Banach 值函数空间的一个乘子

本文研究了从有界正则 Banach 值测度到 Banach 值 p(1≤p≤∞)次可积函数空间的模同态和不变算子.得到了所述的算子和模同态的三个等价关系.此外证明了如下结果:模同态和不变算子等距同构的充要条件是作为值域的 Banach 空间的维数等于一.     

完备随机赋范模上的连续模同态半群

本文首先利用完备随机赋范模的层次结构研究了一致连续模同态半群与其无穷小生成元之间的关系,并进一步给出几乎处处有界半群的指数刻画.在此基础上,建立几乎处处有界半群的微分和积分公式,推广了经典的结论.同时,用反例说明要求上述半群几乎处处有界的条件是必要的.     

完备随机内积模上稠定模同态的共轭算子

对定义在完备随机内积模的稠子模上的模同态引入了共轭算子的概念并讨论其基本性质,尤其证明了共轭算子的闭性.     

Fuzzy概率空间的Fuzzy格刻划

本文研究了Fuzzy概率空间中Fuzzy事件及概率的代数性质.利用Fuzzy概率空间中的概率为集函数这一特征和Fuzzy格的相关理论，得到了Fuzzy概率空间中的概率是从一个Fuzzy格到某个区间的Fuzzy格模同态，并将概率分解成Fuzzy格同态与Fuzzy格模同态的乘积。     

管范畴中的模同态与模分解

本讨论管范畴（ｔｕｂｅ）中的模同态。在不可分解模上定义特殊生成元,并运用它研究了管范畴中模同态的一些性质,得到了关于同态ｆ：Ｍｈ,ｌ→Ｌ的导出的模Ｌ的直和分解及其余核的构造。     

关于随机解析算子函数的正族性质

该文在经典函数的正族理论基础上建立了随机解析算子函数的正族、一致有界和等度连续等概念，并在此意义下，给出了随机解析算子函数族内闭一致有界与等度连续、正族与一致有界的关系，以及随机解析算子函数族为正族的一个充分必要条件。     

Tube中的模同态与模分解

本文讨论管（tube)范畴中的模同态，在不可分解模上运用[4]中特殊生成元的定义，进一步研究了管范畴中模同态的一些性质，得到了关于同态g:L→Mh,l的导出模L的直和分解及其核的构造。     

一类用仿射几何构造的半对称图

图X是一个有限简单无向图,如果图X是正则的且边传递但非点传递,则称X是半对称图.主要利用仿射几何构造了一类2p~n阶连通p~4度的半对称图的无限族,其中p≥n≥11.     

半模的张量积

本文引入了半模的张量积的泛性定义，给出了半模范畴中的有向正向系的上极限以及任意一个半模同态的上核，讨论了半模张量积的若干性质，主要结果是：证明了张量函子保持半模的右正合性和上积，并且上积保持半模的平坦性，半模范畴中的张量函子保持上极限和上核．     

连续半鞅的弱紧性与随机微分方程弱解的存在性

本文研究了连续半鞅在连续函数空间对应的测度族的弱紧性及一般鞅问题解的存在性,弱紧性与存在性的条件是用半鞅的自然特征:转移泛函与扩散泛函来表示的。这些结果可以应用于研究随机微分方程,我们得到了随机微分方程的解对应的测度的弱紧性条件,定理7是随机微分方程弱解的新结果,经典的线性有界条件由于添上了一个对数因子而减弱了。     

A Characterization of Continuous Module Homomorphisms on Random Semi—Normed Modules and Its Applications

In this paper,a characterization of continuous module homomorphisms on random seminormed modules is first given;then the characterization is further used to show that the Hahn-Banach type of extension theorem is still true for continuous module homomorphisms on random semi-normed modules.     

Random duality

The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules. First, the complicated stratification structure of a module over the algebra L(μ, K) frequently makes our investigations into random duality theory considerably different from the corresponding ones into classical duality theory, thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules. Then, we give the representation theorem of weakly continuous canonical module homomorphisms, the theorem of existence of random Mackey structure, and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants.     

Topological modules of continuous homomorphisms

In this paper, we consider the notion of module homomorphisms in the general topological module setting and establish their linearity and continuity under some suitable conditions. We also introduce the strict and uniform topologies on the modules of continuous linear homomorphisms and study their various properties.     

Module Homomorphisms on Random Normed Modules

ＭｏｄｕｌｅＨｏｍｏｍｏｒｐｈｉｓｍｓｏｎＲａｎｄｏｍＮｏｒｍｅｄＭｏｄｕｌｅｓＧｕｏＴｉｅｘｉｎ（郭铁信）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉａｍｅｎＵｎｉｖｅｒｓｉｔｙ，Ｘｉａｍｅｎ，Ｆｕｊｉａｎ，３６１００５）Ａｂｓｔｒａｃｔ...     

一类推广的Virasoro-like李代数

构造了一类无限维李代数,它是Virasoro-like李代数的推广.研究了这类李代数的两类自同构,这两类自同构均关于映射的合成构成自同构群,一类同构于对称群S3,另一类同构于Klein交换群.得到了这类李代数一些特殊的自同态、中心.证明了这类李代数不是半单李代数.     

Dual Formulation of the Lemma on Substitution Homomorphisms

Doklady Mathematics - This paper contains a nonstandard formulation of the well-known lemma on substitution homomorphisms stated as the canonical duality between the family of all smooth mappings...     

Digraph matrix partitions and trigraph homomorphisms

Matrix partitions generalize graph colourings and homomorphisms. Their study has so far been confined to symmetric matrices and undirected graphs. In this paper we make an initial study of list matrix partitions for digraphs; in other words our matrices are not necessarily symmetric. We motivate future conjectures by classifying the complexity of all list matrix partition problems for matrices of size up to three. We find it convenient to model the problem in the language of trigraph homomorphisms.     

Linear maps on operator algebras that preserve elements annihilated by a polynomial

In this paper some purely algebraic results are given concerning linear maps on algebras which preserve elements annihilated by a polynomial of degree greater than 1 and with no repeated roots and applied to linear maps on operator algebras such as standard operator algebras, von Neumann algebras and Banach algebras. Several results are obtained that characterize such linear maps in terms of homomorphisms, anti-homomorphisms, or, at least, Jordan homomorphisms.

     

T-Radicals and E-Radicals in the Category of Modules

We introduce two classes of radicals by means of tensor product of modules and module homomorphisms and prove some properties of these radicals and their connection with attracting modules.