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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.,{3. 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

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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.,{3., 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.

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, Beijing 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.

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., 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.

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.,{3., 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

ELTA-WAVE IN A SIMPLE 1-D 2.x 2.HYPERBOLIC PROBLEM

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Journal of Computational mathematics 1996年第4期14卷 311-318页

作者： S.L. Yang(institute of applied {2.,{3., Beijing, china) institute of applied {2. Chinese Academy of Sciences Beijing China

A simple one-dimensional 2.x 2.hyperbolic system is considered in the *** model contains a linear hyperbolic equation, as well as a hyperbolic equation ofwhich the coefficients are about the solution of the linear one. The exact solution ispresented and discussed, then numerical experiments are given by TVD (or MmB)type schemes for Riemann problems. From the results, we know that the solutionsdo have δ-waves for some suitable initial data.

关键词： Zhang Figure DELTA-WAVE IN A SIMPLE 1-D 2 HYPERBOLIC PROBLEM

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.

How big are the Csorgo-Revesz increments of two-parameter Wiener processes?

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Science china mathematics 2004年第6期47卷 894-907页

作者： WANG WenshengDepartment of mathematics, Hangzhou Teacher’s College, Hangzhou 3.0012. china {2. of applied mathematics, chinese academy of sciences, Beijing 100080, china Dept. of Math. Hangzhou Teacher's Coll. Hangzhou 310012 China Inst. of Appl. Math. Chinese Acad. of Sci. Beijing 100080 China

In this paper, we prove a theorem on the set of limit points of the increments of a two-parameter Wiener process via establishing a large deviation principle on the increments of the two-parameter Wiener process.

关键词： two-parameter Wiener process increment functional law of the iterated logarithm large deviation.

Approximation of dense-n/2.subgraph and table compression problems

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Science china mathematics 2005年第9期48卷 1223-1233页

作者： XU Dachuan~1 HAN Jiye~2.& DU Dongle~3.1. College of applied sciences,Beijing University of Technology,Beijing 10002.,{2. 2. institute of applied mathematics,academy of mathematics and Systems Science,chinese academy of sciences,Beijing 100080,{2. 3. Faculty of Administration,University of New Brunswick,P.O.Box 4400,Fredericton,NB E3. 5A3.Canada College of applied sciences Beijing University of Technology Beijing 100022 China institute of applied {2. Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China Faculty of Administration University of New Brunswick P.O. Box 4400 Fredericton NB E3B 5A3 Canada

We develop improved approximation algorithms for two NP-hard problems: the dense-n/2.subgraph and table *** on SDP relaxation and advanced rounding techniques,we first propose 0. 5982.and 0. 5970-approximation algorithms respec- tively for the dense-n/2.subgraph problem (DSP) and the table compression problem (TCP). Then we improve these bounds to 0. 62.3.and 0. 6708 respectively for DSP and TCP by adding triangle inequalities to strengthen the SDP *** results for TCP beat the 0. 5 bound of a simple greedy algorithm on this problem,and hence answer an open question of Anderson in an affirmative way.

关键词： dense-n/2.subgraph problem(DSP) table compression problem(TCP) SDP approximation ratio