欧氏空间上Co-regular集的表示式

For the computability of co-regular subsets in metric spaces, the properties of the co-regular subsets and several reasonable representations on co-regular sets have been suggested in this paper. As last, the 'weaker or stronger' relations of these representations have been revealed.     

Large Sets and Overlarge Sets of Triangle-Decomposition

There are six types of triangles:undirected triangle,cyclic triangle,transitive triangle,mixed-1triangle,mixed-2 triangle and mixed-3 triangle.The triangle-decompositions for the six types of triangles havealready been solved.For the first three types of triangles,their large sets have already been solved,and theiroverlarge sets have been investigated.In this paper,we establish the spectrum of LT_i(v,λ),OLT_i(v)(i=1,2),and give the existence of LT_3(v,λ)and OLT_3(v,λ)with λ even.     

Invariant Einstein metrics on generalized Wallach spaces

Invariant Einstein metrics on generalized Wallach spaces have been classified except SO(k + l+ m)/SO(k) × SO(l) × SO(m). In this paper, we first give a survey on the study of invariant Einstein metrics on generalized Wallach spaces, and prove that there are infinitely many spaces of the type SO(k + l + m)/SO(k)× SO(l) × SO(m) admitting exactly two, three, or four invariant Einstein metrics up to a homothety.     

MEASURES AND THEIR DIMENSION SPECTRUMS FOR COOKIE-CUTTER SETS IN R~d

0. IntroductionMany theoretical physicists and mathematicians have studied the Hausdorff dimensions,measures and multifractal decompositions of fractals and obtained a lot of satisfactory results. Particularlyl there hajs given thorough and detailed study for self-similar fractals(of. e.g. [1--7]). mom the dynamical system point of view self-similar sets are regarded asthe attractors of iterated function systems consisting of self-similar cofltraction mappings.However, the researches for measu…     

THEORY AND APPLICATIONS OF MONOTONE SEMIFLOWS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS

The theory of monotone semiflows has been widely applied to functional differential equations (FDEs). The studies on the theory and applications of monotone semiflows for FDEs are very important and interesting. A brief des-cription of our recent works are as follows.By using general monotone semiflow theory, several results of positively invariant sets, monotone solutions and contracting rectangles of retarded functional differential equations(RFDEs) with infinite delay are gained under the assumption of quasimonotonicity; sufficient conditions for the existence, un-iqueness and global attractivity of periodic solutions are also established by combining the theory of monotone semiflows for neutral functional differential equations(NFDEs) and Krasnoselskii's fixed point theorem.     

ASYMPTOTIC SOLUTIONS OF THE REDUCED WAVE EQUATION IN THE VICINITY OF A HIGHER CAUSTIC

In this paper the asymptotic solutions of the reduced wave equation (1) in the vicinity of a higher caustic have been found out by means of asymptotic expansions of the generalized Airy function, and the order (or the singularity inder) and the phase's increment of solutions on the higher caustic have been obtained, too.     

Invariant holomorphic extension in several complex variables Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

Two fundamental problems on the invariant holomorphic extensions have been posed, which are naturally arose from our solution of the extended future tube conjecture and closely and deeply related to the general theory of Stein manifolds due to Cartan-Serre. In this paper, the relationship is presented between the two problems, the motivation of considering the problems, and the methods to approach the problems. We have also posed some questions and conjectures related to this two problems.     

Hyperbolicity of C~1 -star invariant sets for C~1 -class dynamical systems

In this paper, we simply prove, in the framework of Liao, the hyperbolicity of C 1 -star invariant sets of C 1 -class differential systems on a closed manifold of dimension≤ 4, without using the C 1 -connecting lemma and even the ergodic closing lemma.     

