on the characteristic polynomial of a random unitary matrix we present a range of fluctuation and large deviations results for the logarithm of the characteristic polynomial z of a random n n unitary matrix as n first we show that evaluated at a finite set of distinct points is asymptotically a collection of i i d complex normal random variables this leads to a refinement of a recent central limit theorem due to keating and snaith and also explains the covariance structure of the eigenvalue counting function next we obtain a central limit theorem for ln z in a sobolev space of generalised functions on the unit circle in this limiting regime lower order terms which reflect the global covariance structure are no longer negligible and feature in the covariance structure of the limiting gaussian measure large deviations results for ln z a evaluated at a finite set of distinct points can be obtained for for higher order scalings we obtain large deviations results for ln z a evaluated at a single point there is a phase transition at a ln n which only applies to negative deviations of the real part reflecting a switch from global to local conspiracy

multistability of second order competitive neural networks with nondecreasing saturated activation functions in this paper second order interactions are introduced into competitive neural networks nns and the multistability is discussed for second order competitive nns socnns with nondecreasing saturated activation functions firstly based on decomposition of state space cauchy convergence principle and inequality technique some sufficient conditions ensuring the local exponential stability of 2n equilibrium points are derived secondly some conditions are obtained for ascertaining equilibrium points to be locally exponentially stable and to be located in any designated region thirdly the theory is extended to more general saturated activation functions with 2r corner points and a sufficient criterion is given under which the socnns can have r 1 n locally exponentially stable equilibrium points even if there is no second order interactions the obtained results are less restrictive than those in some recent works finally three examples with their simulations are presented to verify the theoretical analysis

discrete analogue of high order periodic cohen grossberg neural networks with delay in this paper new discrete analogue of high order cohen grossberg neural networks with varying delay is obtained by analysis and approximation techniques the existence of periodic solution for discrete high order cohen grossberg neural networks with varying delay is studied by continuation theorem of coincidence degree theory and sufficient condition is given to guarantee global exponential stability of periodic solution finally an example is given to show the effectiveness of the results in this paper

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

asymptotical stability of stochastic neural networks with multiple time varying delays the stochastic neural networks can be considered as an expansion of cellular neural networks and hopfield neural networks in real world the neural networks are prone to be instable due to time delay and external disturbance in this paper we consider the asymptotic stability for the stochastic neural networks with multiple time varying delays by employing a lyapunov krasovskii function a sufficient condition which guarantees the asymptotic stability of the state trajectory in the mean square is obtained the criteria proposed can be verified readily by utilising the linear matrix inequality toolbox in matlab and no parameters to be tuned in the end two numerical examples are provided to demonstrate the effectiveness of the proposed method

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

delay dependent exponential stability for a class of neural networks with time delays this paper is concerned with the exponential stability of a class of delayed neural networks described by nonlinear delay differential equations of the neutral type in terms of a linear matrix inequality lmi a sufficient condition guaranteeing the existence uniqueness and global exponential stability of an equilibrium point of such a kind of delayed neural networks is proposed this condition is dependent on the size of the time delay which is usually less conservative than delay independent ones the proposed lmi condition can be checked easily by recently developed algorithms solving lmis examples are provided to demonstrate the effectiveness and applicability of the proposed criteria

random matrix theory and l functions at s 1 2 recent results of katz and sarnak 8 9 suggest that the low lying zeros of families of l functions display the statistics of the eigenvalues of one of the compact groups of matrices u n o n or usp 2n we here explore the link between the value distributions of the l functions within these families at the central point s 1 2 and those of the characteristic polynomials z u of matrices u with respect to averages over so 2n and usp 2n at the corresponding point 0 using techniques previously developed for u n in 10 for any matrix size n we find exact expressions for the moments of z u 0 for each ensemble and hence calculate the asymptotic large n value distributions for z u 0 and log z u 0 the asymptotic results for the integer moments agree precisely with the few corresponding values known for l functions the value distributions suggest consequences for the non vanishing of l functions at the central point

stability and periodicity in high order neural networks with impulsive effects abstract in this paper the global exponential stability and periodicity are investigated for a class generalized high order neural networks with time delays and impulses some sufficient conditions are derived for checking the global exponential stability and existence of periodic solutions for this system using the generalized halanay inequality mathematical induction and a fixed point theorem the criteria given are easily verified and possess many adjustable parameters which provides flexibility for the design and analysis of the system finally an example with numerical simulation is given to show the effectiveness of the proposed method and results

