紧－凸性与紧－光滑性

本文首先通过暴露集和暴露泛函的概念引入了闭凸集的紧－严格凸、紧－强凸、紧－一致凸及紧－非常凸等概念。并用对偶映射给出了Ｂａｎａｃｈ空间的两种新光滑性—紧－一致光滑与紧－非常光滑。然后特别研究了Ｂａｎａｃｈ空间的紧－非常凸与紧－非常光滑。此外还得到关于对偶映射的两个新结果。     

紧—凸性与紧—光滑性

本文首先通过暴露集和暴露泛函的概念引入卫闭凸集的紧－严格凸、紧－强凸、紧－一致凸及紧－非常凸等概念。用对偶映射给出了Ｂａｎａｃｈ空间的两种新光滑性－紧－一致光滑与紧－非常光滑。然后特别研究了Ｂａｎａｃｈ空间的紧－非常凸与紧－非常光滑。此外还得到关于对偶映射的两个新结果。     

超序列紧fts,可数超紧fts和超列紧fts

文献[1]中定义了序列紧fts(每个不分明集序列有收敛的子序列)和可数紧fts(每个可数开覆盖存在有限子覆盖)。对于序列紧fts,得到“每个fts都是序列紧的”病态结果,由此可见这样定义的序列紧fts不是一般拓扑学中序列紧的良扩张。对于可数紧fts,[2]在评论F-紧性时,论证了凡T_1空间都不是F-紧空间,以上的论证也可得到凡T_1空间都不是可数紧fts的病态结果。我们还要指出,[1]定义的可数紧fts也不是一般拓扑学中可数紧的良扩张。     

S紧locale与S紧空间

本文给出Ｓ紧ｌｏｃａｌｅ的内在刻画,作为推论,得到了一般Ｓ紧空间的内在刻画     

p-仿紧空间

本文研究了p-仿紧空间和p-可数仿紧空间的相关问题.利用预开集和覆盖性质理论,得到了p-仿紧空间和p-可数仿紧空间的定义、等价刻画及αp-仿紧子集的性质,推广了一般拓扑学中仿紧空间的部分结果.     

G序列紧空间

基于G方法,在一般的集合中引入了G序列紧集,讨论了其基本性质,研究了在拓扑空间下其与序列紧,可数紧之间的关系,并论证了将方法定义为理想收敛时,G序列紧空间的应用.推广了序列紧与可数紧的一些经典结果.     

仿紧局部紧空间的映象

本文借助于闭映射、伪开映射和商映射建立仿紧局部紧空间和几类具有某些特定性质 k 系空间之间的联系。     

关于紧图和超紧图的几个结果

给出了一些 新的紧图,并对 不是超紧的紧图 作了一些讨论     

仿紧局部紧空间的序列覆盖L-映象

本文利用特定的覆盖性质,建立了仿紧局部紧空的序列覆盖L－映象和紧覆盖L－映象的特征,得到或深化了局部紧度量空间的一些相应结果。     

仿紧局部紧空间映象的若干结论的推广

让ψ是蕴含仿紧性的映射保持的闭遗传性质．本文建立了仿紧局部ψ空间的闭映象、某些序列覆盖L映象的内在特征的一般性定理,推广了仿紧局部紧空间映象等的若干结论．     

Compact optimization can outperform separation: A case study in structural proteomics

In Combinatorial Optimization, one is frequently faced with linear programming (LP) problems with exponentially many constraints, which can be solved either using separation or what we call compact optimization. The former technique relies on a separation algorithm, which, given a fractional solution, tries to produce a violated valid inequality. Compact optimization relies on describing the feasible region of the LP by a polynomial number of constraints, in a higher dimensional space. A commonly held belief is that compact optimization does not perform as well as separation in practice. In this paper, we report on an application in which compact optimization does in fact largely outperform separation. The problem arises in structural proteomics, and concerns the comparison of 3-dimensional protein folds. Our computational results show that compact optimization achieves an improvement of up to two orders of magnitude over separation. We discuss some reasons why compact optimization works in this case but not, e.g., for the LP relaxation of the TSP.Received: April 2003, Revised: January 2004, MSC classification: 65K05, 90C05, 90C90Thanks to Arie Tamir for pointing out to us many relevant references, and to Brian Walenz and Giulio Zanetti for helpful discussions. We thank two anonymous referees for their suggestions which improved this paper considerably. The second author wishes to thank Sandia National Labs, Albuquerque, NM, and the Mathematical Biosciences Institute, Columbus, OH, for their hospitality. Sandia is a multiprogram laboratory, operated by Sandia Corporation, a Lockhead Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000.     

