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Decomposition of integrable holomorphic quadratic differential on Riemann surface of infinite type

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Science china Mathematics 2010年第8期53卷 2039-2044页

作者： CHENG Tao department of Mathematics,East china {2. university,Shanghai 2.02.1,china 1. department of Mathematics East China Normal University Shanghai 200241 China

In this paper,decomposition of the integrable holomorphic quadratic differential on Riemann surface of infinite type is ***,Schleicher and Shishikura gave a thick-thin decomposition on Riemann surface of finite type with an integrable holomorphic quadratic differential and they thought their result might be generalized to arbitrary hyperbolic Riemann surface of infinite *** confirm what they thought is right and give a proposition(Proposition 2.2. of its own interest.

关键词： holomorphic quadratic differential decomposition collar

HOMOCLINIC BIFURCATION WITH CODIMENSION 3

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Chinese Annals of Mathematics,Series B 1994年第2期15卷 205-216页

作者： ZHU DEMING(department of Matehematics,East china {2. university, Shanghai 2.0062. china) E china normal UNIV DEPT MATHSHANGHAI 200062PEOPLES R CHINA

First it is proved that both the integral of the divergence and the Melnikov function are invariants of the C2.transformation. Then, the problem of the planar homoclinic bifurcation with codimension 3 is considered. It is proved that, in a small neighborhood of the origin in the parameter space of a Cr (r≥5) system, there exist exactly two Cr-1 semi- stable- limit- cycle branching surfaces, and their common boundary is a unique Cr-1 three-multiple- limit-cycle branching curve. The bifurcation pictures and the asymptotic expansions of the bifurcation functions are given. The stability criterion for the homoclinic loop is also obtained when the integral of the divergence is zero. The proof of the auxiliary theorems will be presented in [16].

关键词： Homoclinic bifurcation Codimension Semi-stable-limit-cycle branch Three- multiple-limit- cycle branch.

OPTIMIZATION OF ADAPTIVE DIRECT METHOD FOR APPROXIMATE SOLUTION OF INTEGRAL EQUATIONS OF SEVERAL VARIABLES

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Acta Mathematica Scientia 2004年第2期24卷 228-234页

作者：马万房艮孙 departmentofMathematics BeijingNormalUniversityBeijing100875China

This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic So... 详细信息

关键词： Integral equations direct methods anisotropic sobolev classes

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Saturated models

Chinese Science Bulletin 1998年第7期43卷 562-564页

作者： CHEN Guolong department of Mathematics, Beijing normal {2., Beijing 100875, china department of Mathematics Beijing Normal University Beijing China

An equivalent description of saturated models is given, and some properties of countable saturated models, almost saturated models and full models are discussed. New proofs of two important theorems of the related doc... 详细信息

关键词： almost saturated model full model power type.

Moment bounds for IID sequences under sublinear expectations

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Science china Mathematics 2011年第10期54卷 2155-2160页

作者： HU Feng1,2.1department of Mathematics,Qufu normal {2.,Qufu 2.3165,china 2.chool of Mathematics,Shandong {2.,Jinan 2.0100,china 1. department of Mathematics Qufu Normal University Qufu 273165 China2. School of Mathematics Shandong University Jinan 250100 China

With the notion of independent identically distributed(IID) random variables under sublinear expectations introduced by Peng,we investigate moment bounds for IID sequences under sublinear expectations. We obtain a moment inequality for a sequence of IID random variables under sublinear expectations. As an application of this inequality,we get the following result:For any continuous functionsatisfying the growth condition |(x) | C(1 + |x|p) for some C > 0,p 1 depending on ,the central limit theorem under sublinear expectations obtained by Peng still holds.

关键词： moment bound sublinear expectation IID random variables G-normal distribution central limit theorem

Neural Network for Solving Monotone LinearComplementary Problems

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Communications in Nonlinear Science and Numerical Simulation 1999年第2期4卷 128-132页

作者： Xingban GAO(department of Mathematics, Shaanxi normal {2., Xi’an 710062. china) department of Mathematics Shanxi Normal University Xi'an 710062 China

A neural network for solving monotone linear complementary problem isproposed. It has not involved any parameter and is proven to be uniformly, asymptoticallyand stably convergent to an exact solution of the linear co... 详细信息

关键词： linear complementary problems neural network asymptotical stability

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 {2., Nanjing 2.0097, china department of Mathematics, Sichuan {2., Chengdu 610064, china department of Mathematics Nanjing Normal University Nanjing 210097 China department of Mathematics Sichuan University Chengdu 610064 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.

Relations among the category of topological molecular lattices and certain related categories

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Chinese Science Bulletin 1997年第8期42卷 636-640页

作者： WANG Guojun and LI Yongming1. Institute of Mathematics, Shaanxi normal university, Xi’an 710062.{2. 2. department of Basic Science, Northwestern Institute of Architecture Engineering, Xi’an 710061,{2. Institute of Mathematics Shaanxi Normal University Xi’an China department of Basic Science Northwestern Institute of Architecture Engineering Xi’an China

TAKING the theory of fuzzy topology and point set topology as background,the theory of topo-logical molecular lattices was first advanced in 1979,and after several generalizationsrefs.[4,5] are its general *** topology and point set topology are both special casesof topological molecular lattices as pointed out in ref.[4],whereas it seems not clear whetherone can develop the theory of topological molecular lattices by means of methods in

关键词： category pick-up-one principle.

METHOD OF NONCONFORMING MIXED FINITE ELEMENT FOR SECOND ORDER ELLIPTIC PROBLEMS METHOD OF NONCONFORMING MIXED FINITE ELEMENT FOR SECOND ORDER ELLIPTIC PROBLEMS

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Journal of Computational Mathematics 2000年第5期18卷 449-456页

作者： Zhen-dong Luo (department of Mathematics, Capital normal {2., Beijing 100057, china) 首都师范大学北京 100037

In this paper, the method of non-conforming mixed finite element for second order elliptic problems is discussed and a format of real optimal order for the lowest order error estimate.

关键词： Non-conforming mixed finite element Error estimate Second order elliptic problems.