further note on global exponential stability of uncertain cellular neural networks with variable delays for cellular neural networks with time varying delays and uncertainties a recent work for exponential stability with convergence rate k of the networks is extended a new linear matrix inequality criterion for the stability which give information on the delay dependent property is derived

stability analysis and synthesis of nonlinear time delay systems via linear takagi sugeno fuzzy models abstract this paper concerns with the stability analysis and synthesis of nonlinear retarded systems via linear takagi sugeno ts fuzzy model approach first the ts fuzzy models with time delay are present and the stability conditions are derived using lyapunov razumikhin functional approach then a stabilization approach for nonlinear retarded systems through fuzzy state feedback and fuzzy observer based controller is proposed it shows that the analysis results provide an efficient technique for the design of fuzzy controllers sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain of the time delay systems are derived through the numerical solution of a set of coupled linear matrix inequalities

on galerkin difference methods energy stable difference methods for hyperbolic initial boundary value problems are constructed using a galerkin framework the underlying basis functions are lagrange functions associated with continuous piecewise polynomial approximation on a computational grid both theoretical and computational evidence shows that the resulting methods possess excellent dispersion properties in the absence of boundaries the spectral radii of the operators for the first and second derivative matrices are bounded independent of discretization order with boundaries the spectral radius of the first order derivative matrix appears to be bounded independent of discretization order and grows only slowly with discretization order for problems in second order form

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

brief delay dependent robust h control of uncertain linear state delayed systems this paper examines the problems of robust stabilization and robust h control for linear systems with a constant time delay in the state and subject to parameter uncertainty systems with norm bounded parameter uncertainty will be considered and attention is focused on the design of linear memoryless state feedback controllers we develop methods of robust stabilization and robust h control which are dependent on the size of the delay and are based on the solution of linear matrix inequalities the proposed methods can be easily extended to uncertain linear polytopic systems as well as to the case of multiple time delays

gradings derivations and automorphisms of nearly associative algebras abstract in this paper we examine a class of algebras which includes lie algebras lie color algebras right alternative algebras left alternative algebras antiassociative algebras and associative algebras we call this class of algebras algebras and we examine gradings of these algebras by groups with finite support we generalize various results on associative algebras and finite dimensional lie algebras two of our main results are t heorem 2 2 let a be a g graded left algebra and v g g v g a g graded left a module with finite support where g is a torsion free abelian group if a 0 acts nilpotently on v then a also acts nilpotently on v t heorem 2 12 let a be a g graded algebra with finite support where g t z m and t is a torsion free abelian group if the identity component a 0 0 acts nilpotently on a on both sides then a is solvable these results are used to examine the invariants of automorphisms and derivations one such application is c orollary 3 3 let l g g l g be a lie color algebra over a field k of characteristic 0 and let d be a finite dimensional nilpotent lie algebra of homogeneous derivations of l which are algebraic as k linear transformations of l if l d 0 then l is nilpotent we conclude this paper with counterexamples to various questions which arise naturally in light of our results

a high order accurate parallel solver for maxwell s equations on overlapping grids a scheme for the solution of the time dependent maxwell s equations on composite overlapping grids is described the method uses high order accurate approximations in space and time for maxwell s equations written as a second order vector wave equation high order accurate symmetric difference approximations to the generalized laplace operator are constructed for curvilinear component grids the modified equation approach is used to develop high order accurate approximations that use only three time levels and have the same time stepping restriction as the second order scheme discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed the implementation is optimized for component grids that are cartesian resulting in a fast and efficient method the solver runs on parallel machines with each component grid distributed across one or more processors numerical results in two and three dimensions are presented for the fourth order accurate version of the method these results demonstrate the accuracy and efficiency of the approach

global exponential stability of cellular neural networks with variable delays for cellular neural networks with time varying delays the problems of determining the exponential stability and estimating the exponential convergence rate are investigated by employing the lyapunov krasovskii functional and linear matrix inequality lmi technique a novel criterion for the stability which give information on the delay dependent property is derived two examples are given to demonstrate the effectiveness of the obtained results

