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Lie bialgebras of generalized Witt type

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Science China Mathematics 2006年第4期49卷 533-544页

作者： SONG Guang’ai & SU Yucai College of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 2.4005, China department of Mathematics, university of Science and Technology of China, Hefei 2.002., China department of Mathematics,{3., shanghai 2.02.0, China College of Mathematics Information Science Shandong Institute of Business Technology Yantai 264005 China department of Mathematics University of Science Technology of China Hefei 230026 China department of Mathematics Shanghai Jiaotong University Shanghai 200240 China

In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W, W(?)W) is trivial.

关键词： Lie bialgebras, Yang-Baxter equation, Lie algebra of generalized Witt type.

New Exact Solutions to (2.1)-Dimensional Variable Coefficients Broer-Kaup Equations

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Communications in Theoretical physics 2006年第9期46卷 393-396页

作者： ZHU Jia-Min~(1,2.+) MA Zheng-Yi~(1,2. ~1 department of {3., Zhejiang Lishui {2., Lishui 3.0}000, China ~2.{3. Institute of Applied Mathematics and Mechanics, {3. 2.0072. China department of physics Zhejiang Lishui University shanghai Institute of Applied Mathematics and Mechanics

In this paper, using the variable coefficient generalized projected Ricatti equation expansion method, we present explicit solutions of the (2.1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.

关键词： variable coefficient generalized projected Ricatti equation method (2.1)-dimensional variable coefficients Broer Kaup equations Weierstrass function solution solitary wave solution trigonometric function solution

THE ROBUST CONTROL SCHEME FOR FREE-FLOATING SPACE MANIPULATOR TO TRACK THE DESIRED TRAJECTORY IN JOINTSPACE

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Acta Mechanica Solida Sinica 2001年第2期14卷 183-188页

作者： Chen Li (department of Mechanical Engineering, Fuzhou university, Fuzhou 3.0002. China) Liu Yanzhu (department of Engineering Mechanics,{3. jiaotong university, shanghai 20003., China) ***

The control of a free-floating space manipulator system isdiscussed. With the augmentation approach, the nonlinearparameterization problem of the dynamic equations of the spacemanipulator system is overcome. Based on the results, the robustcontrol scheme for free-floating space manipulator with uncer- tainpayload parameters to track the desired trajectory in jointspace isproposed, and the global convergence of the tracking is verified byusing the Lyapunov method.

关键词： free-floating space maniulator augmentation approach robust control

Time of impact of fragment P2.of comet SL 9 on Jupiter

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Chinese Science Bulletin 1997年第5期42卷 396-398页

作者： ZHOU Hongnan,QIAN Bochen, HUANG Keliang and LI Qibin1. department of Astronomy, Nanjing university, Nanjing 2.0093. China 2. {2. Observatory, Chinese Academy of Sciences,{3., China 3. physics department, Nanjing Normal university, Nanjing 2.0097, China 4. Beijing Astronomical Observatory, Chinese Academy of Sciences, Beijing 100080, China department of Astronomy Nanjing University Nanjing China shanghai Observatory Chinese Academy of Sciences Shanghai China physics department Nanjing Normal University Nanjing China Beijing Astronomical Observatory Chinese Academy of Sciences Behijing China

FROM 1994-07-16 to 1994-07-2., 2. fragments of comet SL 9 impacted against Jupiter in succession. During the impact period the impact of fragments D, E, K, N, P2.and S was observed in China. We used a 1.56-m telescope with the CCD camera of {3. Observatory to monitor Jupiter and its Galilean Satellites, obtaining 1000 high-quality images at B, V, I wave bands. Our data on optical wave bands are rather complete and valuable in the world. Specially, we got some images of Jupiter, Io and Europa in the impact time of fragment P2.impacting against Jupiter. This will help us understand the precise time, position, depth and energy of the P2.s collision. In this note, we report the impact time of fragment P2.of comet SL 9 and Jupiter. Since the impact of comet SL 9 was expected to take place on the side of Jupiter

关键词： comet comet Shoemaker-Levy 9 impacting against Jupiter impact time.

Entanglement Involved in Pair Coherent State Studied via Wigner Function Formalism

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Communications in Theoretical physics 2009年第12期52卷 1071-1075页

作者： HU Li-Yun~(1,2.and FAN Hong-Yi~2. College of physics and Communication Electronics, Jiangxi Normal {3., Nanchang 3.002., China2.{2. of physics, shanghai Jiao Tong {3., shanghai 20003., China College of physics and Communication Electronics Jiangxi Normal University Nanchang 330022 China department of physics Shanghai Jiao Tong University Shanghai 200030 China

We calculate Wigner function,tomogram of the pair coherent state by using its Schmidt decompositionin the coherent state *** turns out that the Wigner function can be seen as the quantum entanglement(QE)between two two-variable Hermite polynomials(TVHP)and the tomogram is further simplified as QE of twosingle-variable Hermite *** Husimi function of pair coherent state is also calculated.

