hierarchical pinning models quadratic maps and quenched disorder we consider a hierarchical model of polymer pinning in presence of quenched disorder introduced by derrida et al j stat phys 66 1189 1213 1992 which can be re interpreted as an infinite dimensional dynamical system with random initial condition the disorder it is defined through a recurrence relation for the law of a random variable r n n 1 2 which in absence of disorder i e when the initial condition is degenerate reduces to a particular case of the well known logistic map the large n limit of the sequence of random variables 2 n log r n a non random quantity which is naturally interpreted as a free energy plays a central role in our analysis the model depends on a parameter 0 1 related to the geometry of the hierarchical lattice and has a phase transition in the sense that the free energy is positive if the expectation of r 0 is larger than a certain threshold value and it is zero otherwise it was conjectured in derrida et al j stat phys 66 1189 1213 1992 that disorder is relevant respectively irrelevant or marginally relevant if 1 2 1 2 we find the correct scaling form for weak disorder of the critical point shift

superdiffusivity in first passage percolation in standard first passage percolation on bbb z d with d geq 2 the time minimizing paths from a point to a plane at distance l are expected to have transverse fluctuations of order l xi it has been conjectured that xi d geq 1 2 with the inequality strict superdiffusivity at least for low d and with xi 2 2 3 we prove versions of xi d geq 1 2 for all d and xi 2 geq 3 5

phase transitions for the growth rate of linear stochastic evolutions we consider a discrete time stochastic growth model on d dimensional lattice the growth model describes various interesting examples such as oriented site bond percolation directed polymers in random environment time discretizations of binary contact path process and the voter model we study the phase transition for the growth rate of the total number of particles in this framework the main results are roughly as follows if d 3 and the system is not too random then with positive probability the growth rate of the total number of particles is of the same order as its expectation if on the other hand d 1 2 or the system is random enough then the growth rate is slower than its expectation we also discuss the above phase transition for the dual processes and its connection to the structure of invariant measures for the model with proper normalization

impulsive delay differential inequality and stability of neural networks in this article a generalized model of neural networks involving time varying delays and impulses is considered by establishing the delay differential inequality with impulsive initial conditions and using the properties of m cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of impulsive delay model are obtained the results extend and improve the earlier publications an example is given to illustrate the theory

almost sure exponential behavior of a directed polymer in a fractional brownian environment this paper studies the asymptotic behavior of a one dimensional directed polymer in a random medium the latter is represented by a gaussian field bh on r r with fractional brownian behavior in time hurst parameter h and arbitrary function valued behavior in space the partition function of such a polymer is u t eb exp 0tbh dr br here b is a continuous time nearest neighbor random walk on z with fixed intensity 2 defined on a complete probability space pb independent of bh the spatial covariance structure of bh is assumed to be homogeneous and periodic with period 2 for h 12 we prove that the upper and lower almost sure limits lim supt t 2hlogu t and lim inft t 2hlogt logu t are non trivial in the sense that they are bounded respectively above and below by finite strictly positive constants thus as h passes through 12 the exponential behavior of u t changes abruptly this can be considered as a phase transition phenomenon novel tools used in this paper include sub gaussian concentration theory via the malliavin calculus detailed analyses of the long range memory of fractional brownian motion and an almost superadditivity property

localization for linear stochastic evolutions we consider a discrete time stochastic growth model on the d dimensional lattice with non negative real numbers as possible values per site the growth model describes various interesting examples such as oriented site bond percolation directed polymers in random environment time discretizations of the binary contact path process we show the equivalence between the slow population growth and a localization property in terms of replica overlap the main novelty of this paper is that we obtain this equivalence even for models with positive probability of extinction at finite time in the course of the proof we characterize in a general setting the event on which an exponential martingale vanishes in the limit

superdiffusivity for a brownian polymer in a continuous gaussian environment this paper provides information about the asymptotic behavior of a one dimensional brownian polymer in random medium represented by a gaussian field w on r r assumed to be white noise in time and function valued in space according to the behavior of the spatial covariance of w we give a lower bound on the power growth wandering exponent of the polymer when the time parameter goes to infinity the polymer is proved to be superdiffusive with a wandering exponent exceeding any 3 5

