1 intervals this neural network can have 2k 2m 1 n equilibrium points this result can be applied to the multiobjective optimal control and associative memory in particular several succinct criteria are given to ascertain multistability of cellular neural networks these stability conditions are the improvement and extension of the existing stability results in the literature a numerical example is given to illustrate the theoretical findings via computer simulations

kernels with prescribed surface tension mobility for threshold dynamics schemes abstract we show how to construct a convolution kernel that has a desired anisotropic surface tension and desired anisotropic mobility to be used in threshold dynamics schemes for simulating weighted motion by mean curvature of interfaces including networks of them in both two and three dimensions moreover we discuss necessary and sufficient conditions for the positivity of the kernel which in the case of two phase flow ensures that the resulting scheme respects a comparison principle and implies convergence to the viscosity solution of the level set formulation of the flow in particular we show in a barrier type statement that the kernel cannot possibly be positive unless both the mobility and the surface tension satisfy necessary conditions in three dimensions and give a complete characterization among other results is a threshold dynamics scheme that is guaranteed to dissipate a non local approximation to the interfacial energy in the fully anisotropic multiphase setting using the new kernel construction

robust stability analysis for interval cohen grossberg neural networks with unknown time varying delays in this paper robust stability problems for interval cohen grossberg neural networks with unknown time varying delays are investigated using linear matrix inequality m matrix theory and halanay inequality techniques new sufficient conditions independent of time varying delays are derived to guarantee the uniqueness and the global robust stability of the equilibrium point of interval cohen grossberg neural networks with time varying delays all these results have no restriction on the rate of change of the time varying delays compared to some existing results these new criteria are less conservative and are more convenient to check two numerical examples are used to show the effectiveness of the present results

on the properties of special functions on the linear type lattices abstract we present a general theory for studying the difference analogs of special functions of hypergeometric type on the linear type lattices i e the solutions of the second order linear difference equation of hypergeometric type on a special kind of lattices the linear type lattices in particular using the integral representation of the solutions we obtain several difference recurrence relations for such functions finally applications to q classical polynomials are given

multistability of complex valued recurrent neural networks with real imaginary type activation functions this paper addresses the multistability problem of n dimensional complex valued recurrent neural networks with real imaginary type activation functions sufficient conditions are proposed for checking the existence of 2 1 2 1 n 1 equilibria under these conditions 1 1 n equilibria are locally exponentially stable and the others are unstable attractive basins of equilibria are also investigated complete attractive basins of equilibria in 1 dimensional complex valued recurrent neural networks are obtained the obtained stability results improve and extend the existing ones two numerical examples are given to illustrate the effectiveness of the obtained results

analysis of the cahn hilliard equation with a relaxation boundary condition modeling the contact angle dynamics we analyze the cahn hilliard equation with a relaxation boundary condition modeling the evolution of an interface in contact with the solid boundary an l estimate is established which enables us to prove the global existence of the solution we also study the sharp interface limit of the system the dynamic of the contact point and the contact angle are derived and the results are compared with the numerical simulations

differential equations for generalized jacobi polynomials abstract we look for differential equations of the form m i 0 a i x y i x n i 0 b i x y i x mn i 0 c i x y i x 1 x 2 y x 2 x y x n n 1 y x 0 satisfied by the generalized jacobi polynomials pn m n x n 0 which are orthogonal on the interval 1 1 with respect to the weight function 2 2 1 1 1 1 x 1 x m x 1 n x 1 where 1 1 m 0 and n 0 we give explicit representations for the coefficients ai x i 0 bi x i 0 and ci x i 0 and we show that this differential equation is uniquely determined for m2 n2 0 the order of this differential equation is infinite except for 0 1 2 or 0 1 2 moreover the order equals 2 4 if m 0 n 0 and 0 1 2 2 4 if m 0 n 0 and 0 1 2 2 2 6 if m 0 n 0 and 0 1 2

