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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., chinese academy of sciences, 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.

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., 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.

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.

A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING THE ADVECTION-DIFFUSION EQUATIONS

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Journal of Computational mathematics 2002年第1期20卷 57-64页

作者： Huo-yuan Duan (institute of mathematics, {2. of mathematics and System sciences, chinese academy of sciences, beijing 100080, china) institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 北京 100080

Focuses on a study on the development of a stabilized finite element method for solving the advection-diffusion equations with a zero Dirichlet boundary condition. Problem formulation; Error analysis.

关键词： advection-diffusion equation stabilized finite element method

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, institute of applied {2., chinese academy of sciences, 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.

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 {2.,chinese academy 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

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, {2. of mathematics and System sciences, chinese academy of sciences, beijing 100080, china Graduate School, chinese academy of sciences, beijing 100080, china institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China Graduate School Chinese Academy of Sciences 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.

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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 {2., chinese academy of sciences, beijing 100080, 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.

δ-WAVE FOR 1-D AND 2.D HYPERBOLIC SYSTEMS

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Journal of Computational mathematics 1996年第3期14卷 256-262页

作者： S.L. Yang(institute of applied {2., chinese academy of sciences, beijing, china) 中科院应用数学所北京

Here a new kind of nonlinear wave, which is called δ-wave, is described by some high resolution difference solutions for Riemann problems of one-dimensional (1-D) and two-dimensional (2.D) nonlinear hyperbolic systems in conservation laws. Some phenomena are numerically shown for the solutions of Riemann problems for 2.D gas dynamics systems

关键词： Zhang WAVE FOR 1-D AND 2.D HYPERBOLIC SYSTEMS