hopf bifurcation and stability of periodic solutions for van der pol equation with time delay abstract in this paper the van der pol equation with a time delay is considered where the time delay is regarded as a parameter it is found that hopf bifurcation occurs when this delay passes through a sequence of critical value a formula for determining the direction of the hopf bifurcation and the stability of bifurcating periodic solutions is given by using the normal form method and center manifold theorem

a random matrix model for elliptic curve l functions of finite conductor we propose a random matrix model for families of elliptic curve l functions of finite conductor a repulsion of the critical zeros of these l functions away from the centre of the critical strip was observed numerically by miller 2006 exp math 15 257 79 such behaviour deviates qualitatively from the conjectural limiting distribution of the zeros for large conductors this distribution is expected to approach the one level density of eigenvalues of orthogonal matrices after appropriate rescaling our purpose here is to provide a random matrix model for miller s surprising discovery we consider the family of even quadratic twists of a given elliptic curve the main ingredient in our model is a calculation of the eigenvalue distribution of random orthogonal matrices whose characteristic polynomials are larger than some given value at the symmetry point in the spectra we call this sub ensemble of so 2n the excised orthogonal ensemble the sieving off of matrices with small values of the characteristic polynomial is akin to the discretization of the central values of l functions implied by the formulae of waldspurger and kohnen zagier the cut off scale appropriate to modelling elliptic curve l functions is exponentially small relative to the matrix size n the one level density of the excised ensemble can be expressed in terms of that of the well known jacobi ensemble enabling the former to be explicitly calculated it exhibits an exponentially small on the scale of the mean spacing hard gap determined by the cut off value followed by soft repulsion on a much larger scale neither of these features is present in the one level density of so 2n when n we recover the limiting orthogonal behaviour our results agree qualitatively with miller s discrepancy choosing the cut off appropriately gives a model in good quantitative agreement with the number theoretical data

design of state estimator for bam fuzzy cellular neural networks with leakage and unbounded distributed delays in this paper the state estimation problem is studied for the bidirectional associative memory bam fuzzy cellular neural networks fcnns with delays where the delays include leakage and unbounded distributed delays the problem addressed is to estimate the neuron states through available output measurements such that for all admissible leakage and unbounded distributed delays the dynamics of the estimation error is globally asymptotically stable a delay dependent linear matrix inequality lmi criterion for the existence of the estimator is proposed by using the lyapunovkrasovskii functional method in addition the unknown gain matrix is determined by solving a delay dependent lmi finally numerical examples and simulations are provided to illustrate the effectiveness of the theoretical results

global stability of almost periodic solutions of hopfield neural networks with neutral time varying delays in this paper the global stability and almost periodicity are investigated for hopfield neural networks with neutral time varying delays some sufficient conditions are obtained for the existence and globally exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques the results of this paper are new and they complement previously known results

impulsive stabilization of high order hopfield type neural networks with time varying delays this paper studies the problems of global exponential stability for impulsive high order hopfield type neural networks nns with time varying delays by employing the lyapunov razumikhin technique some criteria ensuring global exponential stability are derived our results are then used to obtain some sufficient conditions under which some nns can be forced to converge by impulsive control numerical examples are also discussed to illustrate our results

new robust stability results for bidirectional associative memory neural networks with multiple time delays in this paper the robust stability problem is investigated for a class of bidirectional associative memory bam neural networks with multiple time delays by employing suitable lyapunov functionals and using the upper bound norm for the interconnection matrices of the neural network system some novel sufficient conditions ensuring the existence uniqueness and global robust stability of the equilibrium point are derived the obtained results impose constraint conditions on the system parameters of neural network independent of the delay parameters some numerical examples and simulation results are given to demonstrate the applicability and effectiveness of our results and to compare the results with previous robust stability results derived in the literature

periodic attractor for reactiondiffusion high order hopfield neural networks with time varying delays this paper is concerned with a class of reactiondiffusion high order hopfield neural networks with time varying delays subject to the dirichlet boundary condition in a bounded domain easily verifiable delay independent criteria are established to ensure the existence of periodic mild solutions and the global exponential stability of the periodic mild solutions is also discussed by using the exponential dissipation property of semigroup of operators the obtained results are easy to check and they effectually complement previously known results a numerical example is given to show the effectiveness of theoretical results