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

lie rings with almost regular automorphisms let l be a lie ring or a lie algebra of arbitrary not necessarily finite dimension let be an automorphism of l and let cl a l a a denote the fixed point subring the automorphism is called regular if cl 0 that is has no non trivial fixed points by kreknin s theorem 20 if a lie ring l admits a regular automorphism of finite order k that is such that 1 and cl 0 then l is soluble of derived length bounded by a function of k actually by 2 2 earlier borel and mostow 3 proved the solubility in the finite dimensional case without a bound for the derived length in the present paper we prove that if a lie ring admits an automorphism of prime power order that is almost regular then l is almost soluble

a quasi hamiltonian discretization of the thermal shallow water equations the rotating shallow water rsw equations are the usual testbed for the development of numerical methods for three dimensional atmospheric and oceanic models however an arguably more useful set of equations are the thermal shallow water equations tsw which introduce an additional thermodynamic scalar but retain the single layer two dimensional structure of the rsw as a stepping stone towards a three dimensional atmospheric dynamical core this work presents a quasi hamiltonian discretization of the thermal shallow water equations using compatible galerkin methods building on previous work done for the shallow water equations structure preserving or quasi hamiltonian discretizations methods that discretize the hamiltonian structure of the equations of motion rather than the equations of motion themselves have proven to be a powerful tool for the development of models with discrete conservation properties by combining these ideas with an energy conserving poisson time integrator and a careful choice of galerkin spaces a large set of desirable properties can be achieved in particular for the first time total mass buoyancy and energy are conserved to machine precision in the fully discrete model

on almost fixed point free automorphisms abstract ideas from the theory of p adic analytic groups are employed in the study of finite groups having automorphisms with few fixed points in particular we prove that the derived length of a finite p group admitting an automorphism of order p k with p m fixed points is bounded in terms of p m k this extends a well known result of alperin dealing with the case k 1 some applications to soluble groups are also given

robust approaches to handling complex geometries with galerkin difference methods abstract the galerkin difference gd basis is a set of continuous piecewise polynomials defined using a finite difference like grid of degrees of freedom the one dimensional gd basis functions are naturally extended to multiple dimensions using a tensor product construction on quadrilateral elements the gd basis can be used to define the solution space for a discontinuous galerkin finite element discretization of partial differential equations in this work we propose two approaches to handling complex geometries within this setting 1 using nonconforming curvilinear gd elements and 2 coupling affine gd elements with curvilinear simplicial elements in both cases the semidiscrete discontinuous galerkin method is provably energy stable even when variational crimes are committed additionally for both element types a weight adjusted mass matrix is used which ensures that only the reference mass matrix must be inverted we also present sufficient conditions on the treatment of metric terms for the curvilinear nonconforming gd elements to ensure that the scheme is both constant preserving and conservative numerical experiments confirm the stability results and demonstrate the accuracy of the coupled schemes

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

chaos and asymptotical stability in discrete time neural networks abstract this paper aims to theoretically prove by applying marotto s theorem that both transiently chaotic neural networks tcnn and discrete time recurrent neural networks drnn have chaotic structure a significant property tcnn and drnn is that they have only one bounded fixed point when absolute values of the self feedback connection weights in tcnn and the difference time in drnn are sufficiently large we show that this unique fixed point can actually evolve into a snap back repeller which generates chaotic structure if several conditions are satisfied on the other hand by using the lyapunov functions we also derive sufficient conditions on asymptotical stability for symmetrical versions of both tcnn and drnn under which tcnn and drnn asymptotically converge to a fixed point furthermore related bifurcations are also considered in this paper since both tcnn and drnn are not special but simple and general the obtained theoretical results hold for a wide class of discrete time neural networks to demonstrate the theoretical results of this paper better several numerical simulations are provided as illustrating examples

