on kullback leibler loss and density estimation discrimination information or kullback leibler loss is an appropriate measure of distance in problems of discrimination we examine it in the context of nonparametric kernel density estimation and show that its asymptotic properties are profoundly influenced by tail properties of the kernel and of the unknown density we suggest ways of choosing the kernel so as to reduce loss and describe the extent to which likelihood cross validation asymptotically minimises loss likelihood cross validation generally leads to selection of a window width of the correct order of magnitude but not necessarily to a window with the correct first order properties however if the kernel is chosen appropriately then likelihood cross validation does result in asymptotic minimisation of kullback leibler loss

the steady states of a non cooperative model arising in reactor dynamics in this work we investigate the existence and stability of coexistence states of a reaction diffusion model originated by the theory of nuclear reactors by converting it to an equivalent system with linear cooperative part we obtain the necessary and sufficient conditions for the existence of coexistence states via lower and upper solutions method in addition stability results and a criterion are also given to enrich and complement those available in the literature

distribution estimation consistent in total variation and in two types of information divergence the problem of the nonparametric estimation of a probability distribution is considered from three viewpoints the consistency in total variation the consistency in information divergence and consistency in reversed order information divergence these types of consistencies are relatively strong criteria of convergence and a probability distribution cannot be consistently estimated in either type of convergence without any restrictions on the class of probability distributions allowed histogram based estimators of distribution are presented which under certain conditions converge in total variation in information divergence and in reversed order information divergence to the unknown probability distribution some a priori information about the true probability distribution is assumed in each case as the concept of consistency in information divergence is stronger than that of convergence in total variation additional assumptions are imposed in the cases of informational divergences

a quasilinear parabolic system arising in modelling of catalytic reactors a system of four quasilinear parabolic equations arising in modelling of catalytic reactors is studied the system is coupled in a nonstandard way we prove that the system has unique global solution the asymptotic behavior as t is studied

on the uniqueness and ordering of steady states of predator prey systems this paper discusses the relationship between the uniqueness and the ordering of strictly positive solutions of elliptic predator prey interacting systems if v and u v are two such solutions with u or v v then u v v when the positive solutions are numerically close to the extreme case the solution is unique

some uniqueness and exact multiplicity results for a predator prey model in this paper we consider positive solutions of a predator prey model with diffusion and under homogeneous dirichlet boundary conditions it turns out that a certain parameter m in this model plays a very important role a good understanding of the existence stability and number of positive solutions is gained when m is large in particular we obtain various results on the exact number of positive solutions our results for large m reveal interesting contrast with that for the well studied casem 0 i e the classical lotka volterra predator prey model

optimal routing under capacity and distance restrictions this paper describes an integer linear programming algorithm for vehicle routing problems involving capacity and distance constraints the method uses constraint relaxation and a new class of subtour elimination constraints two versions of the algorithm are presented depending upon the nature of the distance matrix exact solutions are obtained for problems involving up to sixty cities

global existence for reaction diffusion systems with mass control and critical growth with respect to the gradient abstract in this paper we study the existence of global weak solutions for 2 2 reaction diffusion systems for which two main properties hold the positivity of the solutions and the total mass of the components are preserved with time moreover we suppose that the non linearities have critical growth with respect to the gradient the technique we use here in order to prove global existence is in the same spirit of the method developed by boccardo murat and puel for a single equation

asymptotic behavior of global solutions for a chemical reaction model this paper deals with a system of reaction diffusion equations modeling a chemical reaction process involving three substances the mathematical system consists of three semilinear partial differential equations of parabolic type with homogenous neumann boundary conditions the goal is to determine whether each substance has a positive asymptotic limit by the method of upper and lower solutions

persistence in a periodic competitor competitor mutualist diffusion system in this paper we investigate the existence and the asymptotic behavior of periodic solutions for a periodic reaction diffusion system of a competitor competitor mutualist model under dirichlet boundary conditions we shall prove that under certain conditions this system is persistent and under some other conditions it exhibits extinction or more exactly the species of mutualist extincts