variations and generalizations of bohr s inequality abstract in this paper we provide an account of various results that have been obtained concerning bohr s inequality with emphasis on several generalizations

transversal fluctuations for increasing subsequences on the plane consider a realization of a poisson process in 2 with intensity 1 and take a maximal up right path from the origin to n n consisting of line segments between the points where maximal means that it contains as many points as possible the number of points in such a path has fluctuations of order n where 1 3 bdj here we show that typical deviations of a maximal path from the diagonal x y is of order n with 2 3 this is consistent with the scaling identity 2 1 which is believed to hold in many random growth models

on the partition function of a directed polymer in a gaussian random environment the purpose of this work is the study of the partition function of a dimensional lattice directed polymer in a gaussian random environment being the inverse of temperature in the low dimensional cases we prove that for all the renormalized partition function converges to 0 and the correlation of two independent configurations does not converge to 0 in the high dimensional case a lower tail of has been obtained for small furthermore we express some thermodynamic quantities in terms of the path measure alone

the parisi formula in this chapter we prove the parisi formula which gives the limiting value of the free energy per site for the sherrington kirkpatrick model at each temperature starting with the famous result of guerra that the parisi formula provided a bound for this free energy we make full use of poisson dirichlet cascades we then use the same techniques to prove in a strong sense that in presence of an external field the overlaps are positive

one sided local large deviation and renewal theorems in the case of infinite mean if s n n 0 is an integer valued random walk such that s n a n converges in distribution to a stable law of index 0 1 as n then gnedenko s local limit theorem provides a useful estimate for p s n r for values of r such that r a n is bounded the main point of this paper is to show that under certain circumstances there is another estimate which is valid when r a n in other words to establish a large deviation local limit theorem we also give an asymptotic bound for p s n r which is valid under weaker assumptions this last result is then used in establishing some local versions of generalized renewal theorems

eigenvalue extensions of bohr s inequality abstract we present a weak majorization inequality and apply it to prove eigenvalue and unitarily invariant norm extensions of a version of the bohr s inequality due to vasic and keckic

a new proof of an inequality of bohr for hilbert space operators in this note we present a new proof and an extension of the hilbert space operators version of an inequality by bohr

the effect of disorder on polymer depinning transitions we consider a polymer with monomer locations modeled by the trajectory of a markov chain in the presence of a potential that interacts with the polymer when it visits a particular site 0 we assume that probability of an excursion of length n is given by n c varphi n for some 1 3 2 at high temperature the quenched and annealed curves differ significantly only in a very small neighborhood of the critical point the size of this neighborhood scales as beta 1 2c 3 where is the inverse temperature for c 0 for sufficiently high temperature the quenched and annealed curves are within a factor of 1 epsilon for all u near the critical point in particular the quenched and annealed critical points are equal for c 3 2 the regime depends on the slowly varying function varphi

a note on the diffusion of directed polymers in a random environment a simple martingale argument is presented which proves that directed polymers in random environments satisfy a central limit theorem ford 3 and if the disorder is small enough this simplifies and extends an approach by j imbrie and t spencer

the thermodynamic limit in mean field spin glass models we present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities for a large class of mean field disordered models as for example the sherrington kirkpatrick model and the derrida p spin model the main argument is based on a smooth interpolation between a large system made of n spin sites and two similar but independent subsystems made of n 1 and n 2 sites respectively with n 1 n 2 n the quenched average of the free energy turns out to be subadditive with respect to the size of the system this gives immediately convergence of the free energy per site in the infinite volume limit moreover a simple argument based on concentration of measure gives the almost sure convergence with respect to the external noise similar results hold also for the ground state energy per site

inequalities for absolute value operators abstract we present refinements of an inequality which is due to saito and tominaga linear algebra appl 432 2010 3258 3264 and other inequalities for absolute value operators