robust asymptotic stability of uncertain fuzzy bam neural networks with time varying delays via ordinary takagi sugeno ts fuzzy models complex nonlinear systems can be represented to a set of linear sub models by using fuzzy sets and fuzzy reasoning in this paper the global asymptotic stability problem of ts fuzzy bi directional associative memories bam neural networks with time varying delays and parameter uncertainties is considered first the model of ts fuzzy bam neural networks with time varying delays and parameter uncertainties is established as a modified ts fuzzy model in which the consequent parts are composed of a set of bam neural networks with time varying delays secondly the globally robust asymptotically stable condition is presented in terms of linear matrix inequalities which can be easily solved by some standard numerical packages two numerical examples are also given to validate the theoretical results

almost solubility of lie algebras with almost regular automorphisms the well known theorem of borel mostow kreknin on solubility of lie algebras with regular automorphisms is generalized to the case of almost regular automorphisms it is proved that if a lie algebra l admits an automorphism of finite order n with finite dimensional fixed point subalgebra of dimension dimcl m then l has a soluble ideal of derived length bounded by a function of n whose codimension is bounded by a function of m and n theorem 1 a virtually equivalent formulation is in terms of a n graded lie algebra l whose zero component l0 has finite dimension m the functions of n and of m and n in theorem 1 can be given explicit upper estimates the proof is of combinatorial nature and uses the criterion for solubility of lie rings with an automorphism obtained in e i khukhro siberian math j 42 2001 996 1000 the method of generalized or graded centralizers is developed which was originally created in e i khukhro math ussr sbornik 71 1992 51 63 for almost regular automorphisms of prime order as a corollary we prove a result analogous to theorem 1 on locally nilpotent torsion free groups admitting an automorphism of finite order with the fixed points subgroup of finite rank theorem 3 we also prove an analogous result for lie rings with an automorphism of finite order having finitely many fixed points theorem 2 2003 elsevier inc all rights reserved

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

stability and bifurcation in a neural network model with two delays abstract a simple neural network model with two delays is considered linear stability of the model is investigated by analyzing the associated characteristic transcendental equation for the case without self connection it is found that the hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values the stability and direction of the hopf bifurcation are determined by applying the normal form theory and the center manifold theorem an example is given and numerical simulations are performed to illustrate the obtained results

exponential stability for uncertain cellular neural networks with discrete and distributed time varying delays in this paper the problem of exponential stability of uncertain cellular neural networks with discrete and distribute time varying delays is considered based on the lyapunov function method and convex optimization approach a new delay dependent stability criterion with an exponential convergence rate is derived in terms of lmi linear matrix inequality three numerical examples are given to show the effectiveness of the proposed methods

galerkin differences for acoustic and elastic wave equations in two space dimensions abstract the galerkin difference method a finite element method built using standard galerkin projection techniques but employing nonstandard basis functions was originally developed for one space dimension in 1 here the method is extended to two space dimensions using a tensor product construction theoretical and computational evidence shows the method behaves as expected for the acoustic wave equation for the elastic wave equation the approximations are found to be at least as accurate as predicted but with a free surface the scheme may exhibit an unexpected superconvergence extension to curvilinear mapped grids is also considered for acoustics in all cases the use of a tensor product construction allows for efficient solution of the linear system involving the mass matrix which implies optimal linear time solutions with respect to the number of degrees of freedom

global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays by employing the lyapunov krasovskii functional and linear matrix inequality lmi approach the problem of global asymptotical stability is studied for recurrent neural networks with both discrete time varying delays and distributed time varying delays some sufficient conditions are given for checking the global asymptotical stability of recurrent neural networks with mixed time varying delay the proposed lmi result is computationally efficient as it can be solved numerically using standard commercial software two examples are given to show the usefulness of the results

on almost regular automorphisms of finite p groups abstract in this paper we prove that there are functions f p m n and h m such that any finite p group with an automorphism of order p n whose centralizer has p m points has a subgroup of derived length h m and index f p m n this result gives a positive answer to a problem raised by e i khukhro see also problem 14 96 from the kourovka notebook 1999 e i khukhro and v d mazurov eds the kourovka notebook unsolved problems in group theory 14th ed novosibirsk

