集合$\tau$-标准部分的闭性

In this paper,the closeness of the τ-standard part of a set is discussed.Some related propositions of the τ-neighborhood system of a set are given.And then some related conclusions of the τ-monad of a set and the τ-standard part of a set are presented.And based on it,the necessary and sufficient conditions of the enlarged model and the saturated model are showed.Finally,some sufficient conditions that the τ-standard part of a set is closed are proved in the enlarged model and the saturated model.     

Zero-sum stochastic games with average payoffs: New optimality conditions

In this paper we study zero-sum stochastic games. The optimality criterion is the long-run expected average criterion, and the payoff function may have neither upper nor lower bounds. We give a new set of conditions for the existence of a value and a pair of optimal stationary strategies. Our conditions are slightly weaker than those in the previous literature, and some new sufficient conditions for the existence of a pair of optimal stationary strategies are imposed on the primitive data of the model. Our results are illustrated with a queueing system, for which our conditions are satisfied but some of the conditions in some previous literatures fail to hold.     

QUALITATIVE ANALYSIS OF BOBWHITE QUAIL POPULATION MODEL

In this paper, the qualitative behavior of solutions of the bobwhite quail pop-ulation modelwhere 0   

OSCILLATION AND GLOBAL ATTRACTIVITY OF IMPULSIVE PERIODIC DELAY RESPIRATORY DYNAMICS MODEL

This paper studies the nonlinear delay impulsive respiratory dynamics model. The model describes the sudden changes of the concentration of CO2 in the blood of the mammal. It is proved that the model has a unique positive periodic solution. Some sufficient conditions for oscillation of all positive solutions about the positive periodic solution are established and also some sufficient conditions for the global attractivity of the periodic solution are obtained.     

PERMANENCE AND GLOBAL STABILITY OF POSITIVE SOLUTIONS TO TWO PREDATORSONE PREY SYSTEM WITH A DISCRETE TIME RATIO-DEPENDENT

A three-species ratio-dependent predator-prey discrete model is studied.As a result,sufficient conditions which guarantee the permanence of the model are obtained. In addition,by constructing a suitable Lyapunov function,we derive some sufficient conditions,which ensure that the positive solution of the model is stable and attracts all positive solutions.To illustrate the feasibility of the main results,we introduce an example with corresponding numeric simulations.     

带时滞的比率型的食物链系统的持久性和稳定性

A delayed three-species ratio-dependent predator-prey food-chain model without dominating instantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions, and sufficient conditions are obtained for the local asymptotic stability of a positive equilibrium of the system.     

Existence of two periodic solutions of a ratio-dependent Holling-Taner model with infinite delay and prey harvest

This paper considers a class of ratio-dependent Holling-Taner model with infinite delay and prey harvest, which is of periodic coefficients. By means of the coincidence degree theory, a set of sufficient conditions for the existence of at least two positive periodic solutions of this model is established.     

PERSISTENCE AND PERIODIC SOLUTIONS FOR NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH IMPULSES

In this paper, a nonautonomous Predator-prey model with functional response and impulses is studied. By using comparison theorem and the mono-tonicity, some sufficient conditions which guarantee the permanence and asymptotic behavior of this system are obtained.     

一个具有非线性边界条件的抛物系统整体存在性和爆破

In this paper the nonnegative classical solutions of a parabolic system with nonlinear boundary conditions are discussed. The existence and uniqueness of a nonnegative classical solution are proved. And some sufficient conditions to ensure the global existence and nonexistence of nonnegative classical solution to this problem are given.     

Stability for several type of interval matrices

The robust stability for some types of tlme-varying interval raatrices and nonlineartime-varying interval matrices is considered and some sufficient conditions for robust stability of such interval matrices are given, The main results of this paper are only related to the verticesset of a interval matrices, and therefore, can be easily applied to test robust stability of interval matrices. Finally, some examples are given to illustrate the results.     

