Banach空间X的弱局部ZR性质

本文引入了Ｂａｎａｃｊ空间Ｘ的弱局部Ｚ性质和弱Ｚ性质，得出了：Ｂａｎａｃｈ空间Ｘ是Ｋ－ＮＵＣ空间的一个充分必要条件和Ｂａｎａｃｈ空间Ｘ是ＬＫ－ＮＵＣ空间的一个充分条件，并指出弱Ｚ性质蕴含弱Ｂａｎａｃｈ－Ｓａｋｓ性质．     

局部k-一致凸空间的对偶空间

本文证明了若Ｂａｎａｃｈ空间Ｘ是局部ｋ-一致凸的，则对每个ｘ∈Ｓ（Ｘ），ｆ∈Σ（ｘ）是Ｘ^*的ｋ－强光滑点，并得到局部ｋ－一致凸空间的几个性质．     

关于K—极凸Banach空间

引进Ｋ－极凸Ｂａｎａｃｈ空间，证明了ＸＫ－极凸当且仅当Ｘ自反、Ｋ－严格凸且有（Ｈ）性质，得到了Ｋ－极凸空间的一些性质，并讨论了Ｋ－极凸与Ｋ－Ｋ－强光滑、Ｋ－一致凸及完全Ｋ－凸的关系。     

Banach空间具有Banach—Saks性质的一个充分条件

本文的目标是利用凸性指标给出Ｂａｎａｃｈ空间具有Ｂａｎａｃｈ－Ｓａｋｅ性质的一个充分条件，从而推广Ｋａｎｋｕｔａｎｉ定理。     

一致凸Banach空间中渐近非扩张映象的几乎轨道的渐近行为

设Ｘ是有Ｆｒéｃｈｅｔ可微范数的一致凸Ｂａｎａｃｈ空间，Ｃ是Ｘ的有界闭凸子集，Ｔ：Ｃ→Ｃ是一个渐近非扩张映象．证明了，如果｛ｘ_ｎ：ｎ≥１｝是Ｔ的几乎轨道，则序列｛ｘ０｝弱几乎收敛到集合∩from∞to(ｎ＝１)ｃｏ｛ｘ_i：ｉ≥ｎ｝∩Ｆ（Ｔ）的唯一点，其中，Ｆ（Ｔ）是Ｔ的不动点集．     

Banach空间的接近光滑性,接近凸性和滴性及其应用

本文发现，用在一定条件下序列的相对列紧性可以统一而且十分简捷地处理Ｂａｎａｃｈ空间的局部接近一致光滑性，弱Ｈａｈｎ－Ｂａｎａｃｈ光滑性及滴性等概念。并由此推出了它们之间的一些新关系，得出一些新性质，也得到了Ｂａｎａｃｈ空间自反的一些新等价条件，在讨论了接近一致光滑和接近一致凸之间的关系的基础上，我们还得到了Ｂｏｃｈｎｅｒ空间的相应一些性质。     

次可分与拟可分的Banach空间

Ｘ是Ｂａｎａｃｈ空间，对Ｘ的每一弱可分且弱紧的子集Ｋ，若（ｋ，ω）可度量，则称Ｘ是次可分的。如果对任意的可分，则称Ｘ是拟可分的。本文证明了这两类新引入的空间比可分空间与弱紧生成的Ｂａｎａｃｈ空间都要广泛并且保留了可分空间的许多重要性质。     

B值L′极值鞅变换的Lp收敛性

本文运用 Ｋｒｏｎｅｃｋｅｒ引理的推广形式对取值于 Ｂａｎａｃｈ空间 Ｂ上的 Ｂ值 Ｌ′极限鞅Ｘ＝（Ｘ_ｎ，Ｆ_ｎ）_ｎ≥0，关于实值可预报序列 Ｖ＝（Ｖ_ｎ，Ｆ_ｎ）_ｎ≥１的鞅变换Ｙ＝((?)V_k(X_k-X_k-1)Ｆ_ｎ）_ｎ≥１的Ｌ^p收敛性进行讨论，获得一     

Banach空间的弱*序列紧性

本文研究了Ｂａｎａｃｈ空间的弱序列紧性．Ｂａｎａｃｈ空间Ｘ称为有（ｗ）性质，如果Ｘ（Ｘ的共轭空间）的每个有界序列有弱收敛子列．我们证明了，如果Ｂａｎａｃｈ空间Ｘ有（ｗ）性质，那么ｌｐ（Ｘ）（１≤ｐ＜＋∞）与ｃ０（Ｘ）也有（ｗ）性质．     

一类弱稳定的Banach空间

为了解决什么样的Ｂａｎａｃｈ空间，它的每个无穷维子空间几乎等距地含有Ｃ０或ｌｐ（１≤ｐ＜∞）问题，Ｊ．Ｌ．Ｋｒｉｖｉｎｅ１９７９年在［４］中引进了稳定的Ｂａｎａｃｈ空间的概念．Ｓ．Ａｒｇｙｏｒｓ．在［２］中引进了弱稳定的概念，列举了一个弱稳定而非稳定的Ｂａｎａｃｈ空间，本文引进具有Ｐ－凸完备极小系的Ｂａｎａｃｈ空间，证明了该空间是弱稳定以及可赋等价的稳定范数的充要条件是其自反．最后给出了不自反的具有Ｐ—凸完备极小系的Ｂａｎａｃｈ空间的例子从而推广了［２］中结果．     

6-path-connectivity and 6-generation

We consider simple connected graphs for which there is a path of length at least 6 between every pair of distinct vertices. We wish to show that in these graphs the cycle space over Z₂ is generated by the cycles of length at least 6. Furthermore, we wish to generalize the result for k-path-connected graphs which contain a long cycle.     

