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A global solution of the Ein-stein-Yang-Mills equation on the conformal space

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chinese science Bulletin 2001年第6期46卷 460-461页

作者： LU QikengInstitute of mathematics, chinese academy of sciences, beijing 100080, china Institute of mathematics Chinese Academy of Sciences Beijing China

A global solution of the Einstein-Yang-Mills (EYM) equation on the conformal space is constructed. This solution is conformal invariant under the conformal group.

关键词： Einstein-Yang-Mills equation $12(2)-connection confor- mal space.

Note on families of semistable curves over P^1 with 4 singular fibers whose Jacobian are non-compact

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science china mathematics 2010年第7期53卷 1710-1713页

作者： YU Fei 1, 2 1 academy of mathematics and systems science, chinese academy of sciences, beijing 100190, china 2 Department of mathematics, East china Normal University, Shanghai 200062, china academy of mathematics and systems science Chinese Academy of Sciences Beijing China Department of mathematics East China Normal University Shanghai China

Let f : S → P 1 be a semistable family of curves of genus g 2. We prove that if f admits exactly 5 singular fibers and 4 of them have non-compact Jacobian, then g = 2.

关键词： singular fiber adjoint linear system non-compact Jacobian

On factorizable solution of the differential equation(f')~2-a_0(z)(f-a)1(z))~2f

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chinese science Bulletin 1997年第21期42卷 1779-1782页

作者： YUAN Wenjun and HE YuzanInstitute of mathematics, chinese academy of sciences, beijing 100080, china Institute of mathematics Chinese Academy of Sciences Beijing 100080 China

If the coefficients are transcendental, Bergweiler et al. proved that in all possible non-trivialfactorization f(z)=h(g(z)), the growth of the right factor g(z) can be controlled by thegrowth of the coefficients. In ref. [2], He and Laine proved a similar conclusion for two othertypical kinds of nonlinear differential equations. But for the following equation:

关键词： factorization growth order meromorphic function ordinary differential equation.

Range inclusion of operators on non-archimedean Banach space

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science china mathematics 2010年第12期53卷 3215-3224页

作者： WANG PengHui 1 & ZHANG Xu 2,3 1 School of mathematics, Shandong University, Jinan 250100, china 2 Key Laboratory of systems and Control, academy of mathematics and systems science, chinese academy of sciences, beijing 100190, china 3 School of mathematics, Sichuan University, Chengdu 610064, china School of mathematics Shandong University Jinan China Key Laboratory of systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China School of mathematics Sichuan University Chengdu China

In this paper, we establish some range inclusion theorems for non-archimedean Banach spaces over general valued fields. These theorems provide close relationship among range inclusion, majorization and factorization for bounded linear operators. It is found that these results depend strongly on a continuous extension property, which is always true in the classical archimedean case, but may fail to hold for the non-archimedean setting. Several counterexamples are given to show that our results are sharp in some sense.

关键词： range inclusion majorization factorization non-archimedean Banach space continuous extension property

ASYMPTOTIC ERROR EXPANSION AND DEFECT CORRECTION FOR SOBOLEV AND VISCOELASTICITY TYPE EQUATIONS

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Journal of Computational mathematics 1998年第1期16卷 51-62页

作者： Qun Lin Shu-hua Zhang Ning-ning Yan(Institute of systems science, chinese academy of sciences, beijing, china) 中科院系统科学所北京

In this paper we study the higher accuracy methods - the extrapolation and defect correction for the semidiscrete Galerkin approximations to the solutions of Sobolev and viscoelasticity type equations. The global extrapolation and the correction approximations of third order, rather than the pointwise extrapolation results are presented.

关键词： asymptotic error semidiscrete Galerkin approximation global extrapolation higher accuracy

A COMPREHENSIVE DEA APPROACH FOR THE RESOURCE ALLOCATION PROBLEM BASED ON SCALE ECONOMIES CLASSIFICATION

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Journal of systems science & Complexity 2008年第4期21卷 540-557页

作者： Xiaoya LI Jinchuan CUI Institute of Applied mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China.