an efficient iterative thresholding method for image segmentation abstract we proposed an efficient iterative thresholding method for multi phase image segmentation the algorithm is based on minimizing piecewise constant mumford shah functional in which the contour length or perimeter is approximated by a non local multi phase energy the minimization problem is solved by an iterative method each iteration consists of computing simple convolutions followed by a thresholding step the algorithm is easy to implement and has the optimal complexity o n log n per iteration we also show that the iterative algorithm has the total energy decaying property we present some numerical results to show the efficiency of our method

new exponential stability results for delayed neural networks with time varying delays abstract this paper presents new sufficient conditions for the uniqueness and exponential stability of the equilibrium point for delayed neural networks with time varying delays by employing a more general type of lyapunov krasovskii functional and using lmi linear matrix inequality we derive new results for exponential stability of the equilibrium point for delayed neural networks the results establish a relation between the delay time and the parameters of the network the results are compared with the previous results derived in the literature

multistability of two kinds of recurrent neural networks with activation functions symmetrical about the origin on the phase plane in this paper we investigate multistability of two kinds of recurrent neural networks with time varying delays and activation functions symmetrical about the origin on the phase plane one kind of activation function is with zero slope at the origin on the phase plane while the other is with nonzero slope at the origin on the phase plane we derive sufficient conditions under which these two kinds of n dimensional recurrent neural networks are guaranteed to have 2m 1 n equilibrium points with m 1 n of them being locally exponentially stable these new conditions improve and extend the existing multistability results for recurrent neural networks finally the validity and performance of the theoretical results are demonstrated through two numerical examples

new criteria for global robust stability of delayed neural networks with norm bounded uncertainties in this paper we study the global asymptotic robust stability of delayed neural networks with norm bounded uncertainties by employing the lyapunov stability theory and homeomorphic mapping theorem we derive some new types of sufficient conditions ensuring the existence uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slope bounded activation functions an important aspect of our results is their low computational complexity as the reported results can be verified by checking some properties of symmetric matrices associated with the uncertainty sets of the network parameters the obtained results are shown to be generalizations of some of the previously published corresponding results some comparative numerical examples are also constructed to compare our results with some closely related existing literature results

stability analysis of cohen grossberg neural networks without assuming boundedness and differentiability of the activation functions and any symmetry of interconnections we employ lyapunov functions to establish some sufficient conditions ensuring existence uniqueness global asymptotic stability and even global exponential stability of equilibria for the cohen grossberg neural networks with and without delays our results are not only presented in terms of system parameters and can be easily verified and also less restrictive than previously known criteria and can be applied to neural networks including hopfield neural networks bidirectional association memory neural networks and cellular neural networks

limit relations between q krall type orthogonal polynomials in this paper we consider a natural extension of several results related to krall type polynomials introducing a modification of a q classical linear functional via the addition of one or two mass points the limit relations between the q krall type modification of big q jacobi little q jacobi big q laguerre and other families of the q hahn tableau are established

a method to study the krall and q krall polynomials we describe a method allowing to obtain new results in studying the krall and q krall polynomials in particular we establish the criterion for orthogonal polynomials to be eigenfunctions of 2nth order q differential operator this criterion is an exact q analogue of corresponding krall s criterion

motion of multiple junctions a level set approach abstract a coupled level set method for the motion of multiple junctions is proposed the new method extends the hamilton jacobi level set formulation of osher and sethian it retains the feature of tracking fronts by following level sets and allows the specification of arbitrary velocities on each front the diffusion equation is shown to generate curvature dependent motion and this is used to develop an algorithm to move multiple junctions with curvature dependent speed systems of reaction diffusion equations are shown to possess inherent properties which prohibit efficient numerical solutions when applied to curvature dependent motion

harmless delays in cohen grossberg neural networks without assuming monotonicity and differentiability of the activation functions and any symmetry of interconnections we establish some sufficient conditions for the globally asymptotic stability of a unique equilibrium for the cohen grossberg neural network with multiple delays lyapunov functionals and functions combined with the razumikhin technique are employed the criteria are all independent of the magnitudes of the delays and thus the delays under these conditions are harmless 2002 elsevier science b v all rights reserved msc 34d23 34k20 92b20

