拟连续Domain的拟基及其权

在定向完备偏序集(即dcpo)上引入了拟基的概念,给出了拟基的若干刻画并在此基础上定义了拟连续Domain的权。探讨了拟连续Domain的权与该拟连续Domain上赋予内蕴拓扑时的拓扑空间的权之间的关系。     

拟正规与Hayman 选择

本文证明了亚纯函数族的一个拟正规定则, 推广了Xu-Fang, Chang 与Nevo-Pang-Zalcman 的相应结果; 并应用此拟正规定则得到了一个值分布结果, 推广与改进了著名的Hayman 选择, 以及Wang-Fang, Chang 和Nevo-Pang-Zalcman 的相关结论.     

Banach空间上的框架与拟Riesz基

该文首先给出Ｂａｎａｃｈ空间上的框架与拟Ｒｉｅｓｚ基的充要条件,其次讨论Ｂａｎａｃｈ空间上的框架和拟Ｒｉｅｓｚ基的稳定性,特别地,讨论在Ｂａｎａｃｈ空间上关于框架与拟Ｒｉｅｓｚ基的广义Ｐａｌｅｙ Ｗｉｅｎｅｒ定理．     

有限域上最优正规基的乘法表

本文给出了有限域上最优正规基乘法表的一个计算方法,改进了孙琦的相应结果.在有限域上椭圆曲线密码体制的应用中,本文给出的算法是非常有效的.     

Banach空间二阶周期边值问题的一种拟上下解方法

利用比较结果,通过构造L-拟上下解的单调迭代过程,在L-拟上下解反序的情形下,研究了Banach空间二阶周期边值问题解的存在性,并获得该问题解的存在性与唯一性结果.     

线性层空间的一个刻画

本文利用邻域约定证明了线性层空间是单调正规的,并且从单调正规的角度得到了线性层空间的一个刻画．     

用迹表示研究序列的线性复杂度

本文用迹表示式证明了序列的线性复杂度等于其秩矩阵的秩，并由此导出了正规基的计数公式．     

非线性拟周期方程的Floquet理论

主要研究由如下的微分方程所组成的自治系统: 其中是一个双曲的常矩阵, f是一个关于两个变元都是C^∞的函数, 并且关于变元θ的各个分量都是2π周期的, 还满足当x→0时,通过研究原系统的正规形, 证明了在适当条件下原系统可以变为自治系统 另外, 证明过程自然蕴含了Chen定理在拟周期情形下的推广.     

Frechet拟基与度量空间的闭映象

本利用林寿引入的Frechet拟基的概念,获得了度量空间的确定闭映象和局部可度量空间的确定闭映象的一些新的刻画。     

拟-C半群的结构

本文研究了拟-C半群的结构.利用拟直积的方法,证明了半群S是拟-C半群,当且仅当S是左正规带,Clifford半群和右正规带的拟直积,推广了Clifford半群.     

SOME PROPERTIES OF STRONGLY MONOTONICALLY T2 SPACES

This paper investigates Buck＇s question about which class of spaces is strongly monotonically T2,and if other properties are combined with strongly monotonically T2,which class of spaces could be got. Based on having a cushioned pair-base space and compact strongly monotonically T2 space,some results （Theorems 1--3） are obtained.     

强单调T2空间的几个性质

§1Introduction Theclassofstratifiable(=M3)spacesincludesallmetricspacesandmanytopological groups.Stratifiablespaceholdsmostofthestrongestandusefulpropertiesofmetric space.ThequestionproposedbyCederwhetherstratifiablespaceisM1spaceornotisstill opennow.ManyresearcheshavediscussedthepropertiesofMi(i=1,2,3)spacesthrough monotonenormality(see[2-7]).Borges[6]studiedthemonotonicallynormalproperties,Heath,etal.[5]gavemajorcontributiononmonotonenormality,andBuck,etal.[2]proposedseveraladditionalcha…     

部分模型之间的一些代数关系

我们把部分模型定义成三值逻辑的模型.对于Kleene语义,我们讨论部分模型之间的一些代数关系,并用图方法刻划了这些关系.证明了部分模型上某些算子的不动点定理.文中所讨论的代数关系对发展三值逻辑的模型起一定的作用.     

Relations Between the Ranks and Cranks of Partitions

New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.     

向量变分不等式与广义变分不等式之间的某些关系

文章首先建立了向量变分不等式与广义变分不等式之间的等价关系,然后利用这个结论,建立了向量变分不等式的Levitin-Polyak适定性与广义变分不等式的Levitin-Polyak适定性之间的等价关系.     

Products with linear and countable type factors

The basic theorem presented shows that the product of a linearly ordered space and a countable (regular) space is normal. We prove that the countable space can be replaced by any of a rather large class of countably tight spaces. Examples are given to prove that monotone normality cannot replace linearly ordered in the base theorem. However, it is shown that the product of a monotonically normal space and a monotonically normal countable space is normal.

     

Some Relations Between Packing Premeasure and Packing Measure

Let K be a compact subset of Rⁿ, 0 s n. Let , P^s denote s-dimensional packing premeasure andmeasure, respectively. We discuss in this paper the relationbetween and P^s. We prove:if , then ; and if , then for any > 0, there exists a compact subset F of K such that and P^s(F) P^s(K) – .1991 Mathematics Subject Classification 28A80, 28A78.     

Relations Between Some Dimensions of Semimodular Lattices

The aim of this paper is to present relations between Goldie, hollow and Kurosh-Ore dimensions of semimodular lattices. Relations between Goldie and Kurosh-Ore dimensions of modular lattices were studied by Grzeszczuk, Okiski and Puczyowski.     

Normal Bases and Their Dual-Bases over Finite Fields

In this paper, we prove the following results： 1） A normal basis N over a finite field is equivalent to its dual basis if and only if the multiplication table of N is symmetric; 2） The normal basis N is self-dual if and only if its multiplication table is symmetric and Tr（α^2） = 1, where α generates N; 3） An optimal normal basis N is self-dual if and only if N is a type-Ⅰ optimal normal basis with q = n = 2 or N is a type-Ⅱ optimal normal basis.