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

nonadditive conditional entropy and its significance for local realism based on the form invariance of the structures given by khinchin s axiomatic foundations of information theory and the pseudoadditivity of the tsallis entropy indexed by q the concept of conditional entropy is generalized to the case of nonadditive nonextensive composite systems the proposed nonadditive conditional entropy is classically nonnegative but can be negative in the quantum context indicating its utility for characterizing quantum entanglement a criterion deduced from it for separability of density matrices for validity of local realism is examined in detail by employing a bipartite spin 1 2 system it is found that the strongest criterion is obtained in the limit q

nonextensive triangle equality and other properties of tsallis relative entropy minimization kullback leibler relative entropy has unique properties in cases involving distributions resulting from relative entropy minimization tsallis relative entropy is a one parameter generalization of kullback leibier relative entropy in the nonextensive thermostatistics in this paper we present the properties of tsallis relative entropy minimization and present some differences with the classical case in the representation of such a minimum relative entropy distribution we highlight the use of the q product an operator that has been recently introduced to derive the mathematical structure behind the tsallis statistics one of our main results is the generalization of triangle equality of relative entropy minimization to the nonextensive case

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

quantum work fluctuations versus macrorealism in terms of non extensive entropies abstract fluctuations of the work performed on a driven quantum system can be characterized by the so called fluctuation theorems the jarzynski relation and the crooks theorem are famous examples of exact equalities characterizing non equilibrium dynamics such statistical theorems are typically formulated in a similar manner in both classical and quantum physics leggett garg inequalities are inspired by the two assumptions referred to as the macroscopic realism and the non invasive measurability together these assumptions are known as the macrorealism in the broad sense quantum mechanics is provably incompatible with restrictions of the leggett garg type it turned out that leggett garg inequalities can be used to distinguish quantum and classical work fluctuations we develop this issue with the use of entropic functions of the tsallis type varying the entropic parameter we are often able to reach more robust detection of violations of the corresponding leggett garg inequalities in reality all measurement devices suffer from losses within the entropic formulation detection inefficiencies can naturally be incorporated into the consideration this question also shows advantages that are provided due to the use of generalized entropies

unified entropic measures of quantum correlations induced by local measurements we introduce quantum correlation measures based on the minimal change in unified entropies induced by local rank one projective measurements divided by a factor that depends on the generalized purity of the system in the case of nonadditive entropies in this way we overcome the issue of the artificial increasing of the value of quantum correlation measures based on nonadditive entropies when an uncorrelated ancilla is appended to the system without changing the computability of our entropic correlation measures with respect to the previous ones moreover we recover as limiting cases the quantum correlation measures based on von neumann and renyi entropies i e additive entropies for which the adjustment factor becomes trivial in addition we distinguish between total and semiquantum correlations and obtain some inequalities between them finally we obtain analytical expressions of the entropic correlation measures for typical quantum bipartite systems

asymptotic stability of the stationary solution to the compressible navier stokes equations in the half space we investigate the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for the compressible navier stokes equation in a half space the main concern is to analyze the phenomena that happens when the fluid blows out through the boundary thus it is natural to consider the problem in the eulerian coordinate we have obtained the two results for this problem the first result is concerning the existence of the stationary solution we present the necessary and sufficient condition which ensures the existence of the stationary solution then it is shown that the stationary solution is time asymptotically stable if an initial perturbation is small in the suitable sobolev space the second result is proved by using an l 2 energy method with the aid of the poincare type inequality

nonlinear stability of rarefaction waves for compressible navier stokes equations it is shown that expansion waves for the compressible navier stokes equations are nonlinearly stable the expansion waves are constructed for the compressible euler equations based on the inviscid burgers equation our result shows that navier stokes equations and euler equations are time asymptotically equivalent on the level of expansion waves the result is proved using the energy method making essential use of the expansion of the underlining nonlinear waves and the specific form of the constitutive eqution for a polytropic gas

properties of q entropies basic properties of the q entropy sq q 1 1 1 tr q 0 q 1 for states of a quantum system are established concavity quasi convexity continuity and failure of additivity and subadditivity for composite systems

information theoretic bell inequalities we formulate information theoretic bell inequalities which apply to any pair of widely separated physical systems if local realism holds the two systems must carry information consistent with the inequalities two spin s particles in a state of zero total spin violate these information bell inequalities

