lesche stability of κ entropy abstract the lesche stability condition for the shannon entropy j stat phys 27 1982 419 represents a fundamental test for its experimental robustness for systems obeying the maxwell boltzmann statistical mechanics of course this stability condition must be satisfied by any entropic functional candidate to generate non conventional statistical mechanics in the present effort we show that the entropy recently introduced in literature phys rev e 66 2002 056125 satisfies the lesche stability condition

analysis and design of primal dual assignment networks the assignment problem is an archetypical combinatorial optimization problem having widespread applications this paper presents two recurrent neural networks a continuous time one and a discrete time one for solving the assignment problem because the proposed recurrent neural networks solve the primal and dual assignment problems simultaneously they are called primal dual assignment networks the primal dual assignment networks are guaranteed to make optimal assignment regardless of initial conditions unlike the primal or dual assignment network there is no time varying design parameter in the primal dual assignment networks therefore they are more suitable for hardware implementation the performance and operating characteristics of the primal dual assignment networks are demonstrated by means of illustrative examples

global exponential stability of bidirectional associative memory neural networks with time delays in this paper we consider delayed bidirectional associative memory bam neural networks nns with lipschitz continuous activation functions by applying young s inequality and holder s inequality techniques together with the properties of monotonic continuous functions global exponential stability criteria are established for bam nns with time delays this is done through the use of a new lyapunov functional and an m matrix the results obtained in this paper extend and improve previous results

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

solving the assignment problem using continuous time and discrete time improved dual networks the assignment problem is an archetypal combinatorial optimization problem in this brief we present a continuous time version and a discrete time version of the improved dual neural network idnn for solving the assignment problem compared with most assignment networks in the literature the two versions of idnns are advantageous in circuit implementation due to their simple structures both of them are theoretically guaranteed to be globally convergent to a solution of the assignment problem if only the solution is unique

a novel neural network for variational inequalities with linear and nonlinear constraints variational inequality is a uniform approach for many important optimization and equilibrium problems based on the sufficient and necessary conditions of the solution this paper presents a novel neural network model for solving variational inequalities with linear and nonlinear constraints three sufficient conditions are provided to ensure that the proposed network with an asymmetric mapping is stable in the sense of lyapunov and converges to an exact solution of the original problem meanwhile the proposed network with a gradient mapping is also proved to be stable in the sense of lyapunov and to have a finite time convergence under some mild conditions by using a new energy function compared with the existing neural networks the new model can be applied to solve some nonmonotone problems has no adjustable parameter and has lower complexity thus the structure of the proposed network is very simple since the proposed network can be used to solve a broad class of optimization problems it has great application potential the validity and transient behavior of the proposed neural network are demonstrated by several numerical examples

a neural network model for monotone linear asymmetric variational inequalities a linear variational inequality is a uniform approach for some important problems in optimization and equilibrium problems we give a neural network model for solving asymmetric linear variational inequalities the model is based on a simple projection and contraction method computer simulation is performed for linear programming lp and linear complementarity problems lcp the test results for the lp problem demonstrate that our model converges significantly faster than the three existing neural network models examined in a comparative study paper

analysis and design of a k winners take all model with a single state variable and the heaviside step activation function this paper presents a k winners take all kwta neural network with a single state variable and a hard limiting activation function first following several kwta problem formulations related existing kwta networks are reviewed then the kwta model model with a single state variable and a heaviside step activation function is described and its global stability and finite time convergence are proven with derived upper and lower bounds in addition the initial state estimation and a discrete time version of the kwta model are discussed furthermore two selected applications to parallel sorting and rank order filtering based on the kwta model are discussed finally simulation results show the effectiveness and performance of the kwta model

a novel recurrent neural network with one neuron and finite time convergence for k winners take all operation in this paper based on a one neuron recurrent neural network a novel k winners take all k wta network is proposed finite time convergence of the proposed neural network is proved using the lyapunov method the k wta operation is first converted equivalently into a linear programming problem then a one neuron recurrent neural network is proposed to get the kth or k 1 th largest inputs of the k wta problem furthermore a k wta network is designed based on the proposed neural network to perform the k wta operation compared with the existing k wta networks the proposed network has simple structure and finite time convergence in addition simulation results on numerical examples show the effectiveness and performance of the proposed k wta network

