拓扑空间中的一个非空交定理及其应用

在FC-空间中证明了一新的非空交定理．作为应用，一不动点定理，一极大元定理，一重合点定理和一些极小极大不等式被证明．这些定理推广了近期文献中的结果．     

Fn-H截口定理的改进及其应用

本文首先证明Fn H截口定理的一个改进形式和一些相应的等价形式;其次作为应用,我们得到一个极大极小定理、一些重合定理和一个极大元定理.     

Fan-Ha截口定理的改进及其应用

本文首先证明Ｆａｎ－Ｈａ截口定理的一个改进形式和一些相应的等价形式;其 次作为应用,我们得到一个极大极小定理、一些重合定理和一个极大元定理．     

Fan-Ha截口定理的改进及其应用

本文首先证明Ｆａｎ－Ｈａ截口定理的一个改进形式和一些相应的等价形式;其 次作为应用,我们得到一个极大极小定理、一些重合定理和一个极大元定理．     

转移开,闭集值映象和H—KKM定理的推广及应用

本中，我们引入转移开、闭集值映象的概念、推广了Ｈ－空间中的ＫＫＭ定理。然后用所得的结果证明了几个重合定理、匹配定理和向量值极大极小不等式。这些结论推广了近期献〔１，２，４，５，６，７〕中的相应结果。     

转移开、闭集值映象和H－KKM定理的推广及应用

本文中，我们引入转移开、闭集值映象的概念，推广了Ｈ－空间中的ＫＫＭ定理￣［４］．然后用所得的结果证明了几个重合定理、匹配定理和向量值极大极小不等式。这些结论推广了近期文献［１，２，４，５，６，７］中的相应结果。     

光滑流形的同调论及其推广

在近代光滑流形的理论中,将流形的解析性质与拓扑性质关联起来的著名的DeRham定理起着重要的作用。实际上De Rham定理是Leray首先证明的一个唯一性定理的特殊情形。这个定理Leray是在极大的一般性之下很复杂地证明的。后来J.Fáry在一个简短的报导中在一个比较不顶一般的形式下很简单地证明了唯一性定理。本文的目的就是要详尽地阐明Fáry的证明。     

关于2—因指数群

如果有限群Ｇ的每个极大子群的指数和质因子个数都小于或等于ｎ，则称Ｇ为ｎ－因指数群。本文用单群分类定理证明了。     

初等几何定理机器证明——吴方法简介

吴文俊院士获得2000年国家科学技术最高奖，这对我们数学工作者是极大的鼓舞，他的主要成就包括代数拓扑，应用数学，数学史，几何定理的机器证明等．这里，我们介绍后者．     

关于''抽象的极小极大定理''的注记

本文指出林壮鹏2000年发表的一个抽象的极大极小定理一文中主要结果的证明需要修正,然后改进了该文的结果,同时给出了一个简单的证明。     

Constants related to operators of class Cρ

Let T be a Hilbert-space operator of class $$\left\| {S^{ - 1} TS} \right\| \leqslant 1\,\,\,\,and\,\,\left\| {S^{ - 1} } \right\| \cdot \left\| S \right\| \leqslant \max (1,\rho )$$ in the sense of Sz.-Nagy and Foia?. Then there exists an invertible operator S such that ∥S^?1TS∥≤1 and ∥S^?1∥·∥S∥≤max(1,ρ). The following estimate is valid for the bilateral limit: $$\mathop {lim}\limits_{n \to \infty } \{ \left\| {T^n h} \right\|^2 + \left\| {T*^n h} \right\|^2 \} \leqslant max(2,\rho )\left\| h \right\|^2 .$$ Here the constants max(1,ρ) and max(2,ρ) are the best possible in their respective cases.     

