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Minimal symmetric submanifolds in compact Riemannian symmetric spaces

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Chinese Science Bulletin 1998年第21期43卷 1786-1789页

作者： LIANG Ke 1 and JIN Quanqin 1,2.1. department of mathematics, {2. University, tianjin 300071, china 2. department of mathematics, Hebei University, Baoding 071002. china department of mathematics Nankai University Tianjin China department of mathematics Hebei University Baoding China

A necessary and sufficient condition for a symmetric submanifold to be minimal in its ambient compact Riemannian symmetric space is given. By this condition a complete classification of non- minimal symmetric submanif... 详细信息

关键词： symmetric space symmetric submanifold mean curvature vector.

SOME RESULTS ON INFINITE DIMENSIONAL NOVIKOV ALGEBRAS

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Chinese Annals of mathematics,Series B 2003年第3期24卷 309-314页

作者： ZHAO YUFENG MENG DAOJI department of mathematics, {2. University, tianjin 300071, china. department of mathematics, {2. University, tianjin 300071, china. department of mathematics Nankai University Tianjin 300071 China

This paper gives some sufficient conditions for determining the simplicity of infinite di-mensional Novikov algebras of characteristic 0, and also constructs a class of simple Novikovalgebras by extending the base fie... 详细信息

关键词： Novikov algebra Novikov-Poisson Algebra Algebraic deformation

The mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate-temporal mode

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Science china(Physics,Mechanics & Astronomy) 2005年第5期48卷 614-625页

作者： HUANG Zhangfeng 1, CAO Wei 1,2.& ZHOU Heng 1,2.1. department of Mechanics, tianjin University, tianjin 300072. china 2. Liu-Hui Center of Applied mathematics, nankai University and tianjin University, tianjin 300072. china department of Mechanics Tianjin University Tianjin China Liu-Hui Center of Applied mathematics Nankai University and Tianjin University Tianjin China

Temporal mode direction numerical simulation has been done for the transition of a supersonic boundary layer on a flat plate with Mach number 4.5. Analysis of the result showed that during the breakdown process in laminar-turbulent transition, the mechanism causing the mean flow profile to evolve swiftly from laminar to turbulent was that the modification of mean flow profile by the disturbances,when they became larger,led to a remarkable change of its stability characteristics. Though the most unstable T-S wave was of second mode for laminar flow, the first mode waves played the key role in the breakdown process in laminar-turbulent transition.

关键词： supersonic boundary layer, transition, breakdown.

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, {2. 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, {2. 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, {2. 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.

Direct numerical simulation of a supersonic turbulent boundary layer on a flat plate and its analysis

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Science china(Physics,Mechanics & Astronomy) 2005年第5期48卷 626-640页

作者： HUANG Zhangfeng1, ZHOU Heng1,2.& LUO Jisheng1,2.1. department of Mechanics, tianjin University, tianjin 300072. china 2. Liu-Hui Center of Applied mathematics, nankai University and tianjin University, tianjin 300072. china department of Mechanics Tianjin University Tianjin China Liu-Hui Center of Applied mathematics Nankai University and Tianjin University Tianjin China

Temporal mode direct numerical simulation (DNS) has been done for a supersonic turbulent boundary layer on a flat plate with Mach number 4.5. It was found that the mean flow profile, the normal-wise distribution of turbulent Mach number and the root mean square (RMS) of the fluctuations of various variables, as well as the Reynolds stresses, bore similarity in nature, when the turbulence reached a fully developed state. But the compressibility effect was strong and must be considered. The strong Reynolds analogy (SRA) and the Morkovin hypothesis were no longer valid. From the end of transition to the fully developed state of turbulence, it was in the transient period, for which the similarity did not hold.

关键词： turbulence, similarity, compressibility effect, supersonic boundary layer, direct numerical simulation.

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.

Geometric characterizations for variational minimization solutions of the 3-body problem

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Chinese Science Bulletin 1999年第18期44卷 1653-1655页

作者： LONG Yiming and ZHANG Shiqing1. nankai Institute of mathematics , nankai University , tianjin 300071 , china 2. department of Applied mathematics, Chongqing University, Chongqing 400044, china Associate Member of the ICTP. nankai Institute of mathematics Nankai University Tianjin China department of Applied mathematics Chongqing University Chongqing China

For any given positive masses it is proved that the variational minimization solutions of the 3-body problem in 3 or 2.are precisely the planar equilateral triangle circular solutions found by J. Lagrange in 1772. and that the variational minimization solutions of the circular restricted 3-body problem in 3 or 2.are also planar equilateral triangle circular solutions.

关键词： 3-body problem variational minimization equilateral triangle circular solution.