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Rational Form Solitary Wave Solutions and Doubly Periodic Wave Solutions to (1+1)-Dimensional Dispersive Long Wave Equation

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Communications in Theoretical Physics 2005年第6期43卷 975-982页

作者： WANG Qi CHEN Yong ZHANG Hong-Qing department of Applied mathematics, Dalian university of Technology, Dalian 116024. china department of mathematics, Ningbo university, Ningbo 315211, china department of Physics, shanghai jiao tong university, shanghai 200030, china department of Applied mathematics Dalian University of Technology department of mathematics Ningbo University department of Physics Shanghai Jiao Tong University

In this work we devise an algebraic method to uniformly construct rational form solitary wave solutionsand Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. Withthe aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wavethe (1+1)-dmensional dispesive long wavedelliptic donbly periodc wave solutions as special cases.

关键词： elliptic equation rational expansion method rational form solitary wave solutions rational form Jacobi and Weierstrass doubly periodic wave solutions symbolic computation (1+1)-dimensional dispersive long wave equation

Computational model for perception of objects and motions

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Science china(Life Sciences) 2008年第6期51卷 526-536页

作者： YANG WenLu1,2, ZHANG LiQing1 & MA LiBo1 1 department of Computer Science and Engineering, shanghai jiao tong university, shanghai 20024., china 2 department of Electronic Engineering, shanghai Maritime university, shanghai 200135, china 1. department of Computer Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China 2. department of Electronic Engineering Shanghai Maritime University Shanghai 200135 China

Perception of objects and motions in the visual scene is one of the basic problems in the visual system. There exist 'What' and 'Where' pathways in the superior visual cortex, starting from the simple cells in the primary visual cortex. The former is able to perceive objects such as forms, color, and texture, and the latter perceives 'where', for example, velocity and direction of spatial movement of objects. This paper explores brain-like computational architectures of visual information processing. We propose a visual perceptual model and computational mechanism for training the perceptual model. The compu- tational model is a three-layer network. The first layer is the input layer which is used to receive the stimuli from natural environments. The second layer is designed for representing the internal neural information. The connections between the first layer and the second layer, called the receptive fields of neurons, are self-adaptively learned based on principle of sparse neural representation. To this end, we introduce Kullback-Leibler divergence as the measure of independence between neural responses and derive the learning algorithm based on minimizing the cost function. The proposed algorithm is applied to train the basis functions, namely receptive fields, which are localized, oriented, and bandpassed. The resultant receptive fields of neurons in the second layer have the characteristics resembling that of simple cells in the primary visual cortex. Based on these basis functions, we further construct the third layer for perception of what and where in the superior visual cortex. The proposed model is able to perceive objects and their motions with a high accuracy and strong robustness against additive noise. Computer simulation results in the final section show the feasibility of the proposed perceptual model and high efficiency of the learning algorithm.

关键词： visual perception visual cortex computational model receptive fields simple cells complex cells

Conditional Entropy of Partitions on Quantum Logic

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Communications in Theoretical Physics 2007年第7期48卷 11-13页

作者： ZHAO Yue-Xu Institute of Applied mathematics and Engineering Computation,Hangzhou Dianzi university,Hangzhou 310018,chinaMA Zhi-Hao department of mathematics,shanghai jiao tong university,shanghai 20024.,china Institute of Applied mathematics and Engineering Computation Hangzhou Dianzi University Hangzhou 310018 China

A construction of conditional entropy of partitions on quantum logic is given,and the properties ofconditional entropy are investigated.

关键词： state density operator projector conditional entropy quantum logic lattice

Twisted exponential sums of polynomials in one variable

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Science china mathematics 2010年第9期53卷 2395-2404页

作者： LIU ChunLei1,& LIU WenXin2,3 1department of mathematics,shanghai jiao tong university,shanghai 20024.,china 2department of Fundamental Subject,Tianjin Institute of Urban Construction,Tianjin 300384,china 3School of Mathematical Sciences,Beijing Normal university,Beijing 100875,china 1. department of mathematics Shanghai Jiao Tong University Shanghai 200240 China2. Department of Fundamental Subject Tianjin Institute of Urban Construction Tianjin 300384 China3. School of Mathematical Sciences Beijing Normal University Beijing 100875 China

The twisted T-adic exponential sums associated to a polynomial in one variable are *** explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the C-function of the twisted T-adic exponential *** bound gives lower bounds for the Newton polygon of the L-function of twisted p-power order exponential sums.

