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On some tests-based projection pursuit for elliptical symmetry of a high-dimensional distribution

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Chinese Science Bulletin 1998年第6期43卷 450-458页

作者： JING Ping 1 and ZHU Lixing 2.1. mathematics Lab, china University of Mining & Technology, {2. 100083, china 2. Probability Lab, institute of applied mathematics, Chinese Academy of Sciences, beijing 100080, china mathematics Lab China University of Mining & Technology Beijing China Probability Lab Institute of Applied Mathematics Chinese Academy of Sciences Beijing China

Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. The asymptotic properties of bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on the number theoretic method, is suggested.

关键词： bootstrap approximation projection pursuit type statistic elliptical symmetry.

Mathematical stencil and its application in finite difference approximation to the Poisson equation

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Science china mathematics 2005年第10期48卷 1421-1429页

作者： FENG Hui~1 ZHANG Baolin~(1,2. & LIU Yang~1 1. Department of mathematics,Wuhan University,Wuhan 430072.china 2. Laboratory of {2. Physics,institute of applied Physics and {2. mathematics,beijing 100088. china Department of mathematics Wuhan University Wuhan China Laboratory of computational Physics Institute of Applied Physics and Computational Mathematics Beijing China

The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented, and then a new type of the iteration algorithm is established for the Poisson equation. The new algorithm has not only the obvious property of parallelism, but also faster convergence rate than that of the classical Jacobi iteration. Numerical experiments show that the time for the new algorithm is less than that of Jacobi and Gauss-Seidel methods to obtain the same precision, and the computational velocity increases obviously when the new iterative method, instead of Jacobi method, is applied to polish operation in multi-grid method, furthermore, the polynomial acceleration method is still applicable to the new iterative method.

关键词： mathematical stencil, stencil elimination, Poisson equation, finite difference, iterative algorithm,parallelism.

Two-dimensional Riemann problems of simplified Euler equation

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Chinese Science Bulletin 1998年第6期43卷 441-444页

作者： YANG Xiaozhou 1,2.and HUANG Feimin+1 1. institute of applied {2., Chinese Academy of Sciences, beijing 100080, china 2. Department of {2., Shantou University, Guangdong 515063, china institute of applied {2. Chinese Academy of Sciences Beijing China Department of mathematics Shantou University Guangdong China

The two-dimensional Riemann problem of simplifed Euler equation is discussed, in which initial value contains two different constant states that are separated by a smooth curve. This problem is a natural description of realistic phenomena, but it is hard to study by conventional idea. So a new approach is proposed. Some new properties about two-dimensional rarefaction wave, shock wave and intermediate state of solutions are disclosed.

关键词： D Riemann problem implicit functions cylindrical surface pencil of cylindrical surface.

A note on n-edge chromatic number

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Chinese Science Bulletin 1997年第23期42卷 1952-1954页

作者： SUN Liang and ZHANG Zhongfu1. Department of applied mathematics, {2. institute of Technology, {2. 100081, china 2. institute of applied mathematics, Lanzhou institute of Railway, Lanzhou 730070, china Department of applied mathematics Beijing Institute of Technology Beijing China institute of applied {2. Lanzhou Institute of Railway Lanzhou China

ALL graphs appearing in this note are simple. A graph with p vertices and q edges will becalled a (p, q )-graph. The maximum degree of G is denoted by Δ(G).Let n≥2.be an integer. The n-edge chromatic number X_n (G) of a simple graph G is theminimum cardinality of a set of colors with which one can assign the colors to the edges of Gsuch that the edges on a path of length less than or equal to n receive different *** aim of this note is to explore the bounds for X’_n (G) and X’_n (G) + X’_n (G). It is

关键词： graph complement n-edge chromatic number.

A predict-correct projection method for monotone variant variational inequalities

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Chinese Science Bulletin 1998年第15期43卷 1264-1267页

作者： HAN Qiaoming 1 and HE Bingsheng 2.1. institute of applied {2., Chinese Academy of Sciences, beijing 100080, china 2. Department of {2., Nanjing University, Nanjing 2.0093, china institute of applied {2. Chinese Academy of Sciences Beijing China Department of mathematics Nanjing University Nanjing China

A predict_correct projection method is presented for solving monotone variant variational inequalities, which could exploit the advantages and overcome the difficulties of both explicit and implicit projection methods.

