拟共形映射和弱John域

作为John域的推广,本文定义了弱John域,并讨论了弱John域与拟圆、弱John域与拟共形 映射之间的关系,得到(1)若(?)。中的Jordan域D和它的外部 均是弱John域,则D 是拟圆;(2)R2中的弱John域是拟共不变的;(3)R2中的有界拟圆必是弱John域．最后构造例子 说明R2中的无界拟圆不一定是弱John域．     

拟共形映射和弱John域

作为John域的推广,本文定义了弱John域,并讨论了弱John域与拟圆、弱John域与拟共形映射之间的关系,得到(1)若R2中的Jordan域D和它的外部D*=R2\D均是弱John域,则D是拟圆;(2)R2中的弱John域是拟共不变的;(3)R2中的有界拟圆必是弱John域.最后构造例子说明R2中的无界拟圆不一定是弱John域.     

使用相关内射性对拟连续模的一个刻划

近二十年，许多环与模工作对拟投射模与拟内射模作了各种推广与研究。连续模与拟连续模就是拟内射模的一种推广，拟连续模要比连续模弱。在[2]，作对连续模与拟连续模做了深入的研究。在这篇章中，利用相关内射性给出了拟连续模的一个刻划。     

拟圆的三个充要条件

设D是R2中的Jordan域,D*=R2＼D是D的外部,本文证明了拟圆的下面三个充要条件:(1)D是拟圆当且仅当D和D*都是弱拟凸域;(2)D是拟圆当且仅当D和D*都是弱Cigar域;(3)D是拟圆当且仅当D是弱一致域.     

拟圆的三个充要条件

设D是(-R2)中的Jordan域,D*=(-R2)\(-D)是D的外部,本文证明了拟圆的下面三个充要条件(1)D是拟圆当且仅当D和D*都是弱拟凸域;(2)D是拟圆当且仅当D和D*都是弱Cigar域;(3)D是拟圆当且仅当D是弱一致域.     

外部边界球可达域上拟共形映射的Lipschitz连续性

定义了外部边界球可达域,利用曲线族的模获得如下结果:设D是R~n中的有界拟凸域,f:D→B~n是K-拟共形映射,若D是外部边界球可达域,则f∈Lip_α(D),其中α=K~(1/(1-n)).     

有界凸域上拟共形映射的Hoelder连续性

该文利用曲线族的模,得到了n维空间中的有界凸域D到单位球B^n上的K-拟共形映射f的全局Hoelder连续性,且Hoelder指数α=K^1/1-n是最佳的.     

拟共不变集和拟圆的特征

证明了ＮＥＤ集在拟共形映照下的像仍是ＮＥＤ集，建立了关于拟圆的一个充分必要条件。     

内部边界球可达域和拟共形映射的Hlder连续性

定义了内部边界球可达域,利用曲线族的模证明了D是R~n中的有界Jordan域,f:B~n→D是K-拟共形映射,若D是内部边界球可达域,则f∈H_(1/K)(B~n).     

纯拟内射模

本文引进了纯拟内射模的概念，讨论了该模的一些主要性质，证明了纯拟内射模保持有限直和，进一步地利用这类新模刻画了正则环的特征。     

Monotonicity and complex convexity in Banach lattices

The goal of this article is to study the relations among monotonicity properties of real Banach lattices and the corresponding convexity properties in the complex Banach lattices. We introduce the moduli of monotonicity of Banach lattices. We show that a Banach lattice E is uniformly monotone if and only if its complexification EC is uniformly complex convex. We also prove that a uniformly monotone Banach lattice has finite cotype. In particular, we show that a Banach lattice is of cotype q for some 2?q<∞ if and only if there is an equivalent lattice norm under which it is uniformly monotone and its complexification is q-uniformly PL-convex. We also show that a real Köthe function space E is strictly (respectively uniformly) monotone and a complex Banach space X is strictly (respectively uniformly) complex convex if and only if Köthe-Bochner function space E(X) is strictly (respectively uniformly) complex convex.     

