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A CRITERION FOR TESTING WHETHER A DIFFERENCE IDEAL IS PRIME

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Journal of systems science & Complexity 2009年第4期22卷 627-635页

作者： Chunming YUAN xiao-Shan GAO Key Laboratory of mathematics Mechanization,institute of {3. science academy of mathematics and {3. science,chinese academy of sciences,Beijing 100190,china. Key Laboratory of mathematics Mechanization Institute of Systems Science Beijing China academy of mathematics and systems {3. Chinese Academy of Sciences Beijing 100190 China

This paper presents a criterion for testing the irreducibility of a polynomial over an algebraicextension *** this criterion and the characteristic set method,the authors give a criterion fortesting whether certain difference ascending chains are strong irreducible,and as a consequence,whetherthe saturation ideals of these ascending chains are prime ideals.

关键词： Characteristic set difference prime ideal irreducibility strong irreducibility.

ON THE OBSERVABILITY AND DETECTABILITY OF LINEAR STOCHASTIC systems WITH MARKOV JUMPS AND MULTIPLICATIVE NOISE

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Journal of systems science & Complexity 2010年第1期23卷 102-115页

作者： Yuanhua NI Weihai zhang Haitao FANG Key Laboratory of systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China. College of Information and Electrical Engineering Shandong University of Science and Technology Qingdao China.

This paper presents the notions of exact observability and exact detectability for Markov jump linear stochastic systems of Ito type with multiplieative noise （for short, MJLSS）. Stochastic Popov-Belevith-Hautus （PBH） Criterions for exact observability and exact detectability are respectively obtained. As an application, stochastic H2/H∞ control for such MJLSS is discussed under exact detectability.

关键词： Exact detectability exact observability Markov jump systems multiplicative noise PBH Criterion stochastic H2/H∞ control.

On the ratio of different norms of caloric functions and related eigenfunctions of an integral operator

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science china mathematics 2012年第8期55卷 1597-1612页

作者： DING YuTao 1,2,& zhang LiQun 1,2 1 institute of mathematics,{3. of mathematics and systems science,chinese {3. of sciences,Beijing 100190,china 2 Hua Loo-Keng Key Laboratory of mathematics,chinese {3. of sciences,Beijing 100190,china 1. institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China2. Hua Loo-Keng Key Laboratory of Mathematics Chinese Academy of Sciences Beijing 100190 China

We investigate the ratio of L 1 and L 2 norms of the Cauchy problem solutions of heat equations with compact support initial *** related asymptotic behavior of the eigenvalues and eigenfunctions of certain integral op... 详细信息

关键词： integral operators eigenvalues heat equation

ARTIFICIAL LIVING SYSTEM AND ITS COMPLEXITY

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Journal of systems science & Complexity 2001年第2期14卷 124-131页

作者： zhang Yongguang (institute of systems {3., academy of mathematics and systems science, chinese academy of sciences, Beijing 100080, china) 中科院系统科学所北京 100080

In this paper the author shows some artificial living systems, whose basic life characteristics are explored, especially the differentiation in evolution from single cellular to multi-cellular organism. In addition, the author discusses diversity and evolvability also. The author gives a modified entropy function to measure the diversity. Finally, the author drops an open problem about the structure of "gene" of artificial living systems, so that we can measure the evolutionary order between the artificial living systems.

关键词： Artificial living systems digital creature evolutionary systems diferentia- tion diversity evolvability.

A CHARACTERISTIC SET METHOD FOR SOLVING BOOLEAN EQUATIONS AND APPLICATIONS IN CRYPTANALYSIS OF STREAM CIPHERS

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Journal of systems science & Complexity 2008年第2期21卷 191-208页

作者： Fengjuan CHAI xiao-Shan GAO Chunming YUAN Key Laboratory of mathematics Mechanization Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

This paper presents a characteristic more efficient and has better properties than the set method for solving Boolean equations, which is general characteristic set method. In particular, the authors give a disjoint and monic zero decomposition algorithm for the zero set of a Boolean equation system and an explicit formula for the number of solutions of a Boolean equation system. The authors also prove that a characteristic set can be computed with a polynomial number of multiplications of Boolean polynomials in terms of the number of variables. As experiments, the proposed method is used to solve equations from cryptanalysis of a class of stream ciphers based on nonlinear filter generators. Extensive experiments show that the method is quite effective.

关键词： Boolean equation characteristic set method cryptanalysis finite field stream ciphers.

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.

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 {3. of Technology, Chongqing 63.000, china academy of mathematics systems science Chinese Academy of Sciences Beijing 100080 China Department of Statistics Chongqing Institute of Technology Chongqing 630000 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

PROJECTION-PURSUIT BASED PRINCIPAL COMPONENT ANALYSIS:A LARGE SAMPLE THEORY

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Journal of systems science & Complexity 2006年第3期19卷 365-385页

作者： Jian zhang institute of mathematics,Statistics and Actuarial {3.,University of Kent,Canterbury,Kent CT2 7NF,U.K. institute of systems {3.,academy of mathematics and systems {3.,chinese academy of {13.,Beijing 100080,china institute of mathematics Statistics and Actuarial Science University of Kent Canterbury institute of systems science Academy of Mathematics and Systems Science Chinese Academy of Sciences

The principal component analysis （PCA） is one of the most celebrated methods in analysing multivariate data. An effort of extending PCA is projection pursuit （PP）, a more general class of dimension-reduction techniques. However, the application of this extended procedure is often hampered by its complexity in computation and by lack of some appropriate theory. In this paper, by use of the empirical processes we established a large sample theory for the robust PP estimators of the principal components and dispersion matrix.

关键词： Dispersion matrices eigenvalues and eigenvectors empirical processes principal component analysis projection pursuit (PP).

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 {3., 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