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Bifurcations of Rough Heteroclinic Loops with Three Saddle Points

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Acta Mathematica Sinica,English Series 2002年第1期18卷 199-208页

作者： JIN Yin Lai ZHU De Ming department of mathematics. Linyi Teachers university. Shandong 276005. P. R. china department of mathematics. east china normal university. shanghai 2.0062. P. R. china department of mathematics. east china normal university. shanghai 2.0062. P. R. china department of mathematics Linyi Teachers' University Shandong P. R. China department of mathematics East China Normal University Shanghai P. R. China

In this paper, we study the bifurcation problems of rough heteroclinic loups cormecting threc saddle points for a higher-dimensional system. Under some transversal conditions and the nontwisted condition. the existence. uniqueness. nd incoexistencc of thc l-heteroclinic loop with threc or two saddle pomts. l-homoclinic orbit and l-periodic orbit near T are obtained. Nleanwhile, the bifurcation surfaces and existence regions are also given. Moreover. the above bifurcation results are extended to the case for heteroclinic loop with l saddle points.

关键词： Local coordinates Heteroclinic loop Homoclinic orbit Periodic orbit Bifurcation surface

Extremal problems on the Hua domain of the first type

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Science china mathematics 2005年第z1期48卷 343-354页

作者： SU Jianbing & YIN Weiping mathematics department, Xuzhou normal university, Xuzhou 221116, china mathematics department, Capital normal university, Beijing 100037, china 1. mathematics department Xuzhou Normal University 221116 Xuzhou China 2. mathematics department Capital Normal University 100037 Beijing China

In this paper we study some extremal problems between the Hua domain of the first type and the unit ball.

关键词： extremal problem, Hua domain of the first type, minimal circumscribed Hermitian ellipsoid.

Extremal problems on the generalized Hua domain of the first type

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Progress in Natural Science:Materials International 2006年第4期16卷 352-358页

作者： SU Jianbing and YIN Weiping department of mathematics, Xuzhou normal university, Xuzhou 221116, china department of mathematics, Capital normal university, Beijing 100037, china [a]department of mathematics Xuzhou Normal University Xuzhou China [b]department of mathematics Capital Normal University Beijing China

Some extremal problems between the generalized Hua domain of the first type and the unit ball are studied. The extremal mapping and extremal value in explicit formulas are also obtained.

关键词： extremal problem generalized Hua domain of the first type minimal circumscribed Hermitian ellipsoid.

A categorical interpretation of Yetter-Drinfel'd modules

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Chinese Science Bulletin 1999年第9期44卷 771-778页

作者： KAN Haibin and WANG ShuanhongInstitute of mathematics , Fudan university , shanghai 200433 , china department of mathematics , Henan normal university, Xinxiang 453002, china Institute of mathematics Fudan Univrrsity Shanghai China Dcpartment of mathematics Henun Normal University Xinxiang China

It is known that any strict tensor category （C, I） can determine a strict braided tensor category Z （ C）, the centre of C. When A is a finite Hopf algebra, Drinfel’d has proved that Z（AM） is equivalent to D（A）M as a braided tensor category, where AM is the left A-module category, and D （A） is the Drinfel’d double of A. This is the categorical interpretation of D （A）.Z（4M） is proved to be equivalent to the Yetter-Drinfel’ d module category AY D4 as a braided tensor category for any Hopf algebra A. Furthermore, for right A-comodule category MA , Z（MA） is proved to be equivalent to the Yetter-Drinfel’ d module category AY D4 as a braided tensor category. But, in the two cases, the Yetter-Drinfel’ d module category AY DA has different braided tensor structures.

关键词： Yetter-Drinfel’d module tensor category equivalence.

ON THE UNIQUE SOLVABILITY OF THE NONLINEAR SYSTEMS IN MDBM

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Journal of Computational mathematics 1994年第1期12卷 55-60页

作者： Kuang Jiao-xun Lu Lian-hua (department of mathematics, shanghai normal university, shanghai, china) shanghai normal UNIV DEPT MATHSHANGHAIPEOPLES R CHINA

To obtain the approximate solution of the nonlinear ordinary differential equations requires the solution to systems of nonlinear equations. The authors study the conditions for the existence and uniqueness of the sol... 详细信息

关键词： DL ON THE UNIQUE SOLVABILITY OF THE NONLINEAR SYSTEMS IN MDBM

Functors of the Category of Abelian Sheaves on Regular Affine Scheme

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Acta Mathematica Sinica,English Series 1996年第4期12卷 413-414页

作者： Zhou Caijun department of mathematics shanghai normal university shanghai, 200234 china department of mathematics Shanghai Normal University Shanghai China

In this short paper, we prove that if R is a regular local ring of unequal characteristic, then there exists an additive covariant functor G from the category of abelian sheaves on SpecR to the category of abelian groups such that id_R(G(R))>dimG(R). This result shows that the answer to the question 3.8 (ii) in [3] may be negative.

关键词： Affine scheme Abelian sheaf Additive covariant functor

Lie bialgebras of generalized Witt type

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Science china mathematics 2006年第4期49卷 533-544页

作者： SONG Guang’ai & SU Yucai College of mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264005, china department of mathematics, university of Science and Technology of china, Hefei 230026, china department of mathematics, shanghai Jiaotong university, shanghai 200240, china College of mathematics Information Science Shandong Institute of Business Technology Yantai 264005 China department of mathematics University of Science Technology of china Hefei 230026 China department of mathematics Shanghai Jiaotong University Shanghai 200240 China

In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W, W(?)W) is trivial.

关键词： Lie bialgebras, Yang-Baxter equation, Lie algebra of generalized Witt type.

AN EXTREMAL APPROACH TO BIRKHOFF QUADRATURE FORMULAS

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Journal of Computational mathematics 2001年第5期19卷 459-466页

作者： Ying-guang Shi (department of mathematics, Hunan normal university, Changsha 410081, china) 湖南师范大学湖南长沙 410081

Discusses an extremal problem with Birkhoff interpolation constraints. Quadrature formula derived from an extremal problem; Overview of auxiliary lemmas; Derivation of some properties of polynomials.

关键词： an extremal approach Birkhoff quadrature formulas

GENERAL CAUCHY PROBLEM FOR THE LINEAR SHALLOW-WATER EQUATIONS ON AN EQUATORIAL BETA-PLANE

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Journal of Hydrodynamics 2006年第3期18卷 303-309页

作者： SHEN Chun SHI Wei-hui School of mathematics and Information Yantai Normal University Yantai 264025 China shanghai Institute of Applied mathematics and Mechanics Shanghai University Shanghai 200072 China department of mathematics Shanghai University Shanghai 200444 China

Based on the theory of stratification, the well-posedness of the initial value problem for the linear shallow-water equations on an equatorial beta-plane was discussed. The sufficient and necessary conditions of the existence and uniqueness for the local solution of the equations were presented and the existence conditions for formal solutions of the equations vere also given. For the Cauchy problem on the hyper-plane {t = O}, the local analytic solution were worked out and a special case was discussed. Finally, an example was used to explain the variety of formal solutions for the ill-posed problem.

关键词： stratification initial value problem,well-posedness shallow-water equations