diffusion generated motion using signed distance functions we describe a new class of algorithms for generating a variety of geometric interfacial motions by alternating two steps construction of the signed distance function i e redistancing to the interface and convolution with a suitable kernel these algorithms can be seen as variants of merriman bence and osher s threshold dynamics 25 the new algorithms proposed here preserve the computational efficiency of the original threshold dynamics algorithm however unlike threshold dynamics the new algorithms also allow attaining high accuracy on uniform grids without adaptive refinement

passivity of switched recurrent neural networks with time varying delays this paper is concerned with the passivity analysis for switched neural networks subject to stochastic disturbances and time varying delays first using the multiple lyapunov functions method a state dependent switching law is designed to present a stochastic passivity condition second a hysteresis switching law involving both the current state and the previous value of the switching signal are presented to avoid chattering resulted from the state dependent switching third based on the average dwell time approach a class of switching signals is determined to guarantee the switched neural network stochastically passive finally three numerical examples are provided to illustrate the characteristics of three proposed switching laws

a variational method for multiphase volume preserving interface motions we develop a numerical method for realizing mean curvature motion of interfaces separating multiple phases whose volumes are preserved throughout time the foundation of the method is a thresholding algorithm of the bence merriman osher type the original algorithm is reformulated in a vector setting which allows for a natural inclusion of constraints even in the multiphase case moreover a new method for overcoming the inaccuracy of thresholding methods on non adaptive grids is designed since this inaccuracy becomes especially prominent in volume preserving motions formal analysis of the method and numerical tests are presented

global asymptotic stability of reaction diffusion cohen grossberg neural networks with continuously distributed delays this paper is concerned with the global asymptotic stability of a class of reaction diffusion cohen grossberg neural networks with continuously distributed delays under some suitable assumptions and using a matrix decomposition method we apply the linear matrix inequality lmi method to propose some new sufficient stability conditions for the reaction diffusion cohen grossberg neural networks with continuously distributed delays the obtained results are easy to check and improve upon the existing stability results some remarks are given to show the advantages of the obtained results over the previous results an example is also given to demonstrate the effectiveness of the obtained results

robust stability and boundedness of stochastic differential equations with delay driven by g brownian motion this paper aims to establish the robust stability and boundedness for a class of stochastic differential equations with delay driven by g brownian motion g sddes in short whose coefficients do n

second structure relation for q semiclassical polynomials of the hahn tableau the q classical orthogonal polynomials of the q hahn tableau are characterized from their orthogonality condition and by a first and a second structure relation unfortunately for the q semiclassical orthogonal polynomials a generalization of the classical ones we find only in the literature the first structure relation in this paper a second structure relation is deduced in particular by means of a general finite type relation between a q semiclassical polynomial sequence and the sequence of its q differences such a structure relation is obtained

on the krall type discrete polynomials in this paper we present a unified theory for studying the so called krall type discrete orthogonal polynomials in particular the three term recurrence relation lowering and raising operators as well as the second order linear difference equation that the sequences of monic orthogonal polynomials satisfy are established some relevant examples of q krall polynomials are considered in detail

q classical polynomials and the q askey and nikiforov uvarov tableaus abstract in this paper we continue the study of the q classical discrete polynomials in the hahn s sense started in medem et al this issue comput appl math 135 2001 157 196 here we will compare our scheme with the well known q askey scheme and the nikiforov uvarov tableau also new families of q polynomials are introduced

multistability of recurrent neural networks with time varying delays and the piecewise linear activation function in this brief stability of multiple equilibria of recurrent neural networks with time varying delays and the piecewise linear activation function is studied a sufficient condition is obtained to ensure that n neuron recurrent neural networks can have 4k 1 n equilibrium points and 2k n of them are locally exponentially stable this condition improves and extends the existing stability results in the literature simulation results are also discussed in one illustrative example

factorization method for difference equations of hypergeometric type on nonuniform lattices we study the factorization of the hypergeometric type difference equation of nikiforov and uvarov on nonuniform lattices an explicit form of the raising and lowering operators is derived and some relevant examples are given