model order reduction with preservation of passivity non expansivity and markov moments a new model order reduction technique is presented which preserves passivity and non expansivity it is a projection based method which exploits the solution of linear matrix inequalities to generate a descriptor state space format which preserves positive realness and bounded realness in the case of both non singular and singular systems solving the linear matrix inequality can be replaced by equivalently solving an algebraic riccati equation which is known to be a more efficient approach a new algebraic riccati equation and a frequency inversion technique are also presented to specifically deal with the important singular case the preservation of markov moments is also guaranteed by the judicious choice of a projection matrix three pertinent examples comparing the present approach with positive real balanced truncation show the strength and accuracy of the present approach

dynamics of high order bam neural networks with and without impulses the main aim of this paper is to study the existence and global exponential stability of periodic solution for high order bidirectional associative memory bam neural networks with and without impulses easily verifiable sufficient conditions are established the method is based on coincidence degree theory as well as a priori estimates and lyapunov functional it is shown that the convergence characteristics of periodic solution for the impulsive system are preserved by the corresponding nonimpulsive system with some restriction imposed on the impulse effect numerical simulation results are given to support the theoretical predictions

krylov subspace methods for reduced order modeling in circuit simulation the simulation of electronic circuits involves the numerical solution of very large scale sparse in general nonlinear systems of differential algebraic equations often the size of these systems can be reduced considerably by replacing the equations corresponding to linear subcircuits by approximate models of much smaller state space dimension in this paper we describe the use of krylov subspace methods for generating such reduced order models of linear subcircuits particular emphasis is on reduced order modeling techniques that preserve the passivity of linear rlc subcircuits

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

mixed time delays dependent exponential stability for uncertain stochastic high order neural networks this paper presents a discrete and distributed time delays dependent simultaneous approach to deterministic and uncertain stochastic high order neural networks new results are proposed in terms of linear matrix inequality lmi by exploiting a novel lyapunov krasovskii functional and by making use of novel techniques for time delay systems some constraints of systems are removed and new results cover some recently published works two numerical examples are given to show the usefulness of presented approach

exponential stability of delayed bi directional associative memory networks some sufficient conditions are derived for the global exponential stability in delayed bi directional associative memory bam networks by constructing suitable lyapunov functional and the inequality 2ab

a hybrid euler hadamard product for the riemann zeta function we use a smoothed version of the explicit formula to find an accurate pointwise approximation to the riemann zeta function as a product over its nontrivial zeros multiplied by a product over the primes we model the first product by characteristic polynomials of random matrices this provides a statistical model of the zeta function which involves the primes in a natural way we then employ the model in a heuristic calculation of the moments of the modulus of the zeta function on the critical line for the second and fourth moments we establish all of the steps in our approach rigorously this calculation illuminates recent conjectures for these moments based on connections with random matrix theory

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

periodic solutions for a class of higher order cohen grossberg type neural networks with delays sufficient conditions are obtained for the existence and global attractivity of periodic solutions of a class of higher order cohen grossberg type neural networks with delays the proof is based on gaines and mawhin s continuation theorem of coincidence degree theory the lyapunov functional and a nonsingular m matrix one example is exploited to illustrate the effectiveness of the proposed criteria

neural network for quadratic optimization with bound constraints a recurrent neural network is presented which performs quadratic optimization subject to bound constraints on each of the optimization variables the network is shown to be globally convergent and conditions on the quadratic problem and the network parameters are established under which exponential asymptotic stability is achieved through suitable choice of the network parameters the system of differential equations governing the network activations is preconditioned in order to reduce its sensitivity to noise and to roundoff errors the optimization method employed by the neural network is shown to fall into the general class of gradient methods for constrained nonlinear optimization and in contrast with penalty function methods is guaranteed to yield only feasible solutions

delay dependent stability and h control for uncertain discrete switched singular systems with time delay abstract the robust stability robust stabilization and h control problems for time delay discrete switched singular systems with parameter uncertainties are discussed based on the restricted system equivalent r s e transformation and by introducing new state vectors the switched singular system is transformed into a switched standard linear system and delay dependent linear matrix inequality lmi conditions for the time delay discrete time switched singular systems to be regular causal and uniformly asymptotically stable uniformly robust asymptotically stable with disturbance attenuation are obtained respectively with these conditions robust stabilization problem and robust h control problem are solved based on lmis

