带马氏切换的马氏过程的指数收敛速度

设 (X(t), Z(t))是以[0,∞) ×{1, 2,…, n₀} 为状态空间的强马氏过程, 其第一分量 X(t) 依赖于第二分量 Z(t), 而第二分量 Z(t) 是一个马氏链. 应用耦合方法, 估计了(X(t), Z(t)) 的转移概率依全变差范数收敛于其不变概率测度的指数收敛速度.     

多项式微分系统的周期解

给出了多项式微分系统的反射函数第一分量不依赖于第二变量的的充要条件,并应用所得结论研究了周期多项式系统周期解的几何性态.     

因变量缺失下部分线性变系数变量含误差模型的估计

该文主要考虑部分线性变系数模型在自变量含有测量误差以及因变量存在缺失情形下的估计问题.基于Profile最小二乘技术,针对参数分量和非参数分量提出了多种估计方法.第一种估计方法只利用了完整观测数据,而第二种和第三种估计方法分别利用了插补技术和替代技术.参数分量的所有估计被证明是渐近正态的,非参数分量的所有估计被证明和一般非参数回归函数的估计具有相同的收敛速度.对于因变量的均值,构造了两类估计并证明了它们的渐近正态性.最后,通过数值模拟验证了所提方法.     

方差分量模型参数的广义岭估计

本文先将方差分量模型的方差分量化为派生模型的均值参数，分别作出其相对于ＬＳＥ和ＢＬＵＥ的广义岭估计，再根据二步估计法作出原模型均值参数的广义二乘估计及其进行一步的岭估计。证明了这样不仅使方差分量估计的均方误差减少，而且使原模型均值参数估计的均方误差也不均加和地一步减少。本文还找到了岭参数仅仅依据于样本的估计，这样既将岭估计方法推进至方差分量模型，也改进了方差分量模型参数的离差均值对应方法。     

向量组关系与其构造的齐次线性方程组的解关系探讨

本文定义了一个向量组所能构造的两个齐次线性方程组:分量型和向量型齐次线性方程组.随后得出:向量组之间的线性表示和等价性与它们对应的分量型齐次线性方程组的解之间关系不大,但与它们对应的向量型齐次线性方程组的解之间的关系密切,可以相互刻划.在此基础上指出了教材《线性代数》(第二版,同济大学数学教研室编)中有关部分的安排及叙述的不妥之处.     

向量组关系与其构造的齐次线性方程组的解关系探讨

本定义了一个向量组所能构造的两个齐次线性方程组：分量型和向量型齐次线性方程组．随后得出：向量组之同的线性表示和等价性与它们对应的分量型齐次线性方程组的解之间关系不大,但与它们对应的向量型齐次线性方程组的解之同的关系密切,可以相互刻射．在此基础上指出了教材《线性代数》(第二版,同济大学数学教研室编)中有关部分的安排及叙述的不妥之处．     

阵列代数与高阶矩

阵列代数与高阶矩李作发，罗玉芳（武汉测绘科技大学，武汉４３００７０）在概率中，ｎ维随机变量的协方差阵表达了各分量围绕它们的数学期望的疏散程度，以及各分量间相关程度的一组数字特征．我们将利用阵列代数引进ｔ个ｎ维随机向量的各分量间相关程度的ｔ阶相关中心矩...     

方差分量的Bayes和Minimax二次估计

本文研究方差分量模型(?)其中 Eε=0,Eεε′=V_θ=sum from i=1 to p θ_iV_i,θ=(θ_1,…,θ_p)′∈Θ,而Θ为一开集且使Θ∩{θ:V_θ>0(p.d.)}非空,β∈(?),此处(?)为 R~K 中开集.在第二节,我们发现了∞-MINQE(u)的 Mini-max 性质,从而赋予其一种明确的统计优良性.本文的第二部分主要是引进有偏的 Bayes二次估计,并在 Kleffe(1974)工作的基础上,将其相应的结果推广到一般的方差分量模型.此外,亦导出了最优的 Bayes 二次估计.借助于当今的计算机,所有的计算步骤皆是可行的.     

关于微分方程组解的m-非允许分量

在本文里，我们给出了微分方程组解的非允许分量之定义，探讨了一类微分方程组解的m-非允许分量的存在性问题，得到了几个结果。它是文[9]的进—步讨论．     

多维指数分布

本文讨论了服从多维指数分布的随机向量的各分量间的独立性与相关性，证明了诸分量相互独立的充分必要条件是它们两两无关；并证明了多维指数分布类在弱收敛下的封闭性．     

The spreading frontiers of avian-human influenza described by the free boundary

In this paper,a reaction-diffusion system is proposed to investigate avian-human influenza.Two free boundaries are introduced to describe the spreading frontiers of the avian influenza.The basic reproduction numbers rF0(t)and RF0(t)are defined for the bird with the avian influenza and for the human with the mutant avian influenza of the free boundary problem,respectively.Properties of these two time-dependent basic reproduction numbers are obtained.Sufficient conditions both for spreading and for vanishing of the avian influenza are given.It is shown that if rF0(0)<1 and the initial number of the infected birds is small,the avian influenza vanishes in the bird world.Furthermore,if rF0(0)<1 and RF0(0)<1,the avian influenza vanishes in the bird and human worlds.In the case that rF0(0)<1 and RF0(0)>1,spreading of the mutant avian influenza in the human world is possible.It is also shown that if rF0(t0)>1 for any t0>0,the avian influenza spreads in the bird world.     

