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Correlation and Entanglement

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Acta Mathematicae Applicatae Sinica 2003年第4期19卷 581-598页

作者： Shun-long Luo, You-feng Luoacademy of mathematics and system {3., chinese academy of sciences, beijing 100080, China academy of mathematics and system {3. Chinese Academy of Sciences Beijing China

In quantum mechanics, it is long recognized that there exist correlations between observables which are much stronger than the classical ones. These correlations are usually called entanglement, and cannot be accounted for by classical theory. In this paper, we will study correlations between observables in terms of covariance and the Wigner-Yanase correlation, and compare their merits in characterizing entanglement. We will show that the Wigner-Yanase correlation has some advantages over the conventional covariance.

关键词： Correlation covariance Wigner-Yanase correlation entanglement qubit

Variational Description for the Generating Function Method of First Kind

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 693-702页

作者： Ya-Juan Sun, Meng-Zhao Qinacademy of mathematics and system {3., chinese academy of sciences, beijing 100080, China academy of mathematics and system {3. Chinese Academy of Sciences Beijing China

We propose the variational description of generating function approach of first kind for Hamil-tonian ODEs, and extend the approach to the semi-linear wave equations. In this way, we can construct any finite order accuracy scheme, and show that the resulting numerical scheme is multisymplectic. At last, we present some numerical experiments by using derived new scheme.

关键词： Generating function method inultisyrnplectic variational description

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 {3. 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 Beijing China

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.

ON CONJUGATE SYMPLECTICITY OF MULTI-STEP METHODS

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Journal of Computational mathematics 2000年第4期18卷 431-438页

作者： Yi-fa Tang (LSEC, Institute of Computational mathematics and Scientific/Engineering Computing, academy of mathematics and {3. sciences, chinese academy of sciences, beijing 100080, China) Dedicated to Feng Kang on his 80th birthday 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, we solve a problem on the existence of conjugate symplecticity of linear multi-step methods (LMSM), the negative result is obtained. [ABSTRACT FROM AUTHOR]

关键词： conjugate symplecticity multi-step method

Lattice Boltzmann model for the perfect gas flows with near-vacuum region

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Communications in Nonlinear Science and Numerical Simulation 2000年第2期5卷 58-63页

作者： Guangwu YAN and Li YUAN (LSEC, Institute of Computational mathematics, academy of mathematics and {3. sciences,chinese academy of sciences, beijing 100080, China Department of Mathermatics, Jilin University, Changchun 13.023. China) LSEC Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Department of mathematics Jilin University Changchun 130023 China

It is known that the standard lattice Boltzmann method has near-vacuum limit,i. e., when the density is near zero, this method is invalid. In this letter, we propose a shople lattice Boltzmann model for one-dimensional fiows. It possesses the ability of simulating near vacuum area by setting a limitation of the relaxation factor. Thus, the model overcomes the disadvantage of non-physical pressure and the density. The numerical examples show these results are satisfactory.

关键词： lattice Boltzmann method perfect gas near-vacuum region Roe’s tests

Enumeration of Maximum Acyclic Hypergraphs

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Acta Mathematicae Applicatae Sinica 2002年第2期18卷 215-218页

作者： Jian-fang Wang, Hai-zhu LiInstitute of Applied mathematics, academy of mathematics and {3. sciences, chinese academy of sciences, beijing 100080, China Institute of Applied mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. In this article, the maximum size of an acyclic hypergraph is determined and the number of maximum γ-uniform ac... 详细信息

关键词： Hypergraph Acyclic hypergraph Enumeration formula

Multisymplectic Structure and Multisymplectic Scheme for the Nonlinear Ware Equation

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Acta Mathematicae Applicatae Sinica 2002年第1期18卷 169-176页

作者： Yu-shun WANG, Meng-zhao QINLASG, Institute of Atmospheric Physics, chinese academy of sciences, beijing 100029, ChinaInstitute of Computational mathematics, {3. of mathematics and system sciences, chinese academy of sciences, beijing 100080, China LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China Institute of Computational mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

The multisymplectic structure of the nonlinear wave equation is derived directly from the variational principle. In the numerical aspect, we present a multisymplectic nine points scheme which is equivalent to the multisymplectic Preissman scheme. A series of numerical results are reported to illustrate the effectiveness of the scheme.

关键词： Multisymplectic structure Multisymplectic schemes Nonlinear wave equation

Regular Splitting and Potential Reduction Method for Solving Quadratic Programming Problem with Box Constraints

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Journal of Computational mathematics 2002年第6期20卷 643-652页

作者： Zi-Luan Wei(Institute of Computational mathematics and Scientific / Engineering Computing, academy of mathematics and {3. sciences, chinese academy of sciences, P.O. Box 2719, beijing, 100080) Institute of Computational mathematics and Scientific / Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences P.O. Box 2719 北京 100080

Presents a regular splitting and potential reduction method for solving a quadratic programming problem with box constraints. Discussion on the regular splitting and potential reduction algorithm; Complexity analysis ... 详细信息

关键词： quadratic programming problem regular splitting potential reduction algorithm complexity analysis

Lattice Boltzmann solver of Rossler equation

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Communications in Nonlinear Science and Numerical Simulation 2000年第2期5卷 64-68页

作者： Guangwu YAN and Li RUAN (LSEC Institute of Computational mathematics, academy of mathematics and {3. sciences, chinese academy of sciences, beijing 100080, China Department of mathematics, Jilin University, Changchun 13.023. China) LSEC Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Department of mathematics Jilin University Changchun 130023 China

We proposed a lattice Boltzmann model for the Rossler equation. Using a method of multiscales in the lattice Boltzmann model, we get the ditheion reaction as a special case. If the diffusion effect disappeared, we can obtain the lattice Boltzmann solution of the Rossler equation on the mesescopic scale. The numericale results show the method can be used to simulate Rossler equation.

关键词： lattice Boltzmann method multiscale technique Rossler equation