a grid based particle method for moving interface problems we propose a novel algorithm for modeling interface motions the interface is represented and is tracked using quasi uniform meshless particles these particles are sampled according to an underlying grid such that each particle is associated to a grid point which is in the neighborhood of the interface the underlying grid provides an eulerian reference and local sampling rate for particles on the interface it also renders neighborhood information among the meshless particles for local reconstruction of the interface the resulting algorithm which is based on lagrangian tracking using meshless particles with eulerian reference grid can naturally handle control topological changes moreover adaptive sampling of the interface can be achieved easily through local grid refinement with simple quad oct tree data structure extensive numerical examples are presented to demonstrate the capability of our new algorithm

effective contact angle for rough boundary abstract we provide rigorous justification for the classical wenzel equation for the roughness enhanced effective contact angle the minimization of the total surface energy is reformulated into a variational problem as the size of the roughness becomes small we show convergence of the minimizer the limiting minimizer and effective contact angle are explicitly calculated to verify the wenzel equation

variations around classical orthogonal polynomials connected problems abstract we survey and prove the principal characterizations of the classical orthogonal polynomials with the method of the dual sequence two new characterizations are given connected problems are discussed

difference equations for generalized meixner polynomials abstract in this paper is introduced a system of polynomials orthogonal with respect to the classical discrete weight function for meixner polynomials with an extra point mass added at x 0 a difference operator of infinite order is constructed for which these new polynomials are eigenfunctions and a second order difference equation is given with polynomial coefficients n dependent and of at most degree 2 which these polynomials satisfy

global robust stability criteria for interval delayed full range cellular neural networks this brief considers a class of delayed full range fr cellular neural networks cnns with uncertain interconnections between neurons modeled by means of intervalized matrices using mathematical tools from the theory of differential inclusions a fundamental result on global robust stability of standard s cnns is extended to prove global robust exponential stability for the corresponding class same interconnection weights and inputs of fr cnns the result is of theoretical interest since in general the equivalence between the dynamical behavior of fr cnns and s cnns is not guaranteed

further results on delay dependent stability criteria of neural networks with time varying delays in this brief paper an augmented lyapunov functional which takes an integral term of state vector into account is introduced owing to the functional an improved delay dependent asymptotic stability criterion for delayed neural networks nns is derived in term of linear matrix inequalities lmis it is shown that the obtained criterion can provide less conservative result than some existing ones when linear fractional uncertainties appear in nns a new robust delay dependent stability condition is also given numerical examples are given to demonstrate the applicability of the proposed approach

auction dynamics a volume constrained mbo scheme abstract we show how auction algorithms originally developed for the assignment problem can be utilized in merriman bence and osher s threshold dynamics scheme to simulate multi phase motion by mean curvature in the presence of equality and inequality volume constraints on the individual phases the resulting algorithms are highly efficient and robust and can be used in simulations ranging from minimal partition problems in euclidean space to semi supervised machine learning via clustering on graphs in the case of the latter application numerous experimental results on benchmark machine learning datasets show that our approach exceeds the performance of current state of the art methods while requiring a fraction of the computation time

global asymptotic stability of delayed cellular neural networks a new criterion for the global asymptotic stability of the equilibrium point of cellular neural networks with multiple time delays is presented the obtained result possesses the structure of a linear matrix inequality and can be solved efficiently using the recently developed interior point algorithm a numerical example is used to show the effectiveness of the obtained result

dynamic stability conditions for lotka volterra recurrent neural networks with delays the lotka volterra model of neural networks derived from the membrane dynamics of competing neurons have found successful applications in many winner take all types of problems this paper studies the dynamic stability properties of general lotka volterra recurrent neural networks with delays conditions for nondivergence of the neural networks are derived these conditions are based on local inhibition of networks thereby allowing these networks to possess a multistability property multistability is a necessary property of a network that will enable important neural computations such as those governing the decision making process under these nondivergence conditions a compact set that globally attracts all the trajectories of a network can be computed explicitly if the connection weight matrix of a network is symmetric in some sense and the delays of the network are in l2 space we can prove that the network will have the property of complete stability