stability of boundary layer and rarefaction wave to an outflow problem for compressible navier stokes equations under large perturbation abstract in this paper we investigate the large time behavior of solutions to an outflow problem for compressible navier stokes equations in 2003 kawashima nishibata and zhu s kawashima s nishibata p zhu asymptotic stability of the stationary solution to the compressible navier stokes equations in the half space comm math phys 240 2003 483 500 showed there exists a boundary layer i e stationary solution to the outflow problem and the boundary layer is nonlinearly stable under small initial perturbation in the present paper we show that not only the boundary layer above but also the superposition of a boundary layer and a rarefaction wave are stable under large initial perturbation the proofs are given by an elementary energy method

asymptotic stability of nonlinear wave for the compressible navier stokes equations in the half space in the present paper we investigate the large time behavior of the solution to an initial boundary value problem for the isentropic compressible navier stokes equations in the eulerian coordinate in the half space this is one of the series of papers by the authors on the stability of nonlinear waves for the outflow problem of the compressible navier stokes equations some suitable assumptions are made to guarantee that the time asymptotic state is a nonlinear wave which is the superposition of a stationary solution and a rarefaction wave employing the l2 energy method and making use of the techniques from the paper s kawashima y nikkuni stability of rarefaction waves for the discrete boltzmann equations adv math sci appl 12 1 2002 327 353 we prove that this nonlinear wave is nonlinearly stable under a small perturbation the complexity of nonlinear wave leads to many complicated terms in the course of establishing the a priori estimates however those terms are of two basic types and the terms of each type are good and can be evaluated suitably by using the decay in both time and space variables estimates of each component of nonlinear wave

global exponential stability of cohen grossberg neural networks with piecewise constant argument of generalized type and impulses in this letter we consider a model of cohen grossberg neural networks with piecewise constant argument of generalized type and impulses sufficient conditions ensuring the existence and uniqueness of solutions are obtained based on constructing a new differential inequality with piecewise constant argument and impulse and using the lyapunov function method we derive sufficient conditions ensuring the global exponential stability of equilibrium point with approximate exponential convergence rate an example is given to illustrate the validity and advantage of the theoretical results

generalized quantum entropy the generalized quantum entropies are introduced in this paper some important properties such as nonnegativity continuity and concavity are proved but different from the von neumann entropy the subadditivity and additivity fail for the quantum unified r s entropy in general

contact discontinuity with general perturbations for gas motions the contact discontinuity is one of the basic wave patterns in gas motions the stability of contact discontinuities with general perturbations for the navier stokes equations and the boltzmann equation is a long standing open problem general perturbations of a contact discontinuity may generate diffusion waves which evolve and interact with the contact wave to cause analytic difficulties in this paper we succeed in obtaining the large time asymptotic stability of a contact wave pattern with a convergence rate for the navier stokes equations and the boltzmann equation in a uniform way one of the key observations is that even though the energy norm of the deviation of the solution from the contact wave may grow at the rate it can be compensated by the decay in the energy norm of the derivatives of the deviation which is of the order of thus this reciprocal order of decay rates for the time evolution of the perturbation is essential to close the a priori estimate containing the uniform bounds of the l8 norm on the lower order estimate and then it gives the decay of the solution to the contact wave pattern

nonlinear stability of rarefaction waves for the compressible navier stokes equations with large initial perturbation the expansion waves for the compressible navier stokes equations have recently been shown to be nonlinear stable the nonlinear stability results are called local stability or global stability depending on whether the h1 norm of the initial perturbation is small or not up to now local stability results have been well established however for global stability only partial results have been obtained the main purpose of this paper is to study the global stability of rarefaction waves for the compressible navier stokes equations for this purpose we introduce a positive parameter to in the construction of smooth approximations of the rarefaction wave solutions for the compressible euler equations so that the quantity ty 6 denotes the strength of the rarefaction waves is sufficiently large to control the growth induced by the nonlinearity of the system and the interaction of waves from different families then by using the energy method together with the continuation argument we obtain some nonlinear stability results provided that the initial perturbation satisfies certain growth conditions as oo notice that the assumption that the quantity can be chosen to be sufficiently large implies that either the strength of the rarefaction waves is small or the rarefaction waves of different families are separated far enough initially

