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Asymptotic behavior of the divergence on loop spaces over a compact Riemannian manifold

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chinese Science Bulletin 1998年第4期43卷 272-274页

作者： LI Xiangdong probability laboratory,{2.,{2., beijing 100080, China probability laboratory Institute of Applied Mathematics Chinese Academy of Sciences Beijing China

The asymptotic behavior of the divergence on loop space is studied over a compact Riemannian manifold via quasi_sure analysis. A Sobolev estimate plays a crucial role.

关键词： divergence exponential integrability Sobolev estimate.

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 mathematics, chinese academy of sciences,{2., China 2. Department of mathematics, 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 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 mathematics, chinese academy of sciences,{2., China 2. Department of mathematics, 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.

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,{2., 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.

The proof of FFD(L)≤11/9OPT(L) +7/9

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chinese Science Bulletin 1997年第15期42卷 1262-1265页

作者： LI Rongheng, YUE Minyi1. Department of mathematics, Hunan Normal University, Changsha 410081, China 2. institute of applied mathematics,{2., beijing 100080, China Department of mathematics Hunan Normal University Changsha 410081 China institute of applied {2. Chinese Academy of Sciences Beijing 100080 China

THE one-dimensional bin-packing problem is defined as follows: for a given list L={p1, p2.…, Pn}, where 0i≤1 denotes the item and its size as well, we are to pack all the items in-to bins, each of which has a capaci... 详细信息

THE one-dimensional bin-packing problem is defined as follows: for a given list L={p1, p2./sub>,…, Pn}, where 0i≤1 denotes the item and its size as well, we are to pack all the items in-to bins, each of which has a capacity 1, and the goal is to minimize the number of bins *** first-fit-decreasing （FFD） algorithm is a famous approximate algorithm for the bin-pack-ing problem. The FFD algorithm first sorts all the list into non-increasing order and then pro-cesses the pieces in that order by placing each item into the first bin into which it fits.

关键词： bin-packing minimal counter-example weigtht-function FFD-algorithm.

Quasi-Homeomorphisms and Measures of Finite Energy Integrals of Generalized Dirichlet Forms

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Acta Mathematica Sinica,English Series 2000年第2期16卷 325-336页

作者： Wei Sun institute of applied mathematics,chinese {2. of sciences,beijing,100080,P.R.China institute of applied {2. Chinese Academy of Sciences Beijing 100080 P. R. China

We introduce the quasi-homeomorphisms of generalized Dirichlet forms and prove that any quasi-regular generalized Dirichlet form is quasi-homeomorphic to a semi-regular generalized Dirichlet form. Moreover. we apply this quasi-homeomorphism method to study the measures of finite energy integrals of generalized Dirichlet forms. We show that any 1-coexcessive function which is dominated by a function in is associated with a measure of finite energy integral. Consequently, we prove that a Borel set B is-exceptional if and only if μ(B)=0 for any measure μ of finite energy integral.

关键词： Generalized Dirichlet form Quasi-homeomorphism Measure of finite energy integral

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(r,k)-catching code

chinese Science Bulletin 1998年第10期43卷 812-815页

作者： LI Anping institute of applied mathematics, chinese academy of sciences,{2., China institute of applied {2. Chinese Academy of Sciences Beijing China

A collection of r_words on an alphabet of n letters is called (r,k)_catching code if for every r_word w there is one selected member v such that v coincides with w in at least k places. How large is the smallest size of the (r,k)_catching code and how to find the minimal (r,k)_\%catching code? Some methods are advanced to construct such codes.

关键词： catching code.

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. institute 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 {2. 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.

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. institute of applied mathematics, chinese academy of sciences, beijing 100080, China 3. institute of Systems Science, Chi Department of mathematics Beijing Normal University Beijing China institute of applied {2. 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.