Hahn-Banach定理在V-凸性模定义中的应用

先给出了V-凸性模的两个等价定义,并利用Hahn-Banach定理给出了它们的等价性.其次,在V-凸性模定义的基础上引进了广义V-凸性模的概念,并给出了其两个等价定义.     

GO-空间乘积的子空间

数学家 N.Kemoto,T.Nogura,K.D.Sm ith和 Y .Yajim a 1996年证明了两个序数乘积的子空间的正规性、集体正规性、收缩性是等价的 .本文把这个命题进行了推广 ,得到了两个 GO -空间乘积的任意子空间的正规性、集体正规性、收缩性是等价的 .     

一类二阶非线性摄动微分方程的振动性与渐近性

研究了一类二阶非线性摄动微分方程解的振动性质和渐近性质,建立了两个新的振动性与渐近性定理,推广和改进了已有的一些结果.     

具有连续参数齐次随机场的线性预测与马氏性

本文研究了具有连续参数齐次随机场的3个类型的线性预测问题和两个类型的马氏性问题,并用这3个类型的预测问题的研究结果及[1]的方法,求出了这两个类型的马氏性问题具有马氏性的充分条件和充分必要条件.且深化了[1]中结果.     

LMI优化问题的择一性定理与对偶

考虑目标函数是线性函数约束条件为线性矩阵不等式的LMI优化问题,讨论了LMI优化问题中的四个择一性定理.每种类型的择一性定理包含两个线性不等式和(或)等式系统,一个原始系统和一个对偶系统.弱择一性定理说明两系统中至多只有其一有解;基于凸集分离理论得到的强择一性定理说明两系统有且仅有其一有解.并在此基础上推导了LMI优化...     

GO-空间乘积的子空间的广义仿紧性

20 0 0年 ,数学家 N .Kemoto,K.Tam ano和 Y.Yajima证明了两个特殊的 GO-空间——序数乘积子空间的亚紧性 ,screenability,弱 submetalindelof性是等价的 .本文把这个命题推广到了两个一般的 GO-空间乘积的任意子空间上 ,证明了它们仍然是等价的 .     

Banach空间中Birkhoff正交性的刻画

研究了Banach空间中两元素a和b在Birkhoff意义下正交的性质,给出在Banach空间中两个元素B-正交和线性泛函的关系,然后用线性泛函来研究B-正交性与Banach空间的可微性、凸性、自反性的关系.本文最后定义B-正交性的补,通过B-正交性的补来研究B-正交性和Banach空间的性质.     

函数两种凸性定义等价性的今惑前世之初探

通过研究中点凸函数和一般凸函数这两种凸性定义的早期发展历史和凸性性质来探索两种凸性定义的等价性.结果表明,两种凸性定义不等价;但是,当函数满足连续、可微、半连续和有界这四个条件中的任何一个条件时,两种凸性定义等价.     

关于Devroye－Wagner核估计的一个注记

本文研究了Ｄｅｖｒｏｙｅ和Ｗａｇｎｅｒ提出的两个核估计的有偏性，并给出这两个核估计的Ｐａｒｚｅｎ－Ｒｏｓｅｎｂｌａｔｔ核估计有偏性的一个统一的证明．     

二阶非线性摄动微分方程的振动性定理

研究了一类二阶非线性摄动微分方程解的振动性,建立了两个新的振动性定理,推广和改进了已有的结果.     

Existence of solutions of two generalized riccati operator equations and their representation

The solutions of two generalized Riccati operator equations are discussed in terms of two critical parameter values, which are related to the application of optimal control under unknown disturbances. Explicit formulas for calculating these two critical parameters as well as the closedform solutions of these two generalized Riccati operator equations are given. The connection between these two parameters and a zero-sum differential game is also investigated.     

Complete monotonicity of a function involving the divided difference of digamma functions

In the paper, necessary and sufficient conditions are provided for a function involving the divided difference of two psi functions to be completely monotonic. Consequently, a class of inequalities for sums are presented, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions are derived, and two double inequalities for bounding the ratio of two gamma functions are discovered.     

equivalence of initialized Riemann-Liouville and caputo derivatives

Initialization of fractional differential equations remains an ongoing problem. The initialization function approach and the infinite state approach provide two effective ways of dealing with this issue. The purpose of this paper is to prove the equivalence of the initialized Riemann-Liouville derivative and the initialized Caputo derivative with arbitrary order. By synthesizing the above two initialization theories, diffusive representations of the two initialized derivatives with arbitrary order are derived. The Laplace transforms of the two initialized derivatives are shown to be identical. Therefore, the two most commonly used derivatives are proved to be equivalent as long as initial conditions are properly imposed.     

图的笛卡儿积及字典式积的连通性

文章给出了两个图的笛卡儿积及字典式的积为最大边连通的、最大连通的、super-λ,super-κ及hyper-κ的充分条件,同时证明了其中一些条件也是必要的.此外,对这两种积的局部割集和广义割集的性质也进行了考虑.     

Anticoloring of a family of grid graphs

An anticoloring of a graph is a coloring of some of the vertices, such that no two adjacent vertices are colored in distinct colors. We deal with the anticoloring problem with two colors, in the particular cases of graphs which are strong products of two paths or two cycles, and provide an explicit optimal solution.     

广义扰动映射的上导数

主要讨论了两集值映射和的上导数．在比标准约束品性弱的条件下得到了两个集值映射和的上导数与两集值映射上导数的和之间的包含关系,并将此结论用于讨论广义扰动映射的上导数,得到广义扰动映射的上导数的上界估计．     

涉及两个n维单形的两类不等式

本文给出了涉及两个 n维单形的两类不等式 ,并得到了两个推论 .     

Two Classes of Smooth Objective Penalty Functions for Constrained Problems

This research aims at solving constrained problems by providing two classes of objective penalty functions which respectively approach to a class of exact penalty functions smoothly. Meanwhile, the authors present two algorithms based on the two objective penalty functions, and give the conclusion that all of the cluster points of the two sequences generated by the two algorithms are the optimal points of the original problem. Furthermore, this article discusses that both of the two penalty functions are of well-condition. Finally, the authors report numerical results to show the applicability of the two presented algorithms.     

球型平移网络逼近周期函数

研究了球型平移网络对周期函数的逼近问题．文章首先将基函数eimx分别表示成为两种球型平移网络．进一步,将有关多重Fourier级数的Bochner-Riesz平均表示成为球型平移网络的形式．在此基础上构造出了两类球型平移网络序列,并借助于有关Bochner-Riesz平均对Lp空间中函数的逼近结果给出了这两类球型平移网络序列在Lp空间中的逼近阶．