zero dissipation limit to rarefaction waves for the one dimensional navier stokes equations of compressible isentropic gases we study the zero dissipation limit problem for the one dimensional navier stokes equations of compressible isentropic gases in the case that the corresponding euler equations have rarefaction wave solutions we prove that the solutions of the navier stokes equations with centered rarefaction wave data exist for all time and converge to the centered rarefaction waves as the viscosity vanishes uniformly away from the initial discontinuities in the case that either the effects of initial layers are ignored or the rarefaction waves are smooth we then obtain a rate of convergence which is valid uniformly for all time our method of proof consists of a scaling argument and elementary energy analysis based on the underlying wave structure 1993 john wiley sons inc

convergence to travelling fronts of solutions of the p system with viscosity in the presence of a boundary we study the asymptotic behavior as time goes to infinity of solutions to the initial boundary value problem on the half space r for a one dimensional model system for the isentropic flow of a compressible viscous gas the so called p system with viscosity as boundary conditions we prescribe the constant state at infinity and require that the velocity be zero at the boundary x 0 when the velocity at infinity is negative and satisfies a condition on the magnitude we prove that if the initial data are suitably close to those for the corresponding outgoing viscous shock profile which is suitably far from the boundary then a unique solution exists globally in time and tends toward the properly shifted viscous shock profile as the time goes to infinity the proof is given by an elementary energy method

stability of tsallis entropy and instabilities of renyi and normalized tsallis entropies a basis for q exponential distributions the q exponential distributions which are generalizations of the zipf mandelbrot power law distribution are frequently encountered in complex systems at their stationary states from the viewpoint of the principle of maximum entropy they can apparently be derived from three different generalized entropies the renyi entropy the tsallis entropy and the normalized tsallis entropy accordingly mere fittings of observed data by the q exponential distributions do not lead to identification of the correct physical entropy here stabilities of these entropies i e their behaviors under arbitrary small deformation of a distribution are examined it is shown that among the three the tsallis entropy is stable and can provide an entropic basis for the q exponential distributions whereas the others are unstable and cannot represent any experimentally observable quantities

large time behaviors of solutions to an inflow problem in the half space for a one dimensional system of compressible viscous gas the inflow problem for a one dimensional compressible barotropic flow on the half line r 0 is investigated not only classical waves but also the new wave which is called the boundary layer solution arise large time behaviors of the solutions to be expected have been classified in terms of the boundary values by a matsumura inflow and outflow problems in the half space for a one dimensional isentropic model system of compressible viscous gas to appear in proceedings of ims conference on differential equations from mechanics hong kong 1999 in this paper we give the rigorous proofs of the stability theorems on both the boundary layer solution and a superposition of the boundary layer solution and the rarefaction wave

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

stability of contact discontinuities for the 1 d compressible navier stokes equations in this paper we study the large time asymptotic behavior of solutions of the one dimensional compressible navier stokes system toward a contact discontinuity which is one of the basic wave patterns for the compressible euler equations it is proved that such a weak contact discontinuity is a metastable wave pattern in the sense introduced in 24 for the 1 d compressible navier stokes system for polytropic fluid by showing that a viscous contact wave which approximates the contact discontinuity on any finite time interval for small heat conduction and then runs away from it for large time is nonlinearly stable with a uniform convergence rate provided that the initial excess mass is zero this result is proved by an elaborate combination of elementary energy estimates with a weighted characteristic energy estimate which makes full use of the underlying structure of the viscous contact wave

fundamental properties of tsallis relative entropy fundamental properties for the tsallis relative entropy in both classical and quantum systems are studied as one of our main results we give the parametric extension of the trace inequality between the quantum relative entropy and the minus of the trace of the relative operator entropy given by hiai and petz the monotonicity of the quantum tsallis relative entropy for the trace preserving completely positive linear map is also shown without the assumption that the density operators are invertible the generalized tsallis relative entropy is defined and its subadditivity is shown by its joint convexity moreover the generalized peierls bogoliubov inequality is also proven

classifying 50 years of bell inequalities since john s bell demonstrated the interest of studying linear combinations of probabilities in relation with the epr paradox in 1964 bell inequalities have lead to numerous developments unfortunately the description of bell inequalities is subject to several degeneracies which make any exchange of information about them unnecessarily hard here we analyze these degeneracies and propose a decomposition for bell like inequalities based on a set of reference expressions which is not affected by them these reference expressions set a common ground for comparing bell inequalities we provide algorithms based on finite group theory to compute this decomposition implementing these algorithms allows us to set up a compendium of reference bell like inequalities available online at www faacets com this website constitutes a platform where registered bell like inequalities can be explored new inequalities can be compared to previously known ones and relevant information on bell inequalities can be added in a collaborative manner this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