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

a delayed neural network for solving linear projection equations and its analysis in this paper we present a delayed neural network approach to solve linear projection equations the lyapunov krasovskii theory for functional differential equations and the linear matrix inequality lmi approach are employed to analyze the global asymptotic stability and global exponential stability of the delayed neural network compared with the existing linear projection neural network theoretical results and illustrative examples show that the delayed neural network can effectively solve a class of linear projection equations and some quadratic programming problems

global attractivity in delayed hopfield neural network models two different approaches are employed to investigate the global attractivity of delayed hopfield neural network models without assuming the monotonicity and differentiability of the activation functions liapunov functionals and functions combined with the razumikhin technique are constructed and employed to establish sufficient conditions for global asymptotic stability independent of the delays in the case of monotone and smooth activation functions the theory of monotone dynamical systems is applied to obtain criteria for global attractivity of the delayed model such criteria depend on the magnitude of delays and show that self inhibitory connections can contribute to the global convergence

equivalence of laguerre based model order reduction and moment matching the equivalence between the classical moment matching and the laguerre based reduction approaches is shown in addition this equivalence is generalized to include a family of coefficients known as generalized markov parameters

extreme values of the riemann zeta function and its argument we combine our version of the resonance method with certain convolution formulas for zeta s and log zeta s this leads to a new omega result for zeta 1 2 it the maximum of zeta 1 2 it on the interval 1 le t le t is at least exp left 1 o 1 sqrt log t log log log t log log t right we also obtain conditional results for s t 1 pi times the argument of zeta 1 2 it and s 1 t int 0 t s tau d tau on the riemann hypothesis the maximum of s t is at least c sqrt log t log log log t log log t and the maximum of s 1 t is at least c 1 sqrt log t log log log t log log t 3 on the interval t beta le t le t whenever 0 le beta 1

the maximum size of l functions we conjecture the true rate of growth of the maximum size of the riemann zeta function and other l functions we support our conjecture using arguments from random matrix theory conjectures for moments of l functions and also by assuming a random model for the primes

robust h control for a generic linear rational expectations model of economy large time delay and small disturbance attenuation are very important for macroeconomic system this paper is concerned with the problem of robust h control with large time delay and small disturbance attenuation for a generic linear rational expectations model of economy with uncertainties time varying delay and random shocks the norm bounded uncertainties are used to describe the uncertainties of economic system the concept of two levels of conservatism and the approach of parameters weak coupling linear matrix inequalities pwclmis are developed in this paper the result is presented in terms of pwclmis in this note large time delay and small disturbance attenuation are achieved without increasing conservatism of result furthermore according to the robust h result one will obtain various results readily by employing different games an example is given to show the benefit of the presented approach

bounding s t and s_1 t on the riemann hypothesis let pi s t denote the argument of the riemann zeta function zeta s at the point s frac 1 2 it assuming the riemann hypothesis we present two proofs of the bound begin aligned s t le left frac 1 4 o 1 right frac log t log log t end aligned for large t this improves a result of goldston and gonek by a factor of 2 the first method consists of bounding the auxiliary function s 1 t int 0 t s u text d u using extremal functions constructed by carneiro littmann and vaaler we then relate the size of s t to the size of the functions s 1 t pm h s 1 t when h asymp 1 log log t the alternative approach bounds s t directly relying on the solution of the beurling selberg extremal problem for the odd function f x arctan left frac 1 x right frac x 1 x 2 this draws upon recent work by carneiro and littmann

