两点齐性的Finsler流形

该文证明任何一个两点齐性的Finsler流形一定是黎曼流形．证明过程中作者将泛函分析中经典的Mazur定理推广到不一定是绝对齐次的Minkowski空间上．     

两点齐性的 Finsler 流形

该文证明任何一个两点齐性的 Finsler 流形一定是黎曼流形. 证明过程中作者将泛函分析中经典的Mazur 定理推广到不一定是绝对齐次的 Minkowski 空间上.     

发汗冷却控制系统最优控制元的存在唯一性

通过应用泛函分析中一个重要的Mazur定理,证出了水发汗冷却控制系统在自反的Banach空间中的最优控制元的存在唯一性。     

Mazur-Orlicz定理的一个初等证明

在文献[1]中，作为矩阵求和法的一个重要定理——Mazur—Orlicz定理，其证明是借助于许多工具与手段给出的，十分繁琐。现用初等方法给出一个简化而直接的证明。     

Mazur交性质

主要考虑关于Mazur交性质的问题．我们通过赋范半群的对偶,给出了一个赋范空间只有平凡Mazur集白々等价刻画．另外,我们还讨论乘积空间对Mazur交性质的继承性,对Sersouri和Roy的结论作了一定的改进,将范数推广至更一般的情形．     

无限维Gale—Nikaido—Debreu引理的一个新证明

1 引言 1985年,Yannelis将数理经济学中著名的Gale-Nikaido-Debreu引理推广到商品空间是无限维的情况.这是一个非常广泛的结果,概括了一系列的重要特例。 本文首先利用KyFan不等式与鞍点定理证明了一个定理,应用这个定理与凸集分离定理,我们给出了Yannelis结果的一个新证明。     

超双曲型方程定性研究的一些问题

本文是超双曲型方程定性研究的一个综合报导，它包括L.Asgeirsson中量定理的一个新证法；中量定理的推广；广义势解的非解析性；解的拓展性，境界值问题；基本解问题。     

一类具年龄结构n维食物链模型的最优收获控制

研究一类具有年龄结构n维食物链模型的最优收获控制.利用不动点定理,证明了系统非负解的存在性和唯一性.由Mazur定理,证明了最优控制策略的存在性,同时由法锥概念的特征刻画,还得到了控制问题最优解存在的必要条件.     

微分中值定理历史与发展

本文简述了罗尔微分中值定理、拉格朗日中值定理和柯西中值定理产生的历史背景；详细总结了这些中值定理在各种情形下的推广和进一步发展     

停线及其关系

本文研究了几类停线之间的关系并纠正了文[1]中的几个错误；顺便给出了文[4]中一个定理的推广．     

泛函中的两个对偶定理

本文利用＊隔离定理,证明了Ｍａｚｕｒ定理和凸集的最佳逼近元存在性定理的对偶定理．     

Separating sets with relative interior in Fréchet spaces

A separation theorem, valid in infinite dimensional spaces, and involving the relative interior of the sets to be separated, will be extended to Fréchet spaces. This theorem will be elucidated by means of a few examples. The second separation theorem is a generalization of an existing separation theorem, valid in Fréchet spaces. This paper consists of two parts: part I contains the first theorem, the second part contains the second generalization.     

Extremally distant normed spaces with additional restrictions

We study the relationship between the Banach—Mazur distance and the modified Banach—Mazur distance. We sharpen the Szarek theorem on the construction of invariant norms with specific properties and construct extremally distant normed spaces with norms invariant under groups of automorphisms of small cardinality. We prove that the trivial upper bound for the Banach—Mazur distance obtained in terms of the modified Banach—Mazur distance is order-sharp.     

UNCONDITIONAL CAUCHY SERIES AND UNIFORM CONVERGENCE ON MATRICES

The authors obtain new characterizations of unconditional Cauchy series in termsof separation properties of subfamilies of P(N), and a generalization of the Orlicz-PettisTheorem is also obtained. New results on the uniform convergence on matrices anda new version of the Hahn-Schur summation theorem are proved. For matrices whoserows define unconditional Cauchy series, a better sufficient condition for the basicMatrix Theorem of Antosik and Swartz, new necessary conditions and a new proof ofthat theorem are given.     

关于半自反空间的一个闭图定理

本文给出了一个关于半自反ｉｎｆｒａ－（ｕ）空间的闭图定理．作为推论,证明了从速完备 Ｍａｚｕｒ空间到半自反ｉｎｆｒａ－（ｕ）空间的闭图线性映照为弱连续、Ｍａｃｋｅｙ连续和强连续的．     

Optimal contraception control for a size-structured population model with extra mortality

ABSTRACT

This paper investigates the theoretical aspects for an optimal contraception control problem of a linear size-structured population model with extra mortality. The existence of a unique non-negative solution is established by using the Banach fixed-point theorem. The existence of a unique optimal strategy is derived by the Mazur theorem in convex analysis and the optimality conditions are obtained by means of normal cone and adjoint system techniques. Finally, some numerical results demonstrate the effectiveness of the theoretical results in our paper.     

Polynomials and identities on real Banach spaces

We study the duality theory for real polynomials and functions on Banach spaces. Our approach leads to a unified treatment and generalization of some classical results on linear identities and polynomial characterizations due to Fréchet, Mazur, Orlicz, Reznick, Wilson, and others.     

An Analog of the Poincarée Separation Theorem for Normal Matrices and the Gauss–Lucas Theorem

We establish an analog of the Cauchy–Poincarée separation theorem for normal matrices in terms of majorization. A solution to the inverse spectral problem (Borg type result) is also presented. Using this result, we generalize and extend the Gauss–Lucas theorem about the location of roots of a complex polynomial and of its derivative. The generalization is applied to prove old conjectures due to de Bruijn–Springer and Schoenberg.     

OPTIMAL CONTROL PROBLEM FOR A PERIODIC PREDATOR-PREY MODEL WITH AGE-DEPENDENCE

In this paper,we investigate optimal policy for periodic predator-prey system with age-dependence.Namely,we consider the model with periodic vital rates and initial distribution.The existence of optimal control strategy is discussed by Mazur's theorem and optimality condition is derived by means of normal cone.     

On injections and surjections of continuous function spaces

It is shown that a linear isometry ofC(S) intoC(T) is generated by a linear extension fromS to a quotient space ofT. A dual theorem is proved for a quotient map ofC(S) ontoC(T). An application of the first theorem and a modification of a theorem by Banach and Mazur provide a negative answer to a problem posed by Pelczynski.