半群PT_n(A)的正则性与格林关系

设X_n={1,2,…,n}并赋予自然序,PT_n是X_n上的部分变换半群.设A■X_n非空,令PT_n(A)={α∈PT_n:imα■A}.讨论了半群PT_n(A)的正则性与格林关系.     

一类变换半群的正则元

在等价关系E(∈)F的假设下,给出了变换半群TFE(X)的正则元的性质.利用这些性质,简化了正则元的格林关系,得到了更为简单的描述.     

保持一个等价关系的部分变换半群

设X是一个集合,|X|≥3. Px为集合X上所有部分变换构成的半群.设E是集合X的一个等价关系.定义 PE(X)=｛f∈Px:(A)x,y∈domf,(x,y)∈E(→)f(x),f(y)∈E｝ 则PE(X)作成PX的一个子半群.本文讨论半群PE(X)的格林关系和正则性,并研究当等价关系E满足什么条件时,半群PE(X)是富足半群.     

关于一类半环上的格林关系的若干研究

研究了加法半群是带,乘法半群是完全正则半群的半环上的格林关系,给出了˙L∧+D(+L,+R)是同余关系的充分必要条件,证明了由这些同余关系所决定的半环类都是半环簇,并给出了这些半环簇的Mal′cev积分解.     

CR(n,1)中半环上格林关系的开同余

首先给出了加法半群是带,乘法半群是完全正则半群的半环上的格林关系所确定的开同余的刻画,并对其相关性质做了一定的探讨,最后证明了CR(n,1)中半环上的S/L°,S/R°分别是左、右约简的.     

连续参数随机过程的最优停止问题

设为一个右连续随机过程。本文在和的条件下,给出了最优停时的特征,证明了X的Snell包是右连续正则上鞅和控制X的最小正则上鞅。在最优停时存在时,给出了最优停时为唯一的充要条件。此外,将[1]中的条件减弱为后,得到了相应的结果。 §1 引言 设为一个完备的概率空间,为满足通常条件的域流,X=     

一类变种半群上的格林*关系

研究了一类变换半群POPE(X;θ)上的格林*关系,利用格林*关系的定义,得到了半群POPE(X;θ)上元素之间存在格林*关系的条件,这些结果推广了这类变换半群上的格林关系.     

一类广义变换半群的格林关系

设X是一个全序集,E是X上的一个凸等价关系．令 OE（X）={f∈TE（X）：Ax,y∈X,x≤y→f（x）≤f（y））, 其中TE（X）是E-保持变换半群．对于取定的θ∈OE（X）,在OE（X）上定义运算fog=fθg,使OE（X）成为广义半群OE（X;θ）．对于有限全序集X上的凸等价关系E,本文刻画了广义半群OE（X;θ）的正则元,描述了这个半群的格林关系．     

奇异保序变换半群的极大正则子半群

设On为通常的有限链Xn={1,2,…,n}上的奇异保序变换半群.文中利用格林关系的方法讨论On的极大正则子半群,确定了On的所有的极大正则子半群.     

由仿射线诱导的图的第二次成分

本文研究了有限域上n维仿射空间的仿射线诱导的图Γ的第二次成分Γ2(α)的代数和组合性质.利用在仿射群作用下的轨道的代表元,证明了第二次成分Γ2(α)是连通的、正则的,但不是边正则的.     

一类变换半群的正则元和Green关系

设T_X为X上的全变换半群,E为X上的等价关系,令T_E(X)={f∈T_X:■(x,y)∈E,(f(x),f(y))∈E},则T_E(X)是T_X的子半群,如果X是一个全序集,E是X上的一个凸等价关系,设OP_E(X)为T_E(X)中所有保向映射作成的半群。对于有限全序集X上一类特殊的凸等价关系E,本文刻画了半群OP_E(X)的正则元的特征,并且描述了这个半群上的Green关系。     

On Immediate Extensions of Ultrametric Spaces

The purpose of this paper is to define immediate extensions of ultrametric spaces with a totally ordered value set. It will be proved that an ultrametric space (X, d) with value set F is maximal if and only if it is pseudocomplete, i. e. any pseudoconvergent sequence of (X, d) has a pseudolimit in X. Every ultrametric space will be shown to possess a maximal immediate extension, but its uniqueness can only be obtained within the more specific class of essential extensions.     