positive solutions of the second order differential systems in reactor dynamics abstract in this paper we are concerned with the existence of positive solutions of the second order cooperative system u u u g t f u t 0 1 u t 0 1 u 0 u 1 0 0 1 0 where 2 is a constant 0 is a parameter g 0 1 0 is continuous and g 0 on any subinterval of 0 1 f 0 0 is continuous and f s 0 for s 0 under some suitable conditions on the nonlinearity f we show that above system has at least one positive solution for any 0 the proof of our main results is based upon bifurcation techniques

petrov galerkin methods for systems of nonlinear reaction diffusion equations petrov galerkin method is proposed for solving systems of nonlinear reaction diffusion equations a new concept of ordered pair of supersolution and subsolution is introduced and then the existence of numerical solutions is studied a new monotone iteration is provided for solving the resulting problem the convergence of the petrov galerkin scheme is discussed the numerical results show the advantages of such method

spatial pattern in an ecosystem of phytoplankton nutrient from remote sensing abstract in this paper we consider an ecosystem of phytoplankton nutrient which comes from pelagic zone of the ocean by using remote sensing we are concerned with the pattern formation of the model we first give the asymptotic behavior of positive solutions of parabolic dynamical system then we discuss the stability of constant positive solution and the boundedness of stationary solutions finally the non existence and existence results of the pattern are investigated by considering some parameters the result shows that under certain range of these parameters the pattern of the model occurs

demystifying fixed k nearest neighbor information estimators estimating mutual information from independent identically distributed samples drawn from an unknown joint density function is a basic statistical problem of broad interest with multitudinous applications the most popular estimator is the one proposed by kraskov stogbauer and grassberger ksg in 2004 and is nonparametric and based on the distances of each sample to its k mathrm th nearest neighboring sample where k is a fixed small integer despite of its widespread use part of scientific software packages theoretical properties of this estimator have been largely unexplored in this paper we demonstrate that the estimator is consistent and also identify an upper bound on the rate of convergence of the ell 2 error as a function of a number of samples we argue that the performance benefits of the ksg estimator stems from a curious correlation boosting effect and build on this intuition to modify the ksg estimator in novel ways to construct a superior estimator as a by product of our investigations we obtain nearly tight rates of convergence of the ell 2 error of the well known fixed k nearest neighbor estimator of differential entropy by kozachenko and leonenko

asymptotic distribution theory for nonparametric entropy measures of serial dependence entropy is a classical statistical concept with appealing properties establishing asymptotic distribution theory for smoothed nonparametric entropy measures of dependence has so far proved challenging in this paper we develop an asymptotic theory for a class of kernel based smoothed nonparametric entropy measures of serial dependence in a time series context we use this theory to derive the limiting distribution of granger and lin s 1994 normalized entropy measure of serial dependence which was previously not available in the literature we also apply our theory to construct a new entropy based test for serial dependence providing an alternative to robinson s 1991 approach to obtain accurate inferences we propose and justify a consistent smoothed bootstrap procedure the naive bootstrap is not consistent for our test our test is useful in for example testing the random walk hypothesis evaluating density forecasts and identifying important lags of a time series it is asymptotically locally more powerful than robinson s 1991 test as is confirmed in our simulation an application to the daily s p 500 stock price index illustrates our approach

a monotone iterative scheme for nonlinear reaction diffusion systems having nonmonotone reaction terms abstract a monotone scheme is proposed for the solution of weakly coupled systems of reaction diffusion equations without any monotonicity property of the nonlinear reaction terms the considerations are taken within the framework of weak solutions

nonlinear neutron diffusion with poisoning effects on considere un modele de reacteurs nucleaires dont le comportement evolutif est fortement influence par la presence de noyaux a hautes sections efficaces d absorption

asymptotic behavior of a reaction diffusion system in bacteriology abstract this paper is concerned with the asymptotic behavior of the solution for a coupled system of reaction diffusion equations which describes the bacteria growth and the diffusion of histidine and buffer concentrations under the basic boundary condition of neumann type or mixed type the coupled system can have infinitely many steady state solutions the present paper gives some explicit information on the asymptotic limit of the time dependent solution in relation to these steady states this information exhibits some rather distinct properties of the solutions between the neumann boundary problem and the dirichlet or mixed boundary problem