弱条件下同胚的ACL性质

假设Ｄ是Ｒｎ（ｎ２）中的区域，ｙ＝ｆ（ｘ）：ＤＲｎ是一个同胚．如果ｆ（ｘ）的模伸张Ｋ（ｘ，ｆ）适合条件Ａ，则ｆ（ｘ）是ＡＣＬ的．     

On a Double Complex Sequence of Linear Operators

The main goal of the article is to introduce a class of double complex linear operators of integral type. The technique is based by extension into the complex domain of a real positive approximation process. Involving the first modulus of continuity, we investigate their geometric and approximation properties. The statistical convergence of our sequence is proved. In a particular case, our operators turn into the double complex Gauss-Weierstrass integral operators.     

L-Fuzzy Domain上的广义Scott拓扑

本文研究了L-fuzzy domain上的广义Scott拓扑,利用[1]中引入的L-fuzzy domain.获得了其上的广义Scott拓扑,它是Domain上Scott拓扑的推广,证明了一个L-fuzzy单调映射是L-fuzzy Scott连续映射当且仅当它关于L-fuzzy domain上的广义Scott拓扑连续.     

On a Sufficient Condition for Equality of Two Maximal Monotone Operators

We establish minimal conditions under which two maximal monotone operators coincide. Our first result is inspired by an analogous result for subdifferentials of convex functions. In particular, we prove that two maximal monotone operators T,S which share the same convex-like domain D coincide whenever $T(x)\cap S(x)\not=\emptyset $ for every x?∈?D. We extend our result to the setting of enlargements of maximal monotone operators. More precisely, we prove that two operators coincide as long as the enlargements have nonempty intersection at each point of their common domain, assumed to be open. We then use this to obtain new facts for convex functions: we show that the difference of two proper lower semicontinuous and convex functions whose subdifferentials have a common open domain is constant if and only if their ε-subdifferentials intersect at every point of that domain.     

On the central limit theorem for modulus trimmed sums

We prove a functional central limit theorem for modulus trimmed i.i.d. variables in the domain of attraction of a nonnormal stable law. In contrast to the corresponding result under ordinary trimming, our CLT contains a random centering factor which is inevitable in the nonsymmetric case. The proof is based on the weak convergence of a two-parameter process where one of the parameters is time and the second one is the fraction of truncation.     

Monotonicity and the Expressibility of NP Operators

We investigate why similar extensions of first-order logic using operators (that is, generalized quantifiers) corresponding to NP-complete decision problems apparently differ in expressibility: the logics capture either NP or L^NP. It had been conjectured that the complexity class captured is NP if and only if the operator is monotone. We show that this conjecture is false. However, we provide evidence supporting a revised conjecture involving finite variations of monotone problems. Mathematics Subject Classification: 68Q15, 03D15, 03C13.     

Strict limit types for monotone convolution

We introduce the notion of strict domain of attraction in the context of monotone probability theory and prove that a law has a nonempty strict domain of attraction if and only if it is strictly stable. We also show that the monotonic weak law of large numbers is equivalent to the classical and the free weak laws of large numbers. Finally, a necessary condition for a measure μ to belong to the strict domain of attraction of a nondegenerate strictly stable law is given in terms of the absolute moments of μ.     

Regular Maximal Monotone Operators

The purpose of this paper is to introduce a class of maximal monotone operators on Banach spaces that contains all maximal monotone operators on reflexive spaces, all subdifferential operators of proper, lsc, convex functions, and, more generally, all maximal monotone operators that verify the simplest possible sum theorem. Dually strongly maximal monotone operators are also contained in this class. We shall prove that if T is an operator in this class, then (the norm closure of its domain) is convex, the interior of co(dom(T)) (the convex hull of the domain of T) is exactly the set of all points of at which T is locally bounded, and T is maximal monotone locally, as well as other results.