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

entropic test of quantum contextuality we study the contextuality of a three level quantum system using classical conditional entropy of measurement outcomes first we analytically construct the minimal configuration of measurements required to reveal contextuality next an entropic contextual inequality is formulated analogous to the entropic bell inequalities derived by braunstein and caves phys rev lett 61 662 1988 that must be satisfied by all noncontextual theories we find optimal measurements for violation of this inequality the approach is easily extendable to higher dimensional quantum systems and more measurements our theoretical findings can be verified in the laboratory with current technology

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

on almost periodic processes in uncertain impulsive delay models of price fluctuations in commodity markets we present an impulsive price model for a single commodity market with delays and uncertain terms impulsive perturbations are realized at fixed moments of time and are proposed to model price shocks in the case of continuous time representation to do so the paper resorts to the theory of impulsive differential equations uncertain terms are due to modeling errors measurement inaccuracy mutations in the fluctuation processes and so on we investigate conditions under which the extended model is capable of generating a stable almost periodic process

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

quantum q divergence the quantum q divergence is the nonadditive relative entropy associated with the tsallis entropy indexed by q here its basic properties including the q deformation and quantum group structure convexity and monotonicity are summarized then it is applied to measuring the degree of state purification it is shown that the quantum q divergence is always well defined if the entropic index q is in the range 0 1 whereas the ordinary quantum relative entropy is singular when the reference state is a pure state thus the additive limit q 1 0 does not exist in general

new results concerning the exponential stability of delayed neural networks with impulses employing the matrix measure approach and lyapunov function the author studies the global exponential stability of delayed neural networks with impulses in this paper some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point for such delayed neural networks with impulses finally three examples are given to show the effectiveness of the results obtained here

jarzynski equality for quantum stochastic maps jarzynski equality and related fluctuation theorems can be formulated for various setups such an equality was recently derived for nonunitary quantum evolutions described by unital quantum operations i e for completely positive trace preserving maps which preserve the maximally mixed state we analyze here a more general case of arbitrary quantum operations on finite systems and derive the corresponding form of the jarzynski equality it contains a correction term due to nonunitality of the quantum map bounds for the relative size of this correction term are established and they are applied for exemplary systems subjected to quantum channels acting on a finite dimensional hilbert space

information gain within nonextensive thermostatistics we discuss the information theoretical foundations of the kullback information gain recently generalized within a nonextensive thermostatistical formalism general properties are studied and in particular a consistent test for measuring the degree of correlation between random variables is proposed in addition minimum entropy distributions are discussed and the h theorem is proved within the generalized context

information theoretical properties of tsallis entropies a chain rule and a subadditivity for the entropy of type which is one of the nonadditive entropies were derived by daroczy in this paper we study the further relations among tsallis type entropies which are typical nonadditive entropies the chain rule is generalized by showing it for tsallis relative entropy and the nonadditive entropy we show some inequalities related to tsallis entropies especially the strong subadditivity for tsallis type entropies and the subadditivity for the nonadditive entropies the subadditivity and the strong subadditivity naturally lead to define tsallis mutual entropy and tsallis conditional mutual entropy respectively and then we show again chain rules for tsallis mutual entropies we give properties of entropic distances in terms of tsallis entropies finally we show parametrically extended results based on information theory

some general properties of unified entropies basic properties of the unified entropies are examined the consideration is mainly restricted to the finite dimensional quantum case bounds in terms of ensembles of quantum states are given both the continuity in fannes sense and stability in lesche s sense are shown for wide ranges of parameters in particular uniform estimates are obtained for the quantum renyi entropies stability properties in the thermodynamic limit are discussed as well it is shown that the unified entropies enjoy both the subadditivity and triangle inequality for a certain range of parameters non decreasing of all the unified entropies under projective measurements is proved

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