Continuous Utility Representation Theorems in Arbitrary Concrete Categories

In this paper the continuous utility representation problem will be discussed in arbitrary concrete categories. In particular, generalizations of the utility representation theorems of Eilenberg, Debreu and Estévez and Hervés will be presented that also hold if the codomain of a utility function is an arbitrary totally ordered set and not just the real line. In addition, we shall prove and apply a general result on the characterization of structures that have the property that every continuous total preorder has a continuous utility representation. Finally, generalizations of the utility representation theorems of Debreu and Eilenberg will be discussed that are valid if we consider arbitrary binary relations and allow a utility function to have values in an arbitrary totally ordered set.      

保持序和等价关系的自然偏序变换半群

设X为一个集合,■_X为X上的全变换半群.设E是X上的一个等价关系,定义T_E(X)={f∈■_X:■(x,y)∈E,(f(x),f(y))∈E},则T_E(X)是由等价关系E所确定的■_X的子半群.本文中,所考虑的集合X是一个有限全序集,同时E是非平凡的且所有的E-类都是凸集.显然■_E(X)={f∈T_E(X):■_x,y∈X,x≤y蕴涵f(x)≤f(y)}是T_E(X)的一个子半群.我们赋予■_E(X)自然偏序并讨论何时■_E(X)中的两个元素是关于这个偏序是相关的,然后确定■_E(X)中那些关于≤是相容的元素.此外,还描述了极大(极小)元和覆盖元.     

Alternatives for testing total dual integrality

In this paper we provide characterizing properties of totally dual integral (TDI) systems, among others the following: a system of linear inequalities is TDI if and only if its coefficient vectors form a Hilbert basis, and there exists a test-set for the system’s dual integer programs where all test vectors have positive entries equal to 1. Reformulations of this provide relations between computational algebra and integer programming and they contain Applegate, Cook and McCormick’s sufficient condition for the TDI property and Sturmfels’ theorem relating toric initial ideals generated by square-free monomials to unimodular triangulations. We also study the theoretical and practical efficiency and limits of the characterizations of the TDI property presented here. In the particular case of set packing polyhedra our results correspond to endowing the weak perfect graph theorem with an additional, computationally interesting, geometric feature: the normal fan of the stable set polytope of a perfect graph can be refined into a regular triangulation consisting only of unimodular cones.     

On the Decomposition of Order-Separable Posets of Countable Width into Chains

Order - A partially ordered set X has countable width if and only if every collection of pairwise incomparable elements of X is countable. It is order-separable if and only if there is a countable...     

On coatoms in lattices of quasivarieties of algebraic systems

It is found the necessary condition for the lattice of quasivarieties has a finite set of coatoms. In particular if a quasivariety is generated by a finitely generated abelian-by-polycyclic-by-finite group or a totally ordered group then it has a finite set of proper maximal subquasivarieties. Also it is proved that the set of quasiverbal congruence relations of a finitely defined universal algebra is closed under any meets. Received March 23, 1999; accepted in final form June 7, 1999.     

Automorphism group and dimension of ordered sets

It is shown that a finite groupG is isomorphic to the automorphism group of a two-dimensional ordered set if and only if it is a generalized wreath product of symmetric groups over an ordered index set that is a dual tree. Furthermore, every finite abelian group is isomorphic to the full automorphism group of a three-dimensional ordered set. Also every finite group is isomorphic to the automorphism group of an ordered set that does not contain an induced crown with more than four elements.