关于伪BCI-代数的结合伪滤子与伪a-滤子（英文）

给出伪BCI-代数中结合伪滤子及伪a-滤子的一些新性质,证明了以下重要结果:(1)伪BCI-代数的一个伪滤子是结合的当且仅当它是伪a-滤子;(2)一个伪BCI-代数是结合BCI-代数的充分必要条件是它的每一个伪滤子是结合的(或伪a-滤子);(3)伪BCI-代数的一个伪滤子是结合的(或是伪a-滤子)当且仅当它是群逆伪q-滤子,当且仅当它是群逆T-型伪滤子。     

群伪簇与幂零半群伪簇的两种积

本文确定了群伪簇Ｇ与幂零半群伪簇的Ｎ的半直积Ｇ＊Ｎ,Ｎ＊Ｇ和Ｍａｌｃｅｖ积Ｇ＾－１Ｎ,Ｎ＾－１Ｇ。     

群逆伪BCI-代数与群逆滤子(英文)

伪BCK-代数是非可换模糊逻辑(蕴涵片段)的基本代数框架,伪BCI-代数是伪BCK-代数的推广,本文研究伪BCI-代数的结构。首先,借助BZ-代数(又称弱BCC-代数)给出伪BCI-代数的一个特征性质;其次,通过引入群逆伪BCI-代数的概念,研究了伪BCI-代数与(非可换)群之间的关系;接着,引入群逆滤子、优滤子和正规滤子的概念,并通过它们给出伪BCI-代数成为群逆伪BCI-代数(以及滤子成为p-滤子)的充要条件;最后,证明了如下结论:(1)平均伪BCI-代数等价于p-半单BCI-代数;(2)伪BCI-代数的每一个滤子是p-滤子,当且仅当它是群逆的且其伴随群的每一个子群是正规子群。     

代数结构上的模糊拟伪$b$-度量

研究代数结构上的模糊(拟)伪$b$-度量. 主要结论有: (1)设$G$是一个抽象群, $\tau$是$G$上一个左不变模糊拟伪$b$-度量(伪$b$-度量)诱导的拓扑,如果$(G,\tau)$是右拓扑群,那么$(G,\tau)$是一个仿拓扑群(拓扑群); (2)设$S$是一个半群,如果$\tau$是$S$上一个不变模糊拟伪$b$-度量诱导的拓扑,那么$(S,\tau)$是一个拓扑半群.     

伪内射模与主伪内射模

本文研究了伪内射模与主伪内射模,它们分别是拟内射模与PQ-内射模的推广．伪内射模是对偶于伪投射模的．我们讨论了伪内射模与主伪内射模的性质及其自同态环,并得到了自同态环的Jacobson根的若干性质．     

伪加权Mealy机与伪加权Moore机的关系

给出伪加权序列机、伪加权Mealy机以及伪加权Moore机的定义并分别给出了它们的响应函数.证明伪加权序列机与伪加权Mealy机是不等价的、伪加权序列机与伪加权Moore机是等价的;并以伪加权序列机为桥梁,得到了伪加权Mealy机与伪加权Moore机的关系是不等价的.     

关于伪欧氏空间

本文提出了一些新概念，ｐ—伪转置阵，ｐ—伪正交阵，ｐ—伪对称阵，从而能以这些矩阵为工具研究伪欧氏空间的性质以及空间中两个特殊线性变换，伪正交变换和伪对称变换．本文得到的主要结果是定理２，定理３，定理４及定理６．本文还指出了北大编《高等代数》第二版中的伪正交变换习题的一个错误．     

关于伪欧氏空间

本提出了一些新概念，p-伪转置阵，p-伪正交阵，p-伪对称阵，从而能以这些矩阵为工具研究伪欧氏空间的性质以及空间中两个特殊线性变换，伪正交变换和伪对称变换，本得到的主要结果是定理2，定理3，定理4及定理6，还指出了北大编《高等代数》第二版中的伪正交变换习题的一个错误。     

逆极限空间的伪轨跟踪性

证明了对于由{xi,φi,fi}∞i=l生成的逆极限系统(X∞,f∞),如果每个fi具有伪轨跟踪性,则诱导映射f∞也具有伪轨跟踪性.并构造了一个例子说明它的逆命题不成立.还证明了零维紧致度量群的自同构拓扑共轭于一族有限型子转移生成的逆极限系统.     