globally exponential stability conditions for cellular neural networks with time varying delays in this paper the problems of global exponential stability for cellular neural networks cnn with time varying delays are studied several sufficient conditions guaranteeing the network s global exponential stability are established these results can easily be used to design and verify globally stable networks furthermore the results presented here are independent of the form of specific delays and have important significance in both theory and applications

global exponential stability and global convergence in finite time of delayed neural networks with infinite gain this paper introduces a general class of neural networks with arbitrary constant delays in the neuron interconnections and neuron activations belonging to the set of discontinuous monotone increasing and possibly unbounded functions the discontinuities in the activations are an ideal model of the situation where the gain of the neuron amplifiers is very high and tends to infinity while the delay accounts for the finite switching speed of the neuron amplifiers or the finite signal propagation speed it is known that the delay in combination with high gain nonlinearities is a particularly harmful source of potential instability the goal of this paper is to single out a subclass of the considered discontinuous neural networks for which stability is instead insensitive to the presence of a delay more precisely conditions are given under which there is a unique equilibrium point of the neural network which is globally exponentially stable for the states with a known convergence rate the conditions are easily testable and independent of the delay moreover global convergence in finite time of the state and output is investigated in doing so new interesting dynamical phenomena are highlighted with respect to the case without delay which make the study of convergence in finite time significantly more difficult the obtained results extend previous work on global stability of delayed neural networks with lipschitz continuous neuron activations and neural networks with discontinuous neuron activations but without delays

wetting of rough surfaces a homogenization approach the contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests we study the roughness induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory by relying on a variational formulation of the problem we show that the macroscopic contact angle is associated with the solution of two cell problems giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapor phase our results are valid for both chemically heterogeneous and homogeneous surfaces in the latter case a very transparent structure emerges from the variational approach the classical laws of wenzel and cassie baxter give bounds for the optimal energy and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case to the largest one in the hydrophilic case

lmi based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures global asymptotic stability problem is studied for a class of recurrent neural networks with distributed delays satisfying lebesgue stieljies measures on the basis of linear matrix inequality the concerned network model includes many neural network models with various delays and structures as its special cases such as the delays covering the discrete delays and distributed delays and the network structures containing the neutral type networks and high order networks therefore many new stability criteria for the above neural network models have also been derived from the present stability analysis method all the obtained stability results have similar matrix inequality structures and can be easily checked three numerical examples are used to show the effectiveness of the obtained results

a characterization of the classical orthogonal discrete and q polynomials in this paper we present a new characterization for the classical discrete and q classical discrete polynomials in the hahn s sense

a simple proof of convergence for an approximation scheme for computing motions by mean curvature we prove the convergence of an approximation scheme recently proposed by bence merriman and osher for computing motions of hypersurfaces by mean curvature our proof is based on viscosity solutions methods

q coherent pairs and q orthogonal polynomials in this paper we introduce the concept of q coherent pair of linear functionals we prove that if u 0 u 1 is a q coherent pair of linear functionals then at least one of them has to be a q classical linear functional moreover we present the classification of all q coherent pairs of positive definite linear functionals when u 0 or u 1 is either the little q jacobi linear functional or the little q laguerre wall linear functional finally by using limit processes we recover the classification of coherent pairs of linear functionals stated by meijer

a method of constructing krall s polynomials we propose a method of constructing orthogonal polynomials pn x krall s polynomials that are eigenfunctions of higher order dierential operators using this method we show that recurrence coecients of krall s polynomials pn x are rational functions of n let p a b m n x be polynomials obtained from the jacobi polynomials p a b n x by the following procedure we add an arbitrary concentrated mass m at the endpoint of the orthogonality interval with respect to the weight function of the ordinary jacobi polynomials we nd necessary conditions for the parameters a b in order for the polynomials p a b m n x to obey a higher order dierential equation the main result of the paper is the following let a be a positive integer and b 1 2 an arbitrary real parameter then the polynomials p a b m n x are krall s polynomials