finite groups and lie rings with a metacyclic frobenius group of automorphisms abstract suppose that a finite group g admits a frobenius group of automorphisms fh of coprime order with cyclic kernel f and complement h such that the fixed point subgroup c g h of the complement is nilpotent of class c it is proved that g has a nilpotent characteristic subgroup of index bounded in terms of c c g f and f whose nilpotency class is bounded in terms of c and h only this generalizes the previous theorem of the authors and p shumyatsky where for the case of c g f 1 the whole group was proved to be nilpotent of c h bounded class examples show that the condition of f being cyclic is essential results based on the classification provide reduction to soluble groups then representation theory arguments are used to bound the index of the fitting subgroup lie ring methods are used for nilpotent groups a similar theorem on lie rings with a metacyclic frobenius group of automorphisms fh is also proved

a low storage curvilinear discontinuous galerkin method for wave problems the low storage curvilinear discontinuous galerkin lsc dg method reduces the storage requirements for solving symmetric and linear linear symmetric conservation laws in curvilinear domains when compared to the standard discontinuous galerkin method we perform a semidiscrete a priori convergence analysis of lsc dg and determine sufficient conditions on sequences of meshes to guarantee the same rate of convergence as the original upwind dg method on curvilinear domains computational results confirm the optimal order convergence on sample mesh sequences that satisfy the sufficiency conditions additional results show that the sufficient conditions for optimal order convergence of lsc dg may also be necessary conditions

on discretely entropy stable weight adjusted discontinuous galerkin methods curvilinear meshes abstract we construct entropy conservative and entropy stable discontinuous galerkin dg discretizations for time dependent nonlinear hyperbolic conservation laws on curvilinear meshes the resulting schemes preserve a semi discrete quadrature approximation of a continuous global entropy inequality the proof requires the satisfaction of a discrete geometric conservation law which we enforce through an appropriate polynomial approximation we extend the construction of entropy conservative and entropy stable dg schemes to the case when high order curvilinear mass matrices are approximated using low storage weight adjusted approximations and describe how to retain global conservation properties under such an approximation for certain types of curvilinear meshes these weight adjusted approximations deliver optimal rates of convergence finally the high order accuracy local conservation and discrete conservation or dissipation of entropy for under resolved solutions are verified through numerical experiments for the compressible euler equations on triangular and tetrahedral meshes

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

stabilization role of inhibitory self connections in a delayed neural network abstract in a delayed hopfield neural network that is strongly connected with non inhibitory interconnections fast and inhibitory self connections lead to global convergence to a unique equilibrium of the network by applying monotone dynamical systems theory and an embedding technique we prove that this conclusion remains true without the requirement of strong connectivity or non inhibitory interconnections

dynamics of cohen grossberg neural networks with variable and distributed delays abstract this paper is concerned with the analysis problem for the exponential stability of a class of cohen grossberg neural networks with variable and distributed delays some sufficient conditions ensuring the existence uniqueness and exponential stability of the equilibrium point are obtained by employing brouwer s fixed point theorem and by applying the inequality technique in the results we do not assume that the activation function satisfies the boundedness and the lipschitz condition three numerical examples are given to show the effectiveness of the obtained results

global dynamics of neural nets with infinite gain abstract we consider a model of neural and gene networks where the nonlinearities in the system of differential equations are discontinuous and piecewise constant we develop a framework for study of such systems as a first step we associate to the system a graph g on a hypercube and show how the collection of strongly connected components of g relates to the dynamics of the flow on the set of rays through the origin in the second step we discuss the relationship between the invariant sets of the ray flow and the invariant sets of the original flow we provide a sufficient condition for a one to one correspondence between these sets finally we study the class of binary networks within this framework under certain conditions we can determine the structure of an invariant set corresponding to the lowest strongly connected component of the hypercube graph

