紧空间

Next,it proves that if E is a barrelled space and F〓 is a locally convex space,Kis all the compact operators of L,then the weak operator topology and the uniformly operator topology have the same sub-series convergence series in Kif and only if 〓 contains no copyof 〓.

其次又得到，若E是桶型空间，〓是局部凸空间，那么紧算子空间K中弱算子拓扑与一致算子拓扑具有相同子级数收敛的充要条件是〓不拓扑同胚地包含〓。

In chapter 2, we give some equivalent charcterizations of Bloch space and little Bloch space.

第二章给出有界强拟凸域上Bloch空间、小Bloch空间的等价刻划，也给出了Bergman空间上复合算子紧性的等价描述。

We introduce the notion of fuzzy-valued continuous function on a compact set K in a metric space, and discuss its properties; On this base, we study the uniformly d∞-convergence of a sequence of fuzzy-valued continuous function on K. We prove that the space of fuzzy-valued continuous functions on K, i.e. C(K, E1), is a complete metric space with respect to the metric D.

引入了定义在某度量空间的紧子集K上的模糊数值连续函数和水平连续函数的概念，讨论了它们的某些性质；在此基础上，研究了K上模糊数值连续函数列的一致d∞-收敛性，证明了K上模糊数值连续函数空间C(K， E1)关于度量 D 构成一个完备的度量空间。

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

Using a large data set of 1 894 images,we examine whether the colorspace transformation can increase the compactness of skin distribution and the discriminability between skin and nonskin distributions in fourteen 3D colorspaces and fourteen 2D chrominance planes.

比较结果表明：(1)颜色空间的变换并不能改善肤色紧致性、肤色-非肤色可分辨性以及分类等性能，但RGB及线性变换空间却具有较好的类可分辨性和分类性能；(2)去除亮度信息将明显降低肤色和非肤色之间的可分辨性和分类性能；(3)Bayes决策下的3维SPM的分类性能是最优和空间无关的，而其余分类器则普遍存在类似的"空间偏好性"；(4)同时采用肤色和非肤色模型的分类器的分类性能优于仅使用肤色模型的分类性能。

Firstly,by using the estimating methodfor the compact embedding operators(from weighted Sobolev space to the weighted〓space),we obtain a necessary and sufficient condition for the discreteness of thespectrum of certain differential operators.Secondly,based on the property of thespectrum of difinitizable operators on the Krein space,we consider the left definitedifferential equations with middle deficiency indices,and give a completecharacterization for self-adjoint(J-self-adjoint)differential operators in theindefinite inner product space 〓.Especially,we prove that all the J-self-adjoint differential operators are definitizable.

我们首先运用加权Sobolev空间到加权〓空间嵌入算子紧性的判别方法，证明一类加权自伴微分算子具有离散谱的充要条件；然后，基于Krein空间上可定化算子谱的性质，对于具中间亏指数的左定型微分方程，建立其相应的微分算式在不定度规空间〓上所生成自伴算子的完备性刻画（特别证明了J-自伴微分算子具有可定化性）。

First,we consider the lower semicontinuity property fora functional with linear growth in LDΩthe second, in the SBD space,we discussthe lower semicontinuity of an integral functional that the integrand is a Carathéodoryfunction and that satisfies a symmetric quasi-convex assumption, by the compactnesstheorem of the SBD space,blow-up method and Morrey theorem,prove that integral functional is lower semicontinuous with respect to L~1- convergence;then by using theone-dimentional sections method and the structure theorem of the BD functions, dis-cuss the lower semicontinuity of the integral functional in the whole BD space.

首先我们考虑LD空间满足线性增长的积分泛函的下半连续性；其次在SBD函数空间讨论了被积函数为Carathéodory函数时的积分泛函在满足对称拟凸条件时的下半连续性，主要利用SBD函数空间的紧性定理和blow-up方法以及Morrey定理等给出了积分泛函关于L~1-强收敛的下半连续性；然后利用BD函数的一维截断方法和结构定理，讨论了在BD全空间上的积分泛函的下半连续性。

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。

Since the solutions of this problem are the critical points of the associated energy function. One generally needs some compactness such as PScondition or C-condition to prove the existence of critical points of the energy func-tion, but when we study the elliptic equation in R~N, the compactness condition does not always hold since the imbedding of the Sobolev space H_0~(1,2)into L~(2*) is not compact. In this chapter, based on the nonsmooth critical point theory, and by using the approximation technique with periodic function, the existence of nontrivial solution is obtained.

由于该方程的解就是其所对应的能量泛函的临界点，通常都要在一些紧型条件的基础上来证明其所对应的能量泛函临界点的存在性，但当我们在无界域上考虑该椭圆方程解的存在性时，Sobolev空间H_0~(1，2)到L~(2*)的嵌入非紧，从而导致所对应的能量泛函失去紧性，本章在非光滑临界点理论的基础上，应用周期逼近的方法证明该问题非平凡解的存在性。

Wehave obtained two formulas to express thire relation in different view;at the same time,wegive an explicit description of multiplicative unitary operators corresponding to compactquantum group 〓 and 〓 on concrete Hilbert spaces.

我们首先在第四章讨论了紧量子群对应的乘法酉算子和紧量子群与离散群的交叉积对应乘法酉算子的关系，我们得到了在不同观点下的它们之间的关系式；同时给出了紧量子群〓对应的乘法酉算子和〓对应的乘法酉算子在具体的Hilbert空间上它们之间的表达式。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。