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A class of mechanically decidable problems beyond Tarski's model

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Science china Mathematics 2007年第11期50卷 1611-1620页

作者： Lu YANG~(1,2) Yong FENG~(1+) Yong YAO~1 1 laboratory for automated reasoning and programming,chengdu institute of computer applications,chinese academy of sciences,chengdu 610041,china 2 institute of Theoretical Computing,East china Normal University,Shanghai 200062,china laboratory for automated reasoning programming Chengdu Institute of Computer Applications Chinese Academy of Sciences Chengdu 610041 China institute of Theoretical Computing East China Normal University Shanghai 200062 China

By means of dimension-decreasing method and cell-decomposition,a practical algorithm is proposed to decide the positivity of a certain class of symmetric polynomials,the numbers of whose elements are *** is a class of mechanically decidable problems beyond Tarski *** implement the algorithm,a program nprove written in maple is developed which can decide the positivity of these polynomials rapidly.

关键词： symmetric polynomial inequality cell-decomposition Tarski's sentence Tarski's model mechanically decidable problem

THE EDUCATIONAL SOFTWARE FOR CHEMISTRYBASED ON automated reasoning

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Systems Science and Mathematical sciences 1999年第S1期12卷 78-87页

作者： WANG Xiaojing(chengdu institute of computer Application, chinese academy of sciences,chengdu 610064, china)ZHANG Jingzhong(chengdu institute of computer Application, chinese academy of sciences,chengdu 610064, china)

A new type of the educational software for chemistry based on automatedreasoning with chemical knowledge was successfully developed. This intelligent systemwith the unique style of the interactive functions and the open mode of the knowledgebase has shown not only its notable ability to solve chemical problems, to improve thereasoning performance of itself, but also its advantages to provide more opportunities forthe users to acquire living knowledge through the interactive ways.

关键词： ICAI automated reasoning chemical knowledge-base terminology understanding.

MATRIX ANALYSIS ON LEADING TERM OF CONDITION NUMBER FOR ADDITIVE SCHWARZ METHODS

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Journal of Computational Mathematics 2001年第2期19卷 157-166页

作者： Jia-chang Sun (R & D Center of Paraller Software, laboratory for computer Science, institute of Software, chinese academy of sciences) 中科院软件所

It is well known the order of preconditioned matrix by using additive Schwarz methods. In order to estimate the resulted PCG iteration counts, the related leading term brfore the order is given in this paper.

关键词： additive Schwarz method PCG matrix analysis

THE SPLITTING EXTRAPOLATION FOR FINITEELEMENT METHOD

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Systems Science and Mathematical sciences 1997年第4期10卷 372-382页

作者： LU Tao FENG Yong(institute of chengdu computer Application, Academia Sinica, chengdu 610041, china)

A new splitting extrapolation based on multivariate asymptotic expansionsof finite elemellt eraes for differellt mesh parameters is described. By means of splittingextrapolation, a far 3 scale problem is decomposed into many subproblems, which can besolved in parallel. 111 this paper) we prove that the splitting extrapolation algorithm possesses a high order accuracy and the computation is almost independent of the dimension ofthe problem. Moreover, an extrapolation algorithm at global fine grid points is presented,several numerical examples including interface problems are discussed.

关键词： Splitting extrapolation parallel algorithm domain decomposition.

Frequency/time hopping sequence sets with optimal partial Hamming correlation properties

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Science china(Information sciences) 2012年第10期55卷 2207-2215页

作者： NIU XianHua 1,2,PENG DaiYuan 1 & ZHOU ZhengChun 3 1 The Provincial Key laboratory of Information Coding and Transmission,institute of Mobile Communications,Southwest Jiaotong University,chengdu 610031,china 2 The School of Mathematics and computer Engineering,Xihua University,chengdu 610039,china 3 The College of Maths,Southwest Jiaotong University,chengdu 610031,china 1. The Provincial Key laboratory of Information Coding and Transmission Institute of Mobile Communications Southwest Jiaotong University Chengdu 610031 China 2. The School of Mathematics and computer Engineering Xihua University Chengdu 610039 China 3. The College of Maths Southwest Jiaotong University Chengdu 610031 China

Frequency hopping/time hopping(FH/TH) sequences have found wide applications in various modern FH/TH spread spectrum communications,such as digital cellular mobile communication,short-range wireless communication,personal communication,and multi-user radar,sonar *** order to evaluate the goodness of FH/TH sequences design,the periodic Hamming correlation function is used as an important ***,the length of correlation window is shorter than the period of the chosen FH/TH sequence,so the study of the partial Hamming correlation of FH/TH sequence is particularly *** this paper,a new class of FH/TH sequence sets with good partial Hamming correlation properties is proposed and *** construction of new FH/TH sequence sets is based upon the generalized m-sequence and generalized Gordon-Mills-Welch sequence over a polynomial residue class *** is shown that new FH/TH sequence sets are optimal with respect to the partial Hamming correlation bound.