This paper is concerned with the resource allocation problem based on data envelopment analysis （DEA） which is generally found in practice such as in public services and in production process. In management context, the resource allocation has to achieve the effective-efficient-equality aim and tries to balance the different desires of two management layers： central manager and each sector. In mathematical programming context, to solve the resource allocation asks for introducing many optimization techniques such as multiple-objective programming and goal programming. We construct an algorithm framework by using comprehensive DEA tools including CCR, BCC models, inverse DEA model, the most compromising common weights analysis model, and extra resource allocation algorithm. Returns to scale characteristic is put major place for analyzing DMUs＇ scale economies and used to select DMU candidates before resource allocation. By combining extra resource allocation algorithm with scale economies target, we propose a resource allocation solution, which can achieve the effective-efficient-equality target and also provide information for future resource allocation. Many numerical examples are discussed in this paper, which also verify our work.

关键词： Common weights analysis (CWA) date envelopment analysis (DEA) decision making unit (DMU) efficiency score inverse DEA model multiple-objective linear programming (MOLP) resource allocation problem returns to scale (RTS).

LEAST-SQUARES MIXED FINITE ELEMENT METHOD FOR SADDLE-POINT PROBLEM

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Journal of Computational mathematics 2000年第4期18卷 353-364页

作者： Lie-heng Wang Huo-yuan Duan (LSEC, Institute of Computational mathematics and Scientific/Engineering Computing, academy of mathematics and System sciences, chinese academy of sciences, beijing, 100080, china) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京 100080

In this paper, a least-squares mixed finite element method for the solution of the primal saddle-point problem is developed. It is proved that the approximate problem is consistent ellipticity in the conforming finite element spaces with only the discrete BB-condition needed for a smaller auxiliary problem. The abstract error estimate is derived. [ABSTRACT FROM AUTHOR]

关键词： least-squares method mixed finite element approximation saddle-point problem

Precise Asymptotics of Error Variance Estimator in Partially Linear Models

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Acta Mathematicae Applicatae Sinica 2008年第1期24卷 59-74页

作者： Shao-jun Guo, Min Chen, Feng Liu academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china Department of Statistics, Chongqing Institute of Technology, Chongqing 630000, china academy of mathematics and systems science Chinese Academy of Sciences Beijing China Department of Statistics Chongqing Institute of Technology Chongqing China

In this paper, we focus our attention on the precise asymptotics of error variance estimator in partially linear regression models, yi = xiτβ+ g(ti) +εi, 1≤i≤n, {εi,i = 1,…, n} are i.i.d random errors with mean 0 and positive finite varianceσ2. Following the ideas of Allan Gut and Aurel Spatarut and Zhang, on precise asymptotics in the Baum-Katz and Davis laws of large numbers and precise rate in laws of the iterated logarithm, respectively, and subject to some regular conditions, we obtain the corresponding results in partially linear regression models.

关键词： Precise asymptotics partially linear models error variance estimator

EXPLORATION OF TCM MASTERS KNOWLEDGE MINING

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Journal of systems science & Complexity 2008年第1期21卷 34-45页

作者： Xijin TANG Nan ZHANG Zheng WANG Institute of systems science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China.

Traditional chinese medicine （TCM） has a rich knowledge about human health and disease by its special way evolved along a very long history. As modern medicine is achieving much progress, arguments and disputes toward TCM never end. To avoid losing precious knowledge of living TCM masters, endeavors have been engaged to systematic collection of those knowledge of TCM masters, such as their growth experiences, effective practical cases toward diseases and typical therapeutic principles and methods. Knowledge mining methods have been expected to explore some useful or hidden patterns to unveil some mysteries of the TCM system. In the paper, some computerized methods are applied toward those collected materials about some living TCM masters in china mainland to show a different way of exposing essential ideas of those TCM masters by correspondence visualization which aims to help people understand TCM holistic views toward disease and body, and facilitate tacit knowledge transfer and sense-making of the essence of TCM. The work is one kind of qualitative meta-synthesis of TCM masters＇ knowledge.

关键词： Idea map knowledge mining qualitative meta-synthesis traditional chinese medicine.