Banach空间范数的k-点态粗性和k-粗性

对Banach空间范数引入了k-点态粗和k-粗的概念,利用Banach空间理论的方法,给出了x∈S(X)为范数的k-粗糙点和X的范数是k-粗的一些充分必要条件,证明了(k+1)-粗糙点是k-粗糙点以及k-粗糙点与Fréchet可微性的一些结果.特别地,在k=1的情形下蕴含了关于范数的粗糙点、点态粗范数和粗范数的相应结果.     

Musielak-Orlicz序列空间的粗性

作者给出赋Luxemburg范数Musielak-Orlicz序列空间光滑点的支撑泛函的刻画．进一步,给出赋Orliez范数和赋Luxemburg范数Musielak-Orlicz序列空间的粗性,点态粗的充分必要条件．     

平的Banach空间

本文定义了平的Ｂａｎａｃｈ空间，证明了平的Ｂａｎａｃｈ的空间Ｘ的共轭空间Ｘ没有非常光滑点，而Ｓ（Ｘ）的非光滑点在Ｓ（Ｘ）是稠密的，同时还给出Ｘ具有粗范数的一个充分条件。     

置换空间P_XX_n中的Hahn-Banach光滑性

本文中我们给出了置换空间ＰＸＸｎ中（弱）Ｈａｈｎ－Ｂａｎａｃｈ光滑性提升性质，它们是ｌｐ（Ｘｎ）中相应结果的推广（１＜ｐ＜∞）．     

性质(u)在置换空间P_XX_n上的提升

主要讨论性质 ( u)从 Banach空间 Xn 到 PXXn 的提升问题 ,它是 lp( Xn)中相应结果的推广 .     

关于k-强极凸空间

本文证明k-强极凸是严格介于k-非常极凸和k-极凸之间的凸性.利用k-强极凸的概念,得到k-强极凸的一些特征.     

赋Orlicz范数的Musielak-Orlicz空间的光滑点与强光滑点(英)

给出赋Ｏｒｌｉｃｚ范数的Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｃｚ函数空间中光滑点、光滑性、强（很）光滑点和强（很）光滑性的充 分必要条件．     

赋Orlicz范数的Orlicz—Lorentz空间的严格凸性

本文对于赋Ｌｕｘｅｍｂｕｒｇ范数的Ｏｒｌｉｃｚ－Ｌｏｒｅｎｔｚ空间     

Bergman空间上Hankel算子的本性范数的刻划

在文中,对于Ｃ＾ｍ中有界强拟凸域Ω,得到了Ｂｅｒｇｍａｎ空间Ａ＾２（Ω）上的Ｈａｎｋｅｌ算子Ｈｆ（ｆ∈Ｌ＾２（Ω,ｄｖ）的本性范数∥Ｈｆ∥ｅｓｓ（在Ｌ＾２（Ω,ｄｖ上）的等价刻划。     

具有CF性质的k-半分层空间

给出了k-空间类中具有CF性质的k-半分层空间的一些刻画,证明了k-空间X是具有CF性质的k-半分层空间当且仅当X具有σ-CF闭伪基(闭k-网).作为这个结果的一个应用,本文部分正面回答了k-半分层空间的两个问题.     

置换空间上的滴性和弱滴性

主要给出下面结果．即PzXn。具有滴性和弱滴性的充分必要条件是每个Xn具有滴性和弱滴性条件.     

The impact of product substitution on retail merchandising

We analyze the impact of product substitution on two key aspects of retail merchandising: order quantities and expected profits. To perform this analysis, we extend the basic news-vendor model to include the possibility that a product with surplus inventory can be used as a substitute for out of stock products. This extension requires a definition and an approximation for the resulting effective demand under substitution. A service rate heuristic is developed to solve the extended problem. The performance of this heuristic is evaluated using an upper bound generated by solving the associated Lagrangian dual problem. Our analysis suggests that this heuristic provides a tractable and accurate method to determine order quantities and expected profits under substitution. We apply this heuristic to examine how the level of demand uncertainty and correlation, and the degree of substitution between products affect order quantities and expected profits under substitutable demand. In addition, we use the heuristic to better understand the mechanism by which substitution improves expected profits.     

The divergence of Banach space valued random variables on Wiener space

The domain of definition of the divergence operator δ on an abstract Wiener space (W,H,μ) is extended to include W–valued and – valued “integrands”. The main properties and characterizations of this extension are derived and it is shown that in some sense the added elements in δ’s extended domain have divergence zero. These results are then applied to the analysis of quasiinvariant flows induced by W-valued vector fields and, among other results, it turns out that these divergence-free vector fields “are responsible” for generating measure preserving flows. Mathematics Subject Classification (2000): Primary 60H07, Secondary 60H05 An erratum to this article is available at .     

The Radon transform on hyperbolic space

The Radon transform that integrates a function in ⁿ , the n-dimensional hyperbolic space, over totally geodesic submanifolds with codimension 1 and the dual Radon transform are investigated in this paper. We prove inversion formulas and an inclusion theorem for the range.     

The rack space

The main result of this paper is a new classification theorem for links (smooth embeddings in codimension 2). The classifying space is the rack space and the classifying bundle is the first James bundle.

We investigate the algebraic topology of this classifying space and report on calculations given elsewhere. Apart from defining many new knot and link invariants (including generalised James-Hopf invariants), the classification theorem has some unexpected applications. We give a combinatorial interpretation for of a complex which can be used for calculations and some new interpretations of the higher homotopy groups of the 3-sphere. We also give a cobordism classification of virtual links.

     

The Hardy space decomposition on multiangular domain

In this paper, we consider the problem of Hardy space decomposition on multiangular domain. By using rational approximation, we achieve that a function f in can be decomposed into a sum in the sense of , where are the boundary limits of functions in .