a complex valued projection neural network for constrained optimization of real functions in complex variables in this paper we present a complex valued projection neural network for solving constrained convex optimization problems of real functions with complex variables as an extension of real valued projection neural networks theoretically by developing results on complex valued optimization techniques we prove that the complex valued projection neural network is globally stable and convergent to the optimal solution obtained results are completely established in the complex domain and thus significantly generalize existing results of the real valued projection neural networks numerical simulations are presented to confirm the obtained results and effectiveness of the proposed complex valued projection neural network

inpainting of binary images using the cahn hilliard equation image inpainting is the filling in of missing or damaged regions of images using information from surrounding areas we outline here the use of a model for binary inpainting based on the cahn hilliard equation which allows for fast efficient inpainting of degraded text as well as super resolution of high contrast images

difference equation for modifications of meixner polynomials abstract we consider a modification of meixner moment functional by adding a mass point at x 0 we obtain the resulting orthogonal polynomials identify them as hypergeometric 3f2 functions and derive the second order difference equation which these polynomials satisfy in such a way we give the solution to a problem raised by r askey 1991 in orthogonal polynomials and their applications p 418 baltzer ag scientific basel

on the properties for modifications of classical orthogonal polynomials of discrete variables abstract we consider a modification of moment functionals for some classical polynomials of a discrete variable by adding a mass point at x 0 we obtain the resulting orthogonal polynomials identify them as hypergeometric functions and derive the second order difference equation which these polynomials satisfy the corresponding tridiagonal matrices and associated polynomials were also studied

robust stability for interval hopfield neural networks with time delay the conventional hopfield neural network with time delay is intervalized to consider the bounded effect of deviation of network parameters and perturbations yielding a novel interval dynamic hopfield neural network idhnn model a sufficient condition related to the existence of unique equilibrium point and its robust stability is derived

on stabilization of stochastic cohen grossberg neural networks with mode dependent mixed time delays and markovian switching the globally exponential stabilization problem is investigated for a general class of stochastic cohen grossberg neural networks with both markovian jumping parameters and mixed mode dependent time delays the mixed time delays consist of both discrete and distributed delays this paper aims to design a memoryless state feedback controller such that the closed loop system is stochastically exponentially stable in the mean square sense by introducing a new lyapunov krasovskii functional that accounts for the mode dependent mixed delays stochastic analysis is conducted in order to derive delay dependent criteria for the exponential stabilization problem three numerical examples are carried out to demonstrate the feasibility of our delay dependent stabilization criteria

on the q polynomials a distributed study in this paper we present a uni1ed distributional study of the classical discrete q polynomials in the hahn s sense from the distributional q pearson equation we will deduce many of their properties such as the three term recurrence relations structure relations etc also several characterizations of such q polynomials are presented c

threshold dynamics for networks with arbitrary surface tensions we present and study a new algorithm for simulating the n phase mean curvature motion for an arbitrary set of isotropic surface tensions the departure point is the threshold dynamics algorithm of merriman bence and osher for the two phase case a new energetic interpretation of this algorithm allows us to extend it in a natural way to the case of n phases for arbitrary surface tensions and arbitrary isotropic mobilities for a large class of surface tensions the algorithm is shown to be consistent in the sense that at every time step it decreases an energy functional that is an approximation in the sense of gamma convergence of the interfacial energy a broad range of numerical tests shows good convergence properties an important application is the motion of grain boundaries in polycrystalline materials it is also established that the above mentioned large class of surface tensions contains the read shockley surface tensions both in the two dimensional and three dimensional settings 2015 wiley periodicals inc

factorization of the hypergeometric type difference equation on non uniform lattices dynamical algebra we argue that one can factorize the difference equation of hypergeometric type on non uniform lattices in the general case it is shown that in the most cases of q linear spectrum of the eigenvalues this directly leads to the dynamical symmetry algebra suq 1 1 whose generators are explicitly constructed in terms of the difference operators obtained in the process of factorization thus all models with the q linear spectrum some of them but not all previously considered in a number of publications can be treated in a unified form

