偏序集

证明了偏序集P是连续偏序集当且仅当S-极限是σ（P）拓扑决定的；

It is proved that a poset is continuous iff the S-limits for P are σ( P ) topological determined .

设P是一个有限偏序集，Γ是一个群，保序地作用于P上。

Let P be a finite poset and Γ a permutation group acting on P which preserves the order relation on P .

F（X）上的格拓扑路偏序集的个数

Lattice Topology on Fuzzy set The Number of Path-Posets

点频干扰下GPS接收机捕获性能研究偏序集上的不动点

Research of GPS Receiver Acquisition Performance under Single Frequency Interference Fixed Point on Partially Ordered Sets

并利用MP-滤子和Fuzzy滤子，刻画了一类偏序集上蕴涵代数的结构。

Some characterizes of a kind of Implication Algebra on a partial ordered set are gained by the use of MP-filter and fuzzy filter .

严格偏序集的拆分技术及其在AI中的应用（Ⅱ）

The Partition Technology of Strick Partical Order Set and Application in AI (ⅱ)

DeMorgan偏序集的刻画与同余关系

Characterization of De Morgan posers and congruences

MC型偏序集结构分析

Structure Analysis on MC Type partially Ordered Sets

R-偏序集及其Scott拓扑

R-po set and its Scott Topology

主要结果有：（1）每一FS-偏序集都是有限上集生成的，因而是Scott紧的；

Main results are : ( 1 ) Every FS-poset is finitely upper generated and is Scott compact ;

第三章给出了对应于部分字偏序集P（r，n）的全字上的偏序集P~（n）的嵌套链分解。

The third chapter gives a nested chain decomposition of the posetP ( n ) on total words , which corresponds to the posetP ( r , n ) on partial words .

Z-连续偏序集作为连续格一个推广已被WrightWagner和Thatcher等介绍。

Z-continuous posets were introduced by Wright Wagner and Thatcher as a generalization of continuous lattices .

研究了偏序集（X；≤）的伴随代数；

The adjoint algebra of a partial order set ( X ;≤) is studied , and the author points out that all adjoint algebra of a partial order set are automorphism .

得分向量偏序集上Schur函数和奇异得分向量

Schur Function on the Poset of Score Vectors and Singular Score Vectors

给出了连通代数Domain上相容紧元的等价刻画，证明了连通代数Domain范畴与偏序集范畴等价。

At the same time we give that some equivalent propositions on consistently compact elements of connected algebraic domain and prove that the category of connected algebraic domains is equivalent to the category of posets .

所有n维得分向量集合Ln在优超关系下是一个偏序集。

The set Ln of all n - term score vectors is a poset ( i.e. , partially ordered set ) under the majorization relation .

2003年，这一专著又出版了新的补充版[22]，吸收了最近20多年的成果。Domain理论主要以满足一定条件的偏序集以及它们之间的映射为研究对象。

The complementary version Continuous Lattices and Domains absorbing the results of the latest twenty years was published in 2003.The main objects in domain theory are partially ordered sets ( posets for short ) and the mappings between posets .

本文获得了以下主要成果：（1）在形式背景上建立了三个偏序集：G偏序集、M偏序集和GM偏序集，并将包含度的概念引入到三个偏序集上。

For this , we establish three posets , namely , G poset , M poset as well as GM poset and based on the three posets , we define three inclusion degrees on them .

带Morita对偶的偏序集环

Poset Rings with Morita Duality

近年来，由于序与偏序集理论在组合数学、Fuzzy数学、计算机科学、甚至社会科学中得到了广泛的应用，因而使格论有了较大的发展，逐渐成为现代数学的重要分支之一。

In recent years , as order and partial ordered set theory were widely applied in the combinatorics , Fuzzy mathematics , computer science , and even in the social science , the lattice theory has became an important branch of mathematics . Since F.

最后，用偏序集代数KI的代数性质，给出偏序集I是格的充分必要条件。

Last , a necessary and sufficient condition of a partial ordered set I to be a lattice is given by the algebra properties of KI .

以有上界且有限可分的偏序集为对象，以它们之间的D~△-连续的函数为态射组成的范畴是一个Cartesian闭范畴。

The category FSBP in which objects are finitely separating and upper bounded posets and arrows are D ~ △ - continuous functions between them , is a cartesian closed category .

本文讨论了Z－连续偏序集的一系列性质，主要证明了Z－连续偏序集范畴对偶等价于完全分配格范畴的一个满子范畴。

In this paper , we mainly prove that the category Of z-continuous posets is dually equivalent to a full subcategory of the category of all completely distributive lattices . Some other new properties of z-continuous posets are also investigated .

第二章研究由偏序集生成的自由Dcpo与自由并完备格，由并半格生成的强自由Dcpo与强自由并完备格。

In Chapter 2 , the free dcpo and free join-complete lattice generated by poset are given ;

本文给出了从一个集合构造R-偏序集的方法，并用迁移系统和部分模拟的例子对这一方法的实现作了进一步的说明，同时还给出R-偏序集上的Scott拓扑。

In this paper , we propose an approach to construct a R-poset from a set , and describe this approach further through the examples of transition system and partial simulation . We establish the Scott topology on R-poset .

对于偏序集上蕴涵代数中的蕴涵算子引入了一些逻辑条件，得到了偏序集上具有不同条件的蕴涵代数与MV-代数之间的关系，给出了偏序集上蕴涵代数与MV代数之间的几个等价定理。

Some other conditions which the implicative operator of a Implication Algebra should satisfied in a logic system are given . The relations between MV-Algebra and Distributive Implication Algebra , Implication Algebra with condition ( S ) are gained .

研究了Z-连续偏序集上的Z-Scott开集，Z-Lawson开集，Z-Scott拓扑及Z-Lawson拓扑的一些性质。

Some properties of Z-Scott open set , Z-Lawson open set , Z-Scott topology and Z-Lawson topology are studied .

Sym的同态对分次偏序集的旗向量进行了分类.Bergeron与Sottile[4]也作了类似研究，证明了一个拟对称函数对应于一个边棱标号的偏序集也有一个Hopf代数同态。

A similar construction was made by Bergeron and Sottile given [ 4 ] , They have shown that a quasi-symmetric function associated to an edge-labeled poset also gives a morphism of Hopf algebras .

本节的一个中心问题是提出了一个猜想：一个有限格L同构于一个有限偏序集拟阵的闭集所构成的格当且仅当L是一个半模格。

In this section , we also give a conjecture : A finite lattice is isomorphic to the lattice of flats of a finite poset matroid if and only if it is a semi-modular lattice .

确定了树型偏序集的多重对偶扩张代数的典范模的结构，并描述了其Ringel对偶代数的通常箭图的形状。

This paper determines the structures of canonical modules over dual extension algebras of multi posets of tree type and describes the ordinary quivers of the ringel duals of these algebras .