s shaped global bifurcation curve and hopf bifurcation of positive solutions to a predator prey model where d is a bounded domain in r n 1 with smooth boundary d and a b c d m are positive constants problem 1 0 is known as the predator prey model with holling tanner type interactions where u and v represent the densities of the prey and predator respectively hence we are only interested in positive solutions by which we mean that both u and v are positive in d it is easy to see that a 1 is necessary for the existence of positive solutions to 1 0 and we shall also assume that d 1 the case d 1 is rather different and will not be discussed here we are mainly interested in studying the number of positive solutions of 1 0 and the stability of these solutions in particular we shall show that when b d c and m fall into certain range the solution set u v a of 1 0 forms a s shaped smooth curve and that hopf bifurcation occurs along this curve this not only confirms rigorously similar numerical observations on 1 0 made in 4 but also shows that the corresponding parabolic system

a diffusive competition model with a protection zone this paper is concerned with a two species diffusive competition model with a protection zone for the weak competitor our mathematical results imply that when the protection zone is above a certain critical patch size determined by the birth rate of the weak competitor the weak species almost always survives but it cannot survive when the protection zone is below the critical size and its competitor is strong enough while this is the main feature of the model the actual dynamical behavior of the reaction diffusion system is more complicated the key to reveal the main feature of the system lies in a detailed analysis of the attracting regions of its steady state solutions our mathematical analysis shows that compared with the predator prey model discussed in yihong du junping shi a diffusive predator prey model with a protect zone j differential equations 226 2006 63 91 the protection zone has some essentially different effects on the fine dynamics of the competition model

estimation of nonlinear functionals of densities with confidence this paper introduces a class of k nearest neighbor k nn estimators called bipartite plug in bpi estimators for estimating integrals of nonlinear functions of a probability density such as shannon entropy and renyi entropy the density is assumed to be smooth have bounded support and be uniformly bounded from below on this set unlike previous k nn estimators of nonlinear density functionals the proposed estimator uses data splitting and boundary correction to achieve lower mean square error specifically we assume that t i i d samples xi rd from the density are split into two pieces of cardinality m and n respectively with m samples used for computing a k nn density estimate and the remaining n samples used for empirical estimation of the integral of the density functional by studying the statistical properties of k nn balls explicit rates for the bias and variance of the bpi estimator are derived in terms of the sample size the dimension of the samples and the underlying probability distribution based on these results it is possible to specify optimal choice of tuning parameters m t k for maximizing the rate of decrease of the mean square error the resultant optimized bpi estimator converges faster and achieves lower mean squared error than previous k nn entropy estimators in addition a central limit theorem is established for the bpi estimator that allows us to specify tight asymptotic confidence intervals

on nonlinear coupled reaction diffusion equations this paper is concerned with the existence and uniqueness of solutions of reaction diffusion equations arising in many applications and often coupled our approach to the problem is based on converting the coupled equations into a system of volterra fredholm type integral equations by means of the green s function representation and using the banach fixed point theorem an application to nonlinear second order evolution equations is also indicated

on positive solutions of a nonlinear equilibrium boundary value problem abstract we give necessary and sufficient conditions for the existence of positive solutions to a nonlinear elliptic system arising from mathematical ecology with the dirichlet boundary data assigned by the equilibria of the corresponding ode system the main result is theorem 1 the tools are dancer fixed point index and degree theory

a branch and cut algorithm for the resolution of large scale symmetric traveling salesman problems an algorithm is described for solving large scale instances of the symmetric traveling salesman problem stsp to optimality the core of the algorithm is a polyhedral cutting plane procedure that exploits a subset of the system of linear inequalities defining the convex hull of the incidence vectors of the hamiltonian cycles of a complete graph the cuts are generated by several identification procedures that have been described in a companion paper whenever the cutting plane procedure does not terminate with an optimal solution the algorithm uses a tree search strategy that as opposed to branch and bound keeps on producing cuts after branching the algorithm has been implemented in fortran two different linear programming lp packages have been used as the lp solver the implementation of the algorithm and the interface with one of the lp solvers is described in sufficient detail to permit the replication of our experiments computational results are reported with up to 42 stsps with sizes rangin

