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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., {3. 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 Mathematics 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.

CONSERVATiON LAWS OF NONHOLONOMiC NONCONSERVATiVE DYNAMiCAL SYSTEMS

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Acta Mechanica Sinica 1989年第2期5卷 167-175页

作者： Liu Duan (department of applied {2.,{3. institute of technology) 1. department of applied {2. Beijing Institute of Technology Beijing China

in this paper conservation laws of nonholonomic nonconservative dynamical systems are studied by using the differential variational principles of Jourdain and the generalized Noether's identi- ties of nonconservative ... 详细信息

关键词： conservation law nonholonomic constraint Noether's theorem

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., {3. 100081, China 2. institute of applied Mathematics, Lanzhou institute of Railway, Lanzhou 73.070, China department of applied Mathematics Beijing Institute of Technology Beijing 100081 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.

Non-Noether conserved quantity for differential equations of motion in the phase space

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Chinese Science Bulletin 2002年第24期47卷 2049-2050页

作者： MEi Fengxiangdepartment of applied {2.,{3., beijing 100081, China department of applied {2. Beijing Institute of Technology Beijing China

A non-Noether conserved quantity for the differential equations of motion of mechanical systems in the phase space is studied. The differential equations of motion of the systems are established and the determining equations of Lie symmetry are given. An existence theorem of non-Noether conserved quantity is obtained. An example is given to illustrate the application of the result.

关键词： mechanical system phase space non-Noether conserved quantity.

Lie symmetry and conservation law of Birkhoffian system

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Chinese Science Bulletin 1999年第4期44卷 318-320页

作者： MEi Fengxiangdepartment of applied {2. ,{3., beijing 100081, China department of applied {2. Beijing Institute of Technology Beijing China

The Lie symmetry of Birkhoffian system was studied, the condition under which the system admits the one-parameter Lie group of transformation with infinitesimal generator was given, and the structural equation and the... 详细信息

关键词： symmetry conservation law Birknoffian system.

A trust region algorithm for bilevel programing problems

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Chinese Science Bulletin 1998年第10期43卷 820-824页

作者： LiU Guoshan 1, HAN Jiye 2.and WANG Shouyang 3.1. department of Mathematics, beijing Normal University, beijing 100875, China 2. {3. of applied Mathematics, Chinese Academy of Sciences, beijing 100080, China 3. {3. of Systems Science, Chi department of Mathematics Beijing Normal University Beijing China institute of applied Mathematics Chinese Academy of Sciences Beijing China institute of Systems Science Chinese Academy of Sciences Beijing China

A trust region algorithm is proposed for solving bilevel programming problems where the lower level programming problem is a strongly convex programming problem with linear constraints. This algorithm is based on a tr... 详细信息

关键词： bilevel programming problem trust region algorithm global convergence.

ON THE EXiSTENCE OF SOLUTiONS TO A TYPE OF NONLiNEAR DiFFERENTiAL-iTERATiVE EQUATiONS

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Chinese Annals of Mathematics,Series B 2000年第2期21卷 217-224页

作者： GE WEiGAO(department of applied Mathematics,{2., {3. 100081, China.) Li CUiZHE(department of applied Mathematics,{2., {3. 100081, China.) YU YUANHONG(inditute of applied Mathematics, Acad department of applied Mathematics Beijing Institute of Technology Beijing 100081 China institute of applied Mathematics Academia Sinica Beijing 100080 China

Under the assumption that h(z) is strictly monotone the existence of solutions to a type of nonlinear differential-iterative equations in the form of x’(t) = g(x(t)) -h(x(x(t))) is discussed according to the behavior... 详细信息

关键词： Differential-iterative equation Quasi-isoclinic curve Fixed point

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 Computational Mathematics, {2. {3.8, China 2. department of Modern mechanics, University of Science and technology of China, Hefei 2.002., China) institute of applied Physics and Computational 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.

Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science China Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2.1. department of Mathematics, beijing Normal University, beijing 100875, China 2. {3. of applied Physics and Computational Mathematics, beijing 100080, China 1. department of Mathematics Beijing Normal University Beijing 100875 China 2. institute of applied Physics and Computational Mathematics Beijing 100080 China

in this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.