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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

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, Tianjin 300071, 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

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, Tianjin 300071, China) Department of Mathematics Nankai University Tianjin 300071 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, Tianjin 300071, 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.

Synthesis and Moessbauer Spectra of Four-Coordinated Tin Compounds Containing Tin-Copper Bonds

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Chinese Chemical Letters 1998年第5期9卷 491-494页

作者： Jin Shan LI and (Institute of Elemento-Organic Chemistry, nankai university, Tianin 300071)Jing Kun ZANG (Central Laboratory, nankai university, Tanjin 300071) Inst. of Elemento-Organic Chemistry Nankai University Tianjin 300071 China Central Laboratory Nankai University Tianjin 300071 China

Seven compounds containing tin-copper bonds, namely [Ph2P(CH2)(n)PPh2](CuSnPh3)(2) (n=1-4) and (Ph2PR)CuSnPh3 (R=Ph, Bu, Am), have been synthesized. Tin-119 Moessbauer spectra for these compounds were determined. The results have shown that the QS values for these compounds are all zero, the IS values are between 1.32 and 1.38 mm/s, and the oxidation state of tin is +4.

关键词： Moessbauer spectrum oxidation state electron density

Topological Structures of ω-subsets in Symplectic Groups

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Acta Mathematica Sinica,English Series 1999年第2期15卷 255-268页

作者： Yiming Long, nankai Institute of Mathematics, nankai university, Tianjin 300071, P. R. ChinaE-mail: longym@sun. nankai, edu. cn 南开大学南开数学所天津

All the symplectic matrices possessing a fixed eigenvalue ω on the unit circle form a hypersurface in the real symplectic group Sp(2n). This paper is devoted to the study of the topological structures of this hypersu... 详细信息

关键词： Symplectic groups ω-subsets Toplogical structure

THE ACHILLES’ HEEL OF GATT’S INTERNATIONAL TRADE SYSTEM OF AGRICULTURAL PRODUCTS AND A POSSIBLE REMEDY

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南开经济研究 1994年第S2期 34-41页

作者： Cheng Baoku nankai university Cui Yonglu

The postwar history saw the rapid agricultural developmentand great expansion of production in many developed countriesowing to the impetus provided by the progress in science andtechnology and subsidies in agricultur... 详细信息

关键词：全色

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, Tianjin 300071, 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.

ON THE COASTAL ECONOMIC ZONE AROUND THE YELLOW SEA & BOHAI SEA——Features & Comparative Advantages in Regional Economic Cooperation

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南开经济研究 1994年第S2期 12-20页

作者： Chen Yue nankai university Shen Huan

Since the middle of the nineteen-eighties, there haveemerged in Northeast Asia many circles or economic zones of whichthe concept of the coastal region around the Yellow Sea and

关键词： Features