Equidistribution for meromorphic transforms and the dd~c-method

In this paper we give an introduction to the notion of meromorphic transform. We describe some equidistribution problems and their solution, using the ddc-method. In particular, we give some statistical properties of the equilibrium measure for meromorphic maps on compact Kahler manifolds: K-mixing, exponential decay of correlations and central limit theorem.     

GENERALIZATIONS OF KY FAN＇S THEOREM ON BEST APPROXIMATIONS

In 1969, Ky Fan[3] proved that for any continuous function f from a compact convex subset M of a normed linear space X into X, there exists x ∈ M such that f (x) - x = dist( f (x), M). Since then, there have appeared several generalizations, extensions and applications of this result. This paper also deals with some extensions and generalizations of this result when the underlying spaces are convex metric spaces.     

紧图的两个结果及其应用

双随机矩阵有许多重要的应用, 紧图族可以看作是组合矩阵论中关于双随机矩阵的著名的Birkhoff定理的拓广,具有重要的研究价值． 确定一个图是否紧图是个困难的问题,目前已知的紧图族尚且不多.给出了两个重要结果：任意紧图与任意多个孤立点的不交并是紧图;任意紧图的每一个顶点上各增加一条悬挂边的图是紧图． 利用这两个结果,从已知紧图可构造出无穷多个紧图族．     

Approximation of continuous set-valued maps by constant set-valued maps with image balls

It is shown that the problem of the best uniform approximation in the Hausdorff metric of a continuous set-valued map with finite-dimensional compact convex images by constant set-valued maps whose images are balls in some norm can be reduced to a visual geometric problem. The latter consists in constructing a spherical layer of minimal thickness which contains the complement of a compact convex set to a larger compact convex set.     

Actions symplectiques de groupes compacts (Symplectic Actions of Compact Groups)

For any symplectic action of a compact connected group on a compact connected symplectic manifold, we show that the intersection of the Weyl chamber with the image of the moment map is a closed convex polyhedron. This extends Atiyah–Guillemin–Sternberg–Kirwan's convexity theorems to non-Hamiltonian actions. As a consequence, we describe those symplectic actions of a torus which are coisotropic (or multiplicity free), i.e. which have at least one coisotropic orbit: they are the product of an Hamiltonian coisotropic action by an anhamiltonian one. The Hamiltonian coisotropic actions have already been described by Delzant thanks to the convex polyhedron. The anhamiltonian coisotropic actions are actions of a central torus on a symplectic nilmanifold. This text is written as an introduction to the theory of symplectic actions of compact groups since complete proofs of the preliminary classical results are given. An erratum to this article is available at .     

A compact group which is not Valdivia compact

A compact space is Valdivia compact if it can be embedded in a Tikhonov cube in such a way that the intersection is dense in , where is the sigma-product ( the set of points with countably many non-zero coordinates). We show that there exists a compact connected Abelian group of weight which is not Valdivia compact, and deduce that Valdivia compact spaces are not preserved by open maps.

     

Non-linear traces on the algebra of compact operators and majorization

We study non-linear traces of the Choquet type and the Sugeno type on the algebra of compact operators. They have certain partial additivities. We show that these partial additivities characterize non-linear traces of both the Choquet type and the Sugeno type respectively. There exists a close relation between non-linear traces of the Choquet type and majorization theory. We study trace class operators for non-linear traces of the Choquet type. More generally we discuss Schatten–von Neumann $p$-class operators for non-linear traces of the Choquet type. We determine when they form Banach spaces. This is an attempt at non-commutative integration theory for non-linear traces of the Choquet type on the algebra of compact operators. We also consider the triangle inequality for non-linear traces of the Sugeno type.     

Orlicz空间的若干紧一致凸性和k-drop凸性

给出赋Luxemburg范数的Orlicz函数空间的紧一致凸、弱紧一致凸、紧局部一致凸、弱紧局部一致凸和k-drop凸的判据,并且据此得到在Orlicz函数空间中这些凸性的等价关系.     

Eberlein mulian定理在局部凸空间中的推广

设（Ｅ，Ｔ）是一个分离的局部凸空间．本文主要结果是：（１）如果（Ｅ，Ｔ）是次可分的，那么ＡＥ是相对弱紧集Ａ是相对弱可数紧集Ａ是相对弱序列紧集．（２）如果（Ｅ，Ｔ）是强次可分且（Ｅ，β（Ｅ，Ｅ））是桶型空间，那么ＡＥ是相对弱紧集Ａ是相对弱可数紧集Ａ是相对弱序列紧集．