几个随机算子定理

得到Banach空间中随机隐函数存在定理、随机反函数定理和随机Hahn-Banach定理，它们是著名隐函数定理、反函数定理和Hahn-Banach控制延拓定理的随机化推广，这些定理在随机算子理论中将起重要作用。     

向量在几何中的应用

近期将欧氏平面E2上的正弦定理和余弦定理推广到三维欧氏空间E3中,建立了E3中四面体空间角正弦定理、二面角正弦定理和四面体余弦定理,利用向量给出了三维余弦定理和三维正弦定理的简单证明.     

播挪运算及其性质

在现有的播挪定义基础上,引入了对偶播挪的概念和任意论域子集族的内并、内交两种新运算,提出了十个定理.它们是：平凡播挪空间定理,最小播挪定理,播挪内运算封闭性定理,播挪任意交定理,播挪上确界定理,播挪运算分配性定理,播挪基判定定理,播挪基闭包定理,播挪基约简定理,播挪基内运算封闭性定理.这些定理对于播挪空间的研究具有一定的理论价值.     

一类新的KKM定理及其应用*

本文得到一类新的KKM定理,统一和改进了[2,3,0,7,11]中的结果。作为应用,我们得到了几个匹配定理、重合定理、不动点定理、极大极小不等式定理及截口定理。     

连续型概率度量的特征及其应用

讨论了连续型概率度量空间,给出了连续型概率度量的特征定理.利用这个特征定理,我们获得了连续型概率度量空间的闭球套定理和M enger空间完备性特征定理.作为本文的应用获得了一个局部概率压缩映象不动点定理.     

On the Equivalence of Minimax Theorems

In this note we show that Ky Fan's minimax theorem and its several generalizations such as König's minimax theorem [6], M. Neumann's minimax theorem [8] and Fuchssteiner-König's minimax theorem [3] are equivalent. We also give a direct proof for Fuchssteiner-König's minimax theorem on the basis of Eidelheit's well-known seperation theorem.     

Leray-Schauder不动点定理的一个新证明

给出Leray-Schauder不动点定理的一个新证明.我们首先给出集值映射的焊接引理,利用集值映射的焊接引理和Kakutani不动点定理证明Leray-Schauder不动点定理,并证明Leray-Schauder不动点定理与Brouwer不动点定理等价.     

Whitney定理的一个推广形式

Whitney's theorem is a famous theorem in the local singularity theory. In this paper, as an application of Malgrange preparation theorem, a generalized form of Whitney's theorem will be derived.     

An n-dimensional version of Steinhaus' chessboard theorem

The main result of this paper is an n-dimensional version of the Steinhaus' chessboard theorem. Our theorem implies the Poincaré theorem as well as its parametric extension. But it is known that the Poincaré theorem is equivalent to the Brouwer Fixed-Point theorem.     

A stable theorem of the alternative: an extension of the gordan theorem

A theorem with a number of equivalent alternatives is proposed as an extension of the classical Gordan theorem of the alternative. The theorem can handle nonzero unrestricted variables which cannot be directly treated by ordinary theorems of the alternative. Like the Gordan theorem, the extended theorem has the stability feature that small perturbations in the data will not invalidate an alternative that is in force. The theorem has useful applications in establishing the boundedness and uniqueness of feasible points of polyhedral sets and of solutions to linear programming problems.     

A Generalized Form of Whitney's Theorem

Whitney's theorem is a famous theorem in the local singularity theory.In this paper,as an application of Malgrange preparation theorem,a generalized form of Whitney's theorem will be derived.     

关于“四元数自共轭矩阵与行列式的几个定理”的注记

本刊1985年第4期发表郝稚传的“四元数自共轭矩与行列式的几个定理”(称为〔1〕)的文章的主要工作分为两部分。〔1〕在英文摘要中写到:“(i)This essay has improvedthe conclusion of theorem 8 and theorem 9 in 〔2〕”即〔1〕之第一部分工作在于改进了〔2〕的定理8、9的结果,其根据就是〔1〕的定理1、2.〔1〕称定理1—若     

A Generalized Form of Whitney＇s Theorem

Whitney's theorem is a famous theorem in the local singularity theory.In this paper,as an application of Malgrange preparation theorem,a generalized form of Whitney's theorem will be derived.     

替换定理的推广

对向量组的替换定理进行了推广,在证明过程中给出了向量组替换的方法,比经典替换定理便于应用.     

矩阵秩分解定理的一个证明及其应用

矩阵的秩分解定理是矩阵论中的一个基础性定理.本文给出了秩分解定理的一个证明,描述了其中可逆矩阵P,Q的构造,讨论了秩分解定理及其P,Q的构造在解线性方程组中的应用,以及在判别Sylvester不等式等号成立中的应用.     

On pairs of multidimensional matrices

Recently Bapat applied a topological theorem of Kronecker and generalized a theorem of Sinkhorn on positive matrices. Here we give an alternative proof of a slightly stronger version of his generalization. This proof combines Kakutani's fixed point theorem and the duality theorem of linear programming and gives yet another proof of a theorem of Bacharach and Menon on pairs of nonnegative matrices.     

Short proofs of classical theorems

We give proofs of Ore's theorem on Hamilton circuits, Brooks' theorem on vertex coloring, and Vizing's theorem on edge coloring, as well as the Chvátal-Lovász theorem on semi-kernels, a theorem of Lu on spanning arborescences of tournaments, and a theorem of Gutin on diameters of orientations of graphs. These proofs, while not radically different from existing ones, are perhaps simpler and more natural. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 159–165, 2003     

两个泛函优化定理的证明

在泛函优化理论中,Lagrange乘子定理、对偶定理占有重要地位.建立了带有等式和不等式约束的泛函优化问题,并给出了广义Lagrange乘子定理、广义Lagrange对偶定理的证明.     

Existence of the optimal measurable coupling and ergodicity for Markov processes

The existence theorem of the optimal measurable coupling of two probability kernels on a complete separable metric measurable space is proved. Then by this theorem, a general ergodicity theorem for Markov processes is obtained. And as an immediate application to particle systems the uniqueness theorem of the stationary distribution is supplemented, i.e. the uniqueness theorem also implies the existence of the stationary distribution.