拟阵

The rank function is introduced for poset greedoids on the base of poset matroids,and the closure operator s are defined and a series of properties of closure operaters of poset greedoids are discussed.

在偏序集拟阵的基础上，引入了偏序集广义拟阵的函数，定义了偏序集广义拟阵的闭包算子，讨论了偏序集广义拟阵的一系列性质。

This paper gives definitions of the closure operator, interior operator and complement operator in poset matroids, of which the underlying posets have an order-reversing involution, and then studies some properties of these operators.

本文将主要研究偏序集拟阵和模糊拟阵中的这些生成运算，要点及主要内容如下：一、给出了限制和收缩作用相等的一个充要条件，显示了秩函数在研究偏序集拟阵中的重要作用。

This thesis including four chapters: Chapter Ⅰ, Introduction: Chapter Ⅱ, bases and Circuits of Poset Matroids; Chapter Ⅲ, A Class of Functions Associated with Poset Matroids: Chapter Ⅳ, Dependence and Closure Operator of Poset Matroids.

本文包括四章内容，第一章，引言。第二章，偏序集拟阵的基和圈。第三章，一类与偏序集拟阵相关的函数。第四章，偏序集拟阵的相关性和闭包算子。

The study includes the fuzzy independent set, fuzzy bases, fuzzy circuits, fuzzy rank, fuzzy hyperplanes, fuzzy closure operator, fuzzy submatroid, quasi-fuzzy graph matroids, fuzzy graphic matroids, fuzzy dual matroid and so on.

研究的内容包括模糊拟阵的独立集，模糊基，模糊圈，模糊秩函数，模糊超平面，模糊闭包算子，模糊子拟阵，准模糊图拟阵，模糊图拟阵，模糊拟阵的对偶和模糊拟阵的运算等等。

The study includes fuzzy bases, fuzzy circuits, fuzzy rank function, fuzzy hyperplanes, fuzzy closure operator, fuzzy submatrods, quasi-fuzzy graph matroid, fuzzy graphic matroids, fuzzy dual matroid and so on.

研究的内容包括模糊拟阵的模糊基，模糊圈，模糊秩函数，模糊超平面，模糊闭包算子，模糊子拟阵，准模糊图拟阵，模糊图拟阵，模糊拟阵的对偶等等。

The exchange theorem of bases of closed regular fuzzy matroids is obtained with the help of "the exchange theorem of bases" of crisp matroids. Then,the relations between the fuzzy bases and the fuzzy circuits in closed regular fuzzy matroids are studied, and some necessary and sufficient conditions for some fuzzy independent set to be a fuzzy base; some fuzzy circuits from a fuzzy base, and some fuzzy bases from a fuzzy circuit are investigated.

根据传统拟阵的基交换定理，作者给出了闭正规模糊拟阵的基交换定理，得到了一系列结论，并在此基础上进一步研究了闭正规模糊拟阵的模糊基与模糊圈之间的关系，然后给出了闭正规模糊拟阵中某模糊独立集是模糊基、从一个模糊基得到一些模糊圈、以及从一个模糊圈得到一些模糊基的充要条件。

The fundamental sequence, fuzzy bases and its algorithm, fuzzy circuits and its algorithm are studied in this thesis are all important topics in the research fields of fuzzy matroids. They enrich the theory of fuzzy matroids and it is very useful for them to push the change of fuzzy matroid from basic research to application research.

本论文研究的模糊拟阵的基本序列、模糊基及算法、模糊圈及算法都是模糊拟阵的重要内容，丰富了模糊拟阵理论，对于推动模糊拟阵从基础研究逐渐向应用研究的转变起着重要作用。

At the same time, they proved that a multipartite matroid is representable if and only if the corresponding discrete polymatroid is representable.

他们的工作具有令人振奋的结果：通过研究多部拟阵和离散多拟阵之间的关系，他们得到了多部存取结构为理想存取结构的一个必要条件和一个充分条件，并且证明了一个多部拟阵是可表示的当且仅当其对应的离散多拟阵是可表示的。

We apply this general result to Vamos matroid and obtain a family of non-representable multipartite matroids.

我们将这一结论应用于Vamos拟阵，于是得到了一族不可表示的多部拟阵，同时我们利用向量的线性相关和线性无关性对Vamos拟阵的不可表示性给出了新的证明。

Based on the existed theory of mareoids and fuzzy matroids, this thesis studies the closed regular fuzzy matroid and its fundamental sequence, the fuzzy base and its algorithm of closed fuzzy matroids, the fuzzy circuit and its algorithm of closed fuzzy matroids and so on. The main contributions of this thesis are as follows: 1 The necessary and sufficient condition of closed regular fuzzy matroid and a property of its fuzzy dual matroid are found by studying some properties of closed regular fuzzy matroid. 2 By studying some properties of fuzzt bases of closed fuzzy matroid, the necessary and sufficient condition of judging fuzzy bases of closed fuzzy matroids and some corollaries are found. In the end, an algorithm of obtaining a fuzzy base is given. 3 By studying some properties of fuzzt circuits of closed fuzzy matroid, some necessary and sufficient conditions of using its fundamental sequence to express fuzzy circuits are found. An algorithm of obtaining a fuzzy circuit is given. 4 By studying the fundamental sequence of closed regular fuzzy matroid, some necessary and sufficient conditions of fundamental sequence of closed regular fuzzy matroid are found.

本文在现有拟阵和模糊拟阵理论的基础上，研究了闭正规模糊拟阵及其基本序列，闭模糊拟阵的模糊基及算法、模糊圈及算法等内容，现分述如下： 1研究了闭正规模糊拟阵的一些性质，得到了闭正规模糊拟阵的充要条件及其模糊对偶拟阵的一个性质； 2研究了闭模糊拟阵模糊基的性质，找到了闭模糊拟阵模糊基的充要条件和几个推论，最后还给出了求模糊基的算法； 3研究了闭模糊拟阵模糊圈的性质，找到了用基本序列来表达模糊圈的几个充要条件，并给出了求模糊圈的算法； 4研究了闭正规模糊拟阵的基本序列，找到了闭正规模糊拟阵的基本序列的几个充要条件。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了