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

freezing transition characteristic polynomials of random matrices and the riemann zeta function we argue that the freezing transition scenario previously explored in the statistical mechanics of 1 f noise random energy models also determines the value distribution of the maximum of the modulus of the characteristic polynomials of large n ifmmode times else texttimes fi n random unitary matrices we postulate that our results extend to the extreme values taken by the riemann zeta function ensuremath zeta s over sections of the critical line s 1 2 it of constant length and present the results of numerical computations in support our main purpose is to draw attention to possible connections between the statistical mechanics of random energy landscapes random matrix theory and the theory of the riemann zeta function

uniform asymptotics of the coefficients of unitary moment polynomials keating and snaith showed that the 2kth absolute moment of the characteristic polynomial of a random unitary matrix evaluated on the unit circle is given by apolynomial of degree k2 in this articl

elliptic curves with large rank over function fields we produce explicit elliptic curves over fp t whose mordell weil groups have arbitrarily large rank our method is to prove the conjecture of birch and swinnerton dyer for these curves or rather the tate conjecture for related elliptic surfaces and then use zeta functions to determine the rank in contrast to earlier examples of shafarevitch and tate our curves are not isotrivial asymptotically these curves have maximal rank for their conductor motivated by this fact we make a conjecture about the growth of ranks of elliptic

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

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

state estimation for neural networks of neutral type with interval time varying delays in this paper the design problem of state estimator for a class of neural networks of neutral type with interval time varying delays is studied the interval time varying delay does not have constraint that its derivative is less than 1 the constraint is widely used to deal with time varying delays in many papers a delay dependent linear matrix inequality lmi criterion for existence of the estimator is proposed by using lyapunov method the criterion can be easily solved by various convex optimization algorithms a numerical example is given to show the effectiveness of proposed method

on controllability of delayed boolean control networks this paper is devoted to studying the trajectory and state controllability of boolean control networks bcns with time delay in contrast to bcns without time delay the dynamics of delayed bcns are determined by a sequence of initial states named here trajectories trajectory controllability means that there exists a control signal steering a system from an initial trajectory to a desired trajectory while state controllability means that there exists a control signal steering an initial state to a given state here both trajectory controllability and state controllability will be studied it should be noted that in this paper trajectory controllability does not mean tracking or following a given trajectory in fact it means to control bcns to a destination trajectory of length mu at the k th step using the semi tensor product of matrices the delayed bcns are first converted into an equivalent algebraic description and then some necessary and sufficient conditions are derived for the trajecto

matrix nearness based guaranteed passive system approximation abstract in this paper we present a new approach towards global passive approximation in order to find a passive real rational transfer function g s that is an arbitrarily close approximation of the passive transfer function nearest to a non passive square transfer function h s it is based on existing solutions to pertinent matrix nearness problems it is shown that the key point in constructing the passive real rational transfer function g s is to find a good rational approximation of the well known ramp function over an interval defined by the minimum and maximum dissipation of h s the proposed algorithms rely on the stable anti stable decomposition of a given transfer function pertinent examples are given to show the scope and accuracy of the proposed algorithms

novel global stability criteria for high order hopfield type neural networks with time varying delays abstract this paper discusses a generalized model of high order hopfield type neural networks with time varying delays some novel global stability criteria of the system is derived by using lyapunov method linear matrix inequality lmi and analytic technique the lmi based criteria obtained here are computationally more flexible and more generic than many other existing criteria a numerical example is given to illustrate our result

neural networks orientations of the hypercube and algebraic threshold functions a class of possible generalizations of current neural networks models is described using local improvement algorithms and orientations of graphs a notation of dynamical capacity is defined and by computing bounds on the number of algebraic threshold functions it is proven that for neural networks of size n and energy function of degree d this capacity is o n sup d 1 stable states are studied and it is shown that for the same networks the storage capacity is o n sup d 1 in the case of random orientations it is proven that the expected number of stable states is exponential applications to coding theory are indicated and it is shown that usual codes can be embedded in neural networks but only at high cost cycles and their storage are also examined

lmi optimization approach on stability for delayed neural networks of neutral type in this paper the global asymptotic stability of delayed cellular neural networks of neutral type is investigated a novel delay dependent criterion for the stability using the lyapunov stability theory and linear matrix inequality lmi framework is presented since the condition is dependent on the size of time delay it is usually less conservative than delay independent ones two numerical examples are given to show the effectiveness of proposed method

