局部凸空间

Suppose that f is a real-valued ω〓-lower semicontinuous function defined on a ω〓closed bounded subset A〓 of the dual E〓 of a locally convex space E, which is bounded below on A〓, and suppose every ω〓 closed convex subset of C〓≡ω〓-clcoA〓 is the ω〓closed convex hull of its w〓-β-exposed points.

假设X是一个局部凸空间，X〓是其对偶。A〓是X〓上的ω〓有界闭子集，f是A〓上的ω〓-下半连续实值函数且在A〓上下有界。

For the compact operators series and Eberlein-Smulian theorem,first,it presents acharacterization of unconditional convergent series for the case of sequentially complete lo-cally convex spaces.

关于紧算子级数与〓定理，首先给出了序列完备局部凸空间中无条件收敛级数的一个特征。

Let X be a Banach space, be a locally convex linear topological space, C is a τ-sequence compact convex subset of X, and S an asymptotically nonexpansive type semigroups from C onto itself.

X是一Banach空间，是局部凸线性拓扑空间，C是X上的τ-序列紧凸集，S是C上的Γ类渐近非扩张型半群。

Duality invariants theories are the core of functional analysis space theories, especially the core of locally convex space theories.

对偶不变性理论是泛函分析空间理论特别是局部凸空间理论的核心内容。

And then,let E be a locally convex space and 〓 be the space of all sequentially continuous linearfunctional defined on E.

其次，设E是一个局部凸空间，〓是E上序列连续的线性泛函全体。

The generalization in locally convex space, restricted p-centers, of restricted Chebyshev centers of a set in normed linear spaces has been studied for only about a little bit more than ten years.

一。赋范空间中集的限制Chebyshev中心在局部凸空间中的推广—限制p-中心—问题的研究只有十余年的历史。

We investigate strong wellposedness and solvability of higher order ab-stract Cauchy proublems in a sequentially complete locally convex space,estab-lishing a Hille-Yosida-Phillips type characterization theoremand obtaining a solvability result.

研究序列完备局部凸空间中高阶抽象Cauchy问题的强适定性与可解性。关于强适定性建立了一个Hille-yosida-phillips型特征刻划定理，并获得一个可解性结果。

In chapter 4 , with S-KKM mapping , a new Ky Fan\'s minimax inequality is proved , the locally convex H-space with uniform structure is introduced , s-HKKM mapping is defined as the generalization of KKM mapping, with the H-convexity of Hausdorff locally convex H-space , a new fixed point theorem for the compact andclosed mapping belonging to the class s-HKKM is established ;with local intersection property of muti-function ,K-H-quasi-convexity of mapping , connectedness of set and condensing correspondences, some new vector quasi-variational inequalities are established , respectively .

第四章利用S-KKM映射，建立了新的Ky Fan极小极大不等式；定义了带有一致结构的局部凸H-空间，利用Hausdorff局部凸H-空间的H-凸性，对于属于s-HKKM中紧的闭映射建立了新的不动点定理，利用对应的局部交性质、映射的K-拟-凸性、集合的连通性以及φ-condensing对应分别建立了相应的拟向量变分不等式。

We avoid of assuming that the interior of the ordering cone is not empty and the cone has a compact base or a weakly compact base, but consider Benson proper efficiency in the framework of sparable locally convex metric spaces.

本文回避了以往需要序锥内部非空并且有紧基或弱紧基的条件，转而把目光从局部凸拓扑向量空间投向可分局部凸距离空间，在这个框架下，先利用Polarity定理给出了Benson真有效点的标量化定理。

By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem,several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces.

应用局部凸H－空间内具有闭零调值的上半连续集值映象的Fan－Glicksberg型不动点定理和极大化定理，对无限最优化总理2和约束对策问题在没有线性结构的局部凸H－空间内证明了解的某些新的存在定理，这些定理改进和推广了最近文献中的许多重要结果。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。