抽象基上的伪e拓扑与伪ρ拓扑

在抽象基上引入了伪e拓扑和伪ρ拓扑,研究了这两种内蕴拓扑的性质以及与其它内蕴拓扑的关系。利用伪e拓扑与伪ρ拓扑得到具有辅助关系的偏序集的辅助基的若干等价刻画。证明了具有辅助关系的偏序集的辅助基恰是伪ρ拓扑的稠子集。     

Pseudo Availability of Repairable System

Availability is a very basic characteristic of a system for measuring its performance. Various traditional availabilities have been defined in the literature. This article considers repairable system, the failure of which can be detected only by inspection, and incorporates both inspection and repair into consideration. The concept of pseudo availability is introduced and studied. Pseudo availability differs from the traditional availabilities in that once the system is in ‘up’ state it will remain there forever without change. The expression and/or its Laplace transform are derived. The limiting behavior of pseudo availability is also studied. AMS 2000 Subject Classification Primary 60K10, Secondary 60E10     

伪概周期函数二十年

伪概周期函数是1992年在我的博士论文中定义的，大多数人是在1994年我的两篇文章得知此函数的．从那以来，伪概周期函数引起国内外许多数学工作者的兴趣，成为一个活跃的研究领域．文中将介绍伪概周期函数是如何定义的，并且综述近20年它的发展．     

Pseudo S-asymptotically ω-periodic solution for a differential equation with piecewise constant argument in a Banach space

ABSTRACT

In this paper, we give sufficient conditions for the existence and uniqueness of Pseudo S-Asymptotically ω-periodic solutions for a differential equation with piecewise constant argument in a Banach space. This result is obtained using the Pseudo S-asymptotically ω-periodic sequences.     

Pseudo duality in mathematical programming: Unconstrained problems and problems with equality constraints

In this work non-convex programs are analyzed via Legendre transform. The first part includes definitions and the classification of programs that can be handled by the transformation. It is shown that differentiable functions that are represented as a sum of strictly concave and convex functions belong to this class. Conditions under which a function may have such representation are given. Pseudo duality is defined and the pseudo duality theorem for non linear programs with equality constraints is proved.The techniques described are constructive ones, and they enable tocalculate explicitly a pseudo dual once the primal program is given. Several examples are included. In the convex case these techniques enable the explicit calculation of the dual even in cases where direct calculation was not possible.     

On Varieties of Pseudo MV-Algebras

In this paper we investigate the relation between the lattice of varieties of pseudo MV-algebras and the lattice of varieties of lattice ordered groups.     

几类亚交换序半群

本文研究几类亚交换序半群的性质,并将具有单位元的亚交换序半群的一些结果扩张到这几类亚交换序半群上,使得这些结果更加细化,其中主要证明了以下定理：伪交换序半群可以分解成阿基米德序半群的半格．并且,一般来说,这种分解不是唯一的．     

Pseudo Leja sequences

We study pseudo Leja sequences attached to a compact set in the complex plane. The requirements are weaker than those of ordinary Leja sequences, but these sequences still provide excellent points for interpolation of analytic functions and their computation is much easier. We also apply them to the construction of excellent sets of nodes for multivariate interpolation of analytic functions on product sets.     

Pseudo equality algebras

A new structure, called pseudo equality algebras, will be introduced. It has a constant and three connectives: a meet operation and two equivalences. A closure operator will be introduced in the class of pseudo equality algebras; we call the closed algebras equivalential. We show that equivalential pseudo equality algebras are term equivalent with pseudo BCK-meet-semilattices. As a by-product we obtain a general result, which is analogous to a result of Kabziński and Wroński: we provide an equational characterization for the equivalence operations of pseudo BCK-meet-semilattices. Our result treats a much more general algebraic structure, namely, pseudo BCK-meet-semilattice instead of Heyting algebras, on the other hand, we also need to use the meet operation. Finally, we prove that the variety of pseudo equality algebras is a subtractive, 1-regular, arithmetical variety.     

Pseudo generalized Youden designs

Youden square designs, or Youden rectangles, are classical objects in design theory. Extensions of these were introduced in 1958 by Kiefer and in 1981 by Cheng, in the form of generalized Youden designs (GYDs) and pseudo Youden designs (PYDs), respectively. In this paper, we introduce a common generalization of both these objects, which we call a pseudo generalized Youden design (PGYD). PGYDs share the statistically desirable optimality properties of GYDs and PYDs, and we show that they exist in situations where neither GYDs nor PYDs do. We determine some numerical necessary conditions for the existence of PGYDs, classify their existence for small parameter sets, and provide constructions for families of PGYDs using patchwork methods based on affine planes.