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Some new results on planar harmonic mappings

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Science china Mathematics 2010年第3期53卷 597-604页

作者： CHEN HuaiHui department of Mathematics, nanjing normal university, {2. 2.0097, china department of Mathematics Nanjing Normal University

This survey paper contains some new results on the Landau theorem, Bloch theorem and Schwarz-Pick lemma for planar harmonic mappings.

关键词： harmonic mapping Landau theorem Bloch constant Schwarz-Pick lemma quasi-regularity

normal Functions and α-normal Functions

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Acta Mathematica Sinica,English Series 2000年第3期16卷 399-404页

作者： Yan Xu department of Mathematics,nanjing {2. university,nanjing 2.0097 P.R.china department of Mathematics Nanjing Normal University Nanjing 210097 P. R. China

This paper has studied two open questions about normal functions due to Lappan,and obtained two corresponding results for α-normal functions.

关键词： Spherical derivative normal function α-normal function

Completely regular paracompact reflection of locales

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Science china Mathematics 2006年第6期49卷 820-826页

作者： HE Wei & LUO Maokang department of Mathematics, nanjing normal university, {2. 2.0097, china department of Mathematics, Sichuan university, Chengdu 610064, china department of Mathematics Nanjing Normal University Nanjing China department of Mathematics Sichuan University Chengdu China

We give an explicit construction of the completely regular paracompact reflection pL of a completely regular locale L described as a sublocale of the Stone-tech compactification βL of L.

关键词： completely regular paracompact locale, nucleus.

L-R smash products for bimodule algebras

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Progress in Natural Science:Materials International 2006年第6期16卷 580-587页

作者： ZHANG Liangyun (department of Mathematics, nanjing Agricultural {2., nanjing 2.0095, china department of Mathematics, nanjing {2., nanjing 2.0008, china) department of Mathematics Nanjing Agricultural University Nanjing 210095 China department of Mathematics Nanjing University Nanjing 210008 China

In this paper, we prove that the L-R smash product A(?)H is exactly the twisted smash product A * H if H is a finite dimensional cocommutative Hopf algebra, and give a sufficient and necessary condition for L-R smash products to be bialgebras (Hopf algebras) . For any finite dimensional coquasitriangular Hopf algebra (H,σ), we prove that the L-R smash product H(?)H is semisimple Artinian if H is semisimple and H * is unimodular. In particular, the L-R smash product D(H)* (?)D(H)* semisimple Artinian if the Drin-fel'd double D(H) is semisimple.

关键词： bimodule algebras L-R smash products coquasitriangular Hopf algebras Long bialgebras.

On the variational principle for the topological pressure for certain non-compact sets

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Science china Mathematics 2010年第4期53卷 1117-1128页

作者： PEI Yu 1 & CHEN ErCai 1,2.1 department of Mathematics,nanjing {2. university,nanjing 2.0097,china 2.Center for Nonlinear Science,nanjing university,nanjing 2.0093,china department of Mathematics Nanjing Normal University Center for Nonlinear Science Nanjing University

Let (X,d,T) be a dynamical system,where (X,d) is a compact metric space and T:X → X is a continuous *** assume that the dynamical system satisfies g-almost product property and the uniform separation *** compute the topological pressure of saturated sets under these two *** the uniform separation property does not hold,we compute the topological pressure of the set of generic *** give an application of these results to multifractal analysis and finally get a conditional variational principle.

关键词： uniform separation property g-almost product property topological pressure of non-compact sets variational principle BS-dinmension

THE SECOND EXPONENT SET OF PRIMITIVE DIGRAPHS

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Chinese Annals of Mathematics,Series B 2000年第2期21卷 233-236页

作者： MIAO ZHENGKE(department of Mathematics, nanjing {2., nanjing 2.0093, china.)(department of Mathematics, Xuzhou normal {2., Xuzhou 2.1009, china.) ZHANG KEMIN(department of Mathematics, nanjing {2., nanjing 2.0093, china.) department of Mathematics Nanjing University Nanjing 210093 China department of Mathematics Xuzhou Normal University Xuzhou 221009 China

Let D = (V, E) be a primitive digraph. The exponent of D, denoted byγ(D), is the least integer k such that for any u, v∈ V there is a directed walk of length k from u to v. The local exponent of D at a vertex u∈ V, denoted by exp_D (u), is the least integer k such that there is a directed walk of length k from u to v for each v ε V. Let V = {1,2.….,n}. Following [1], the vertices of V are ordered so that exp_D (1) ≤exp_D (2. ≤…≤exp_D(n) =λ(D). Let E_n(i):= {exp_D (i) ∈D PD_n}, where PD_n is the set of all primitive digraphs of order n. It is known that E_n(n) = {γ(D) D∈PD_n} has been completely settled by [7]. In 1998, E_n(1) was characterized by [5]. In this paper, the authors describe E_n(2. for all n≥2.

关键词： Primitive digraph Local exponent Gap

Nonlinear ergodic theorem for semitopological semigroups of non-Lipschitzian mappings in Banach spaces

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Chinese Science Bulletin 1997年第1期42卷 8-11页

作者： LI Gang and MA Jipu1. department of Mathematics, Yangzhou normal College, Yangzhou 2.5002.{2. 2. department of Mathematics, nanjing university, nanjing 2.0093,{2. department of Mathematics Yangzhou Normal College Yangzhou China department of Mathematics Nanjing University Nanjing China

LET G be a semitopological semigroup, i. e. G is a semigroup with a Hausdorff topology such that for each s∈G the mapping s|→s·t and s|→t·s from G to G are continuous. G is called right reversible if any two closed left ideals of G have non-void intersection. In this case, (G,≤) is a directed system when the binary relation '≤' on G is defined by a≤b if and only if Let E be the uniformly convex Banach space

关键词： nonlinear semigroup ergodic theorem non-Lipschitzian mapping.

A GOLDSTEIN'S TYPE PROJECTION METHOD FOR A CLASSOF VARIANT VARIATIONAL INEQUALITIES

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Journal of Computational Mathematics 1999年第4期17卷 425-434页

作者： Bing-sheng He(department of Mathematics, nanjing {2., nanjing 2.0008, china) department of Mathematics Nanjing University Nanjing 210008 China

Some optimization problems in mathematical programming can be translated to a variant variational inequality of the following form: Find a vectoru*, such that This paper presents a simple iterative method for solving this class of variational inequalities. The method can be viewed as an extension of theGoldstein's projection method. Some results of preliminary numerical experiments are given to indicate its applications.

关键词： Variational inequality Goldstein projection method.

Uniquely ergodic property of minimal probability measure in positive definite Lagrangian systems

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Science china Mathematics 2006年第12期49卷 1864-1866页

作者： CHEN Jing & BAI Yuzhen department of Mathematics, nanjing {2., nanjing 2.0093, china department of Mathematics, Qufu normal {2., Qufu 2.3165, china department of Mathematics Nanjing University Nanjing China department of Mathematics Qufu Normal University Qufu China

Mane conjectured that every minimal measure in the generic Lagrangian systems is uniquely ergodic. In this paper, we will show that the answer to the Mane's conjecture is negative by analyzing the structure of the sup... 详细信息

关键词： minimal probability measure,uniquely ergodic,Mather theory,Lagrangian systems.