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Transformations and non-degenerate maps

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Science china mathematics 2005年第z1期48卷 195-205页

作者： LI Baokui & WANG Yuefei institute of mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china Graduate School, chinese academy of sciences, beijing 100080, china 1. institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 2. Graduate School Chinese Academy of Sciences 100080 Beijing China

We shall prove the equivalences of a non-degenerate circle-preserving map and a M(o)bius transformation in ^Rn, of a non-degenerate geodesic-preserving map and an isometry in Hn of a non-degenerate line-preserving map and an affine transformation in Rn. That a map is non-degenerate means that the image of the whole space under the map is not a circle, or geodesic or line respectively. These results hold without either injective or surjective, or even continuous assumptions, which are new and of a fundamental nature in geometry.

关键词： M(o)bius transformation, circle-preserving map, non-degenerate map.

Central simple Poisson algebras

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Science china mathematics 2004年第2期47卷 245-263页

作者： SU Yucai & XU XiaopingDepartment of mathematics, Shanghai Jiaotong University, Shanghai 200030, china institute of mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china 1.Department of mathematics Shanghai Jiaotong University 200030 Shanghai China 2.Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China

Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic *** Lie algebra structures of these Poisson algebras are in general not finitely-graded.

关键词： Poisson algebra, locally-finite operator, derivation, finitely-graded, isomorphism class.

ON THE ERROR ESTIMATE OF LINEAR FINITE ELEMENT APPROXIMATION TO THE ELASTIC CONTACT PROBLEM WITH CURVED CONTACT BOUNDARY

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Journal of Computational mathematics 2000年第6期18卷 561-566页

作者： Lie-heng Wang (State Key Laboratory of Scientific and Engineering Computing, institute of Computational mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china) 中科院计算数学所科学与工程计算国家重点实验室北京 100080

In this paper, the linear finite element approximation to the elastic contact problem with curved contact boundary is considered. The error bound O(h[sup ?]) is obtained with requirements of two times continuously differentiable for contact boundary and the usual regular triangulation, while *** et. al. Obtained the error bound O(h[sup ?]) with requirements of three times continuously differentiable for contact boundary and extra regularities of triangulation (c.f. [2]). [ABSTRACT FROM AUTHOR]

关键词： contact problem finite element approximation

Adaptive computation for convection dominated diffusion problems

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Science china mathematics 2004年第z1期47卷 22-31页

作者： CHEN Zhiming & Jl GuanghuaLSEC, institute of Computational mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china institute of Computational mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china (email:ghji@***) 1. LSEC Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 2. institute of Computational mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China

We derive sharp L∞(L1) a posteriori error estimate for the convection dominated diffusion equations of the formThe derived estimate is insensitive to the diffusion parameter ε→0. The problem is dis-cretized implicitly in time via the method of characteristics and in space via continuous piecewise linear finite elements. Numerical experiments are reported to show the competitive behavior of the proposed adaptive method.

关键词： a posteriori error estimator, characteristics, adaptive.

Global asymptotic stability of a two species competitive system with stage structure and harvesting

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Communications in Nonlinear Science and Numerical Simulation 2001年第2期6卷 81-87页

作者： Xinyu SONG and Lansun CHEN Department of mathematics, Xinyang Teachers College, Henan 464000, china institute of mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china Department of mathematics Xinyang Teachers College Henan 464000 China institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China

The dynamics of a two species competitive system, where the species one has two stages, a immature stage and a mature stage with harvesting, and the growth of the species two is of Lotka-Volterra nature, is modelled by a system of retarded functional differential equations. We obtain the conditions for global asymptotic stability of three nonnegative equilibria and the threshold of harvesting mature population. The effect of the delay on the population at equilibrium and the optimal harvesting of mature population are also considered.

关键词： optimal harvesting stage structure competitive system global asymptotic stability.

Recovery of the scale-ε2 pattern by lattice BGK model

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Communications in Nonlinear Science and Numerical Simulation 2001年第1期6卷 40-44页

作者： Guangwu YAN and Li YUAN (institute of Computational mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china Department of mathematics, Jinn University, Chongchun 130023, china) Inst. of Computational mathematics Acad. of Math. and System Sciences Chinese Academy of Sciences Beijing 100080 China Department of mathematics Jilin University Changchun 130023 China

A lattice BGK method for nonlinear chemical reactions is described. Since the equation does not possess the convect terms, we can easily get the equilibrium distribution functions of the lattice BGK models. Using this... 详细信息

关键词： lattice BGK method Turing pattern mosaic structure

ON THE HYPER ORDER OF SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS

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chinese Annals of mathematics,Series B 2003年第4期24卷 501-508页

作者： CHEN ZONGXUAN Department of mathematics, Jiangxi Normai University, Nanchang 330027, china. institute of mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china. Jiangxi Normal Univ Dept Math Nanchang 330027 Peoples R China chinese Acad Sci Acad Math & Syst Sci Inst Math Beijing 100080 Peoples R China

The author investigates the hyper order of solutions of the higher order linear equation, andimproves the results of M. Ozawa[15], G. Gundersen[6] and J. K. Langley[12].

关键词： Differential equation Entire function Hyper order

A V-CYCLE MUTIGRID FOR QUADRILATERAL ROTATED Q_1 ELEMENT WITH NUMERICAL INTEGRATION

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Journal of Computational mathematics 2003年第5期21卷 545-554页

作者： Zhong-ci Shi Xue-jun Xu(LSEC, institute of Computational mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china) 中科院数学与系统科学院 LSEC CAS 北京 100080

In this paper, a V-cycle multigrid method is presented for quadrilateral rotated elements with numerical integration.

关键词： Multigrid Rotated Q1 elements Numerical integration.

Lattice Boltzmann solver of Rossler equation

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Communications in Nonlinear Science and Numerical Simulation 2000年第2期5卷 64-68页

作者： Guangwu YAN and Li RUAN (LSEC institute of Computational mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china Department of mathematics, Jilin University, Changchun 130023, china) LSEC Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Department of mathematics Jilin University Changchun 130023 China

We proposed a lattice Boltzmann model for the Rossler equation. Using a method of multiscales in the lattice Boltzmann model, we get the ditheion reaction as a special case. If the diffusion effect disappeared, we can obtain the lattice Boltzmann solution of the Rossler equation on the mesescopic scale. The numericale results show the method can be used to simulate Rossler equation.

关键词： lattice Boltzmann method multiscale technique Rossler equation