关键词： variant variational inequality explicit projection method implicit projection method predict_correct projection method.

Two-dimensional simulation of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect

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Progress in Natural Science:Materials International 2007年第12期17卷 1389-1396页

作者： Hu Jun1 and Yin Xieyuan2.1. institute of applied Physics and {2. mathematics, beijing 100088, china 2. Department of Modern Mechanics, University of Science and Technology of china, Hefei 2.002., china) institute of applied Physics and {2. mathematics Beijing 100088 China Department of Modern Mechanics University of Science and Technology of China Hefei 230027 China

Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect are directly simulated by a mixed finite element method. A temperature perturbation is used as an initial disturbed source for the basic parallel flows. The whole spatio-temporal evolution of the binary fluid flows is exhibited: initially only the disturbed mode with the wavenumber k=π is amplified while others are damped, and continuously the amplified mode grows further and the nonlinear effect becomes important; after a nonlinear evolution transition the flow system evolves finally into a periodic right traveling wave.

关键词： Poiseuille-Rayleigh-Bénard flow Soret effect through-flow.

Global convergence property of s-dependent GFR conjugate gradient method

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Chinese Science Bulletin 1998年第23期43卷 1959-1965页

作者： WANG Changyu 1,2.and ZHANG Yuzhong\+1 1. institute of Operations Research in Qufu Normal University, Qufu 2.3165, china 2. institute of applied mathematics, Chinese Academy of Sciences, beijing 100080, china institute of Operations Research Qufu Normal University Qufu China institute of applied {2. Chinese Academy of Sciences Beijing China

An \%S\%_dependent GFR method and a generalized conjugate gradient method are designed. Two estimated values of upper bounds for the ratio of β k to β FR k are given. The two convergence theorems are proved. The global convergent properties of \%s\%_dependent GFR method are obtained adopting several choice strategies of steplength and some results in recent literature are extended.

关键词： steplength linear search global convergence conjugate gradient.

On the periodic solutions of a type of differential-iterative equations

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Chinese Science Bulletin 1998年第3期43卷 204-206页

作者： GE Weigao 1, LIU Zhengrong 2.and YU Yuanhong 3 1. Department of applied mathematics, {2. institute of Technology, {2. 100081, china 2. Department of mathematics, Yunnan University, Kunming 650091, china 3. institute of applied mathematics, C Department of applied mathematics Beijing Institute of Technology Beijing China Department of mathematics Yunnan University Kunming China institute of applied {2. Chinese Academy of Sciences Beijing China

Sufficient conditions for the existence of periodic solutions to a type of nonautonomous differential_iterative equations are given.

关键词： differential_iterative equation periodic solution fixed point.

Existence of solutions for the dynamic equation of ferrimagnets

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Progress in Natural Science:Materials International 2007年第11期17卷 1279-1283页

作者： Zeng Ming1, Guo Boling2.and Cheng Caozong1(1. College of applied Sciences, beijing University of Technology, beijing 10002., china 2. Center for Nonlinear Studies, institute of applied Physics and computational mathematics, beijing 100088, china) College of applied Sciences Beijing University of Technology Beijing 100022 China Center for Nonlinear Studies Institute of Applied Physics and Computational Mathematics Beijing 100088 China

Ferrimagnet is a kind of basic and important multi-sublattice magnet material. It has attracted more and more attention of physicists and mathematicians. Many results of solitons and numerical computations on this topic have appeared. In this article, the dynamic equation for an isotropic ferrimagnet with two non-equivalent sublattices is studied, existence of weak solutions in multi dimension case is proved through the penalized method, the uniqueness and smoothness of the solution in one dimension case are also obtained by the relation between this equation and hyperbolic equation.

关键词： ferrimagnet weak solutions penalized method finite difference method