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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.

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.

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 {3. 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 {3. 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

Modeling and verifying Web services driven by requirements:An ontology-based approach

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Science in china(Series F) 2006年第6期49卷 792-820页

作者： HOU Lishan1,3.JIN ZHi1,2.& WU Budan1,4 1. academy of mathematics and Systems Science, Chinese academy of sciences, beijing 100080, china 2. institute of Computing Technology, Chinese academy of sciences, beijing 100080, china 3. institute of Software, Chinese academy of sciences, beijing 100080, china 4. Graduate University of Chinese academy of sciences, beijing 100049, china academy of mathematics and Systems Science Chinese Academy of Sciences Beijing China institute of Software Chinese Academy of Sciences Beijing China institute of Computing Technology Chinese Academy of Sciences Bejing China Graduate University of Chinese academy of sciences Beijing China

Automatic discovery and composition of Web services is an important research area in Web service technology, in which the specification of Web services is a key issue. This paper presents a Web service capability description framework based on the environment ontology. This framework depicts Web services capability in two aspects： the operable environment and the environment changes resulting from behaviors of the Web service. On the basis of the framework, a requirement-driven Web service composition model has been constructed. This paper brings forward the formalization of Web service interactions with π calculus. And an automatic mechanism converting conceptual capability description to the formal process expression has been built. This kind of formal specification assists in verifying whether the composite Web service model matches the requirement.

关键词： Web service environment ontology automatic composition π calculus formal verification.

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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 {3. 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.

Some properties on multivariate filter banks with a matrix factorization

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Progress in Natural Science:Materials International 2005年第2期15卷 20-30页

作者： LIAN Qiaofang1, XIAO Hongying2. and CHEN Qiuhui3.1. Department of mathematics, beijing Jiaotong University, beijing 100044, china 2. institute of mathematics, academy of mathematics and System sciences, Chinese academy of sciences,{13., china 3. Department of Scientific Computing and Computer Applications, Zhongshan University, Guangzhou 5102.5, china) Dept. of mathematics Beijing Jiaotong Univ. Beijing 100044 China Inst. of mathematics Acad. of Math. and System Sci. Chinese Acad. of Sciences Beijing 100080 China Dept. of Scientific Computing Zhongshan Univ. Guangzhou 510275 China

A class of multivariate filter banks with a matrix factorization has been developed by Chen et al. The main purpose of this paper is to discuss some further properties of this kind of filter bank, such as the completeness, accuracy of the corresponding scaling functions and the relationships with Daubechies' wavelets and the multi-wavelets provided by Chui and Lian. Moreover, some examples are given to show that this kind of filter bank has a higher accuracy for the scaling functions.

关键词： filter banks completeness accuracy matrix factorization

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,{2. University of Technology,{2. 10002.,china 2. institute of applied mathematics,academy of mathematics and Systems Science,Chinese academy of sciences,{2. {13.,china 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

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 {2. of sciences, beijing 100080, china Graduate School, Chinese {2. 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.