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

global exponential stability in continuous time and discrete time delayed bidirectional neural networks convergence dynamics of continuous time bidirectional neural networks with constant transmission delays are studied without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions lyapunov functionals and halanay type inequalities are constructed and employed to derive delay independent sufficient conditions under which the continuous time networks converge exponentially to the equilibria associated with temporally uniform external inputs to the networks discrete time analogues of the continuous time networks are formulated and we study their dynamical characteristics it is shown that the convergence dynamics of the continuous time networks are preserved by the discrete time analogues without any restriction on the discretization step size several examples are given to illustrate the advantages of the discrete time analogues in numerically simulating the continuous time networks

stable coupling of nonconforming high order finite difference methods a methodology for handling block to block coupling of nonconforming multiblock summation by parts finite difference methods is proposed the coupling is based on the construction of projection operators that move a finite difference grid solution along an interface to a space of piecewise defined functions we specifically consider discontinuous piecewise polynomial functions the constructed projection operators are compatible with the underlying summation by parts energy norm using the linear wave equation in two dimensions as a model problem energy stability of the coupled numerical method is proven for the case of curved nonconforming block to block interfaces to further demonstrate the power of the coupling procedure we show how it allows for the development of a provably energy stable coupling between curvilinear finite difference methods and a curved triangle discontinuous galerkin method the theoretical results are verified through numerical simulations on curved meshes as well as eigenval

solving optimization problems with variable constraint by an extended cohen grossberg model abstract a variety of real world problems can be formulated as continuous optimization problems with variable constraint it is however well known that it is quite hard to develop a unified method for obtaining their feasible solutions we have recognized that the recent work of solving the traveling salesman problem by the hopfield model explores an innovative approach to them as well as combinatorial optimization problems the hopfield model is generalized into the cohen grossberg model to which a specific liapunov function has been found this paper thus extends the hopfield method onto the cohen grossberg model in order to develop a unified solving method of continuous optimization problems with variable constraint specifically we consider a certain class of continuous optimization problems with a constraint equation including the hopfield version of the traveling salesman problem as a particular member then we theoretically develop a method that from any given problem of that class derives a network of an extended cohen grossberg model to provide feasible solutions to it the main idea for constructing that extended cohen grossberg model lies in adding to the cohen grossberg model a synapse dynamical system concurrently operating with its current unit dynamical system so that the constraint equation can be enforced to satisfaction at final states this construction is also motivated by previous neuron models in biophysics and learning algorithms in neural networks

delay dependent state estimation for delayed neural networks in this letter the delay dependent state estimation problem for neural networks with time varying delay is investigated a delay dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable the proposed method is based on the free weighting matrix approach and is applicable to the case that the derivative of a time varying delay takes any value an algorithm is presented to compute the state estimator finally a numerical example is given to demonstrate the effectiveness of this approach and the improvement over existing ones

stability in delayed cohen grossberg neural networks lmi optimization approach in this paper stability problems are further discussed for a class of delayed cohen grossberg neural networks on the basis of the linear matrix inequality lmi optimization approach and also the lyapunov krasovskii functional method combined with the halanay inequality technique several new sufficient criteria are given for ascertaining the global asymptotic stability and exponential stability of the equilibrium point for this system the proposed results are less restrictive than those given in the earlier literature and are easier to verify in practice in addition four examples and their numerical simulations are given two of them are used to demonstrate the effectiveness of the proposed results and another two show that there exist stable bifurcating periodic solutions if the given conditions do not hold

new delay dependent stability criteria for neural networks with time varying delay using delay decomposition approach this brief is concerned with the problem of asymptotic stability of neural networks with time varying delays the activation functions are monotone nondecreasing with known lower and upper bounds novel stability criteria are derived by employing new lyapunov krasovskii functional and the integral inequality the developed stability criteria have delay dependencies and the results are characterized by linear matrix inequalities new and less conservative solutions to the global stability problem are provided in terms of feasibility testing numerical examples are finally given to demonstrate the effectiveness of the proposed method

taming the cfl number for discontinuous galerkin methods on structured meshes the upwind discontinuous galerkin method is an attractive method for solving time dependent hyperbolic conservation laws it is possible to use high order explicit time stepping methods and high order spatial approximations without incurring heavy numerical linear algebra overheads however the courant friedrichs lewy cfl condition for these methods depends on the polynomial order used and there is a somewhat excessive cost for using very high order spatial approximation we discuss the impact of a covolume mesh based filter on the cfl number for these methods and present an algorithm which has a cfl number independent of the spatial order of approximation we present computational results for the advection equation and the wave equation on one dimensional meshes using up to tenth order in space and time