global exponential stability analysis on impulsive bam neural networks with distributed delays using m matrix and topological degree tool sufficient conditions are obtained for the existence uniqueness and global exponential stability of the equilibrium point of bidirectional associative memory bam neural networks with distributed delays and subjected to impulsive state displacements at fixed instants of time by constructing a suitable lyapunov functional the results remove the usual assumptions that the boundedness monotonicity and differentiability of the activation functions it is shown that in some cases the stability criteria can be easily checked finally an illustrative example is given to show the effectiveness of the presented criteria

the sherrington kirkpatrick model of spin glasses and stochastic calculus the high temperature case we study the fluctuations of free energy energy and entropy in the high temperature regime for the sherrington kirkpatrick model of spin glasses we introduce here a new dynamical method with the help of brownian motions and continuous martingales indexed by the square root of the inverse temperature as parameter thus formulating the thermodynamic formalism in terms of random processes the well established technique of stochastic calculus leads us naturally to prove that these fluctuations are simple gaussian processes with independent increments a generalization of a result proved by aizenman lebowitz and ruelle 1

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

broken replica symmetry bounds in the mean field spin glass model by using a simple interpolation argument in previous work we have proven the existence of the thermodynamic limit for mean field disordered models including the sherrington kirkpatrick model and the derrida p spin model here we extend this argument in order to compare the limiting free energy with the expression given by the parisi ansatz and including full spontaneous replica symmetry breaking our main result is that the quenched average of the free energy is bounded from below by the value given in the parisi ansatz uniformly in the size of the system moreover the difference between the two expressions is given in the form of a sum rule extending our previous work on the comparison between the true free energy and its replica symmetric sherrington kirkpatrick approximation we give also a variational bound for the infinite volume limit of the ground state energy per site

localization in log gamma polymers with boundaries consider the directed polymer in one space dimension in log gamma environment with boundary conditions introduced by seppalainen ann probab 40 1 19 73 2012 in the equilibrium case we prove that the end point of the polymer converges in law as the length increases to a density proportional to the exponent of a zero mean random walk this holds without space normalization and the mass concentrates in a neighborhood of the minimum of this random walk we have analogous results out of equilibrium as well as for the middle point of the polymer with both ends fixed the existence and the identification of the limit relies on the analysis of a random walk seen from its infimum

non coincidence of quenched and annealed connective constants on the supercritical planar percolation cluster in this paper we study the abundance of self avoiding paths of a given length on a supercritical percolation cluster on mathbb z d more precisely we count z n the number of self avoiding paths of length n on the infinite cluster starting from the origin which we condition to be in the cluster we are interested in estimating the upper growth rate of z n limsup n rightarrow infty z n 1 n which we call the connective constant of the dilute lattice after proving that this connective constant is a s non random we focus on the two dimensional case and show that for every percolation parameter p in 1 2 1 almost surely z n grows exponentially slower than its expected value in other words we prove that limsup n rightarrow infty z n 1 n lim n rightarrow infty mathbb e z n 1 n where the expectation is taken with respect to the percolation process this result can be considered as a first mathematical attempt to understand the influence of disorder for self avoiding walks on a quenched dilute lattice our method which combines change of measure and coarse graining arguments does not rely on the specifics of percolation on mathbb z 2 so our result can be extended to a large family of two dimensional models including general self avoiding walks in a random environment

diffusion of directed polymers in a random environment we consider a system of random walks or directed polymers interacting weakly with an environment which is random in space and time in spatial dimensionsd 2 we establish that the behavior is diffusive with probability one the diffusion constant is not renormalized by the interaction

global exponential stability of hybrid bidirectional associative memory neural networks with discrete delays in this paper the dynamical characteristics of hybrid bidirectional associative memory neural networks with constant transmission delays are investigated without assuming symmetry of synaptic connection weights and monotonicity and differentiability of activation functions halanay type inequalities which are different from the approach of constructing lyapunov functionals are employed to derive the delay independent sufficient conditions under which the networks converge exponentially to the equilibria associated with temporally uniform external inputs our results are less conservative and restrictive than previously known results

continuous model for homopolymers we consider the model for the distribution of a long homopolymer in a potential field the typical shape of the polymer depends on the temperature parameter we show that at a critical value of the temperature the transition occurs from a globular to an extended phase for various values of the temperature including those at or near the critical value we consider the limiting behavior of the polymer when its size tends to infinity