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 note on strict passivity we show that there exists an explicit descriptor state space format which actually describes all strictly passive transfer functions a key advantage of this explicitly strictly passive descriptor state space format resides in its relation with congruence projection based reduced order modeling where the resulting reduced order model is also cast in this same format another advantage of the format is that it allows for a simple construction of strictly passive random systems generators

stability and robust stabilization of discrete time switched systems with time delays lmi approach we present sufficient linear matrix inequality conditions for asymptotic stability and stabilizability of switched discrete time linear systems subject to time delays and norm bounded uncertainties namely if these lmis are solvable then the switched system is exponentially stable for arbitrary switching in fact we show that any family of switched time delay systems satisfying these conditions possesses a quadratic common lyapunov function we also discuss the implication of this result on the stabilizability of this class of systems by switching controllers that use common lyapunov functions we show that even the analysis is carried out through a common lyapunov function the applied controller is mode dependent

computational estimation of the order of frac 1 2 the paper describes a search for increasingly large extrema ile of 1 2 it in the range 0 t 10 13 for t 10 6 the complete set of ile 57 of them was determined in total 162 ile were found and they suggest that 1 2 it t 2 log t log t there are several regular patterns in the location of ile and arguments for these regularities are presented the paper concludes with a discussion of prospects for further computational progress

stability bifurcation and global existence of a hopf bifurcating periodic solution for a class of three neuron delayed network models in this paper a system of three delay differential equations representing a hopfield type general model for three neurons with two way bidirectional time delayed connections between the neurons and time delayed self connection from each neuron to itself is studied delay independent and delay dependent sufficient conditions for linear stability instability and the occurrence of a hopf bifurcation about the trivial equilibrium are addressed the partition of the resulting parametric space into regions of stability instability and hopf bifurcation in the absence of self connection is realized to extend the local hopf branches for large delay values a particular bidirectional delayed tri neuron model without self connection is investigated sufficient conditions for global existence of multiple non constant periodic solutions are obtained for such a model using the global hopf bifurcation theorem for functional differential equations due to j wu and the bendixson criterion for higher dimensional ordinary differential equations due to li and muldowney and following the approach developed by wei and li

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

further improvement of free weighting matrices technique for systems with time varying delay a novel method is proposed in this note for stability analysis of systems with a time varying delay appropriate lyapunov functional and augmented lyapunov functional are introduced to establish some improved delay dependent stability criteria less conservative results are obtained by considering the additional useful terms which are ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices the resulting criteria are extended to the stability analysis for uncertain systems with time varying structured uncertainties and polytopic type uncertainties numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

new convergence behavior of high order hopfield neural networks with time varying coefficients in this paper the convergence behavior of the delayed high order hopfield neural networks hhnns with time varying coefficients are considered some sufficient conditions are established to ensure that all solutions of the networks converge to zero point which are new and complement of previously known results

global asymptotic stability of high order hopfield type neural networks with time delays abstract this paper studies the problem of global asymptotic stability of a class of high order hopfield type neural networks with time delays by utilizing lyapunov functionals we obtain some sufficient conditions for the global asymptotic stability of the equilibrium point of such neural networks in terms of linear matrix inequality lmi numerical examples are given to illustrate the advantages of our approach

integral moments of l functions we give a new heuristic for all of the main terms in the integral moments of various families of primitive l functions the results agree with previous conjectures for the leading order terms our conjectures also have an almost identical form to exact expressions for the corresponding moments of the characteristic polynomials of either unitary orthogonal or symplectic matrices where the moments are defined by the appropriate group averages this lends support to the idea that arithmetical l functions have a spectral interpretation and that their value distributions can be modelled using random matrix theory numerical examples show good agreement with our conjectures

refinements of gal s theorem and applications abstract we give a simple proof of a well known theorem of gal and of the recent related results of aistleitner berkes and seip 1 regarding the size of gcd sums in fact our method obtains the asymptotically sharp constant in gal s theorem which is new our approach also gives a transparent explanation of the relationship between the maximal size of the riemann zeta function on vertical lines and bounds on gcd sums a point which was previously unclear furthermore we obtain sharp bounds on the spectral norm of gcd matrices which settles a question raised in 2 we use bounds for the spectral norm to show that series formed out of dilates of periodic functions of bounded variation converge almost everywhere if the coefficients of the series are in l 2 log log 1 l with 2 this was previously known with 4 and is known to fail for 2 we also develop a sharp carleson hunt type theorem for functions of bounded variations which settles another question raised in 1 finally we obtain almost sure bounds for partial sums of dilates of periodic functions of bounded variations improving 1

