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THE STABILITY OF THE PERIODIC SOLUTIONS OF SECOND ORDER HAMILTONIAN SYSTEMS

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Chinese Annals of mathematics,Series B 2000年第2期21卷 225-232页

作者： LIU CHUNGEN(Department of mathematics, nankai university, {2., china.) Department of mathematics Nankai University Tianjin 300071 China

This paper studies the stability of the periodic solutions of the second order Hamiltonian systems with even superquadratic or subquadratic potentials. The author proves that in the subquadratic case, there exist infinite geometrically distinct elliptic periodic solutions, and in the superquadratic case, there exist infinite geometrically distinct periodic solutions with at most one instability direction if they are half period non-degenerate, otherwise they are elliptic.

关键词： Krein type Stability Periodic elliptic solution Hamitonian systems

η-INVARIANT AND CHERN-SIMONS CURRENT

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Chinese Annals of mathematics,Series B 2005年第1期26卷 45-56页

作者： ZHANGWEIPING nankaiInstituteofmathematics NankaiUniversityTianjin300071China

The author presents an alternate proof of the Bismut-Zhang localization formula of η invariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localization techniques of Bismut-Lebeau. As a consequence, it is shown that the R/Z part of the analytically defined η invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, the author discusses the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles, and proves an R refinement in the case where the Dirac operator is replaced by the Signature operator.

关键词： Direct image η-Invariant Chern-Simons current mod k index theorem

Another solution of Yang-Baxter equation on set and "metahomomorphisms on groups

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Chinese Science Bulletin 1997年第22期42卷 1852-1855页

作者： GU PeiDepartment of mathematics, nankai university, {2., china Department of mathematics Nankai University Tianjin China

1 Another solution of Yang-Baxter equation on setIN ref [1], Drinfeld said that up to now there exist just two examples on the solution R of theYang-Baxter

关键词： Yang-Baxter equation solution metahomomorphism finite simple group.

THE FULL DISCRETE DISCONTINUOUS FINITE ELEMENT ANALYSIS FOR FIRST-ORDER LINEAR HYPERBOLICEQUATION

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Journal of Computational mathematics 1999年第1期17卷 97-112页

作者： Che Sun Shu-jie Qin(Department of mathematics, nankai university, {2., china. nankai Univ Dept Math Tianjin 300071 Peoples R China

In this paper, the full discrete discontinuous Galerkin finite element method to solove 2.dimensional first-order linear hyperbolic problem is considered. Two practical schemes, Euler scheme and Crank-Nicolson scheme, are constructed. For each of them, the stability and error estimation with optimal order approximation is established in the norm stronger than L-2.norm.

关键词： hyperbolic equation discontinuous FEM Euler scheme

On homotopy regular monomorphisms

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Chinese Science Bulletin 1998年第1期43卷 27-30页

作者： CHEN Jixiang Department of mathematics, nankai university, {2., china Department of mathematics Nankai University Tianjin China

A concept of homotopy regular monomorphism is introduced which is strictly between homotopy monomorphism and homotopy equivalence. And it characterizes homotopy equivalence in some sense.

关键词： homotopy monomorphism homotopy equalizer homotopy regular monomorphism homotopy pull back.

CRITERION FOR SL(2.Z)-MATRIX TO BE CONJUGATE TO ITS INVERSE

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Chinese Annals of mathematics,Series B 2002年第4期23卷 455-460页

作者： LONG YIMINGnankai Institute of mathematics, {2., tianjin 300071, china. E-mail: longym@***. nankai Institute of mathematics Nankai University Tianjin 300071 China

This paper gives a necessary and sufficient condition for a matrix in SL(2. Z) to be conjugateto its inverse. This condition reduces the determination of the conjugation to solving some indeterminate equation of second degree. It yields an algorithm to determine this conjugation in finite steps based on the elementary number theory.

关键词： SL(2 Z) matrix Inverse Mixed stability

Complete Lie algebras

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Chinese Science Bulletin 1999年第11期44卷 961-964页

作者： MENG DaojiDepartment of mathematics , nankai university, {2., china Department of Mathemtics Nankai University Tianjin China

A remark on complete Lie algebras is given. Since the theory of complete Lie algebras is still developing, this remark cannot be complete.

关键词： complete Lie algebra derivation center.

Automorphisms with order three of affine Lie algebras

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Chinese Science Bulletin 1998年第21期43卷 1793-1798页

作者： JIN Quanqin 1,2.and HOU Zixin 2.1. Department of mathematics, Hebei university, Baoding 071002.{2.2. Department of mathematics, nankai university, tianjin 300071, china Department of mathematics Hebei University Baoding China Department of mathematics Nankai University Tianjin China

Some properties of automorphisms of affine Lie algebras are presented. Automorphisms with order three are classified up to conjugacy, and their fixed point sets are also computed. As a corollary, it is proved that two... 详细信息

关键词： affine Lie algebra automorphism of order three first (second) kind of automorphism.

The realization and structure of complete Lie algebras whose nilpotent radicals are Heisenberg algebras

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Chinese Science Bulletin 1998年第5期43卷 383-385页

作者： JIANG Cuibo 1 and MENG Daoji 2.1.Department of mathematics,Yantai Teachers university, Yantai 2.402.,{2.2.Department of mathematics,nankai university,tianjin 300071,{2. Department of mathematics Yantai Teachers University Yantai China Department of mathematics Nankai University Tianjin China

The realization and structure of complete Lie algebras whose nilpotent radicals are Heisenberg algebras over the complex field C are given.

关键词： complete Lie algebra Heisenberg algebra nilpotent radical.