Two Hardy-Bennett-Type Theorems

The factorization of inequalities is a new and very effective method proving the best possible version of classical and recent inequalities. Presently we shall slightly improve two factorization theorems proved by us, and simultaneously verify the theorem of [2] in its original form. This revised version was published online in June 2006 with corrections to the Cover Date.     

Hartogs Extension Theorems on Stein Spaces

We discuss various known generalizations of the classical Hartogs extension theorem on Stein spaces with arbitrary singularities and present an analytic proof based on \(\overline{\partial}\)-methods.     

锥线性算子的延拓定理

建立了一种锥分离定理,据此证明了锥线性算子的延拓定理,作为应用,给出了正线性算子的延拓定理。     

Two Theorems of Rokhlin

Two theorems due to V. A. Rokhlin are proved: the theorem on the third stable homotopy group of spheres: ; and the theorem on the divisibility by 16 of the signature of a spin 4-manifold. The proofs use immersion theory. Bibliography 17 titles.     

Two Theorems of Hardy-Bennett-Type

The factorization of inequalities, introduced by G. Bennett, is a new and very effective method providing the best possible version of several classical and latest inequalities. Here two theorems of G. Bennett are extended into factorized forms up to the exact values of the constants. In the proofs we construct appropriate sequence spaces and utilize one of our recent theorems.     

一致连续映射的两个扩张定理

把文[1],[2]中的两个定理进行了拓广和改进,给出两个一致连续映射的扩张定理:(i)任一集合A到一个完备度量空间的一致连续映射可一致连续扩张到A珡上.(ii)任一闭集A到Rn的一致连续映射可一致连续扩张到A与任一紧集的并.     

Embedding Theorems for General Multianisotropic Spaces

An integral representation and embedding theorems for functions in multianisotropic Sobolev spaces are proved. Unlike in previous works, the general case where the characteristic Newton polyhedron in ?ⁿ has an arbitrary number of vertices is considered.     

Limit Theorems for General Markov Chains

Siberian Mathematical Journal -     

关于Gelfand-Mazur型的两个定理

证明了两个Gelfand-Mazur型的定理，其一是：设A是一单位C^*- wa ovt ,AH≌R，且h∈AK时，e^h具有凸谱集。则A≌C。这一结果回答了Bhatt等人的问题，给出了他们的结果在实情形中的结论。其二，部分地回答了Bhatt等人的另一个问题。结果是：设A是一复单位厄米Banach^*- 代数，假设（i)对任意x∈AH，谱集σA(x)的内部是空集，且C\σA（x)是连通的，（ii)A没有非零零因子，则A同构到C。     

Two Theorems about Similarity Maps

One of the problems arising when exploring toponome or other multivariate-image data is the following: Given a family of n gray-value images of, e.g., a given sample of cell tissue, indexed by a collection of n proteins under investigation (so-called MELK data) — each single image representing the varying local concentration of one of those n proteins at the various sites (pixels) of the given sample, how should one quantify, for any two pixels (or clusters of pixels), the (dis)similarity between the corresponding “vectors” of local protein concentrations in question. Some (dis)similarity mappings defined on allowing for fast OpenGL texture mapping turned out to be useful in visual inspection of toponome data. Here, we derive two rather general results regarding similarity and dissimilarity mappings and, as a corollary, the fact that the functions that were used for visual inspection of MELK data are, indeed, metrics. We believe that our results are, however, also of more general interest within the ongoing program of elucidating the structure of metrics from a more abstract point of view. Received April 01, 2005     

一般拓扑空间上的KKM定理,匹配定理,重合点定理

引进没有任何凸结构的拓扑空间上的广义R-KKM映射的定义,并利用古典的KKM原理得到一般拓扑空间上的KKM型定理,然后利用该结果得到Lassonde型匹配定理和Klee型相交定理,最后作为应用给出非紧的拓扑空间上不动点定理和重合点存在定理.推广和改进了文献中的相应结果.     

概念粒计算系统外延的判别定理

概念粒计算系统是基于两个完备格之间的外延内涵算子和内涵外延算子构成的模型系统,它包括经典概念格,L模糊概念格及变精度概念格等.本文以三种概念粒计算系统为模型研究了概念外延的特征及其相互关系,给出了外延为经典集、内涵为模糊集和外延为模糊集、内涵为经典集这两种概念粒计算系统的概念外延判别定理,并且讨论了几种模型概念之间的关系与性质.     

Extension Theorems for Large Scale Spaces via Coarse Neighbourhoods

We introduce the notion of (hybrid) large scale normal space and prove coarse geometric analogues of Urysohn’s Lemma and the Tietze Extension Theorem for these spaces, where continuous maps are replaced by (continuous and) slowly oscillating maps. To do so, we first prove a general form of each of these results in the context of a set equipped with a neighbourhood operator satisfying certain axioms, from which we obtain both the classical topological results and the (hybrid) large scale results as corollaries. We prove that all metric spaces are hybrid large scale normal, and characterize those locally compact abelian groups which (as hybrid large scale spaces) are hybrid large scale normal. Finally, we look at some properties of the Higson compactifications and coronas of hybrid large scale normal spaces.     

积分型中值定理的推广及统一表示

通过减弱连续的条件,推广了一类积分型中值定理,在适当的条件下,用一个式子将Lagrange中值定理、Cauchy微分中值定理、积分型Cauchy中值定理、积分中值定理、积分第一中值定理、Lagrange型积分中值定理、Cauchy型积分中值定理及推广的积分第一中值定理这8个中值定理统一起来.     

An Asymptotic Version of General Commutator Theorems

An operator generalization of the asymptotic version of Fuglede's theorem is given for an arbitrary complex Banach algebra.