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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 {3.,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.

CONVERGENCE OF VORTEX METHODS FOR 3.D EULER EQUATIONS

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Journal of Computational mathematics 2000年第3期18卷 239-250页

作者： Jia-fu Lin (institute of System science, {2. of {3. and System sciences, chinese academy of sciences, beijing, 100080, China School of Mathematical sciences, Peking University, beijing 100871, China) 中科院系统科学所北京 100080

Presents a study on the convergence of vortex methods for the three-dimensional Euler equations in bounded domains. Related studies on the convergence of vortex methods; Formulation of vortex methods; Convergence for ... 详细信息

关键词： Euler equations vortex methods convergence initial-boundary value problem

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 {3., chinese academy of sciences, beijing 100080, China 3. institute of systems science, Chi Department of mathematics Beijing Normal University Beijing China institute of ap.lied {2. Chinese Academy of Sciences Beijing China institute of systems {2. 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.

Remarks on Hard Lefschetz conjectures on Chow groups Dedicated in celebration of science CHINA on the occasion of its 60th birthday

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science China mathematics 2010年第1期53卷 105-114页

作者： FU BaoHua institute of mathematics, {2. of Mathematic and {3. science, chinese academy of sciences, beijing 100190, China institute of mathematics Academy of Mathematic and Systems Science Chinese Academy of Sciences Beijing China

We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we show that they are equivalent to the well-known conjectures of Beauville and Murre.

关键词： Chow groups abelian varieties Bloch-Beilinson conjectures Beauville conjecture Murre conjecture

Study on the generator f of the operators I_n and I_t

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science China mathematics 2010年第10期53卷 2589-2603页

作者： CHEN HanLin academy of mathematics and systems science,chinese academy of sciences,{2. 100190,China 1. academy of mathematics and systems science Chinese Academy of Sciences Beijing 100190 China

Define two operators In and It,the inner product operator In(g)(x) := j∈Zs(g,f(·-j))f(x-j) and the interpolation operator It(g)(x) := j∈Zs g(j)f(x-j),where f belongs to some space and integer s *** call f the generator of the operators In and *** is well known that there are many results on operators In and *** there remain some important problems to be further *** application we first need to find the available generators (that can recover polynomials as It(p) = p or In(p) = p,p ∈Πm-1) for constructing the relative *** this paper,we focus on the available generator in the class of spline *** shall see that not all spline functions can be used to construct available ***,we do find a spline function in S,of degree m-1,where m is even and S is a class of *** for odd m the problem is still *** on spline functions in this paper are new.

关键词： generator available generator inner product operator spline interpolation operator two-closed refinable

Multi-dimensional versions of a formula of Popoviciu

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science China mathematics 2007年第2期50卷 285-291页

作者： Zhi-qiang XU institute of Computational Math and Sci/Eng Computing, academy of mathematics and systems science, {2., {3., China 1. institute of Computational Math and Sci/Eng Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

In this paper, an explicit formulation for multivariate truncated power functions of degree one is given firstly. Based on multivariate truncated power functions of degree one, a formulation is presented which counts the number of non-negative integer solutions of s×(s + 1) linear Diophantine equations and it can be considered as a multi-dimensional versions of the formula counting the number of non-negative integer solutions of ax + by = n which is given by Popoviciu in 1953.

关键词： multivariate splines discrete truncated power linear Diophantine equations 41A15 05A15

CONGRATULATIONS TO ACADEMICIAN JUNZHI CUI ON HIS 70^(th) BIRTHDAY

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Journal of Computational mathematics 2008年第3期26卷 259-260页

作者： institute of Computational mathematics and Scientific/Engineering Computing {2. {3. institute of Computational mathematics and Scientific/Engineering Computing {2. {3.

Professor Junzhi Cui was born on June 15, 193. in Xinxiang, Henan Province in China. He graduated from the Department of mathematics and Mechanics, Northwestern Polytechnic University in 1962. Since then, he has been ... 详细信息

关键词： BIRTHDAY CONGRATULATIONS TO ACADEMICIAN JUNZHI CUI ON HIS 70 th HIS

On Stability and Trajectory Boundedness in Mean-square Sense for ARMA Processes

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Acta Mathematicae applicatae Sinica 2003年第4期19卷 573-580页

作者： Han-Fu Chenacademy of mathematics and systems science, chinese academy of sciences, {2., China academy of mathematics and systems science Chinese Academy of Sciences Beijing 100080 China

For the multidimensional ARMA system A(z)y k = C(z)w k it is shown that stability (det A(z) = 0, z : |z| 1) of A(z) is equivalent to the trajectory boundedness in the mean square sense (MSS) which, as a rule, is a consequence of a successful stochastic adaptive control leading the closed-loop of an ARMAX system to a steady state ARMA system. In comparison with existing results the stability condition imposed on C(z) is no longer needed. The only structural requirement on the system is that det A(z) and det C(z) have no unstable common factor.

关键词： ARMA stability boundedness in MSS equivalence

ON THE CENTRAL RELAXING SCHEME Ⅱ: systems OF HYPERBOLIC CONSERVATION LAWS

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Journal of Computational mathematics 2001年第6期19卷 571-582页

作者： Hua-zhong Tang (School of Mathematical sciences, Peking University, beijing 100871, China) (LSEC,ICMSEC {2.s, {3., beijing 100080, China) School of Mathematical sciences Peking University Beijing 100871 China

This paper continues to study the central relaxing schemes for system of hyperbolic conservation laws, based on the local relaxation approximation. Two classes of relaxing systems with stiff source term are introduced to approximate system of conservation laws in curvilinear coordinates. Based on them, the semi-implicit relaxing schemes are con- structed as in [6, 12. without using any linear or nonlinear Riemann solvers. Numerical experiments for one-dimensional and two-dimensional problems are presented to demon- strate the performance and resolution of the current schemes.

关键词： Hyperbolic conservation laws The relaxing system The central relaxing schemes The Euler equations.