entropy based kernel mixture modeling for topographic map formation a new information theoretic learning algorithm for kernel based topographic map formation is introduced in the one dimensional case the algorithm is aimed at uniformizing the cumulative distribution of the kernel mixture densities by maximizing its differential entropy a nonparametric differential entropy estimator is used on which normalized gradient ascent is performed both differentiable and nondifferentiable kernels are in principle supported such as gaussian and rectangular on off kernels the relation is shown with joint entropy maximization of the kernel outputs the learning algorithm s performance is assessed and compared with the theoretically optimal performance a fixed point rule is derived for the case of heterogeneous kernel mixtures finally an extension of the algorithm to the multidimensional case is suggested

a reaction diffusion system of a competitor competitor mutualist model we investigate the homogeneous dirichlet problem and neumann problem to a reactiondiffusion system of a competitor competitor mutualist model the existence uniqueness and boundedness of the solutions are established by means of the comparison principle and the monotonicity method for the dirichlet problem we study the existence of trivial and nontrivial nonnegative equilibrium solutions and their stabilities for the neumann problem we analyze the contant equilibrium solutions and their stabilities the main method used in studying of the stabilities is the spectral analysis to the linearized operators the o d e problem to the same model was proposed and studied by b rai h i freedman and j f addicott

existence of coupled quasi solutions of systems of nonlinear reaction diffusion equations systems of nonlinear parabolic initial boundary value problems arise in many applications such as epidemies ecology biochemistry biology chemical and nuclear engineering constructive methods of proving existence results for such problems which can also provide numerical procedures for the computation of solutions are of greater value than theoretical existence results the method of upper and lower solutions coupled with monotone iterative technique has been employed successfully to prove existence of multiple solutions of nonlinear reaction diffusion equations in special cases by various authors 335 10 11 15 181 recently in 6 171 weakly coupled systems of reaction diffusion equations when the nonlinear terms are independent of gradient terms are discussed and some special type of results are obtained we in this paper investigate general systems of nonlinear reaction diffusion problems when the nonlinear terms possess a mixed quasi monotone property we discuss a very general situation and obtain coupled extremal quasi solutions which in special cases reduce to minimal and maximal solutions we shall also indicate how one step cyclic monotone iterative schemes can be generated which yield accelerated rate of convergence of iterates this work is in the spirit of our recent paper 12 for elliptic systems

best asymptotic normality of the kernel density entropy estimator for smooth densities in the random sampling setting we estimate the entropy of a probability density distribution by the entropy of a kernel density estimator using the double exponential kernel under mild smoothness and moment conditions we show that the entropy of the kernel density estimator equals a sum of independent and identically distributed i i d random variables plus a perturbation which is asymptotically negligible compared to the parametric rate n sup 1 2 an essential part in the proof is obtained by exhibiting almost sure bounds for the kullback leibler divergence between the kernel density estimator and its expected value the basic technical tools are doob s submartingale inequality and convexity jensen s inequality

a new subtour elimination constraint for the vehicle routing problem abstract vehicle routing problems vrp are concerned with the delivery of a single commodity from a centralized depot to a number of specified customer locations with known demands in this paper we consider the vrp characterized by fixed or variable number of vehicles common vehicle capacity distance restrictions and minimization of total distance travelled by all vehicles as the objective we develop an exact algorithm based on a new subtour elimination constraint the algorithm is implemented using the cplex package for solving the relaxed subproblems computational results on 1590 simulated problems and 10 literature problems without distance restrictions are reported and a comparative analysis is carried out

numerical methods for coupled systems of nonlinear parabolic boundary value problems abstract a system of nonlinear finite difference equations corresponding to a class of coupled parabolic equations in a bounded domain is investigated using the method of upper lower solutions we construct two monotone sequences for the finite difference equations it is shown that when the reaction function is quasimonotone nondecreasing nonincreasing or mixed quasimonotone these two sequences converge monotonically to a unique solution of the finite difference system this monotone convergence leads to an existence comparison theorem as well as iterative numerical algorithms for the computation of the solution it also gives error estimates for the finite difference solution in each iteration without explicit knowledge of the solution moreover the monotone convergence property is used to prove the convergence of the finite difference solution to the corresponding solution of the differential system as the mesh size decreases to zero