generalizations of bohr inequality for hilbert space operators abstract let b h be the space of all bounded linear operators on a complex separable hilbert space h bohr inequality for hilbert space operators asserts that for a b b h and p q 1 real numbers such that 1 p 1 q 1 a b 2 p a 2 q b 2 with equality if and only if b p 1 a in this paper a number of generalizations of bohr inequality for operators in b h are established moreover bohr inequalities are extended to multiple operators and some related inequalities are obtained the results in this paper generalize results known so far the idea of transforming problems in operator theory to problems in matrix theory which are easy to handle is the key role

directed polymers in random environment are diffusive at weak disorder in this paper we consider directed polymers in random environment with discrete space and time for transverse dimension at least equal to 3 we prove that diffusivity holds for the path in the full weak disorder region i e where the partition function differs from its annealed value only by a non vanishing factor deep inside this region we also show that the quenched averaged energy has fluctuations of order 1 in complete generality arbitrary dimension and temperature we prove monotonicity of the phase diagram in the temperature

on the bohr inequality of operators abstract this paper is focused on the operator inequalities of the bohr type we will give a new and transparent proof for the operator bohr inequality through an absolute value operator identity show some related operator inequalities by means of 2 2 block operator matrices and finally we will present a generalization of the operator bohr inequality for multiple operators

a replica coupling approach to disordered pinning models we consider a renewal process 0 1 on the integers where the law of i i 1 has a power like tail p i i 1 n n 1 l n with 0 and l slowly varying we then assign a random n dependent reward penalty to the occurrence of the event that the site n belongs to in such generality this class of problems includes among others 1 d dimensional models of pinning of directed polymers on a one dimensional random defect 1 1 dimensional models of wetting of disordered substrates and the poland scheraga model of dna denaturation by varying the average of the reward the system undergoes a transition from a localized phase where occupies a finite fraction of mathbb n to a delocalized phase where the density of vanishes in absence of disorder i e if the reward is independent of n the transition is of first order for 1 and of higher order for 1 2 11 in physical terms disorder is relevant in this situation in agreement with the heuristic harris criterion on the other hand for 0 1 2 it has been proven recently by k alexander 2 that if disorder is sufficiently weak critical exponents are not modified by randomness disorder is irrelevant in this work generalizing techniques which in the framework of spin glasses are known as replica coupling and interpolation we give a new simpler proof of the main results of 2 moreover we partially justify a small disorder expansion worked out in 9 for 1 2 showing that it provides a free energy upper bound which improves the annealed one

global exponential stability of bidirectional associative memory neural networks with distributed delays a bidirectional associative memory neural network model with distributed delays is considered by constructing a new lyapunov functional employing the homeomorphism theory m matrix theory and the inequality email protected k 1 mb k q k 0 b k 0 q k 0 with k 1 mq k r 1 and r 1 a sufficient condition is obtained to ensure the existence uniqueness and global exponential stability of the equilibrium point for the model moreover the exponential converging velocity index is estimated which depends on the delay kernel functions and the system parameters the results generalize and improve the earlier publications and remove the usual assumption that the activation functions are bounded two numerical examples are given to show the effectiveness of the obtained results

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 remark on the bound for the free energy of directed polymers in random environment in 1 2 dimension we consider the behavior of the quantity p the free energy of directed polymers in random environment in 1 2 dimension where is inverse temperature we know that the free energy is strictly negative when is not zero in this paper we will prove that p is bounded from above by exp c 2 for small where ce 0 is a constant depending on e 0 also we will suggest a strategy to get a sharper asymptotics we denote by f p a probability space

strong localization and macroscopic atoms for directed polymers in this article we derive strong localization results for directed polymers in random environment we show that at low temperature the polymer measure is asymptotically concentrated at a few points of macroscopic mass we call these points epsilon atoms these results are derived assuming weak conditions on the tail decay of the random environment

