弱条件下马氏链收敛速度的界

以m-骨架(m≥1)代替1-骨架,计算出马氏链Ф的几何收敛速度的界,从而推广了已有结论.

Abstract：

Assume that φ is a time-homogeneous discrete-time Markov chain with m-skeleton φm on the state space [0, ∞). Meyn and Tweedie have studied the bounds on convergence rates of Markov chains φ with conditions of 1-skeleton. This paper is an attempt to weaken those conditions, that is, it manages to change 1-skeleton into m-skeleton. At the same time, it calculates the bounds on geometric convergence rates of Markov chain φ with weak conditions of m-skeleton (m ≥ 1) in order to generalize the result ofM-eyn and Tweedie.     

lp空间中严格伪压缩Mann迭代过程的弱收敛

证明了lp空间中M小迭代序列弱收敛到严格伪压缩映射的不动点的定理.

Abstract：

The purpose of this paper is to prove the weak convergence theorem of the MANN iteration sequence to a fixed point for a strict pseudo-contraction in lp space.     

Hilbert空间中平衡问题和不动点问题的弱收敛定理

在Hilbert空间中,给出关于寻找平衡问题解集和两族无限非扩张映射不动点集的公共元的Ishikswa迭代格式,并得出此迭代的弱收敛定理.

Abstract：

A new Ishikawa iteration scheme is proposed for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of two infinitely nonexpansive mappings in Hilbert space. A weak convergence theorem is established for this iteration.     

判别一类不变凸函数的充分条件

利用微分几何的分析工具,给出了判别一类不变凸函数的充分条件.如果一个可微函数在г-凸集上的г-Hf矩阵是(正定)半正定的,则函数是(严格)不变凸函数.特别地,若函数没有临界点,则函数是局部严格不变凸的.

Abstract：

With the help of differential geometrical tools,a sufficient condition is given to determine the invexity of differentiable functions．A differentiable function is(strictly)invex function if its г-Hf is positive(definite)semidefinite in a г-convex set.Particularly,a function with no critical points is a locally strictly invex function.     

关于三个问题的混合粘性迭代

在Hilbert空间中,对求解混合平衡问题、非扩张映射不动点问题及单调L-Lipschitz连续映射变分不等式问题解的公共元,引入了由粘性迭代方法确定的迭代序列.在一些参数控制条件下获得了一个强收敛定理.

Abstract：

This paper introduces an iterative sequence for finding a common element of the set of solutions of a mixed equilibrium problem,the set of fixed point problem of nonexpansive mapping and the set of solutions of the variational inequality problem.A strong convergence theorem is obtained under some parameter controlling conditions.     

利用周期边界函数对弦振动方程混沌化

给出了用周期边界函数对一阶线性双曲方程混沌化的结果,利用迭代函数混沌特性的结论对该结果进行了严格的证明,并进一步对满足简单条件的初始函数做了数值模拟,模拟结果与理论结论相吻合.

Abstract：

The problem of chaotifying the hyperbolic systems of linear partial differential equations with periodic boundary functions is proposed in this paper.It is verified by the chaotic properties of iterative functions.Numerical simulation results well fit the theoretical analysis.     

正则Markov链的收敛与逼近(英文)

研究Markov链中概率转移函数的收敛性,用算子半群的方法证明了正则概率转移函数的收敛与其对应的预解函数的收敛等价,并给出了概率转移函数收敛的q-矩阵条件.     

关于预不变拟凸函数的一些特征

给出了预不变拟凸函数的必要条件,并利用该必要务件证明了严格预不变拟凸函数的等价条件,最后给出了中间点预不变拟凸函数的充分必要条件.

Abstract：

Some characterizations about prequasiinvex functions are obtained.Firstly,a necessary condition about prequasiinvex functions is established.Secondly,a necessary and sufficient condition of strictly prequasiinvex func-tions is provided by making use of the necessary condition.Finally,a necessary and sufficient condition is estab-lished about intermediate-point prequasiinvex functions.     

相依结构熵及联合熵的分解

把Copula函数引入熵理论,并定义了相依结构熵来度量随机变量之间的相依结构,计论了二维随机向量在单调变换下相依结构熵的不变性并推广到多维的情形.

Abstract：

The copula functions are employed to study the entropy theory and a conception of dependence structure entropy is defined for measuring the dependence structure of random variables.The joint entropy is divided into the dependence structure entropy and the marginal entropy,which is useful of investigating the dependence structure of random variables.In addition,the invariability of dependence structure entro-py of bivariate variables under monotonous transforming is discussed and extended to muhivariable cases.     

具有两种免疫来源的乙肝病毒模型的全局动力学

研究了免疫反应具有两种来源的乙肝病毒模型.通过对相应特征方程的分析,讨论了感染平衡态和未感染平衡态的局部稳定性,证明了基本再生数>1时疾病的持续性.通过几何方法的应用,得到了感染平衡点全局稳定性的充分条件.

Abstract：

In this paper,an HBV model with activated immune response of two sources is studied.By analyzing the corresponding characteristic equations,the local stability of an infected steady state and an uninfected steady state is discussed.It is proved that if the basic reproductive number is more than one,the disease is persistent.By applying a geometric method,sufficient conditions are obtained for the global stability of the endemic equilibrium.