existence uniqueness and stability of positive solutions to sublinear elliptic systems reaction diffusion systems are used to model many chemical and biological phenomena in the natural world 25 26 and systems of coupled partial differential equations are also used in other physical models such as nonlinear schrodinger systems in multi component bose einstein condensates and nonlinear optics 19 23 the steady state solutions or standing wave solutions of such systems of nonlinear partial differential equations satisfy a nonlinear elliptic system with more than one equation much effort has been devoted to the existence of solutions of such systems see for example 4 8 10 11 13 15 17 24 30 33 34 but it is usually difficult to determine whether or not the solution is unique we consider the positive solutions of a semilinear elliptic system of the form

on nonlinear reaction diffusion systems abstract this paper presents a qualitative analysis for a coupled system of two reaction diffusion equations under various boundary conditions which arises from a number of physical problems the nonlinear reaction functions are classified into three basic types according to their relative quasi monotone property for each type of reaction functions an existence comparison theorem in terms of upper and lower solutions is established for the time dependent system as well as some boundary value problems three concrete physical systems arising from epidemics biochemistry and engineering are taken as representatives of the basic types of reacting problems through suitable construction of upper and lower solutions various qualitative properties of the solution for each system are obtained these include the existence and bounds of time dependent solutions asymptotic behavior of the solution stability and instability of nontrivial steady state solutions estimates of stability regions and finally the blowing up property of the solution special attention is given to the homogeneous neumann boundary condition

maximum likelihood estimation of smooth monotone and unimodal densities we study the nonparametric estimation of univariate monotone and unimodal densities using the maximum smoothed likelihood approach the monotone estimator is the derivative of the least concave majorant of the distribution corresponding to a kernel estimator we prove that the mapping on distributions with density the derivative of the least concave majorant of is a contraction in all l p norms 1 p and some other distances such as the hellinger and kullback leibler distances the contractivity implies error bounds for monotone density estimation almost the same error bounds hold for unimodal estimation

numerical solutions for some coupled systems of nonlinear boundary value problems in the well known volterra lotka model concerning two competing species with diffusion the densities of the species are governed by a coupled system of reaction diffusion equations the aim of this paper is to present an iterative scheme for the steady state solutions of a finite difference system which corresponds to the coupled nonlinear boundary value problems this iterative scheme is based on the method of upper lower solutions which leads to two monotone sequences from some uncoupled linear systems it is shown that each of the two sequences converges to a nontrivial solution of the discrete equations the model under consideration may have one two or three nonzero solutions and each of these solutions can be computed by a suitable choice of initial iteration numerical results are given for these solutions under both the dirichlet boundary condition and the mixed type boundary condition

on positive solutions of the lotka volterra cooperating models with diffusion abstract in this paper using the existence and comparison conclusion for the time periodic quasimonotone nondecreasing systems given by pao c v and iterative method we investigate the time periodic lotka volterra cooperating model and present some existence uniqueness and nonexistence results we also use similar methods to treat the corresponding stationary system to give parallel results

nonlinearly smoothed em density estimation with automated smoothing parameter selection for nonparametric deconvolution problems abstract we study a nonparametric deconvolution density estimation problem the estimator is obtained by an em algorithm for a smoothed maximum likelihood estimation problem which has a unique continuous solution we present an implementation of the procedure incorporating a data driven discrepancy principle for selecting the smoothing parameter simulations illustrate the good properties of the resulting estimator when the unknown distribution is smooth and has regularly varying thin tails comparisons with a fourier kernel deconvolution method are made for the case of normal noise we show that under mild smoothness conditions the estimator based on the data driven smoothing parameter is strongly consistent

roles of weight functions in a nonlinear nonlocal parabolic system abstract this paper deals with a semilinear parabolic system with coupled nonlinear nonlocal sources subject to weighted nonlocal dirichlet boundary conditions we establish the conditions for global and non global solutions it is interesting to observe that the weight functions for the nonlocal dirichlet boundary conditions play substantial roles in determining not only whether the solutions are global or non global but also whether for the non global solutions the blowing up occurs for any positive initial data or just for large ones

positive solutions of a lotka volterra competition model with cross diffusion abstract this paper concerns a lotka volterra competition reaction diffusion system with nonlinear diffusion effects we first briefly discuss the stability of trivial solutions by spectrum analysis based on the boundedness of the solutions the existence of the positive steady state solution is also investigated by the monotone iteration method