cycle symmetric matrices and convergent neural networks abstract this work investigates a class of neural networks with cycle symmetric connection strength we shall show that by changing the coordinates the convergence of dynamics by fiedler and gedeon physica d 111 1998 288 is equivalent to the classical results this presentation also addresses the extension of the convergence theorem to other classes of signal functions with saturations in particular the result of cohen and grossberg ieee trans syst man cybernet smc 13 1983 815 is recast and extended with a more concise verification

almost nilpotency of an associative algebra with an almost nilpotent fixed point subalgebra abstract let a be an associative algebra of arbitrary dimension over a field f and g a finite group of automorphisms of a of order n prime to the characteristic of f denote by a g a a a g a for all g g the fixed point subalgebra by the classical bergman isaacs theorem if a g is nilpotent of index d i e a g d 0 then a is also nilpotent and its nilpotency index is bounded by a function depending only on n and d we prove under the additional assumption of solubility of g that if a g contains a two sided nilpotent ideal i a g of nilpotency index d and of finite codimension m in a g then a contains a nilpotent two sided ideal h a of nilpotency index bounded by a function of n and d and of finite codimension bounded by a function of m n and d an even stronger result is provided for graded associative algebras if g is a finite not necessarily soluble group of order n and a g g a g is a g graded associative algebra over a field f i e a g a h a g h such that the identity component a e has a two sided nilpotent ideal i e a g of nilpotency index d and of finite codimension m in a e then a has a homogeneous nilpotent two sided ideal h a of nilpotency index bounded by a function of n and d and of finite codimension bounded by a function of n d and m

on the superconvergence of galerkin methods for hyperbolic ibvp finite element galerkin methods using b splines of order r for periodic first order hyperbolic equations exhibit superconvergence on uniform grids mesh size h at the nodes i e there is an error estimate cal o h 2r instead of the expected convergence rate cal o h r in this paper it will be shown that no matter how the approximating subspace s h is modified in a boundary layer 0 s 1 h s arbitrary but fixed the superconvergence property is lost for the hyperbolic model problem u t u x 0 leq x infty t geq 0 we shall also discuss the implications of this result when constructing compact implicit difference schemes

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

global stability for cellular neural networks with time delay a sufficient condition related to the existence of a unique equilibrium point and its global asymptotic stability for cellular network networks with delay dcnns is derived it is shown that the condition relies on the feedback matrices and is independent of the delay parameter furthermore this condition is less restrictive than that given in the literature

generalized lyapunov approach for convergence of neural networks with discontinuous or non lipschitz activations the paper considers a class of additive neural networks where the neuron activations are modeled by discontinuous functions or by continuous non lipschitz functions some tools are developed which enable us to apply a lyapunov like approach to differential equations with discontinuous right hand side modeling the neural network dynamics the tools include a chain rule for computing the time derivative along the neural network solutions of a nondifferentiable lyapunov function and a comparison principle for this time derivative which yields conditions for exponential convergence or convergence in finite time by means of the lyapunov like approach a general result is proved on global exponential convergence toward a unique equilibrium point of the neural network solutions moreover new results on global convergence in finite time are established which are applicable to neuron activations with jump discontinuities or neuron activations modeled by means of continuous non lipschitz holder functions

a class of convergent neural network dynamics abstract we consider a class of systems of differential equations in r n which exhibits convergent dynamics we find a lyapunov function and show that every bounded trajectory converges to the set of equilibria our result generalizes the results of cohen and grossberg 1983 for convergent neural networks it replaces the symmetry assumption on the matrix of weights by the assumption on the structure of the connections in the neural network we prove the convergence result also for a large class of lotka volterra systems these are naturally defined on the closed positive orthant we show that there are no heteroclinic cycles on the boundary of the positive orthant for the systems in this class