limiting results for the free energy of directed polymers in random environment with unbounded jumps we study asymptotic behaviors of the free energy for the directed polymer in random environment the polymer is allowed to make unbounded jumps and the environment is given by the bernoulli variables we first establish the existence and continuity including the negative infinity value of the coupling constant our proof of existence at differs from existing ones in that it avoids the direct use of subadditivity secondly we identify the asymptotics of the free energy at in the limit of the success probability of the bernoulli variables tending to one it is described by using the so called time constant of a certain directed first passage percolation our proof relies on a certain continuity property of the time constant which is of independent interest

inequalities for sums and direct sums of hilbert space operators abstract we prove several singular value inequalities and norm inequalities involving sums and direct sums of hilbert space operators it is shown among other inequalities that if x and y are compact operators then the singular values of x y 2 are dominated by those of x y applications of these inequalities are also given

characterization of equality in a generalized dunkl williams inequality abstract we establish a generalization of the dunkl williams inequality and its inverse in the framework of hilbert c modules and characterize the equality case as applications we get some new results and some known results due to j e pecaric and r rajic the dunkl williams equality in pre hilbert c modules linear algebra appl 425 1 2007 16 25

influence of spatial correlation for directed polymers in this paper we study a model of a brownian polymer in x d introduced by rovira and tindel j funct anal 222 2005 178 201 our investigation focuses mainly on the effect of strong spatial correlation in the environment in that model in terms of free energy fluctuation exponent and volume exponent in particular we prove that under some assumptions very strong disorder and superdiffusivity hold at all temperatures when d 3 and provide a novel approach to petermann s superdiffusivity result in dimension one superdiffusivity of directed polymers in random environment 2000 ph d thesis we also derive results for a brownian model of pinning in a nonrandom potential with power law decay at infinity

stability of artificial neural networks with impulses sufficient conditions are obtained for the existence and asymptotic stability of a unique equilibrium of a hopfield type neural network with lipschitzian activation functions without assuming their boundedness monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time both the continuous time and their corresponding discrete time networks are considered the sufficient conditions of the discrete time network do not restrict the step size appearing in the discretization process and these conditions approach as the step size tends to zero those of the conditions of the continuous time networks the sufficient conditions are in terms of the parameters of the network only and are easy to verify also when the impulsive jumps are absent the results reduce to those of the non impulsive systems

infinite moments of the partition function for random walks in a random potential we consider a system of random walks directed polymers in a potential which is random in space and time investigations into untypical behavior and the inverse of the partition function leads to the result that regardless of the strength of the potential and in all dimensions all higher moments of the partition function are unbounded as time goes to infinity one can interpret this result in a many body quantum mechanical setting as saying that no matter how small the strength of an attractive potential in any dimension one can find n the number of particles large enough so that there is a bound state

bohr s inequalities for hilbert space operators abstract the classical bohr s inequality states that z w 2 p z 2 q w 2 for all z w c and all p q 1 with 1 p 1 q 1 in this paper bohr s inequality is generalized to the context of hilbert space operators for all positive conjugate exponents p q r in particular the parallelogram law is recovered and some other interesting operator inequalities and established

on the brownian directed polymer in a gaussian random environment in this paper we introduce a model of brownian polymer in a continuous random environment the asymptotic behavior of the partition function associated to this polymer measure is studied and we are able to separate a weak and strong disorder regime under some reasonable assumptions on the spatial covariance of the environment some further developments concerning some concentration inequalities for the partition function are given for the weak disorder regime

the sherrington kirkpatrick model a challenge for mathematicians the sherrington kirkpatrick sk model for spin glasses is deceptively simple to state yet its rigorous study represents a considerable challenge we report here some modest progresses obtained through elementary methods even in the supposedly simple high temperature region a number of basic questions remain unsolved

a brownian motion version of the directed polymer problem consider a brownian particle in three dimensions in a random environment the environment is determined by a potential random in space and time it is shown that at small noise the large time behavior of the particle is diffusive the diffusion constant depends on the environment this work generalizes previous results for random walk in a random environment in these results the diffusion constant does not depend on the environment