asymptotic stability for an integrodifferential reaction diffusion system abstract a reaction diffusion system involving an integrodifferential linear parabolic equation and a nonlinear ordinary differential equation is studied under third type boundary conditions such a system may be used to describe the evolution of a class of man environment epidemics conditions are given for the existence and the asymptotic stability of a unique nontrivial equilibrium solution by using monotone iteration techniques

a reaction diffusion system with mixed type coupling this paper deals with asymptotic behavior of solutions to a reaction diffusion system coupled via localized and local sources u t du v p x t t v t dv u q both the initial boundary problem with null dirichlet boundary condition and the cauchy problem are considered to study the interaction between the two kinds of sources for the initial boundary problem we prove that the nonglobal solutions blow up everywhere in the bounded domain with uniform blow up profiles in addition it is interesting to observe that the cauchy problem admits an infinity fujita exponent namely the solutions blow up under any nontrivial and nonnegative initial data whenever pq 1 all these imply that the blow up behavior of solutions is governed by the localized source for the two problems with mixed type coupling

asymptotic stability of reaction diffusion systems in chemical reactor and combustion theory abstract some coupled reaction diffusion systems arising from chemical diffusion processes and combustion theory are analyzed this analysis includes the existence and uniqueness of positive time dependent solutions upper and lower bounds of the solution asymptotic behavior and invariant sets and the stability of steady state solutions including an estimate of the stability region explicit conditions for the asymptotic behavior and the stability of a steady state solution are given these conditions establish some interrelationship among the physical parameters of the diffusion medium the reaction mechanism the initial function and the type of boundary condition under the same set of physical parameters and reaction function a comparison between the neumann type and dirichlet or third type boundary condition exhibits quite different asymptotic behavior of the solution for the general nonhomogeneous system multiple steady state solutions may exist and only local stability results are obtained however for certain models it is possible to obtain global stability of a steady state solution by either increasing the diffusion coefficients or decreasing the size of the diffusion medium this fact is demonstrated by a one dimensional tubular reactor model commonly discussed in the literature

existence of steady state solutions to predator prey equations in a heterogeneous environment is considered here x t e 52 x r where 52 is a bounded domain in ky u u u urn is an m tuple of functions d is a constant positive definite matrix and the a are continuous matrix valued functions in 4 it is shown that if this system admits a bounded invariant region in r and a certain quantity 0 is positive then the solution of the initial boundary value problem with initial condition u x 0 u x and homogeneous neumann boundary condition will converge to its own spatial average exponentially in l or l as t co this result implies that when the diffusion is sufficiently strong any spatially nonconstant steady state solution of the parabolic system above is unstable

global bifurcation of positive radial solutions for an elliptic system in reactor dynamics in this paper we are concerned with the existence of positive radial solutions of the elliptic system email protected email protected f x u r 1 0 is a constant m 0 is a parameter and 0 0 is continuous and f t s 0 for all t s r 1 r 2 x 0 under some appropriate conditions on the nonlinearity f we show that the above system possesses at least one positive radial solution for any email protected 0 the proof of our main results is based upon bifurcation techniques

global existence and blow up for a nonlinear reaction diffusion system abstract we consider the nonlinear reaction diffusion system u t u u m 1 v n 1 v t v u m 2 v n 2 subject to dirichlet boundary conditions andm2 m1 1 n1 n2 1 we prove that ifm1 1 n2 1 andm2n1 1 m1 1 n2 all nonnegative solutions are global while ifm1 1 orn2 1 orm2n1 1 m1 1 n2 both global existence and finite time blow up coexist

quasi steady state approximation for a reaction diffusion system with fast intermediate abstract we consider a prototype reaction diffusion system which models a network of two consecutive reactions in which chemical components a and b form an intermediate c which decays into two products p and q such a situation often occurs in applications and in the typical case when the intermediate is highly reactive the species c is eliminated from the system by means of a quasi steady state approximation in this paper we prove the convergence of the solutions in l 2 as the decay rate of the intermediate tends to infinity for all bounded initial data even in the case of initial boundary layers the limiting system is indeed the one which results from formal application of the qssa the proof combines the recent l 2 approach to reaction diffusion systems having at most quadratic reaction terms with local l bounds which are independent of the decay rate of the intermediate we also prove existence of global classical solutions to the initial system

