关于四元数EP矩阵偏序的研究

本文利用四元数矩阵的奇异值分解给出四元数EP矩阵的一个刻画,并得到四元数EP矩阵减序,左（右）星序,星序的相应刻画定理与性质定理．     

T-S-Ferrers性质与区间序指标

集中于T-S-Ferrers性质指标以及与之相关的区间序指标的研究。首先给出T-S-Ferrers性质指标的性质,包括T-S-Ferrers性质指标的等价形式、T-S-Ferrers性质指标与S-强完全指标的关系以及大偏好关系与严格偏好关系的T-S-Ferrers性质指标之间关系。然后定义区间序指标,并讨论区间序指标的性质以及T-S-Ferrers性质与区间序指标之间的关系。     

几类随机序关系关于随机最大与随机最小的反向封闭性质

研究了右扩展序、TTT序、单调增凸序和单调增凹序分别关于随机最大与随机最小的反向封闭性质, 并讨论了相关年龄概念关于随机最大与随机最小的反向封闭性质.     

扩散过程的随机序及其在偏微分方程上的应用（英文）

随机序用于比较分布函数的中心位置和分散程度,而这两个特征反映了两个变量或随机过程的大小关系.由于随机过程的不确定性性质,其随机序的研究相对较为困难.因此,本文旨在分析扩散过程随机序关系,以随机微分方程为媒介,利用条件期望的性质,直接证明了扩散过程的强序、增凸序、增凹序及Laplace-Stieltjes转移序的性质.然后将随机序方法应用到扩散过程的Fokker-Planck方程中,验证了一类偏微分方程解的弱比较定理.     

格序代数的商及其代数性质

研究了格序代数的商及其一些重要的代数性质.给出了格序代数的商的概念,定义了商f-代数、商几乎f-代数和商d-代数,并给出其等价刻画.讨论了这三类格序代数的商的半素性和交换性质,得到了这些性质的若干刻画.     

对n-colour有序分拆的一些注记(英文)

本文研究了A.K.Agawarl在文献[1]中给出的n-colour有序分拆的组合性质.利用反例说明其中一个性质的不完全性,并纠正了此性质.此外,还给出了n-colour有序分拆组合性质的两个双射.     

LF拓扑空间的S-序同态和S-连续性

王国俊教授在文献[1]中引进序同态及序同态映射的连续性定义及其性质,本文把它推广到LF拓扑空间的半开集理论中去,引入几种S-序同态映射和几种S-连续性,并讨论它们的性质及其相互关系.     

Fuzzy边界与序同态的特征性质

本文首先给出Fuzzy拓扑空间中元的边界定义和它的一般性质,而后讨论Fuzzy拓扑空间之间保边界、保内部、保闭包等序同态的若干特征性质,及其与开、闭序同态,连续序同态,同胚序同态之间的关系。     

记录值中的随机序与年龄性质

研究记录值中的随机序与年龄性质．证明了任何通过两个分布函数的行为所定义的随机序,均可以被它们相应的记录值所保持,而两个随机变量之间的剩余财富序,可以导致其相应记录值序列的平均连续增量的序关系．也讨论了K-记录值的连续增量的年龄性质．     

可换群的完整子半群

本文提出了正则完整子半群的概念,得到了它的若干基本性质。同时将这些性质应用于域的序函数的拓展及确定无扭可换的线性序。     

Linear Extensions of Additive Partial Orders

Addive partial orders arise naturally in theories of comparativeprobability and subset preferences. An additive partial order is a partialorder on the family of subsets of ann-element set that satisfies . This is reformulated as a subset P of {1,0,–1}ⁿ that excludes 0 and containsx+y whenever x,y P and x+y {1,0,–1}ⁿ. Additional conditions of positivity andcompleteness give rise to positive additive partial orders and additivelinear orders respectively. The paper investigates conditions under which anadditive partial order is included in, or extendable to, an additive linearorder. The additive dimension of an extendable additive partial order isdefined and computed for several classes of additive orders.     

The diamond partial order in rings

In this paper we introduce a new partial order on a ring, namely the diamond partial order. This order is an extension of a partial order defined in a matrix setting in [J.K. Baksalary and J. Hauke, A further algebraic version of Cochran’s theorem and matrix partial orderings, Linear Algebra and its Applications, 127, 157–169, 1990]. We characterize the diamond partial order on rings and study its relationships with other partial orders known in the literature. We also analyse successors, predecessors and maximal elements under the diamond order.     

The L* Partial Order on the Set of Group Matrices

In this paper,we use the L(o)wner partial order and the star partial order to introduce a new partial order (denoted by "L*") on the set of group matrices,and get some characteristics and properties of the new partial order.In particular,we prove that the L* partial order is a special kind of the core par-tial order and it is equivalent to the star partial order under some conditions.We also illustrate its difference from other partial orders with examples and find out under what conditions it is equivalent to other partial orders.     

A Characterization and the Intersection of the Maximal Compatible Extensions of a Partial Order

We present a characterization of the maximal compatible extensions of a given compatible partial order ≤  _r on a unary algebra (A,f ). These extensions can be constructed by using the compatible linear extensions of ≤  _r*, where (A*,f*) is the so called contracted quotient algebra of (A,f) and the compatible partial order ≤  _r* on (A*,f*) is naturally induced by ≤  _r . Using this characterization, we determine the intersection of the maximal compatible extensions of ≤  _r .      

Cycle Orders

Let X, T and C be, respectively, a finite set with at least three points, a set of ordered triples of distinct points from X, and a cyclic ordering of the points in X. Define T C to mean that, for every a b c T, the elements a, b, c occur in that cyclic order in C, and let C(T) denote the set of cyclic orderings of X for which T C. We say that T is noncyclic if C(T) is empty, cyclic if C(T) is nonempty, uniquely cyclic if | C(T) | = 1, a partial cycle order if it is cyclic and T ={a b c :{a b c} C for all C C(T)}, and a total cycle order if it is a uniquely cyclic partial cycle order. Many years ago E. V. Huntington axiomatized total cycle orders by independent necessary and sufficient conditions on T. The present paper studies the more relaxed structures of cyclic T sets and partial cycle orders. We focus on conditions for cyclicity, a theory of cycle dimension of partial cycle orders, and extremal problems that address combinatorial structures of T sets.     

Small integral relation algebras generated by a partial order

The main purpose of this note is to exhibit a concrete representation for a four atom relation algebra which was known to be representable without an actual representation having been found. Along the way, representations are given for all integral relation algebas with four atoms which are generated by a partial order.