deformed exponentials and logarithms in generalized thermostatistics abstract criteria are given that deformed logarithmic and exponential functions should satisfy with a pair of such functions one can associate another function called the deduced logarithmic function it is shown that generalized thermostatistics can be formulated in terms of deformed exponential functions together with the associated deduced logarithmic functions

nonsmooth neural network for convex time dependent constraint satisfaction problems this paper introduces a nonsmooth ns neural network that is able to operate in a time dependent td context and is potentially useful for solving some classes of ns td problems the proposed network is named nonsmooth time dependent network ntn and is an extension to a td setting of a previous ns neural network for programming problems suppose c t t ge 0 is a nonempty td convex feasibility set defined by td inequality constraints the constraints are in general ns nondifferentiable functions of the state variables and time ntn is described by the subdifferential with respect to the state variables of an ns td barrier function and a vector field corresponding to the unconstrained dynamics this paper shows that for suitable values of the penalty parameter the ntn dynamics displays two main phases in the first phase any solution of ntn not starting in c 0 at t 0 is able to reach the moving set c cdot in finite time t h whereas in the second phase the solution tracks the moving set i e it stays within c t for all subsequent times t ge t h ntn is thus able to find an exact feasible solution in finite time and also to provide an exact feasible solution for subsequent times this new and peculiar dynamics displayed by ntn is potentially useful for addressing some significant td signal processing tasks as an illustration this paper discusses a number of examples where ntn is applied to the solution of ns td convex feasibility problems

solving quadratic programming problems by delayed projection neural network in this letter the delayed projection neural network for solving convex quadratic programming problems is proposed the neural network is proved to be globally exponentially stable and can converge to an optimal solution of the optimization problem three examples show the effectiveness of the proposed network

stability analysis of quaternion valued neural networks decomposition and direct approaches in this paper we investigate the global stability of quaternion valued neural networks qvnns with time varying delays on one hand in order to avoid the noncommutativity of quaternion multiplication the qvnn is decomposed into four real valued systems based on hamilton rules ij ji k jk kj i ki ik j i 2 j 2 k 2 ijk 1 with the lyapunov function method some criteria are respectively presented to ensure the global mu stability and power stability of the delayed qvnn on the other hand by considering the noncommutativity of quaternion multiplication and time varying delays the qvnn is investigated directly by the techniques of the lyapunov krasovskii functional and the linear matrix inequality lmi where quaternion self conjugate matrices and quaternion positive definite matrices are used some new sufficient conditions in the form of quaternion valued lmi are respectively established for the global mu stability and exponential stability of the considered qvnn besides some assumptions are presented for the two different methods which can help to choose quaternion valued activation functions finally two numerical examples are given to show the feasibility and the effectiveness of the main results

a new one parameter deformation of the exponential function abstract recently in kaniadakis physica a 296 2001 405 a new one parameter deformation for the exponential function exp x 1 2 x 2 x 1 exp 0 x exp x which presents a power law asymptotic behaviour has been proposed the statistical distribution f z 1 exp e has been obtained both as stable stationary state of a proper nonlinear kinetics and as the state which maximizes a new entropic form in the present contribution starting from the algebra and after introducing the analysis we obtain the exponential exp x as the eigenstate of the derivative and study its main mathematical properties

robust convex optimization we study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set u yet the constraints must hold for all possible values of the data from u the ensuing optimization problem is called robust optimization in this paper we lay the foundation of robust convex optimization in the main part of the paper we show that if u is an ellipsoidal uncertainty set then for some of the most important generic convex optimization problems linear programming quadratically constrained programming semidefinite programming and others the corresponding robust convex program is either exactly or approximately a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods

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

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

an improved dual neural network for solving a class of quadratic programming problems and its k winners take all application this paper presents a novel recurrent neural network for solving a class of convex quadratic programming qp problems in which the quadratic term in the objective function is the square of the euclidean norm of the variable this special structure leads to a set of simple optimality conditions for the problem based on which the neural network model is formulated compared with existing neural networks for general convex qp the new model is simpler in structure and easier to implement the new model can be regarded as an improved version of the dual neural network in the literature based on the new model a simple neural network capable of solving the k winners take all k wta problem is formulated the stability and global convergence of the proposed neural network is proved rigorously and substantiated by simulation results

delay derivative dependent stability for delayed neural networks with unbound distributed delay in this brief based on lyapunov krasovskii functional approach and appropriate integral inequality a new sufficient condition is derived to guarantee the global stability for delayed neural networks with unbounded distributed delay in which the improved delay partitioning technique and general convex combination are employed the lmi based criterion heavily depends on both the upper and lower bounds on time delay and its derivative which is different from the existent ones and has wider application fields than some present results finally three numerical examples can illustrate the efficiency of the new method based on the reduced conservatism which can be achieved by thinning the delay interval

a recurrent neural network for solving bilevel linear programming problem in this brief based on the method of penalty functions a recurrent neural network nn modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem blpp compared with the existing nns for blpp the model has the least number of state variables and simple structure using nonsmooth analysis the theory of differential inclusions and lyapunov like method the equilibrium point sequence of the proposed nns can approximately converge to an optimal solution of blpp under certain conditions finally the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent nns

generalized exponential function and discrete growth models abstract here we show that a particular one parameter generalization of the exponential function is suitable to unify most of the popular one species discrete population dynamic models into a simple formula a physical interpretation is given to this new introduced parameter in the context of the continuous richards model which remains valid for the discrete case from the discretization of the continuous richards model generalization of the gompertz and verhulst models one obtains a generalized logistic map and we briefly study its properties notice however that the physical interpretation for the introduced parameter persists valid for the discrete case next we generalize the scramble competition ricker discrete model and analytically calculate the fixed points as well as their stabilities in contrast to previous generalizations from the generalized ricker model one is able to retrieve either scramble or contest models

neurocomputing with time delay analysis for solving convex quadratic programming problems this paper presents a neural network computational scheme with time delay consideration for solving convex quadratic programming problems based on some known results a delay margin is explicitly determined for the stability of the neural dynamics under which the states of the neural network does not oscillate the configuration of the proposed neural network is provided operational characteristics of the neural network are demonstrated via numerical examples

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

robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances in recent years the global stability of recurrent neural networks rnns has been investigated extensively it is well known that time delays and external disturbances can derail the stability of rnns in this paper we analyze the robustness of global stability of rnns subject to time delays and random disturbances given a globally exponentially stable neural network the problem to be addressed here is how much time delay and noise the rnn can withstand to be globally exponentially stable in the presence of delay and noise the upper bounds of the time delay and noise intensity are characterized by using transcendental equations for the rnns to sustain global exponential stability moreover we prove theoretically that for any globally exponentially stable rnns if additive noises and time delays are smaller than the derived lower bounds arrived at here then the perturbed rnns are guaranteed to also be globally exponentially stable three numerical examples are provided to substantiate the theoretical results

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

on cones of nonnegative quadratic functions we derive linear matrix inequality lmi characterizations and dual decomposition algorithms for certain matrix cones which are generated by a given set using generalized co positivity these matrix cones are in fact cones of nonconvex quadratic functions that are nonnegative on a certain domain as a domain we consider for instance the intersection of a upper level set of a quadratic function and a half plane consequently we arrive at a generalization of yakubovich s s procedure result although the primary concern of this paper is to characterize the matrix cones by lmis we show as an application of our results that optimizing a general quadratic function over the intersection of an ellipsoid and a half plane can be formulated as semidefinite programming sdp thus proving the polynomiality of this class of optimization problems which arise e g from the application of the trust region method for nonlinear programming other applications are in control theory and robust optimization