Map Preserving Local Properties of a Digital Image

In order to study digital topological properties of a k-surface in Z ⁿ , we generalize the topological number in Bertrand (Pattern Recogn. Lett. 15:1003–1011, 1994). Furthermore, we show that a local (k ₀,k ₁)-isomorphism preserves some digital-topological properties, such as a generalized topological number and a simple k ₀-point, and prove that a local (k ₀,k ₁)-isomorphism takes a simple k ₀-surface in into a simple k ₁-surface in .      

A note in approximative compactness and midpoint locally k-uniform rotundity in Banach spaces

In this article, we prove the following results: (1) A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; (2) A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.     

Ordered semigroups having the <Emphasis Type="Italic">P</Emphasis>-property

In this paper we obtain the following main results. The ordered semigroups which have the P-property are decomposable into archimedean semigroups. Moreover, they are decomposable into semigroupswith the P-property. Conversely, if an ordered semigroup S is a complete semilattice of semigroups which have the P-property, then S itself also has the P-property. An ordered semigroup is CS-indecomposable and has the P-property if and only if it is archimedean. If S is an ordered semigroup, then the relation N:= {(a, b) | N(a) = N(b)} (here N(a) is a filter of S generated by a (a ∈ S)) is the least complete semilattice congruence on S and the class (a) _N is a CS-indecomposable subsemigroup of S for each a ∈ S. We introduce the notion of the P _m -property and describe it in terms of the P-property. Our approach simplifies the proofs of the corresponding results about unordered semigroups. The text was submitted by the authors in English.     

空间的几种超投影性质及其局部化

讨论Banach空间几种超投影性质(及其相应的局部化性质)之间的关系,证明了在Banach空间X自反的条件下,X是l_p-次投影空间的充要条件是X^*是l_p-超投影空间,X是局部l_p-次投影空间的充要条件是X^*是局部l_p-超投影空间,以及X是局部次投影空间的充要条件是X^*是局部超投影的。其中1/p+1/q=1(p>1,q>1)。     

KI,k-FACTORIZATION OF BIPARTITE GRAPHS

in this paper a necesssary condition for a bipartite graph λK,to be K1-factorizable and a sufficient condition for kk to have a k -factonrization whenever k is a prime number are given.     

Estimates of Disjoint Sequences in Banach Lattices and R.I. Function Spaces

We introduce UDS _p -property (resp. UDT _q -property) in Banach lattices as the property that every normalized disjoint sequence has a subsequence with an upper p-estimate (resp. lower q-estimate). In the case of rearrangement invariant spaces, the relationships with Boyd indices of the space are studied. Some applications of these properties are given to the high order smoothness of Banach lattices, in the sense of the existence of differentiable bump functions     

Asymptotic structure, -estimates of sequences, and compactness of multilinear mappings

We relate the moduli of asymptotic uniform smoothness and convexity of a Banach space with the existence of upper and lower ℓ_p-estimates of sequences in the space. To this end, we introduce two properties which are related to the (m_p)-property defined by Kalton and Werner. In this way we obtain a connection between the moduli of asymptotic uniform smoothness and convexity, and compactness or weak-sequential continuity of multilinear mappings. Finally, we give some applications to the existence of analytic and asymptotically flat norms on a Banach space.     

Tightness,torsion, and tubes

We give examples of spaces with 3-torsion in the homology admitting Z₃-tight polyhedral immersions into euclidean space. Polyhedral tubes are used to construct embedded hypersurfaces of this kind.     

Cartesian P-property and Its Applications to the Semidefinite Linear Complementarity Problem

We introduce a Cartesian P-property for linear transformations between the space of symmetric matrices and present its applications to the semidefinite linear complementarity problem (SDLCP). With this Cartesian P-property, we show that the SDLCP has GUS-property (i.e., globally unique solvability), and the solution map of the SDLCP is locally Lipschitzian with respect to input data. Our Cartesian P-property strengthens the corresponding P-properties of Gowda and Song [15] and allows us to extend several numerical approaches for monotone SDLCPs to solve more general SDLCPs, namely SDLCPs with the Cartesian P-property. In particular, we address important theoretical issues encountered in those numerical approaches, such as issues related to the stationary points in the merit function approach, and the existence of Newton directions and boundedness of iterates in the non-interior continuation method of Chen and Tseng [6]. This work is supported by the annual grant A2004/23 of University of Southampton.