Weak Pullback Attractors for Asymptotically Upper Semicompact Nonautonomous Multivalued Semiflow

1 IntroductionIn this paper we study the existence of pullback attractors for multivalued nonautonomousand multivalued random semiflow.In[1]and[2],the authors have proved the existenceof pullback attractors of multivalued nonantonomous semiflow(random semiflow)underthe assumption of the existence of compact absorbing set.In[3],the authors have provedthe existence of pullback attractors of multivalued nonantonomous semiflow and randomsemiflow under the assumptions of uniformly pullback asymptotically upper semicompactand closed graph.In[4],the authors consider the existence of pullback attractor of singl-     

Global dynamics of a competitive system of rational difference equations

In this paper, we study the qualitative behavior of a competitive system of second‐order rational difference equations. More precisely, we investigate the boundedness character, existence and uniqueness of positive equilibrium point, local asymptotic stability and global stability of the unique positive equilibrium point and rate of convergence of positive solutions of the system. Some numerical examples are given to verify our theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Existence of complex ℓ2 solutions of linear delay systems of difference equations

We give sufficient conditions for the existence of complex ?₂ solutions of a non-homogeneous system of linear difference equations and of two general classes of delay systems of linear difference equations. In some cases, bounds of the established solutions are also given. As a consequence of the space ?₂ where we work, information can be obtained about the asymptotic behavior of the established solutions and, the asymptotic stability of the zero equilibrium point of the systems under consideration. The method we use is a functional-analytic one.     

一类具有两阶段结构的自治SIS传染病系统

讨论了具有两阶段结构的自治SIS传染病系统,证明了该系统的边界平衡态和正平衡态的全局渐近稳定性,得到了使其渐近稳定的阈值.     

Extrapolation algorithm for affine-convex feasibility problems

The convex feasibility problem under consideration is to find a common point of a countable family of closed affine subspaces and convex sets in a Hilbert space. To solve such problems, we propose a general parallel block-iterative algorithmic framework in which the affine subspaces are exploited to introduce extrapolated over-relaxations. This framework encompasses a wide range of projection, subgradient projection, proximal, and fixed point methods encountered in various branches of applied mathematics. The asymptotic behavior of the method is investigated and numerical experiments are provided to illustrate the benefits of the extrapolations.     

New stability conditions for neural networks with constant and variable delays

In this paper, by utilizing Lyapunov functional method, we analyze global asymptotic stability of neural networks with constant delays. A new sufficient condition ensuring global asymptotic stability of the unique equilibrium point of delayed neural networks is obtained. Furthermore, based on the method of delay differential inequality, the conditions checking global exponential stability of the equilibrium point of neural networks with variable delays are given. The results extend and improve the earlier publications.     

New stability conditions for neural networks with constant and variable delays

In this paper, by utilizing Lyapunov functional method, we analyze global asymptotic stability of neural networks with constant delays. A new sufficient condition ensuring global asymptotic stability of the unique equilibrium point of delayed neural networks is obtained. Furthermore, based on the method of delay differential inequality, the conditions checking global exponential stability of the equilibrium point of neural networks with variable delays are given. The results extend and improve the earlier publications.     

Stabilization and Practical Asymptotic Stability of Abstract Differential Equations

This article studies the problem of stabilization of the infinite-dimension time-varying control systems in Hilbert spaces. We consider the problem of practical asymptotic stability with respect to a continuous functional for a class of abstract nonlinear infinite-dimensional processes with multivalued solutions on a metric space when the origin is not an equilibrium point. In the case of the existence of a differentiable Lyapunov functional, we obtain sufficient conditions for the practical stability of continuous semigroups in a Banach space.     

广义的Lotka—Volterra方程的全局渐近稳定性

通过构造李亚普诺夫函数的方法,研究了广义的Lotka—Volterra时滞模型方程,而且给出了正平衡点的全局渐近稳定性的充分必要条件,同时对前人的结果进行了改进和推广．     

Dynamics of the density dependent predator-prey system with Beddington-DeAngelis functional response

Two models of a density dependent predator-prey system with Beddington-DeAngelis functional response are systematically considered. One includes the time delay in the functional response and the other does not. The explorations involve the permanence, local asymptotic stability and global asymptotic stability of the positive equilibrium for the models by using stability theory of differential equations and Lyapunov functions. For the permanence, the density dependence for predators is shown to give some negative effect for the two models. Further the permanence implies the local asymptotic stability for a positive equilibrium point of the model without delay. Also the global asymptotic stability condition, which can be easily checked for the model is obtained. For the model with time delay, local and global asymptotic stability conditions are obtained.     

一类具有Allee影响的捕食者-食饵扩散系统研究

讨论一类具有Allee影响的捕食者-食饵扩散模型解的整体性态.通过线性化方法和Lyapunov泛函方法分别证明了该模型正平衡点的局部渐近稳定性和全局渐近稳定性.