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According to the existence results of general equilibrium problems and vector equilibrium problems have been studied more and more. Inspired and motivated by these research results, this paper is devoted to study systematically a class of equilibrium problems, which is unify and extension of a large number of known equilibrium problems and variational inequalities problems. The research is carried on from three aspects.Firstly, in finitely continuous topological spaces, we introduce four new types of the system of generalized vector quasi-equilibrium problems, and we derive some existence results of a solution for the system of generalized vector quasi-equilibrium problems via the maximal element theorems in product finitely continuous topological spaces.Secondly, in complete metric spaces, we provide the Ekeland variational principle to equilibrium problems with set-valued maps. And via the Ekeland variational principle, existence results for vector equilibrium problem with set-valued maps and the system of vector equilibrium problem with set-valued maps.

针对一般的均衡问题和向量均衡问题解的存在性，已有许多研究成果，受这些成果的启发，本文主要从理论上较为系统地研究了一类均衡问题，它统一和推广了许多已有的均衡问题和变分不等式问题，研究分有三个方面；首先，在有限连续拓扑空间中，我们提出了四类广义向量拟均衡系，并借助于有限连续拓扑空间中的极大元定理讨论了这四类均衡系问题的解的存在性问题，然后，在完备度量空间中，我们给出了关于集值均衡问题的Ekeland变分原理，并利用Ekeland变分原理分别讨论了集值向量均衡问题和集值向量均衡系问题的解的存在性。

From the point of view of measure theory, this paper gives the unified definition of measurable real fuzzy set-valued function and n-dimensional measurable real fuzzy set-valued function, and discusses the fundamental properties of them and their invers fuzzy set-valued function by combining with fuzzy σ-algebra.

5研究了有界闭复模糊数的四则运算、交并运算以及上下确界、上下极限与极限运算的若干基本性质

University ,Changsha 410075,HunanAbstract: In view of the deficiency in methods for choosing zonation indicators of mudflow danger degrees,a new method for choosing zonation indicators of mudflow danger degrees is put forward based on the rough set theory in this paper.Firstly,according to the environmental conditions of forming mudflows,an indicator choice system is established.Then the indicators for choice are discretized by indicator grading.Finally,based on the discernable matrix of the rough set,a core set of the indicators is found and the representative indicators are sieved out.

摘 要：针对现有泥石流危险度区划指标选取方法的不足，本文基于粗糙集原理，提出了一种新的区划指标选取方法，即首先根据泥石流形成的环境背景条件，建立备选指标体系，然后根据指标等级对备选指标离散化处理，最后利用粗糙集的分辨矩阵对指标进行求核约简，筛选出代表性指标。

In this paper, thereare four sections. In the first section, we introduce the basic theory. Inthe second section, we give out the recent main results of multivariateLagrange interpolation. In the third section, we get some theories ofno posed set of nodes from a kind of recursive method of constructingposed set of nodes for bivariate Lagrange interpolation, and we get akind of abnormal posed set of nodes for interpolation form the reversethought of that theory.

本文共分为四章，第一章介绍了有关多元插值的基本理论和方法，第二章讲述了有关多元Lagrange插值和多元切触插值的近期主要结果，第三章我们从有关适定结点组的添加曲线法考虑，得到了一些有关Lagrange插值不适定的结论，并从该结论的反方向思考，得到了一种非常规型插值适定结点组。

Concerning these problems, this paper proposed a new reduction strategy for large-scale training sample set according to the analysis on the structure of the training sample set based on the point set theory.

针对这些问题，通过在点集理论的基础上分析训练样本集的结构，提出了一种新的支持向量机大规模训练样本集缩减策略。

Now our workshop area is about 100, 000 square meters and our main production equipment is two sets of German MAN Roland R904-7B type outsize four color offset press which is the biggest paper range(1.6m*1.2m) of offset printing machine in the world, one set of Heidelberg speed master four color sheet-fed offset press, one set of Roybi four color offset press, two sets of automatic folder gluer, two sets of film blowing machines, one set of UV machine and nine sets of die-cutting and creasing machines.

现在我们的车间面积约10万平方米，主要生产设备有两套德国男子罗兰r904-106型outsize四色胶印机，是最大的纸张范围(1.6m*1.2m)胶印机在世界上一部海德堡速霸四色单张纸胶印机，一套roybi四色胶印机，两套糊盒机，两套吹塑机，一台机器紫外线和9套模切和压纹机器。

After explained that attention "bottleneck" had exerted a restriction on information obtaining in information receiving process, this paper brings forward a viewpoint that information set is decided by attention namely a subjective resource can deviate investors' expectation from the real, and blurs action set and state set, then irrationalize economic activities.

分析了信息接收过程中，注意力&瓶颈&对信息获取施加的约束，提出信息集的注意力主观资源决定性使决策者预期偏差化，行动空间和状态空间模糊化，进而使经济行为非理性化的观点。

The work of this present paper mainly includes the investigation of the structure of KDD system, the study of the basic concepts of rough set theory, the research of the questions in the heuristic reduct finding algorithms based the rough set theory used in the data reduction and the discretization in the field of KDD, and the development of the system which is used to study the algorithms of the rough set.

论文的主要工作是了解知识发现的体系结构，学习粗糙集理论的基本概念，研究基于粗糙集理论的约简算法在知识发现领域中进行数据约简和离散化两个方面存在的问题，开发用于粗糙集理论算法研究的实验平台。

This paper disproves the conclusion by a counterexample, and with the help of the concept of upper-semicontinuity, proves the connectedness of efficient point set and weak efficient point set of the set.

据此，借助于点集映射的上半连续性，本文给出了集合的Pareto有效点集和Pareto弱有效点集的另一形式的连通性结果。

A new concept of convex set and its some characteristic properties This paper give a new definition, the support direction of a boundary point of convex set. Then use it to prove a characteric properties of convex set and some other characteric properties.

1凸集的一个新概念与凸集的某些特征性质本文引进支持方向这一新概念并利用它来证明凸集的一个特征性质，最后再用它来证明凸集的另外一些特征性质。

The witness also told the jury at the Royal Courts of Justice in London that he saw a paparazzo fighting with a member of the public who was trying to stop him taking pictures in the minutes before the emergency services arrived.

他还告诉在伦敦皇家法庭的陪审团，在急救服务到来之前，他当时看见一个狗仔队正和一群阻止他拍照的人打架。

The entire N／C program on a tape is made up of an accumulation of these successive data blocks.

纸带上的整个数控程序由这些连续数据单元连接而成。