multivariate nonnegative quadratic mappings in this paper we study several issues related to the characterization of specific classes of multivariate quadratic mappings that are nonnegative over a given domain with nonnegativity defined by a prespecified conic order in particular we consider the set cone of nonnegative quadratic mappings defined with respect to the positive semidefinite matrix cone and study when it can be represented by linear matrix inequalities we also discuss the applications of the results in robust optimization especially the robust quadratic matrix inequalities and the robust linear programming models in the latter application the implementational errors of the solution are taken into account and the problem is formulated as a semidefinite program

continuous growth models in terms of generalized logarithm and exponential functions abstract consider the one parameter generalizations of the logarithmic and exponential functions which are obtained from the integration of non symmetrical hyperboles these generalizations coincide to the one obtained in the context of non extensive thermostatistics we show that these functions are suitable to describe and unify the great majority of continuous growth models which we briefly review physical interpretation to the generalization function parameter is given for the richards model which has an underlying microscopic model to justify it

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

solving generally constrained generalized linear variational inequalities using the general projection neural networks generalized linear variational inequality glvi is an extension of the canonical linear variational inequality in recent years a recurrent neural network nn called general projection neural network gpnn was developed for solving glvis with simple bound often box type or sphere type constraints the aim of this paper is twofold first some further stability results of the gpnn are presented second the gpnn is extended for solving glvis with general linear equality and inequality constraints a new design methodology for the gpnn is then proposed furthermore in view of different types of constraints approaches for reducing the number of neurons of the gpnn are discussed which results in two specific gpnns moreover some distinct properties of the resulting gpnns are also explored based on their particular structures numerical simulation results are provided to validate the results

a new constrained independent component analysis method constrained independent component analysis cica is a general framework to incorporate a priori information from problem into the negentropy contrast function as constrained terms to form an augmented lagrangian function in this letter a new improved algorithm for cica is presented through the investigation of the inequality constraints in which different closeness measurements are compared the utility of our proposed algorithm is demonstrated by the experiments with synthetic data and electroencephalogram eeg data

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

a delayed projection neural network for solving linear variational inequalities in this paper a delayed projection neural network is proposed for solving a class of linear variational inequality problems the theoretical analysis shows that the proposed neural network is globally exponentially stable under different conditions by the proposed linear matrix inequality lmi method the monotonicity assumption on the linear variational inequality is no longer necessary by employing lagrange multipliers the proposed method can resolve the constrained quadratic programming problems finally simulation examples are given to demonstrate the satisfactory performance of the proposed neural network

approximating quadratic programming with bound and quadratic constraints we consider the problem of approximating the global maximum of a quadratic program qp subject to bound and simple quadratic constraints based on several early results we show that a 4 7 approximate solution can be obtained in polynomial time

a q generalization of laplace transforms the laplace transform is generalized by using the q exponential function eqx 1 1 q x 1 1 q that emerges from tsallis non extensive statistical mechanics and some of its properties are obtained the usual transform is recovered as a limiting case q1 the use of the q laplace transform is illustrated by establishing a relation between the classical canonical q partition function and the density of states

some properties of q logarithm and q exponential functions in tsallis statistics we present some formulae which q logarithmic and q exponential functions introduced in tsallis statistics satisfy exact expression of the mellin transform of q exponential function is given moreover the q generalization of the digamma function is presented

tsallis entropy induced metrics and cat k spaces abstract generalizing the group structure of the euclidean space we construct a riemannian metric on the deformed set r q n induced by the tsallis entropy composition property we show that the tsallis entropy is a hyperbolic analogue of the euclidean boltzmann gibbs shannon entropy and find a geometric interpretation for the nonextensive parameter q we provide a geometric explanation of the uniqueness of the tsallis entropy as reflected through its composition property which is provided by the abe and the santos axioms for two or more interacting systems described by the tsallis entropy having different values of q we argue why a suitable extension of this construction is provided by the cartan alexandrov toponogov metric spaces with a uniform negative curvature upper bound

