(弱)诱导空间的r连通性

本文研究了分明拓扑空间与其诱导空间,弱诱导空间与其底空间之间的关系.利用LF-r开集定义了r连通性,得出了弱诱导的LF拓扑空间是r连通的当且仅当其底空间是r连通的,并且分析(弱)诱导空间的结构.     

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．     

Norm attaining operators

Every Banach space is isomorphic to a space with the property that the norm-attaining operators are dense in the space of all operators into it, for any given domain space. A super-reflexive space is arbitrarily nearly isometric to a space with this property.     

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.     

The dual of C ps (X)

This is a study of the dual space of continuous linear functionals on the function space C_ps(X) with a natural norm inherited from a larger Banach space. Here ps denotes the pseudocompact-open topology on C(X), the set of all real-valued continuous functions on a Tychonoff space X. The lattice structure and completeness of this dual space have been studied. Since this dual space is inherently related to a space of measures, the measure-theoretic characterization of this dual space has been studied extensively. Due to this characterization, a special kind of topological space, called pz-space, has been studied. Finally the separability of this dual space has been studied.      

Q spaces and Morrey spaces

We characterize functions in Morrey space by p-Carleson measures. We then reveal a simple relation between Q space and Morrey space, that is Q space can be viewed as a fractional integration of the Morrey space. Therefore, many results for Morrey space can be translated onto Q space. For example, we show that Q space is a dual space by identifying its predual.     

Some generalizations of locally and weakly locally uniformly convex space

In this paper, we prove that strongly convex space and almost locally uniformly rotund space, very convex space and weakly almost locally uniformly rotund space are respectively equivalent. We also investigate a few properties of k-strongly convex space and k-very convex space, and discuss the applications of strongly convex space and very convex space in approximation theory.     

连通度量空间的映象

拓扑空间X称为s连通,若X不能表示为两个非空的不相交的序列开集之并.本文纠正了A.Fedeli 和A.Le Donne关于连通度量空间映象的错误论证,证明了s连通性可刻画为连通度量空间的连续的序列覆盖映象,从而导出连通的序列空间(或FrEchet空间)可刻画为连通度量空间的商映象(或伪开映象),回答了V.V.Tkachuk在Proc.Amer.Math Soc.上提出的问题.     

Banach空间的Lipschitz对偶及其应用

本文引进Banach空间E的一个全新对偶空间概念—Lipschitz对偶空间,并证明：任何Banach空间的Lipschitz对偶空间是某个包含E的Banach空间的线性对偶空间,以所引进的新对偶空间为框架,本文定义了非线性Lipschitz算子的Lipshitz对偶算子,证明：任何非线性Lipschitz算子的Lipschitz对偶算子是有界线性算子．所获结果为推广线性算子理论到非线性情形（特别,运用线性算子理论研究非线性算子的特性）开辟了一条新的途径．作为例证,我们应用所建立的理论证明了若干新的非线性一致Lipschitz映象遍历收敛性定理.     

Differentiable spaces that are subcartesian

We show that the differential structure of the orbit space of a proper action of a Lie group on a smooth manifold is weakly reflexive. This implies that the orbit space is a differentiable space in the sense of Smith, which ensures that the orbit space has an exterior algebra of differential forms, that satisfies Smith’s version of de Rham’s theorem. Because the orbit space is a locally closed subcartesian space, it has vector fields and their flows.     

Geometry of the structure of linear complements

Two geometries can be considered in the structure of linear complements: an affine spine space and an affine space. An affine spine space arises from a space of pencils. In terms of this geometry an affine partial line space may be defined. It is extensible to the affine space. Automorphisms of the affine spine space are automorphisms of appropriate affine space.     

非欧空间中双基本图形的度量方程及其应用

本文提出了n维球面型空间和双曲空间中双基本图形的概念,建立了球面型空间与双曲空间中双基图形的度量方程,并给出度量方程的一些应用.     

强零维度量空间的刻画

本文研究了强零维度量空间,借助点星弱邻域网刻画了强零维度量空间,获得了强零维度量空间等价于具有离散覆盖列的点星弱邻域网的非空正则空间,回答了葛英提出的一个问题.     

一致覆盖和度量空间的紧映象

本文利用一致覆盖的概念,讨论了度量空间的序列覆盖紧映象的结构.主要结果有: (1)空间X是局部可分度量空间的序列覆盖紧映象当且仅当X具有由cosmic子空间构成的一致sn网; (2)空间X是局部可分度量空间的序列覆盖,商紧映象当且仅当X是度量空间的序列覆盖,商紧映象且是局部cosmic空间.     

非常极凸空间

本文使用非常极凸的定义，证明了非常极凸和非常光滑是互为对偶空间且严格介于弱k凸和非常凸之间的空间，最后得到了非常极凸的一些特征．     

Some Notes on G-cone Metric Spaces

In this paper, we introduce a G metric on the G-cone metric space and then prove that a complete G-cone metric space is always a complete G metric space and verify that a contractive mapping on the G-cone metric space is a contractive mapping on the G metric space. At last, we also give a new way to obtain the unique fixed point on G-cone metric space.     

单位球面间的等距延拓

本文证明了在一定条件下赋范线性空间与其共轭空间的单位球面之间的等距算子可以延拓为全空间的实线性等距算子。进而,刻画了光滑的自反空间的单位球面到其共轭空间的单位球面上的等距算子。     

Prolate spheroidal wave functions,Sonine spaces,and the Riemann zeta function

In this paper we study underlying spaces associated with A. Connes? trace formula (see Connes (1999) [3], Li (2010) [14]). In particular the explicit formula in the theory of prime numbers is expressed as the trace of an operator acting on a Hilbert space, which is a direct sum of a Sonine space, the space of prolate spheroidal wave functions, and a variant of the space of prolate spheroidal wave functions. A formula is obtained for the orthogonal projection of the Hilbert space onto the Sonine space. A base is given for the variant space of the space of prolate spheroidal wave functions.     

约束离散空间的试验设计方案研究

目前的试验设计大体在连续空间或者无约束的离散空间下进行研究,但实际工程中不少场景都需要在离散空间中挑选试验点来进行试验设计,通常的试验设计方法无法应用于约束的离散空间中.文章立足于实际工程背景,基于连续空间下的均匀试验设计,采用Gale-Shapley算法,给出了连续空间到离散空间的映射设计方案.最后,结合实例进行了Gale-Shapley算法与经验方法所得设计的对比验证研究,在约束的离散空间下,Gale-Shapley算法所得到的映射设计具有更好的均匀性,且计算效率满足工程实际需求.     

Spaces of geodesics: products, coverings, connectedness

We continue our study of the space of geodesics of a manifold with linear connection. We obtain sufficient conditions for a product to have a space of geodesics which is a manifold. We investigate the relationship of the space of geodesics of a covering manifold to that of the base space. We obtain sufficient conditions for a space to be geodesically connected in terms of the topology of its space of geodesics.