连续时间集值(上、下)鞅Doob-停时定理

本文首先给出了Ｊ_L意义下的集值鞅的正则性,然后证明了几种连续时间集值（上、下）鞅Ｄｏｏｂ－停时定理．     

集值映射空间上的(ξ)0特征

应用k-网的概念证明了:若X,Y为(ξ)0空间且Y为局部紧的,则X到Y上满足条件(G)的点紧致的族连续集值映射族依紧开拓扑是(ξ)0空间.     

实$q$-一致光滑Banach空间中一类新的涉及广义 增生映射的集值变分包含组的近似可解性

A new system of set-valued variational inclusions involving generalized H(·, ·)-accretive mapping in real q-uniformly smooth Banach spaces is introduced, and then based on the generalized resolvent operator technique associated with H(·, ·)-accretivity, the existence and approximation solvability of solutions using an iterative algorithm is investigated.     

集值映射空间上的基数函数

讨论了集值映射空间在赋予点态收敛拓扑或紧开拓扑下的权数,特征,网络权,稠密度等基数函数,利用自然映射,诱导映射和嵌入等方法将单值连续映射空间的有关结论推广到集值映射空间类上.     

锥似凸映射下集值优化Henig有效解的高阶最优性条件(英文)

This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.     

集值映射空间在紧开拓扑下的N性质(英文)

本文研究了点紧连续集值映射族在紧开拓扑下的N性质.利用cs-σ网方法获得了如下结果:若X是N0空间,Y是N空间,则C_k(X,Y)是N空间.该结论将J.A.Guthrie关于单值连续映射空间的结论推广到了集值映射空间上,并且改进了相关结论.     

集值映射空间上的仿紧性和(Ж)特征

本文研究了集值映射空间类上的仿紧性和(Ж)特征.利用k网的概念及Paul O'Meara等人的结论,得到了点紧致连续集值映射族依紧开拓扑下的仿紧性和(Ж)特征的刻画.     

集值映射的次微分的性质及其应用(英文)

本文讨论了文章Subgradient of S-convex set-valued mappings and weak efficientsolutions(Appl.Math.J.Chinese Univ.1998,13(4):463-472)中引入的集值映射的次微分的性质及应用.利用相依导数的性质,讨论次微分的性质,并得到了两个集值映射的和、复合以及交的次微分的运算法则.最后,通过这种次微分得到了集值优化问题最优性条件的充要条件,同时推广了此文中的定理7.     

集值映射空间上的Tightness和Fan Tightness

本文讨论了连续集值映射空间在赋予点态收敛拓扑和紧开拓扑下的tightness和fan tightness, 将关于连续单值映射空间的某些结果推广到连续集值映射空间.     

集值映射空间上的■0特征1

应用k-网的概念证明了:若X,Y为■0空间且Y为局部紧的,则X到Y上满足条件(G)的点紧致的族连续集值映射族依紧开拓扑是■0空间.     

The Derived Mappings and the Order of a Set-Valued Mapping Between Topological Spaces

Previous investigations of, in particular, continuous selections have led to the definition of the derived mappings and, here, the order of a set-valued mapping between topological spaces. The relation between the topological spaces and the possible orders of set-valued mappings between them is considered and examples are constructed to show that each ordinal number is the order of some set-valued mapping.     

基于集值映射的形式概念分析

Formal concept analysis (FCA) is a discipline that studied the hierarchical structares induced by a binary relation between a pair of sets,and applies in data analysis,information retrieval,knowledge discovery,etc.In this paper,it is shown that a formal context T is equivalent to a set-valued mapping S :G →P(M),and formal concepts could be defined in the set-valued mapping S.It is known that the topology and set-valued mapping are linked.Hence,the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.     

集值映射下的向量均衡问题解的存在性

利用广义的截口定理,本讨论集值映射和变序下的向量均衡问题解的存在性。     

基于模糊集值映射的粗糙近似算子

给出基于模糊集值映射F的模糊集的下(上)近似等概念,研究F-下(上)近似算子aprF(aprF)的性质,探讨求它们的方法,得到若干结果.     

集值映射的对称向量拟均衡问题

研究向量集值映射的拟均衡问题的有效解,利用数值化方法与不动点定理,得到解的存在性定理.作为应用,得到广义向量鞍点,向量变分不等式与向量互补问题的存在性定理.     

参数集值变分不等式的解映射的有界性和连续性

本文借助于非空闭凸集序列的外极限集和极大单调集值映射的外极限研究了参数集值变分不等式的集值解映射的有界性和外半连续性．     

Banach空间中的隐式集值变分包含的一种扰动算法

在Banach空间中研究了一类新的变分包含——隐式集值变分包含问题，得到了隐式变分包含解的等价性与存在性命题及其解的扰动算法，推广、改进了国内外近期获得的一些结果．     

Locally Compact Path Spaces

It is shown that the space X^[0,1], of continuous maps [0,1]X with the compact-open topology, is not locally compact for any space X having a nonconstant path of closed points. For a T₁-space X, it follows that X^[0,1] is locally compact if and only if X is locally compact and totally path-disconnected. Mathematics Subject Classifications (2000) 54C35, 54E45, 55P35, 18B30, 18D15.     

集值映射的可测性与连续性

引进《集D关于集β对于关系《是正常的》这个概念,由两个单值映射组成,再通过取凸包和闭包,构造了可测集值映射、上下半连续集值映射和连续集值映射.