局部凸空间

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〓。

It investigates mainly the dualinvariant of λ- multiplier convergent series, the full invariant ofλ-multiplier convergent series, the λ- multiplier convergent series in spaceswith a basis, the compact sets in the infinite matrix topological algebras, thecharacteristics of have the same compact sets in different topologies,the weak sequentially completeness of , the characteristics ofSchur-matrices, the characteristics of p- uniform Toeplitz matrices and theEberlein-Smulian theorem in the locally convex spaces, etc.

主要研究了〓数乘收敛级数的对偶不变性，〓数乘收敛级数的全程不变性，有基空间中的〓数乘收敛级数，无穷矩阵拓扑代数〓中的紧集，〓在不同拓扑下具有相同紧集的刻划，〓的弱序列完备性，Schur—矩阵的刻划，p-一致Toeplitz矩阵的刻划以及局部凸空间上的Eberlein—Smulian定理等。

Every weakly countably compact closed convex set in a locally convex space has the quasi-weak drop property.

局部凸空间中每个弱可数紧闭凸集具拟弱滴状性质。

Applying the convexification of nonconvex function and the theorem in Chapter 2, we establish the perturbed optimization in the bounded subsets of the dual of locally convex spaces

运用非凸函数凸化的方法以及第二章给出的命题，在局部凸空间的对偶空间的有界子集上建立相应的的扰动优化和变分原理

Upward dual pairs, dual theorem, positive extension, L-topology, semi-bounded, ordered locally convex spaces.

上偶对，对偶定理，正延拓，L-拓扑，半有界，半序局部凸空间，局部体空间

Meantime, the Namioka-Bauer's and Wong's positive extension theorem are generalized to ordered locally convex spaces (see Theorem 5.1) and hence some new necessary and sufficient conditions of positive extension in ordered locally convex spaces are obtained

同时Namioka-Bauer 定理和 Wong定理也被推广到半序局部凸空间中(定理5.1)，从而得到了一些新的关于半序局部凸空间中正延拓的充分必要条件

Finally, for the following studies and in order to study the nonlinear problems in a widespread space, the relationship between the convexity and the smoothness is studied in the locally convex space.

最后，为了今后在更广泛的空间中研究非线性问题，我们讨论了局部凸空间中凸性与光滑性之间的关系。

In this paper, a varieties of concepts of compactness of sets and sunsets are introduced in a complex locally convex space, which are respectively the generalizations of the known sunsets and convex sets. By establishing the relationship between restricted p-centers of a set in a complex locally convex space and restricted Chebyshev centers of the corresponding set in the quotient space with respect to ker, characterizations and uniqueness of restricted p-centers of sets in a complex locally convex space are obtained. These results are better than any other known ones when we restrict them in real normed linear spaces and real locally convex space.

本文首先在复局部凸空间中引入了几种紧性及几种太阳集的概念，它们分别是已有紧性和凸集概念的推广；然后通过建立局部凸空间中集的限制p-中心和关于ker的商空间中对应集的限制Chebyshev中心的关系，来研究局部凸空间中集的限制p-中心问题，本文即使是在实赋范空间和在实局部凸空间中所得的结果都分别是有关已知结果的深化和推广。

The concepts of the S-simplest form of a seminorm family P and the P-reflexive locally convex space are introduced. The seminorm family P and its every S-simplest form generate the same locally convex separated topology on X are proved.

引入半范数族P的S-最简形式和P-自反局部凸空间的概念，证明了半范数族P和它的每一个S-最简形式都生成X上相同的局部凸拓扑。

Note on relation of seminorm and norm in vector space;2. The functional representation of some seminorms such as the continuous seminorms, the beundedseminorms and the lower semicontinuous seminorms are given out.

给出了局部凸空间上连续半范数，有界半范数和下半连续半范数等的泛函表示，应用这些表示定理，我们得到了Banach－Mackey空间的一个全局特征和囿空间的对偶特征，最后还给出了局部凸空间理论中一些重要定理的简化证明。

Objective: To study the effect of polycythemia on blood oxygen saturation.

裴蕾目的：观察RBC剧增而引起的高粘血症对血氧饱和度的影响。

Based on SIMPLER algorithm in the curvilinear body-fitted coordinates, the calculations were performed for Pr=0.7, Re=10~1000 on non-orthogonal non-staggered grids which are generated by elliptic equation systems.

采用曲线坐标系下压力与速度耦合的SIMPLER算法，数值研究了周期性渐扩渐缩波纹通道内脉动流动与换热情况，流动Re数的范围为10~1000，Pr数为0.7。