existence and global exponential stability of periodic solution for impulsive cohen grossberg type bam neural networks with continuously distributed delays this paper is concerned with the existence and global exponential stability of periodic solution for a class of impulsive cohen grossberg type bam neural networks with continuously distributed delays some sufficient conditions ensuring the existence and global exponential stability of periodic solution are derived by constructing a suitable lyapunov function and a new differential inequality the proposed method can also be applied to study the impulsive cohen grossberg type bam neural networks with finite distributed delays the results in this paper extend and improve the earlier publications finally two examples with numerical simulations are given to demonstrate the obtained results

directed polymers in a random environment some results on fluctuations we consider a polymer model on where to each edgee is associated a random variable v e a polymer configuration is represented by a directed pathr and has a weight exp e r e with 1 t the inverse temperature we extend some rigorous results that have been obtained for the ground state of this model to finite temperatures in particular we obtain some upper and lower bounds on sample to sample free energy fluctuations and also rigorous scaling inequalities between the exponents describing free energy fluctuations and transversal displacements of polymer configurations

brownian directed polymers in random environment we study the thermodynamics of a continuous model of directed polymers in random environment the environment is given by a space time poisson point process whereas the polymer is defined in terms of the brownian motion we mainly discuss i the normalized partition function its positivity in the limit which characterizes the phase diagram of the model ii the existence of quenched lyapunov exponent its positivity and its agreement with the annealed lyapunov exponent iii the longitudinal fluctuation of the free energy some of its relations with the overlap between replicas and with the transversal fluctuation of the path the model considered here enables us to use stochastic calculus with respect to both brownian motion and poisson process leading to handy formulas for fluctuations analysis and qualitative properties of the phase diagram we also relate our model to some formulation of the kardar parisi zhang equation more precisely the stochastic heat equation our fluctuation results are interpreted as bounds on various exponents and provide a circumstantial evidence of super diffusivity in dimension one we also obtain an almost sure large deviation principle for the polymer measure

localization transition for polymers in poissonian medium we study a model of directed polymers in random environment in dimension 1 d given by a brownian motion in a poissonian potential we study the effect of the density and the strength of inhomogeneities respectively the intensity parameter of the poisson field and the temperature inverse our results are i fine information on the phase diagram with quantitative estimates on the critical curve ii pathwise localization at low temperature and or large density iii complete localization in a favourite corridor for large 2 and bounded

the burgers equation with a random force and a general model for directed polymers in random environments the study of the burgers equation with a random force leads via a hopf cole type transformation to a stochastic heat equation having a white noise with spatial parameters type potential the latter can be studied by means of a general model of directed polymers in random environments with two point random potentials these models exhibit a gaussian behavior at large times and have certain stationary distributions which yield the corresponding results for the above stochastic heat and burgers equations

stationary cocycles and busemann functions for the corner growth model we study the directed last passage percolation model on the planar square lattice with nearest neighbor steps and general i i d weights on the vertices outside of the class of exactly solvable models stationary cocycles are constructed for this percolation model from queueing fixed points these cocycles serve as boundary conditions for stationary last passage percolation solve variational formulas that characterize limit shapes and yield existence of busemann functions in directions where the shape has some regularity in a sequel to this paper the cocycles are used to prove results about semi infinite geodesics and the competition interface

ratios of partition functions for the log gamma polymer we introduce a random walk in random environment associated to an underlying directed polymer model in 1 1 dimensions this walk is the positive temperature counterpart of the competition in terface of percolation and arises as the limit of quenched polymer measures we prove this limit for the exactly solvable log gamma polymer as a consequence of almost sure limits of ratios of parti tion functions these limits of ratios give the busemann functions of the log gamma polymer and furnish centered cocycles that solve a variational formula for the limiting free energy limits of ratios of point to point and point to line partition functions manifest a duality between tilt and velocity that comes from quenched large deviations under polymer measures in the log gamma case we identify a fam ily of ergodic invariant distributions for the random walk in random environment

a dunkl williams type inequality for absolute value operators abstract dunkl and williams showed that for any nonzero elements x y in a normed linear space x x x y y 4 x y x y pecaric and rajic gave a refinement and moreover a generalization to operators a b b h such that a b are invertible as follows a a 1 b b 1 2 a 1 p a b 2 q a b 2 a 1 where p q 1 with 1 p 1 q 1 in this note we shall investigate the inequality and also equality conditions under the assumption that the existence of a 1 and b 1 is not required moreover we give a refinement of the equality conditions