distributivity and deformation of the reals from tsallis entropy we propose a one parameter family rq of deformations of the reals which is motivated by the generalized additivity of the tsallis entropy we introduce a generalized multiplication which is distributive with respect to the generalized addition of the tsallis entropy these operations establish a one parameter family of field isomorphisms q between r and rq through which an absolute value on rq is introduced this turns out to be a quasisymmetric map whose metric and measure theoretical implications are pointed out

a possible deformed algebra and calculus inspired in nonextensive thermostatistics we present a deformed algebra related to the q exponential and the q logarithm functions that emerge from nonextensive statistical mechanics we also develop a q derivative and consistently a q integral for which the q exponential is an eigenfunction the q derivative and the q integral have a dual nature that is also presented

global exponential stability of neural networks with globally lipschitz continuous activations and its application to linear variational inequality problem this paper investigates the existence uniqueness and global exponential stability ges of the equilibrium point for a large class of neural networks with globally lipschitz continuous activations including the widely used sigmoidal activations and the piecewise linear activations the provided sufficient condition for ges is mild and some conditions easily examined in practice are also presented the ges of neural networks in the case of locally lipschitz continuous activations is also obtained under an appropriate condition the analysis results given in the paper extend substantially the existing relevant stability results in the literature and therefore expand significantly the application range of neural networks in solving optimization problems as a demonstration we apply the obtained analysis results to the design of a recurrent neural network rnn for solving the linear variational inequality problem vip defined on any nonempty and closed box set which includes the box constrained quadratic programming and the linear complementarity problem as the special cases it can be inferred that the linear vip has a unique solution for the class of lyapunov diagonally stable matrices and that the synthesized rnn is globally exponentially convergent to the unique solution some illustrative simulation examples are also given

a generalized hopfield network for nonsmooth constrained convex optimization lie derivative approach this paper proposes a generalized hopfield network for solving general constrained convex optimization problems first the existence and the uniqueness of solutions to the generalized hopfield network in the filippov sense are proved then the lie derivative is introduced to analyze the stability of the network using a differential inclusion the optimality of the solution to the nonsmooth constrained optimization problems is shown to be guaranteed by the enhanced fritz john conditions the convergence rate of the generalized hopfield network can be estimated by the second order derivative of the energy function the effectiveness of the proposed network is evaluated on several typical nonsmooth optimization problems and used to solve the hierarchical and distributed model predictive control four tank benchmark

blind image deconvolution through support vector regression this letter introduces a new algorithm for the restoration of a noisy blurred image based on the support vector regression svr experiments show that the performance of the svr is very robust in blind image deconvolution where the types of blurs point spread function psf support and noise level are all unknown

non linear kinetics underlying generalized statistics abstract the purpose of the present effort is threefold firstly it is shown that there exists a principle that we call kinetical interaction principle kip underlying the non linear kinetics in particle systems independently on the picture kramers boltzmann used to describe their time evolution secondly the kip imposes the form of the generalized entropy associated to the system and permits to obtain the particle statistical distribution both as stationary solution of the non linear evolution equation and as the state which maximizes the generalized entropy thirdly the kip allows on one hand to treat all the classical or quantum statistical distributions already known in the literature in a unifying scheme and on the other hand suggests how we can introduce naturally new distributions finally as a working example of the approach to the non linear kinetics here presented a new non extensive statistics is constructed and studied starting from a one parameter deformation of the exponential function holding the relation f x f x 1

on maximization of quadratic form over intersection of ellipsoids with common center we demonstrate that if a1 a m are symmetric positive semidefinite n n matrices with positive definite sum and a is an arbitrary symmetric n n matrix then the relative accuracy in terms of the optimal value of the semidefinite relaxation max x tr ax mid tr a ix le1 i 1 m x succeq0 eqno hbox sdp of the optimization program x tax to max mid x ta ix le 1 i 1 m eqno hbox p is not worse than 1 frac 1 2 ln 2m 2 it is shown that this bound is sharp in order as far as the dependence on m is concerned and that a feasible solution x to p with x tax ge frac opt hbox rm sdp 2 ln 2m 2 eqno can be found efficiently this somehow improves one of the results of nesterov 4 where bound similar to is established for the case when all ai are of rank 1

