模糊过程与模糊微分方程的解法

本文在模糊变量和动态模糊集合的基础上定义了模糊过程、构造了它的F样本函数,然后用F样本函数定义了模糊过程的a.f.s微积分,并讨论了它们的性质;在此基础上,本文提出了非齐次项是模糊过程的微分方程的基本解法,从而为分析动态系统受模糊干扰的响应提供了基础。     

结构的失效可能度及模糊概率计算方法

依据模糊可能性理论,系统地建立含模糊变量时结构的可靠性计算模型。旨在解决模糊结构、模糊-随机结构和模糊状态假设下结构的可靠性计算问题。所建模型可给出模糊结构失效的可能度和模糊-随机结构失效概率的可能性分布。研究表明:对同时含模糊变量和随机变量的混合可靠性计算问题,把失效概率(或可靠度)作为模糊变量,能更客观地反映系统的安全状况。算例分析说明了文中方法的合理性和有效性。     

普遍型模糊随机规划

本文提出了一种求解多目标模糊随机规划问题的普遍方法。这种方法在同一个理论框架内处理约束与目标中的随机性和模糊性,因此它具有相当的普遍性。确定性规划,模糊规划和随机规划都可看成是它的特例。     

模糊随机变量值凸函数的性质及判定

定义了模糊随机变量值凸函数概念,讨论了它的基本性质。此外,给出了判定模糊随机变量值函数凸性的充分必要条件。     

关于G-V模糊拟阵的对偶模糊拟阵概念的推广

模糊拟阵的研究方法之一就是通过基本序列和导出拟阵序列将模糊拟阵问题转化为普通拟阵问题来进行研究。本文正是采用这个研究方法,主要完成了三项工作:一是给出并证明了闭正规模糊拟阵和正规模糊拟阵的几个充要条件;二是将对偶模糊拟阵概念从闭正规模糊拟阵推广到正规模糊拟阵并讨论了有关性质和计算;三是证明了除正规模糊拟阵外,其他模糊拟阵不存在这样的对偶模糊拟阵。     

模糊信息处理方法在纯随机统计中应用的探讨

本文用模糊信息处理的信息分配手段作了改进随机统计精度的尝试。研究结果表明:模糊集的基本思想不仅可以用来描述模糊现象,还可用来处理纯随机问题。     

动态模糊综合评判法及其在故障预测中的应用

提出了种动态模糊综合评判法,讨论动态模糊关系矩阵的确定方法,通过实例证明了该方法的有效性和实用性。     

直觉模糊S-粗集的一般结构及性质

在一般等价关系下,给出单向直觉模糊S-集合、双向直觉模糊S-集合的概念,利用这些概念,提出直觉模糊S-粗集,给出直觉模糊S-粗集的数学结构和有关结论,对有关性质进行了讨论。直觉模糊S-粗集为研究动态信息系统中大量的不确定性问题提供了新的途径和方法。     

模糊随机向量凸集的结构和性质

在模糊随机向量凸集概念的基础上,分析了模糊随机向量凸集的结构,研究了模糊随机向量凸集的基本性质.     

基于模糊数分析的时机捕捉型的证券投资模型

以时机捕捉型的投资者的投资理念和操作经验为背景,本文模拟他们的证券分析和决策过程。我们视证券价格的波动为动态的模糊系统,利用模糊数的概念来定义股价波动的预测集。通过模糊数分析,我们详尽地讨论了证券价格的变化规律和显著投资时机等概念。我们获得了模糊集理论下的证券价格的期望值、投资收益率期望值、预期风险系数、风险率和损益比等数据。利用这些结果,我们得到了三个时机捕捉型的证券投资模型,为证券投资者的决策问题提供了一种新的方法。这些模型的建立依赖于投资者的知识和经验,它们的求解过程简单易行。     

关于局部随机吸引子若干性质的注记(英文)

In this note, we study some properties of local random pull-back attractors on compact metric spaces. We obtain some relations between attractors and their fundamental neighborhoods and basins of attraction. We also obtain some properties of omega-limit sets, as well as connectedness of random attractors. A simple deterministic example is given to illustrate some confusing problems.     