二次微分系统的反射函数及其周期解

本文给出了二镒多项式微分系统具有满足特定关系式的反射函数和存在周期解的充要条件，以及在此条件下反射函数的具体表达式及周期解的稳定性态。     

一类二阶非线性非自治微分方程周期解的存在唯一性

本文证明了一类二阶非线性非自治系统x+ RF′(x) x+ 1L F (x) =e(t)在一定条件下存在唯一渐近稳定的ω周期解 ,推广了已有结果     

一类非线性微分系统的反射函数与周期解

采用一种新方法-反射函数法给出了一类非线性微分系统具有满足特定关系式的反射函数和存在周期解的充要条件,得到了此条件下反射函数的具体表达式和周期解的稳定性态.     

Master–slave synchronization of continuously and intermittently coupled sampled-data chaotic oscillators

In this paper, we consider the problem of synchronizing a master–slave chaotic system in the sampled-data setting. We consider both the intermittent coupling and continuous coupling cases. We use an Euler approximation technique to discretize a continuous-time chaotic oscillator containing a continuous nonlinear function. Next, we formulate the problem of global asymptotic synchronization of the sampled-data master–slave chaotic system as equivalent to the states of a corresponding error system asymptotically converging to zero for arbitrary initial conditions. We begin by developing a pulse-based intermittent control strategy for chaos synchronization. Using the discrete-time Lyapunov stability theory and the linear matrix inequality (LMI) framework, we construct a state feedback periodic pulse control law which yields global asymptotic synchronization of the sampled-data master–slave chaotic system for arbitrary initial conditions. We obtain a continuously coupled sampled-data feedback control law as a special case of the pulse-based feedback control. Finally, we provide experimental validation of our results by implementing, on a set of microcontrollers endowed with RF communication capability, a sampled-data master–slave chaotic system based on Chua’s circuit.     

具有扩散的捕食与被捕食系统的持续性和稳定性

本文研究了一类具有扩散和时滞的捕食与被捕食系统,证明了在适当条件下系统 是一致持续的,利用同伦技术证明了正平衡点的存在性,构造适当的Lyapunov函数获得 了正平衡点的局部和全局稳定的充分条件.     

Existence,uniqueness and stability results of random impulsive semilinear differential systems

In this paper, we consider semilinear differential systems with random impulses. We study the existence and uniqueness of the solutions by relaxing the linear growth conditions, sufficient conditions for stability through continuous dependence on initial conditions and the exponential stability of this system have been established.     

Novel Controllability Conditions for a Class of Singularly-Perturbed Systems with Small State Delays

A singularly-perturbed linear time-dependent controlled system with small pointwise and distributed delays in the state variable is considered. Two simpler parameter-free systems, the slow and fast ones, can be associated with the original system. It was established in the literature that the Euclidean space controllability of the original system, valid for all sufficiently small values of the parameter of singular perturbations, follows from the controllability properties of the slow and fast systems. It also was established that such a connection between the controllability properties of the original system and the slow and fast systems is correct, in general, only in one direction. Namely, the controllability of the slow and fast systems provides the controllability of the original system, while the controllability of the original system not always yields the controllability of both the slow and fast systems. In this paper, we consider the original system such that the respective fast system is uncontrollable, meaning that the previously established controllability conditions are not applicable to this original system. In this case, novel parameter-free sufficient conditions for the Euclidean space controllability of the original system, robust with respect to the small parameter of singular perturbations, are derived. Illustrative examples are presented.     

Permanence of a discrete multispecies Lotka–Volterra competition predator–prey system with delays

In this paper, we propose a discrete multispecies Lotka–Volterra competition predator–prey system with delays. For general nonautonomous case, sufficient conditions are established for the permanence of the system.     

Permanence and extinction of a nonautonomous impulsive plankton model with help

In this paper, we consider a nonautonomous impulsive plankton model with mutual help of preys. Sufficient conditions ensuring permanence and global attractivity of the model are established by the relation between solutions of impulsive system and corresponding nonimpulsive system. Also, we propose the conditions for which the species of system are driven to extinction. Numerical simulations are given to verify the main results.