关键词： exponential sum L-function Newton polygon

Hamiltonian type Lie bialgebras

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Science china mathematics 2007年第9期50卷 1267-1279页

作者： Bin XIN~(1+) Guang-ai SONG~2 Yu-cai SU~3 1 department of mathematics,shanghai jiao tong university,shanghai 20024.,china 2 College of mathematics and Information Science,Shandong Institute of Business and Technology,Yantai 264005,china 3 department of mathematics,university of Science and Technology of china,Hefei 230026,china department of mathematics Shanghai Jiao Tong University Shanghai 200240 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

We first prove that,for any generalized Hamiltonian type Lie algebra H,the first co- homology group H^1(H,H(?)H) is *** then show that all Lie bialgebra structures on H are triangular.

关键词： Lie bialgebra Yang-Baxter equation Hamiltonian Lie algebra 17B62 17B05 17B37 17B66

Lie Point Symmetries of Differential-Difference Equations

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Communications in Theoretical Physics 2004年第5期41卷 645-648页

作者： DING Wei~1 TANG Xiao-Yan~(2,3) 1 department of Applied mathematics,shanghai jiao tong university,shanghai 200030,china2 department of Physics,shanghai jiao tong university,shanghai 200030,china3 State Key Laboratory of Scientific and Engineering Computing,Institute of Computational mathematics and Scientific Engineering Computing,Academy of mathematics and System Sciences,the Chinese Academy of Sciences,P.O.Box 2719,Beijing 100080,china State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and System Sciences the Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 China

In this paper,the classical Lie group approach is extended to find some Lie point symmetries of differential-difference *** reveals that the obtained Lie point symmetries can constitute a Kac-Moody-Virasoro algebra.

关键词： Lie point symmetry differential-difference equation Kac Moody-Virasoro algebra

Computer Simulation of the Structure and Propertiesof Nanocrystals

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Journal of Materials Science & Technology 1994年第6期10卷 418-424页

作者： Da CHEN(Dept. of Materials Science, shanghai jiao tong university, shanghai, 200030, china) shanghai jiao tong Univ Shanghai China

This paper provides a computer modeling method for the study of nanocrystals. Structural features,such as the boundary component proportion, the reduced density proportion, the excess lattice parameter, and the radial distribution function, have been atomistically simulated. The energy and elastic properties also have been investigated. Simulation results indicate that the structure of grain boundaries in nanocrystals is different from those of the amorphous and the gas, or rather, it is a special structure with some degree of short-range order. Moreover, the structure of crystallites is not entirely the same as that in the perfect crystal lattice. The present simulation method may become one of the foundations of the theoretical study of nanocrystals.

关键词： Simulation Computer Simulation of the Structure and Propertiesof Nanocrystals BDV

EFFECT OF REINFORCEMENT VOLUME FRACTION ON PRECIPITATION IN MATRIX OF SiC_p/AI COMPOSITE

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Acta Metallurgica Sinica(English Letters) 1993年第8期6卷 161-167页

作者： LIN Junshan LI Pengxing WU Renjie shanghai jiao tong university,shanghai,china postdoctoral,Institute of Composite Materials,shanghai jiaotong university,shanghai 200030,china shanghai jiaotong Univ Shanghai China

The differential scanning calorimetric(DSC) and transmission electron microanalysis (TEM) techniques were used to study the kinetic process of precipitation in matrix of cast SiC_p/2024 *** results showed that precipitation reactions of GP zone and intermediate phase S'(Al_2CuMg)in the composites were accelerated compared with SiC-free material,the peak temperatures of both reactions were *** reaction enthalpies of both the GP zone and intermediate phase S' formation in the matrix were substantially decreased after the addition of *** analysis found that the alloying element Mg segregated at the SiC/Al interfaces,and was depleted in the matrix near the *** precipitation-free zones(PFZ) and precipitation-sparse zones(PSZ) formed near the interfaces,as a results,the volume fraction of precipitates in matrix was reduced.

关键词： SiC_p/2024 composite differential scanning calorimetry precipitation in matrix

Maximally parallel attribute on P Systems: Properties and applications

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Progress in Natural Science:Materials International 2008年第5期18卷 629-632页

作者： Chunyi Huang, Xiaoju Dong BASICS, shanghai jiao tong university, shanghai 20024., china BASICS Shanghai Jiao Tong University Shanghai 200240 China

In this paper, we investigate the maximally parallel attribute of P Systems. Some properties of P Systems are introduced, which are the lter property and the enumeration property. The two properties are applied to sol... 详细信息

关键词： Membrane computing P Systems Maximally parallel