关键词： pair coherent state Wigner function Tomogram Husimi function

The complex variable reproducing kernel particle method for elasto-plasticity problems

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Science China(physics,Mechanics & Astronomy) 2010年第5期53卷 954-965页

作者： CHEN Li1 & CHENG YuMin2.1 department of Engineering Mechanics,Chang’an university,Xi’an 710064,China 2.{2. Institute of Applied Mathematics and Mechanics,{2. university,{2. 2.0072.China 1. department of Engineering Mechanics Chang’an University Xi’an 710064 China2. Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China

On the basis of reproducing kernel particle method(RKPM),using complex variable theory,the complex variable reproducing kernel particle method(CVRKPM) is discussed in this *** advantage of the CVRKPM is that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is *** the CVRKPM is applied to solve two-dimensional elasto-plasticity *** Galerkin weak form is employed to obtain the discretized system equation,the penalty method is used to apply the essential boundary *** then,the CVRKPM for two-dimensional elasto-plasticity problems is formed,the corresponding formulae are obtained,and the Newton-Raphson method is used in the numerical *** numerical examples are given to show that this method in this paper is effective for elasto-plasticity analysis.

关键词： meshless method reproducing kernel particle method(RKPM) complex variable reproducing kernel particle method(CVRKPM) correction function elasto-plasticity

Deriving new operator identities by alternately using normally,antinormally,and Weyl ordered integration technique

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Science China(physics,Mechanics & Astronomy) 2010年第9期53卷 1626-1630页

作者： FAN HongYi1,YUAN HongChun1 & JIANG NianQuan2.1department of physics,{2. Jiao Tong {3.,{2. 20003.,China 2.ollege of physics and Electric Information,Wenzhou {3.,Wenzhou 3.0}03.,China 1. department of physics Shanghai Jiao Tong University Shanghai 200030 China2. College of Physics and Electric Information Wenzhou University Wenzhou 325035 China

Dirac's ket-bra formalism is the language of quantum *** have reviewed how to apply Newton-Leibniz integration rules to Dirac's ket-bra projectors in previous *** this work,by alternately using the technique of integration within normal,antinormal,and Weyl ordering of operators we not only derive some new operator ordering identities,but also deduce some new integration formulas regarding Laguerre and Hermite *** may open a new route of directly deriving some complicated mathematical integration formulas by virtue of the quantum mechanical operator ordering technique,without really performing the integrations in the ordinary way.

关键词： operator ordering identities Laguerre and Hermite polynomials the IWOP technique

Simulation of nuclei morphologies for binary alloy

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Science China Mathematics 2010年第11期53卷 2927-2936页

作者： LI DaMing1, & ZHANG PingWen2.1department of Mathematics, shanghai jiaotong university, {2. 2.02.0, China 2.ey Lab of Mathematics and Applied Mathematics, Center for Applied {3. and Technology and School of Mathematical Sciences, Peking university, Beijing 100871, China 1. department of Mathematics Shanghai Jiaotong University Shanghai 200240 China2. Key Lab of Mathematics and Applied Mathematics Center for Applied Physics and Technology and School of Mathematical Sciences Peking University Beijing 100871 China

We study the critical nuclei morphologies of a binary alloy by the string method. The dynamic equation of the string, connecting the metastable phase (liquid) and stable phase (solid), is governed by Helmholtz free energy for the binary alloy system at a given temperature. The stationary string through the critical nucleus (saddle point) is obtained if the relaxation time of the string is su?ciently large. The critical nucleus radius and energy barrier to nucleation of a pure alloy with isotropic interface energy in two and three dimensions are calculated, which are consistent with the classical nucleation theory. The critical nuclei morphologies are sensitive to the anisotropy strength of interface energy and interface thickness of alloy in two and three dimensions. The critical nucleus and energy barrier to nucleation become smaller if the anisotropy strength of the interface energy is increased, which means that it is much easier to form a stable nucleus if the anisotropy of the interface energy is considered.

关键词： nucleation crystal morphology string method

NONLINEAR MODELING AND CONTROLLING OF ARTIFICIAL MUSCLE SYSTEM USING NEURAL NETWORKS

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Chinese Journal of Mechanical Engineering 2004年第2期17卷 306-310页

作者： Tian Sheping Ding Guoqing Yan Detian Lin Liangming department of Information Measurement and Instrumentation,shanghai {2. {3.,shanghai 20003., China department of Information Measurement and Instrumentation Shanghai Jiaotong University 上海 200030

The pneumatic artificial muscles are widely used in the fields of medicalrobots, etc. Neural networks are applied to modeling and controlling of artificial muscle system. Asingle-joint artificial muscle test system is designed. The recursive prediction error (RPE)algorithm which yields faster convergence than back propagation (BP) algorithm is applied to trainthe neural networks. The realization of RPE algorithm is given. The difference of modeling ofartificial muscles using neural networks with different input nodes and different hidden layer nodesis discussed. On this basis the nonlinear control scheme using neural networks for artificialmuscle system has been introduced. The experimental results show that the nonlinear control schemeyields faster response and higher control accuracy than the traditional linear control scheme.

关键词： Artificial muscle Neural networks Recursive prediction error algorithm Nonlinear modeling and controlling