exponential stability of impulsive cellular neural networks with time delay via lyapunov functionals this paper investigates the problem of exponential stability for a class of impulsive cellular neural networks with time delay by dividing the network state variables into subgroups according to the characters of the neural networks some sufficient conditions for exponential stability are derived by lyapunov functionals and the method of variation of parameters these conditions are given in terms of some blocks of the interconnection matrix which extend and improve some of the known results in the literature our results show that impulses may be used to stabilize the cellular neural networks with time delay if they are not stable or exponentially stable on the other hand if impulses are input disturbances criteria on the magnitude and frequency of the impulses are also established to maintain the stability property of the original system our results generalize and improve some known results two examples with numerical simulations are given to illustrate our results

stability analysis of cohen grossberg neural network with both time varying and continuously distributed delays in this paper the cohen grossberg neural network model with both time varying and continuously distributed delays is considered without assuming both global lipschitz conditions on these activation functions and the differentiability on these time varying delays applying the idea of vector lyapunov function m matrix theory and inequality technique several new sufficient conditions are obtained to ensure the existence uniqueness and global exponential stability of equilibrium point for cohen grossberg neural network with both time varying and continuously distributed delays these results generalize and improve the earlier publications two numerical examples are given to show the effectiveness of the obtained results it is believed that these results are significant and useful for the design and applications of the cohen grossberg neural networks

lmi conditions for global asymptotic stability results for neutral type neural networks with distributed time delays abstract in this paper the global asymptotic stability of neutral type neural networks with unbounded distributed delays is analyzed by utilizing the lyapunov krasovskii functional and the linear matrix inequality lmi approach a new sufficient condition ensuring the global asymptotic stability for neutral type neural networks is obtained by using the powerful matlab lmi toolbox two examples are provided to illustrate the applicability of the stability results

extreme values of zeta and l functions we introduce a resonance method to produce large values of the riemann zeta function on the critical line and large and small central values of l functions

existence and global attractivity of almost periodic solution for cellular neural network with distributed delays this paper is devoted to the existence and global attractivity of almost periodic solution for a class of cellular neural network with distributed delays and variable coefficients some sufficient conditions ensuring the existence and global attractivity of almost periodic solution are derived by employing banach fixed point theory and using differential inequality technique the results allow for the consideration of all unbounded neuron signal functions but not necessarily surjective thus these conditions obtained have highly important significance in designs and applications of the networks we extend and improve previously known results an example is also worked out to demonstrate the advantages of our results

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

on the equivalence between strict positive realness and strict passivity of linear systems this technical note presents a proof of the equivalence between the strict passivity of linear time invariant lti controllable and observable systems and the strict positive realness of their transfer function matrices where the direct feedthrough d is possibly a non zero matrix although both properties guarantee asymptotic stability the former is a time domain condition and the latter is a frequency domain concept a numerical example illustrates our main results

lyapunov lanczos and inertia abstract we present a new proof of the inertia result associated with lyapunov equations furthermore we present a connection between the lyapunov equation and the lanczos process which is closely related to the schwarz form of a matrix we provide a method for reducing a general matrix to schwarz form in a finite number of steps o n 3 hence we provide a finite method for computing inertia without computing eigenvalues this scheme is unstable numerically and hence is primarily of theoretical interest

random matrix theory and ζ 1 2 it we study the characteristic polynomials z u of matrices u in the circular unitary ensemble cue of random matrix theory exact expressions for any matrix size n are derived for the moments of z and z z and from these we obtain the asymptotics of the value distributions and cumulants of the real and imaginary parts of log z as n in the limit we show that these two distributions are independent and gaussian costin and lebowitz 15 previously found the gaussian limit distribution for im log z using a different approach and our result for the cumulants proves a conjecture made by them in this case we also calculate the leading order n asymptotics of the moments of z and z z these cue results are then compared with what is known about the riemann zeta function s on its critical line re s 1 2 assuming the riemann hypothesis equating the mean density of the non trivial zeros of the zeta function at a height t up the critical line with the mean density of the matrix eigenvalues gives a connection between n and t invoking this connection our cue results coincide with a theorem of selberg for the value distribution of log 1 2 it in the limit t they are also in close agreement with numerical data computed by odlyzko 29 for large but finite t this leads us to a conjecture for the moments of 1 2 it finally we generalize our random matrix results to the circular orthogonal coe and circular symplectic cse ensembles