THE RELATION OF DIMENSION,ENTROPY AND LYAPUNOV EXPONENT IN RANDOM CASE

We consider random systems generated by two-sided compositions of random surface diffeomorphisms, together with an ergodic Borel probability measure μ. Let D（μω） be its dimension of the sample measure, then we prove a formula relating D（μω） to the entropy and Lyapunov exponents of the random system, where D （μω） is dimHμω, dimBμm, or dimBμm.     

The relation of dimension,entropy and Lyapunov exponent in random case

We consider random systems generated by two-sided compositions of random surface diffeomorphisms,together with an ergodic Borel probability measure μ.Let D(μω)be its dimension of the sample measure,then we prove a formula relating D(μω)to the entropy and Lyapunov exponents of the random system,where D(μω)is dimHμω,-/dinBμω,or-/dimBμω.     

The attractor of the stochastic generalized Ginzburg-Landau equation

The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system.Then we prove the random system possesses a global random attractor in H_0~1.     

Sample-Path Stability of Non-Stationary Dynamic Economic Systems

The goal of this paper is to introduce and illustrate a new approach to the stability analysis of sample-paths of non-linear stochastic economic models with non-stationary components. We place our study within the mathematical theory of random dynamical systems and apply the concept of a random fixed point which is tailor-made for the study of the long-term behavior of sample-paths in stochastic systems. The main tool for the application of this approach is a Banach-type fixed point theorem for non-stationary random dynamical systems which is proved here. The concept and the theorem are thoroughly explained and illustrated by examples from stochastic growth theory.     

随机耗散Camassa-Holm方程的吸引子

可以接轨道得到带白噪声的随机耗散Camassa-Holm方程的唯—解并且可以检验该解产生随机动力系统,从而证明了该随机动力系统在H₀²中存在紧的随机吸引子.     

模糊随机桁架结构的动力特性双因子分析法

针对模糊随机桁架结构的动力特性分析,提出了一种新的模糊随机有限元方法．当结构的物理参数和几何尺寸同时具有模糊随机性时,利用模糊因子法和随机因子法建立了结构刚度矩阵和质量矩阵;从结构振动的Rayleigh商表达式出发,利用区间运算推导出结构动力特性模糊随机变量的计算表达式;之后利用随机变量的矩法和代数综合法,推导出结构特征值的数字特征的计算式．通过算例分析了模糊随机桁架结构参数的模糊随机性对其动力特性的影响．该方法的优点是能准确反映结构某一参数的模糊随机性对结构特征值及其数字特征的影响．     

Random Attractor for Stochastic Partly Dissipative Systems on Unbounded Domains

In this paper, we consider the long time behaviors for the partly dissipative stochastic reaction diffusion equations. The existence of a bounded random absorbing set is firstly discussed for the systems and then an estimate on the solution is derived when the time is sufficiently large. Then, we establish the asymptotic compactness of the solution operator by giving uniform a priori estimates on the tails of solutions when time is large enough. In the last, we finish the proof of existence a pullback random attractor in L²(R^n) × L²(R^n). We also prove the upper semicontinuity of random attractors when the intensity of noise approaches zero. The long time behaviors are discussed to explain the corresponding physical phenomenon.     

Reconstructibility of a general DNA evolution model

In this paper, we analyze the tree reconstruction problem, to identify whether there is non-vanishing information of the root, as the level of the tree goes to infinity. Although it has been studied in numerous contexts, the existing literature with rigorous reconstruction thresholds established are very limited, and it becomes extremely challenging when the model under investigation has 4 states, one of whose interpretations is the four main bases found in Deoxyribonucleic acid (DNA) and Ribonucleic acid (RNA): guanine [G], cytosine [C], adenine [A], and thymine [T]. In this paper, we study a general DNA evolution model, which distinguishes between transitions and transversions, and allow transversions to occur at the same rate but that rate can be different from the rates for transitions. The sufficient condition for reconstruction is rigorously established.     

Random attractor of stochastic Zakharov lattice system

In this paper, we consider a lattice system of stochastic Zakharov equation with white noise. We first show that the solutions of the system determine a continuous random dynamical system with random absorbing set. And then we prove the random  asymptotic compact on the random absorbing set. Finally, we obtain the existence of a random attractor for the system.