GLOBAL ASYMPTOTICAL STABILITY OF AN OBLIGATE LOTKA-VOLTERRA MUTUALISM MODEL

By constructing a suitable Lyapunov function,sufficient conditions which ensure the global asymptotical stability of the positive equilibrium and boundary equilibrium of an obligate Lotka-Volterra mutualism model are obtained,respectively.It is shown that the conditions which ensure the local stability of the nonnegative equilibria is enough to ensure their global asymptotical stability.Our result supplements and complements some known result.     

General admissibility for linear estimators in a general multivariate linear model under balanced loss function

A generalization of Zellner’s balanced loss function is proposed. General admissibility in a general multivariate linear model is investigated under the generalized balanced loss function. And the sufficient and necessary conditions for linear estimators to be generally admissible in classes of homogeneous and nonhomogeneous linear estimators are given, respectively.     

具有时滞的食饵捕食系统的Hopf分支及分支周期解的稳定性（英文）

In this paper, a predator-prey model of three species is investigated, the necessary and sufficient of the stable equilibrium point for this model is studied. Further, by introducing a delay as a bifurcation parameter, it is found that Hopf bifurcation occurs when τ cross some critical values. And, the stability and direction of hopf bifurcation are determined by applying the normal form theory and center manifold theory. numerical simulation results are given to support the theoretical predictions. At last, the periodic solution of this system is computed.     

THE GENERALIZED REFLEXIVE SOLUTION FOR A CLASS OF MATRIX EQUATIONS （AX- B, XC- D）

In this article, the generalized reflexive solution of matrix equations （AX = B, XC = D） is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved.     

THE SURVIVAL ANALYSIS FOR SINGLE-SPECIES SYSTEM IN A POLLUTED ENVIRONMENT

This article concentrates on the study of a mathematical model for the effect of toxicant levels on a single-species ecosystem in the case where there is a constant emission of a toxicant. Some sufficient conditions for weak persistence and extinction are found. The threshold between persistence and extinction can be established in some cases.     

共振条件下2k阶微分方程周期边值问题解的存在唯一性(英文)

In this paper, a new set of sufficient conditions related to an initial value problem and global homeomorphism is obtained in discussing the existence and uniqueness of 2π-periodic solution for 2kth order differential equations with resonance. The key role is played by nonnegative auxiliary scalar coercive function. The result of this paper generalizes some existed theorems.     

PERSISTENCE AND GLOBAL STABILITY FOR A THREE-SPECIES RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH TIME DELAYS IN TWO-PATCH ENVIRONMENTS

A three-species ratio-dependent predator-prey diffusion model with time de-lays is investigated. It is shown that the system is uniformly persistent under some ap-propriate conditions, and sufficient conditions are obtained for the global stability of the positive equilibrium of the system.     

GAMMA-MINIMAX ESTIMATORS FOR THE MEAN VECTOR OF A MULTIVARIATE NORMAL DISTRIBUTION

Γ-minimax estimators are determined for the mean vector of a multivariate normaldistribution under arbitrary squared error loss.Thereby the set Γ consists of all priorswhose vector of first moments and matrix of second moments satisfy some given restric-tions.Necessary and sufficient conditions are derived which ensure a prior being leastfavourable in Γ and the unique Bayes estimator with respect to this prior being Γ-minimax.By applying these results the Γ-minimax estimator is explicitly found in some special casesor can be computed by solving a system of non-linear equations or by minimizing a quad-ratic form on a compact and convex set.     

（g,f）-FACTORS WITH SPECIAL PROPERTIES IN BIPARTITE （mg,mf）-GRAPHS

Let G be a bipartite graph and g and f be two positive integer-valued functions defined on vertex set V(G) of G such that g(x)≤f(x). In this paper,some sufficient conditions related to the connectivity and edge-connectivity for a bipartite (mg,mf)-graph to have a (g,f)-factor with special properties are obtained and some previous results are generalized.Furthermore,the new results are proved to be the best possible.     

Attractivity in a Delayed Three—species Ratio—dependent Predator—prey System without Dominating Instantaneous Negative Feedback

A delayed three-species ratio-dependent predator-prey food-chain model without dominating in-stantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions, and sufficient conditions are derived for the global attractivity of the positive equilibrium of the system.