recurrent neural network for non smooth convex optimization problems with application to the identification of genetic regulatory networks a recurrent neural network is proposed for solving the non smooth convex optimization problem with the convex inequality and linear equality constraints since the objective function and inequality constraints may not be smooth the clarke s generalized gradients of the objective function and inequality constraints are employed to describe the dynamics of the proposed neural network it is proved that the equilibrium point set of the proposed neural network is equivalent to the optimal solution of the original optimization problem by using the lagrangian saddle point theorem under weak conditions the proposed neural network is proved to be stable and the state of the neural network is convergent to one of its equilibrium points compared with the existing neural network models for non smooth optimization problems the proposed neural network can deal with a larger class of constraints and is not based on the penalty method finally the proposed neural network is used to solve the identification problem of genetic regulatory networks which can be transformed into a non smooth convex optimization problem the simulation results show the satisfactory identification accuracy which demonstrates the effectiveness and efficiency of the proposed approach

a definition of the coupled product for multivariate coupled exponentials abstract the coupled product and coupled exponential of the generalized calculus of nonextensive statistical mechanics are defined for multivariate functions the nonlinear statistical coupling is indexed such that d 1 d where d is the dimension of the argument of the multivariate coupled exponential the coupled gaussian distribution is defined such that the argument of the coupled exponential depends on the coupled moments but not the coupling parameter the multivariate version of the coupled product is defined such that the output dimensions are the sum of the input dimensions this enables construction of the multivariate coupled gaussian from univariate coupled gaussians the resulting construction forms a model of coupling between distributions generalizing the product of independent gaussians

a mathsf d induced duality and its applications this paper attempts to extend the notion of duality for convex cones by basing it on a prescribed conic ordering and a fixed bilinear mapping this is an extension of the standard definition of dual cones in the sense that the nonnegativity of the inner product is replaced by a pre specified conic ordering defined by a convex cone mathsf d and the inner product itself is replaced by a general multi dimensional bilinear mapping this new type of duality is termed the mathsf d induced duality in the paper we further introduce the notion of mathsf d induced polar sets within the same framework which can be viewed as a generalization of the mathsf d induced dual cones and is convenient to use for some practical applications properties of the extended duality including the extended bi polar theorem are proven furthermore attention is paid to the computation and approximation of the mathsf d induced dual objects we discuss as examples applications of the newly introduced mathsf d induced duality concepts in robust conic optimization and the duality theory for multi objective conic optimization

convergence of nonautonomous cohen grossberg type neural networks with variable delays this paper is concerned with the global convergence of the solutions of a nonautonomous system with variable delays arising from the description of the states of neurons in delayed cohen grossberg type in a time varying situation by exploring intrinsic features between nonautonomous system and its asymptotic equation several novel sufficient conditions are established to ensure that all solutions of the networks converge to a periodic function or a constant vector for delayed cohen grossberg type neural network nn models in time varying situation the results can be applied directly to group of nns models including hopfield nns bidirectional association memory nns and cellular nns our results are not only presented in terms of system parameters and can be easily verified but also are less restrictive than previously known criteria numerical simulations have also been presented to demonstrate the theoretical analysis

on a q generalization of circular and hyperbolic functions a generalization of the circular and hyperbolic functions is proposed based on the tsallis statistics and on a consistent generalization of the euler formula some properties of the presently proposed q trigonometry are then investigated the generalized functions are exact solutions of a nonlinear oscillator original circular and hyperbolic relations are recovered as the limiting case

algebra and calculus for tsallis thermo statistics abstract we construct generalized additions and multiplications forming fields and division algebras inspired by the tsallis thermo statistics we also construct derivations and integrations in this spirit these operations do not reduce to the naively expected ones when the deformation parameter approaches zero