关键词： frequency hopping/time hopping(FH/TH) sequence partial Hamming correlation optimal FH/TH sequence set

An improved method for progressive animation models generation

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Science china(Information sciences) 2010年第7期53卷 1312-1321页

作者： ZHANG ShiXue1,2, ZHAO JinYu1 & WU EnHua2,3 1Changchun institute of Optics, Fine Mechanics and Physics, chinese academy of sciences, Changchun 130033, china 2Department of computer and Information Science, University of Macau, Macao, china 3State Key laboratory of computer Science, institute of Software, chinese academy of sciences, Beijing 100190, china 1. Changchun institute of Optics Fine Mechanics and Physics Chinese Academy of Sciences Changchun 130033 China2. Department of Computer and Information Science University of Macau Macao China3. State Key Laboratory of Computer Science Institute of Software Chinese Academy of Sciences Beijing 100190 China

In computer graphics, animated models are widely used to represent time-varying data. And the progressive representation of such models can accelerate the speed of processing, transmission and storage. In this paper, we propose an efficient method to generate progressive animation models. Our method uses an improved curvature sensitive quadric error metric (QEM) criterion as basic measurement, which can preserve more local features on the surface. We append a deformation weight to the aggregated edge contraction cost during the whole animation to preserve more motion features. At last, we introduce a mesh optimization method for the animation sequence, which can efficiently improve the temporal coherence and reduce visual artifacts between adjacent frames. The results show our approach is efficient, easy to implement, and good quality progressive animation models can be generated at any level of detail.

关键词： animation models LOD progressive mesh mesh optimization

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, Beijing 100080, china 3. Department of Scientific Computing and computer applications, Zhongshan University, Guangzhou 510275, china) Department of Mathematics Beijing Jiaotong University Beijing 100044 China. institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China. Department of Scientific Computing and computer applications Zhongshan University 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

A new class of three-variable orthogonal polynomials and their recurrences relations

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Science china Mathematics 2008年第6期51卷 1071-1092页

作者： SUN JiaChang State Key laboratory of computer Science,R&D Center for Parallel Computing,institute of Software,chinese academy of sciences,Beijing 100080,china State Key laboratory of computer Science R & D Center for Parallel Computing Institute of Software Chinese Academy of Sciences Beijing 100080 China

A new class of three-variable orthogonal polynomials, defined as eigenfunctions of a second order PDE operator, is studied. These polynomials are orthogonal over a curved tetrahedron region, which can be seen as a mapping from a traditional tetrahedron, and can be taken as an extension of the 2-D Steiner domain. The polynomials can be viewed as Jacobi polynomials on such a domain. Three-term relations are derived explicitly. The number of the individual terms, involved in the recurrences relations, are shown to be independent on the total degree of the polynomials. The numbers now are determined to be five and seven, with respect to two conjugate variables z, $ \bar z $ and a real variable r, respectively. Three examples are discussed in details, which can be regarded as the analogues of the Chebyshev polynomials of the first and the second kinds, and Legendre polynomials.

关键词： 3-D PDE eigen-problem three-variable Chebyshev polynomials Legendre polynomial Jacobi polynomials recurrence relations 65N25 42C05 33C45

NONPARAMETRIC APPROACH TO IDENTIFYING NARX SYSTEMS

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Journal of Systems Science & Complexity 2010年第1期23卷 3-21页

作者： Qijiang SONG·Han-Pu CHEN Key laboratory of Systems and Control,institute of Systems Science,academy of Mathematics and Systems Science,chinese academy of sciences,Beijing 100190,china Key laboratory of Systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences

This paper considers identification of the nonlinear autoregression with exogenous inputs(NARX system).The growth rate of the nonlinear function is required be not faster than linear withslope less than *** value of f(·) at any fixed point is recursively estimated by the stochasticapproximation (SA) algorithm with the help of kernel *** consistency of the estimatesis established under reasonable conditions,which,in particular,imply stability of the *** simulation is consistent with the theoretical analysis.

关键词： α-mixing geometrically ergodic Markov chains NARX nonparametric recursive estimate stochastic approximation strongly consistent.