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

a spectral element method for fluid dynamics laminar flow in a channel expansion a spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible navier stokes equations in the spectral element discretization the computational domain is broken into a series of elements and the velocity in each element is represented as a high order lagrangian interpolant through chebyshev collocation points the hyperbolic piece of the governing equations is then treated with an explicit collocation scheme while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle the implementation of the technique is demonstrated on a one dimensional inflow outflow advection diffusion equation and the method is then applied to laminar two dimensional separated flow in a channel expansion comparisons are made with experiment and previous numerical work

robust exponential stability of uncertain fuzzy cohen grossberg neural networks with time varying delays in this paper the takagi sugeno t s fuzzy model representation is extended to the stability analysis for uncertain cohen grossberg neural networks cgnns with time varying delays a novel linear matrix inequality lmi based stability criterion is obtained by using lyapunov functional theory to guarantee the exponential stability of uncertain cgnns with time varying delays which are represented by t s fuzzy models finally the proposed stability conditions are demonstrated with numerical examples

multi patch discontinuous galerkin isogeometric analysis for wave propagation explicit time stepping and efficient mass matrix inversion abstract we present a class of spline finite element methods for time domain wave propagation which are particularly amenable to explicit time stepping the proposed methods utilize a discontinuous galerkin discretization to enforce continuity of the solution field across geometric patches in a multi patch setting which yields a mass matrix with convenient block diagonal structure over each patch we show how to accurately and efficiently invert mass matrices in the presence of curved geometries by using a weight adjusted approximation of the mass matrix inverse this approximation restores a tensor product structure while retaining provable high order accuracy and semi discrete energy stability we also estimate the maximum stable timestep for spline based finite elements and show that the use of spline spaces results in less stringent cfl restrictions than equivalent c 0 or discontinuous finite element spaces finally we explore the use of optimal knot vectors based on l 2 n widths we show how the use of optimal knot vectors can improve both approximation properties and the maximum stable timestep and present a simple heuristic method for approximating optimal knot positions numerical experiments confirm the accuracy and stability of the proposed methods

a note on stability of analog neural networks with time delays this note presents a generalized sufficient condition which guarantees stability of analog neural networks with time delays the condition is derived using a lyapunov functional and the stability criterion is stated as the equilibrium of analog neural networks with delays is globally asymptotically stable if the product of the norm of connection matrix and the maximum neuronal gain is less than one

lie type algebras with an automorphism of finite order abstract an algebra l over a field f in which product is denoted by is called a lie type algebra if for all elements a b c l there exist f depending on a b c such that 0 and a b c a b c a c b examples of lie type algebras include associative algebras lie algebras leibniz algebras etc it is proved that if a lie type algebra l admits an automorphism of finite order n with finite dimensional fixed point subalgebra of dimension m then l has a soluble ideal of finite codimension bounded in terms of n and m and of derived length bounded in terms of n

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

lmi based stability criteria for neural networks with multiple time varying delays abstract in this paper the stability of neural networks with multiple time varying delays is studied a new class of lyapunov krasovskii functionals is constructed and the s procedure and free weighting matrix method are employed to derive a delay dependent stability criterion from which a delay independent criterion is obtained as a special case moreover the result is also extended to delay dependent and rate independent stability criteria for multiple unknown time varying delays finally numerical examples are given to illustrate the effectiveness of our methods and improvement over the existing ones

simple central pattern generator model using phasic analog neurons many biological neurons called phasic or adapting neurons display neural adaptation their response to a constant input diminishes with time a simple method of adding adaptive firing thresholds to existing analog or graded response neural models is described a half center central pattern generator is modeled using two mutually inhibitory phasic analog neurons hopf bifurcation analysis shows that oscillatory solutions will arise if the mutual inhibition is sufficiently strong and allows us to characterize the stability of the cycles which arise

stability in asymmetric hopfield nets with transmission delays sufficient conditions are derived for the delay independent stability of the equilibria in hopfield s graded response networks of the type dxi t dt bixi t nj 1aijfj jxj t ij fi t i 1 2 n when the external inputs fi are held temporally uniform a generalization to continuously distributed delays is briefly indicated several illustrative examples are numerically simulated and the results of simulations are graphically displayed