可分集

In this paper,with the aid of the w~*- sequential compactness of bounded closed balls in the conjugate space of a separable space,we proved that the convex hull of a finite union of bounded closed balls in l~∞ is closed.

借助可分空间的共轭空间中有界闭球的弱星序列紧性，证明在无穷维数列空间l∞中有限个闭球之并的凸包仍为闭集

The details are as following.The three necessary conditions for clustering are technical divisibility of production process, rich opportunity of product differentiation and low transportation cost.

本项目得到的一些重要学术成果包括：集群产生的三个必要条件是产品的技术可分性、存在丰富的产品差异化机会以及低运输成本。

In chapter 3, we give a unifying proof for some known difference sets by using Gauss sums, and we construct a new family of divisible difference sets.

在第三章中，我们用Gauss和给出了几个已知差集的统一的代数证明，它们原有的证明要么是用组合设计的方法，要么是用很技巧性的计数方法得到的。同时我们构造了一族新的可分差集。

A new SVM is presented in this paper to solve the approximately linear separable problem of pattern recognition:First,we transform the two convex hulls which are made up of the approximately separable training set to make them separable;Second,we can figure out a separating hyperplane by halving the nearest points method or maximal margin method;Then,we get the approximately linear SVM by solving the dual problem of maximal margin method.

对模式分类中的近似线性可分问题提出了一种新的近似线性支持向量机：先对近似线性分类中的训练集所形成的两类凸壳进行了相似变形，使变形后的凸壳线性可分，再用平分最近点和最大间隔法求出理想的分划超平面，然后再通过求解最大间隔法的对偶问题得到基于相似压缩的近似线性SVM。

First, the two convex hulls from the training set of approximate linear classification are similarly squeezed into the linearly separable ones, and based on the two similarly squeezed linearly separable convex hulls, an optimal separating hyperplane is figured out by using the method of halving the nearest points and the maximal margin method.

首先对近似线性分类中的训练集所形成的两类凸壳进行了相似压缩，使压缩后的凸壳线性可分；基于压缩后线性可分的凸壳，再用平分最近点和最大间隔法求出最优的分划超平面。

At first, the existence of extended form of approach to continuous selection for any set valued mapping without any continuity restriction in para-compact metric space is proved ;by the topologically separated mappings , the approximate selection theorem of sub-lower-semi-continuous mapping is established, furthermore , continuous selection problem in H-space is studied. Next, with W-correspondence, an improved variational inequality is obtained ; by the H-KKM mapping ,Ky Fan\'s minimax inequality is generalized to H-space . At last, with H-convexity instead of the linear topological structure, a new version of Browder fixed point theorem is established.Chapter 3 deals with set-valued mapping vector variational inequality and minimax problems.

第二章首先在仿紧的度量空间上对任意的集值映射建立了新的逼近连续选择定理，利用映射的拓扑可分性，在H-空间上建立了次下半连续映射的逼近连续选择定理和一个新的连续选择定理；然后利用W-对应，在H-空间上建立了广义的变分不等式；利用H-KKM映射，在H-空间上建立了广义的KyFan极小极大不等式；最后，利用H-凸性代替拓扑线性结构，在H-空间上建立了一个新型的Browder不动点定理。

In order to study vector-valued optimization problem, in chapter 5, a class of vector -valued function, that is, uniformly same-order set-valued function is introduced , which includes the separated functions as its proper subset; without hypothesis of convexity, new minimax theorem and saddle point theorem for uniformly same-order set-valued function are established. Next, by employing Ky Fan\'s lemma and H-KKM mapping , several existence results for generalized vector equilibrium problem established.

为了研究向量优化问题，作为可分函数的推广，第五章引入了一致同阶集值函数类，在没有凸性条件的假设下，对一致同阶集值函数建立了新的极小极大定理与鞍点存在定理；利用H-KKM映射，对一般向量均衡问题建立了(来源：A73BcbC论文网www.abclunwen.com)几个存在性定理；最后讨论了集值向量均衡问题系统，利用集值映射的拟凸性，在较弱的条件下证明了解的存在性。

The computational complexity of the algorithm is polynomial growing with the sample size and the solution is the maximal margin one in the high dimensional space.

其主要的内容是：当问题是线性可分时，给出一个求解最大间隔解的方法以及当问题不是线性可分时，提出利用一核函数将样本集映

Based on the limitation and tightness of computational time, it is concluded that the neighborhood of the equation solution is solvable under the condition of open solvable set.

研究了用差分法求解自治的发展方程时稳定性和收敛性这两个基本概念之间的联系，利用计算时间的有限性和紧致性，在可解集为开集的条件下，得出方程解的邻近也可解的结论。

As for the reason, the phenomenon of industrial clusters comes into being owing to aseries of social and cultural factors that lies in the final products such as technologicalclassification, the possibility of product difference, the interconnection of technologicalinnovation, the taciturnity of knowledge, the dynamic changes of the competitiveenvironment of enterprise and the economy of development, the low transportation costof the final products, and the fashion and artistry.

究其原因，产业集群现象的出现是由于多方面因素的综合作用而造成的，其中包括产品存在着技术上的可分性、产品具有差异化机会、技术创新的网络性、知识的缄默性，以及企业竞争环境的动态多变和速度经济性、集群产品的低运输成本并具有时尚性和艺术性等一系列社会文化因素。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。