一类K-单调系统产生的K-单调算子

本文研究了K-单调系统的解的渐近性质.应用K-单调算子的性质,得到了保证K-单调系统的正周期解的存在性、唯一性、全局渐近稳定性的充分条件.     

具饱和传染率的脉冲免疫接种SIRS模型

研究了具饱和传染率的脉冲免疫接种SIRS模型的一致持续生存和周期解,得到了无病周期解全局渐近稳定的充分条件和系统一致持续生存的充分条件,并应用分支理论得到了正周期解存在的分支参数.     

一类具有饱和传染力的Schoner竞争系统的概周期解

对一类具有饱和传染力的Schoner竞争系统进行了研究,得到了系统持久生存和任一正解全局渐近稳定的充分条件;同时当系统是概周期系统时,通过构造适当的Liapunov函数,建立了相应系统存在唯一、全局渐近稳定的概周期正解的充分判据.     

一类Lotka-Volterra竞争生态系统的周期解

讨论一类特殊的n种群LotkaVolterra竞争生态系统的周期解,应用拓扑度理论中的延拓定理和Lyapunov泛函方法,得到了这类系统周期解的存在性和全局渐近稳定性的充分判据.     

一类具有阶段结构的非自治捕食-食饵系统的持久性与周期解

研究了一类具有阶段结构的非自治的捕食-食饵系统的渐近性质,得到了在适当条件下该系统的持久性,对应周期系统正周期解的存在性、唯一性以及全局渐近稳定性.     

一类具logistic增长率的SIS传染病模型的概周期解

研究了一类具 logistic增长率的 SIS传染病模型 .得到持久性与概周期解存在以及全局一致渐近稳定的充分条件 .     

一类具有常数脉冲投放的三种群捕食系统

考虑了一类两食饵种群具有密度制约和常数脉冲投放的三种群捕食系统,证明了当无捕食者时系统存在一个正周期解,并讨论了这个正周期解的全局渐近稳定性及其条件.     

具有反馈控制和功能反应的两种群竞争系统的解的渐近性

讨论了具有反馈控制和功能反应的两种群竞争系统的解的渐近性质,获得了在一定条件下该种群持续生存的充分条件,以及该系统为周期系统时,存在全局渐近稳定的正周期解。     

捕食者-食Lotka-Volterra系统的概周期解(英文)

研究了有m个捕食者n个食饵的概周期Lotka-Volterra系统.得到了系统共存的条件.此外,还得到了系统概周期解存在唯一并且全局渐近稳定的条件.     

具有时滞和避难所的比率型-捕食者-两竞争食饵模型

讨论了一类具有时滞和避难所的比率型非自治三种群捕食者-食饵模型,运用Liapunov函数方法得到了该模型一致持久和全局渐近稳定的充分条件;并讨论了其周期系统正周期解的存在唯一性和全局吸引性.     

隐马尔可夫模型在语音识别中的应用

隐马尔可夫模型 (HMM)的基本技术是语音识别中较为成功的算法 .主要是它具有较强的对时间序列结构的建模能力 .本文首先深入浅出地介绍了 HMM的基本技术和一个基于 HMM的孤立词语音识别系统的构成方法 ,其次 ,基于 HMM尚存有一些缺陷 ,造成语音识别能力较弱 ,为此本文又进一步阐述了语音识别应用中的几种改进的 HMM系统及目前的热点方法—— HMM与 ANN构成的混合网络     

Three Dimensional Interface Problems for Elliptic Equations

The author studies the structure of solutions to the interface problems for second order linear elliptic partial differential equations in three space dimension.The set of singular points consists of some singular lines and some isolated singular points.It is proved that near a singular line or a singular point,each weak solution can be decomposed into two parts,a singular part and a regular part.The singular parts are some finite sum of particular solutions to some simpler equations,and the regular parts are bounded in some norms,which are slightly weaker than that in the Sobolev space H~2.     

限制李三系的半单元

研究了限制李三系的半单元的一些重要性质,给出了若干个限制李三系是可换的条件,得到了限制李三系的有环面元基的几个条件,刻划了限制李三系的Frattini p-子系的一些性质.同时,研究了中心为零的所有元素是半单元的限制李三系的一些重要性质.     

J—自共轭微分算子谱的定性分析

本文对J－自共轭微分算子谱理论研究情况做一些概要性的介绍,第一部分简要回顾了J－自共轭微分算子理论研究的发展过程,第二,三部分介绍了J－自共轭微分算子的本质谱和离散谱定性分析的主要方法和结论;第四部分扼要叙述J－自共轭微分算子其它方面的一些工作,以及J－自共轭微分算子谱理论研究中尚待解决的问题。     

矩阵逆半群

讨论矩阵逆半群的一些基本性质, 证明矩阵逆半群的幂等元集是有限布尔格的子半格, 从而证明等秩矩阵逆半群是群, 然后完全确定二级矩阵逆半群的结构：一个二级矩阵逆半群或者同构于二级线性群,或者同构于二级线性群添加一个零元素,或者是交换线性群的有限半格, 或者满足其他一些性质; 对于由某些二级矩阵构成的集合, 我们给出了它们成为矩阵逆半群的充分必要条件.     

关于r-平均凸函数的一些性质

继续研究r-平均凸函数,得到了r-平均凸函数的几个等价条件及若干个性质,并改进了相关文献的结果,同时对基本不等式进行了加细.     

The multiplicity of solutions for perturbed second-order Hamiltonian systems with impulsive effects

In this paper, we study the existence of multiple solutions for a class of second-order impulsive Hamiltonian systems. We give some new criteria for guaranteeing that the impulsive Hamiltonian systems with a perturbed term have at least three solutions by using a variational method and some critical points theorems of B. Ricceri. We extend and improve on some recent results. Finally, some examples are presented to illustrate our main results.     

Fixed points of a mapping and Hyers–Ulam stability

We show that many general results on Hyers–Ulam stability of some functional equations in a single variable follow immediately from a simple fixed point theorem. The theorem is formulated for self-maps of some subsets of the space of functions from a nonempty set into the set of reals. We also give some applications of that theorem, e.g., in investigations of solutions of some difference equations and functional inequalities.     

The existence of multiple equilibrium points in a global attractor for some p-Laplacian equation

In this paper, we are mainly concerned with some properties of the global attractor for some p-Laplacian equation with a Lyapunov function in a Banach space. Under some suitable assumptions, we prove the existence of multiple equilibrium points in a global attractor for some p-Laplacian equation.     

Contact topology and holomorphic invariants via elementary combinatorics

In recent times a great amount of progress has been achieved in symplectic and contact geometry, leading to the development of powerful invariants of 3-manifolds such as Heegaard Floer homology and embedded contact homology. These invariants are based on holomorphic curves and moduli spaces, but in the simplest cases, some of their structure reduces to some elementary combinatorics and algebra which may be of interest in its own right. In this note, which is essentially a light-hearted exposition of some previous work of the author, we give a brief introduction to some of the ideas of contact topology and holomorphic curves, discuss some of these elementary results, and indicate how they arise from holomorphic invariants.