非线性四阶两点边值问题的一个正解存在定理

本文利用锥压缩锥拉伸型的Krasnosel’skii不动点定理证明了非线性四阶两点边值问题的一个正解存在定理．     

超有效意义下向量集值优化修整的Lagrange乘子型对偶

给出了一类加细的向量集值优化超有效解的最优性条件,由此给出了一种改进的Lagrange乘子型对偶,并建立了对偶的弱定理,正定理及逆定理。     

Pinchings and Norms of Scaled Triangular Matrices

Suppose U is an upper-triangular matrix, and D a nonsingular diagonal matrix whose diagonal entries appear in nondescending order of magnitude down the diagonal. It is proved that $$\|D^{-1}UD\|\ge\|U\|$$ for any matrix norm that is reduced by a pinching. In addition to known examples -weakly unitarily invariant norms - we show that any matrix norm defined by $$\| A \|^{\underline{\underline {{\rm def}}} } \mathop {\max }\limits_{x \ne 0,y \ne 0} {{{\mathop{\rm Re}\nolimits} (x^*Ay)} \over {\phi (x)\psi (y)}},$$ where θ (.) and y (.) are two absolute vector norms, has this property. This includes l p operator norms as a special case.     

Fourier Inversion Formulas in Option Pricing and Insurance

Several authors have used Fourier inversion to compute prices of puts and calls, some using Parseval’s theorem. The expected value of max (S – K, 0) also arises in excess-of-loss or stop-loss insurance, and we show that Fourier methods may be used to compute them. In this paper, we take the idea of using Parseval’s theorem further: (1) formulas requiring weaker assumptions; (2) relationship with classical inversion theorems for probability distributions; (3) formulas for payoffs which occur in insurance. Numerical examples are provided.      

Methods for knowledge reduction in inconsistent ordered information systems

Knowledge reduction is one of the most important problems in the study of rough set theory. However, in real-world, most of information systems are based on dominance relations in stead of the classical equivalence relation because of various factors. The ordering of properties of attributes plays a crucial role in those systems. To acquire brief decision rules from the systems, knowledge reductions are needed. The main objective of this paper is to deal with this problem. The distribution reduction and maximum distribution reduction are proposed in inconsistent ordered information systems. Moreover, properties and relationship between them are discussed. Furthermore, judgment theorem and discernibility matrix are obtained, from which an approach to knowledge reductions can be provided in inconsistent ordered information systems.     

Surrogate duality for robust optimization

Robust optimization problems, which have uncertain data, are considered. We prove surrogate duality theorems for robust quasiconvex optimization problems and surrogate min–max duality theorems for robust convex optimization problems. We give necessary and sufficient constraint qualifications for surrogate duality and surrogate min–max duality, and show some examples at which such duality results are used effectively. Moreover, we obtain a surrogate duality theorem and a surrogate min–max duality theorem for semi-definite optimization problems in the face of data uncertainty.     

关于Hilbert空间上无限维线性定常系统的典型分解

有限维线性定常系统的典型分解定理是控制理论的重要成果之一 [1] ,也是计算机控制的重要理论基础之一 ,本文将这一结果推广到 Hilbert空间上的无限维线性定常系统 .     

拓扑空间中的连续逼近选择和几乎不动点

本文研究连续逼近选择问题 研究结果表明 ,几乎下半连续的集值映射有连续逼近选择 .从而 ,著名的Michael连续逼近选择定理被改进 .应用这个结果 ,一个几乎不动点定理被获得     

A proof of Markov's theorem for polynomials on Banach spaces

Our object is to present an independent proof of the extension of V.A. Markov's theorem to Gâteaux derivatives of arbitrary order for continuous polynomials on any real normed linear space. The statement of this theorem differs little from the classical case for the real line except that absolute values are replaced by norms. Our proof depends only on elementary computations and explicit formulas and gives a new proof of the classical theorem as a special case. Our approach makes no use of the classical polynomial inequalities usually associated with Markov's theorem. Instead, the essential ingredients are a Lagrange interpolation formula for the Chebyshev nodes and a Christoffel-Darboux identity for the corresponding bivariate Lagrange polynomials. We use these tools to extend a single variable inequality of Rogosinski to the case of two real variables. The general Markov theorem is an easy consequence of this.