analysis of a prey predator model with disease in prey abstract in this paper a system of reaction diffusion equations arising in eco epidemiological systems is investigated the equations model a situation in which a predator species and a prey species inhabit the same bounded region and the predator only eats the prey with transmissible diseases a number of existence and non existence results about the non constant steady states of a reaction diffusion system are given it is proved that if the diffusion coefficient of the predator is treated as bifurcation parameter non constant positive steady state solutions may bifurcate from the constant steady state solution under some conditions

dynamics of a diffusive predator prey model with modified leslie gower and holling type iii schemes abstract the diffusive predator prey system with modified leslie gower and holling type iii schemes is considered here firstly stability analysis of the equilibrium for a reduced ode system is discussed secondly we obtain that the system is permanent thirdly sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the system are derived by using the method of lyapunov function finally we establish the existence and nonexistence of nonconstant positive steady states of this reaction diffusion system which indicates the effect of large diffusivity

entropy expressions and their estimators for multivariate distributions entropy expressions for several continuous multivariate distributions are derived point estimation of entropy for the multinormal distribution and for the distribution of order statistics from d g weinman s ph d dissertation ariz state univ tempe az 1966 exponential distribution is considered the asymptotic distribution of the uniformly minimum variance unbiased estimator for multinormal entropy is obtained simulation results on convergence of the means and variances of these estimators are provided

asymptotic behavior and positive solutions of a chemical reaction diffusion system abstract this paper is concerned with some qualitative analysis for a coupled system of three reaction diffusion equations which arises from certain chemical reactions first discovered by belousov and zhabotinskii the analysis includes the existence of a bounded global time dependent solutions the stability and instability of the zero solution and the existence and nonexistence of a positive steady state solution including a global attractor of the system the global existence and stability problem is determined by the method of upper and lower solutions and the existence of a positive steady state solution is based on the fixed point index and bifurcation theory this analysis leads to a necessary and sufficient condition for the existence and nonexistence of a positive steady state solution in relation to the various physical parameters of the system

coexistence theorems of steady states for predator prey interacting systems on donne des conditions necessaires et suffisantes pour l existence des solutions positives des etats stationnaires pour des systemes predateur proie sous des conditions aux limites de dirichlet sur r n

the global existence and blowing up property of solutions for a nuclear model abstract in this paper we study the global existence and blowing up property of solutions for a coupled system of two reaction diffusion equations under the neumann conditions which arises from nuclear reactor dynamics the estimates of stability regions obtained are the best at the moment for constant initial data representations of solutions are given for a solution blowing up in finite time an upper bound and a lower bound on the blowing up time are povided

estimation of the entropy and information of absolutely continuous random variables a method is proposed for estimating the entropy and the mutual information of absolutely continuous random vectors and an upper bound of the mean risks for the proposed estimators under strong mixing conditions is given

periodic solutions of coupled semilinear parabolic boundary value problems the study of periodic solutions to parabolic differential systems goes back to j fourier who investigated the linear heat equation for the determination of temperature oscillation on earth cf 141 in recent years attention has been given to nonlinear parabolic boundary value problems cf l 2 4 6 7 15 16 however most of the discussions in the literature are concerned with a single parabolic equation under dirichlet type boundary condition due to the recent development in the biochemical and biological fields there arise various types of reactiondiffusion systems e g see lo 121 an interesting problem in some of these systems such as the belousov zhabotinskii reaction model is an understanding of the oscillating nature of the solution in this paper we investigate periodic solutions for a coupled system of parabolic boundary value problems in a one dimensional domain under various boundary conditions specifically the equations under consideration are given by

positive solutions of systems of semilinear elliptic equations the pendulum method abstract conditions are formulated which guarantee the existence of positive solutions for simultaneous systems on an open domain with each constant is a positive measure the main tools used are probabilistic potential theory markov processes and an iterative scheme which is not a generalization of the one used for quasi monotone systems quasi monotonicity is not assumed and new results are obtained