a comprehensive review of stability analysis of continuous time recurrent neural networks stability problems of continuous time recurrent neural networks have been extensively studied and many papers have been published in the literature the purpose of this paper is to provide a comprehensive review of the research on stability of continuous time recurrent neural networks including hopfield neural networks cohen grossberg neural networks and related models since time delay is inevitable in practice stability results of recurrent neural networks with different classes of time delays are reviewed in detail for the case of delay dependent stability the results on how to deal with the constant variable delay in recurrent neural networks are summarized the relationship among stability results in different forms such as algebraic inequality forms m matrix forms linear matrix inequality forms and lyapunov diagonal stability forms is discussed and compared some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed concluding remarks and future directions of stability analysis of recurrent neural networks are given

a variational level set approach to multiphase motion a coupled level set method for the motion of multiple junctions of e g solid liquid and grain boundaries which follows the gradient flow for an energy functional consisting of surface tension proportional to length and bulk energies proportional to area is developed the approach combines the level set method of s osher and j a sethian with a theoretical variational formulation of the motion by f reitich and h m soner the resulting method uses as many level set functions as there are regions and the energy functional is evaluated entirely in terms of level set functions the gradient projection method leads to a coupled system of perturbed by curvature terms hamilton jacobi equations the coupling is enforced using a single lagrange multiplier associated with a constraint which essentially prevents a regions from overlapping and b the development of a vacuum the numerical implementation is relatively simple and the results agree with and go beyond the theory as given in 12 other applications of this methodology including the decomposition of a domain into subregions with minimal interface length are discussed finally some new techniques and results in level set methodology are presented

global stability of complex valued recurrent neural networks with time delays since the last decade several complex valued neural networks have been developed and applied in various research areas as an extension of real valued recurrent neural networks complex valued recurrent neural networks use complex valued states connection weights or activation functions with much more complicated properties than real valued ones this paper presents several sufficient conditions derived to ascertain the existence of unique equilibrium global asymptotic stability and global exponential stability of delayed complex valued recurrent neural networks with two classes of complex valued activation functions simulation results of three numerical examples are also delineated to substantiate the effectiveness of the theoretical results

a diffusion generated approach to multiphase motion in this article we present a diffusion generated approach for evolving multiple junctions this work generalizes an earlier method by merriman bence and osher which alternately diffuses and sharpens characteristic functions for each phase region to produce pure mean curvature flow specifically our new method produces a normal velocity which depends on a positive multiple of the curvature of the interface plus the difference in bulk energy densities for prescribed junction angles this simple method naturally treats topological mergings and breakings produces no overlapping regions or vacuums and can be made very fast numerical studies are provided which show that our method agrees with front tracking and a recent variational approach for a variety of examples asymptotic expansions are also carried out near junctions to justify our algorithms

on some necessary and sufficient conditions for a recurrent neural network model with time delays to generate oscillations in this paper the existence of oscillations for a class of recurrent neural networks with time delays between neural interconnections is investigated by using the fixed point theory and liapunov functional we prove that a recurrent neural network might have a unique equilibrium point which is unstable this particular type of instability combined with the boundedness of the solutions of the system will force the network to generate a permanent oscillation some necessary and sufficient conditions for these oscillations are obtained simple and practical criteria for fixing the range of parameters in this network are also derived typical simulation examples are presented

robust stability of delayed markovian switching genetic regulatory networks with reaction diffusion terms abstract robust stochastic stability of delayed genetic regulatory networks with reaction diffusion terms uncertainties terms and markovian jumping parameters under dirichlet boundary conditions is researched in this article based on lyapunov krasovskii functions and linear matrix inequalities sufficient conditions are given to ensure the robust stability for the continuous time delayed genetic regulatory networks in addition it is discussed that the stability criteria proposed in this paper are less conservative than the existing ones numerical examples are presented to illustrate the effectiveness of the proposed approach

global exponential convergence of cohen grossberg neural networks with time delays in this paper we derive a general sufficient condition ensuring global exponential convergence of cohen grossberg neural networks with time delays by constructing a novel lyapunov functional and smartly estimating its derivative the proposed condition is related to the convex combinations of the column sum and the row sum of the connection matrices and also relaxes the constraints on the network coefficients therefore the proposed condition generalizes some previous results in the literature