global asymptotic stability of bi directional associative memory networks with distributed delays in this paper several sufficient conditions are derived for the global asymptotic stability in bi directional associative memory bam networks with distributed delays by constructing suitable lyapunov functional and the young inequality technique these conditions have an important leading significance in the design and applications of globally asymptotically stable neural circuits for bam with distributed delays

existence of an exponential periodic attractor of periodic solutions for general bam neural networks with time varying delays and impulses abstract by applying inequality analysis technique constructing a suitable lyapunov functional and combing the continuation theorem due to mawhin and gaines some novel sufficient conditions are obtained to ensure the existence of an exponential periodic attractor of periodic solutions for general neural networks with time varying including bounded and unbounded delays and impulses an example is employed to illustrate our feasible results

large deviation rate functions for the partition function in a log gamma distributed random potential we study right tail large deviations of the logarithm of the partition function for directed lattice paths in i i d random potentials the main purpose is the derivation of explicit formulas for the 1 1 dimensional exactly solvable case with log gamma distributed random weights along the way we establish some regularity results for this rate function for general distributions in arbitrary dimensions

weak majorization inequalities and convex functions abstract let f be a convex function defined on an interval i 0 1 and a b n n complex hermitian matrices with spectrum in i we prove that the eigenvalues of f a 1 b are weakly majorized by the eigenvalues of f a 1 f b further if f is log convex we prove that the eigenvalues of f a 1 b are weakly majorized by the eigenvalues of f a f b 1 as applications we obtain generalizations of the famous golden thomson trace inequality a representation theorem and a harmonic geometric mean inequality some related inequalities are discussed

existence of an exponential periodic attractor of a class of impulsive differential equations with time varying delays abstract by using the continuation theorem due to mawhin and gaines some analysis techniques and the lyapunov functional method the sufficient conditions ensuring the existence of an exponential periodic attractor of a class of impulsive differential equations with time varying delays are established the results are interesting and very different from previously known results xia and wong 2009 7 tan and tan 2009 19 huang et al 2005 20 liu and huang 2006 22 finally applications and an example are given to illustrate the effectiveness of the results

non commutative operator bohr inequality abstract it is shown that if a b x are hilbert space operators such that x i for the positive real number and p q 1 with 1 p 1 q 1 then a b 2 p a 2 q b 2 with equality if and only if 1 p a b and a b 2 p a 2 x qx b 2 for every unitarily invariant norm moreover if in addition a b are normal and x is any hilbert schmidt operator then a b 2 x 2 p a 2 x qx b 2 2 with equality if and only if 1 p ax xb

an analysis on the global exponential stability and the existence of periodic solutions for non autonomous hybrid bam neural networks with distributed delays and impulses in this paper by utilizing the lyapunov functional method applying m matrix young inequality technique and other analysis techniques we analyze the exponential stability and the existence of periodic solutions for non autonomous hybrid bam neural networks with distributed delays and impulses sufficient conditions are obtained for the global exponential stability and the existence of periodic solutions for non autonomous hybrid bidirectional associative memory bam neural networks with lipschitzian activation functions without assuming their boundedness monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time finally two examples are also provided to demonstrate the effectiveness of the results obtained

variational formulas and cocycle solutions for directed polymer and percolation models we discuss variational formulas for the law of large numbers limits of certain models of motion in a random medium namely the limiting time constant for last passage percolation and the limiting free energy for directed polymers the results are valid for models in arbitrary dimension steps of the admissible paths can be general the environment process is ergodic under spatial translations and the potential accumulated along a path can depend on the environment and the next step of the path the variational formulas come in two types one minimizes over gradient like cocycles and another one maximizes over invariant measures on the space of environments and paths minimizing cocycles can be obtained from busemann functions when these can be proved to exist the results are illustrated through 1 1 dimensional exactly solvable examples periodic examples and polymers in weak disorder