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Bifurcation method for solving multiple positive solutions to boundary value problem of p-Henon equation on the unit disk

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Applied Mathematics and Mechanics(English Edition) 2010年第4期31卷 511-520页

作者：李昭祥杨忠华 Department of Mathematics Scientific Computing Key Laboratory of Shanghai UniversityShanghai Normal University

In this paper, an algorithm is proposed to solve the 0（2） symmetric positive solutions to the boundary value problem of the p-Henon equation. Taking 1 in the p- Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation point on the branch of the O（2） symmetric positive solutions is found via the extended systems. The other symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.

关键词： p-Henon equation symmetry-breaking bifurcation extended system branch switching multiple solutions

Large-scale video compression： recent advances and challenges

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Frontiers of Computer Science 2018年第5期12卷 825-839页

作者： Tao TIAN Hanli WANG Department of Computer Science and Technology Tongji University Shanghai 201804 China key laboratory of Embedded system and Service computing Ministry of Education Tongji University Shanghai 200092 China shanghai Engineering Research Center of Industrial Vision Perception & Intelligent computing Shanghai 200092 China

The evolution of social network and multimedia technologies encourage more and more people to generate and upload visual information, which leads to the generation of large-scale video data. Therefore, preeminent compression technologies are highly desired to facilitate the storage and transmission of these tremendous video data for a wide variety of applications. In this paper, a systematic review of the recent advances for large-scale video compression （LSVC） is presented. Specifically, fast video coding algorithms and effective models to improve video compression efficiency are introduced in detail, since coding complexity and compression efficiency are two important factors to evaluate video coding approaches. Finally, the challenges and fu- ture research trends for LSVC are discussed.

关键词： large-scale video compression fast video coding compression efficiency

Nonlocal Symmetries and Explicit Solutions of the Boussinesq Equation

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Chinese Annals of Mathematics,Series B 2014年第6期35卷 841-856页

作者： Xiangpeng XIN Junchao CHEN Yong CHEN shanghai key laboratory of Trustworthy computing East China Normal University

The nonlocal symmetry of the Boussinesq equation is obtained from the known Lax pair. The explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetry. Some other types of solutions, such as rational solutions and error function solutions, are given by using the fourth Painlev~ equation with special values of the parameters. For some interesting solutions, the figures are given out to show their properties.

关键词： Nonlocal symmetry Lax pair Prolonged system Explicit solution

ONEOptimal:A Maple Package for Generating One-Dimensional Optimal system of Finite Dimensional Lie Algebra

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Communications in Theoretical Physics 2014年第2期61卷 160-170页

作者：苗倩胡晓瑞陈勇 shanghai key laboratory of Trustworthy computing East China Normal University

We present a Maple computer algebra package, ONEOptimal, which can calculate one-dimensional optimal system of finite dimensional Lie algebra for nonlinear equations automatically based on Olver's theory. The core of this theory is viewing the Killing form of the Lie algebra as an invariant for the adjoint representation. Some examples are given to demonstrate the validity and efficiency of the program.

关键词： group-invariant solutions optimal system group classification Lie algebra symbolic computation

An Integrable Discrete Generalized Nonlinear Schr¨odinger Equation and Its Reductions

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Communications in Theoretical Physics 2014年第11期61卷 641-648页

作者：李红敏李玉奇陈勇 shanghai key laboratory of Trustworthy computing East China Normal University

An integrable discrete system obtained by the algebraization of the difference operator is studied. The system is named discrete generalized nonlinear Schr¨odinger(GNLS) equation, which can be reduced to classical discrete nonlinear Schr¨odinger(NLS) equation. Furthermore, all of the linear reductions for the discrete GNLS equation are given through the theory of circulant matrices and the discrete NLS equation is obtained by one of the reductions. At the same time, the recursion operator and symmetries of continuous GNLS equation are successfully recovered by its corresponding discrete ones.

关键词： discrete equation recursion operator symmetry conservation quantities

One-Dimensional Optimal system and Similarity Reductions of Wu–Zhang Equation

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Communications in Theoretical Physics 2016年第7期65卷 1-11页

作者：熊娜李玉奇陈俊超陈勇 shanghai key laboratory of Trustworthy computing East China Normal University

The one-dimensional optimal system for the Lie symmetry group of the(2+1)-dimensional Wu–Zhan equation is constructed by the general and systematic approach. Based on the optimal system, the complete and inequivalent symmetry reduction systems are presented in the form of table. It is noteworthy that a new Painlev integrable equation with constant coefficient is in the table besides the classic Boussinesq equation and the steady cas of the Wu–Zhang equation.

关键词： Wu–Zhang equation optimal system similarity reduction Painlev integrability

Symmetry Analysis and Conservation Laws to the(2+1)-Dimensional Coupled Nonlinear Extension of the Reaction-Diffusion Equation

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Communications in Theoretical Physics 2014年第8期61卷 173-182页

作者：陈俊超辛祥鹏陈勇 shanghai key laboratory of Trustworthy computing East China Normal University

In this paper, a detailed Lie symmetry analysis of the(2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation is presented. The general finite transformation group is derived via a simple direct method,which is equivalent to Lie point symmetry group actually. Similarity reduction and some exact solutions of the original equation are obtained based on the optimal system of one-dimensional subalgebras. In addition, conservation laws are constructed by employing the new conservation theorem.

关键词： (2+1)-dimensional coupled nonlinear reaction-diffusion equation Lie symmetry invariant solutions optimal system conservation laws

Parallel computation of determinants of matrices with multivariate polynomial entries

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Science China(Information Sciences) 2013年第11期56卷 158-173页

作者： CHEN LiangYu ZENG ZhenBing shanghai key laboratory of Trustworthy computing East China Normal University

In this paper we present an extension to the work of Bjrck et *** computing the determinants of matrices with univariate or bivariate polynomials as entries to multivariate *** algorithm supports parallel computation and has been implemented on a multi-core cluster computer *** show how to use our approach to calculate two unsolved problems,which arise from computational geometry optimization and electric power engineering,and analyze the time complexity as well as bits complexity.

关键词： determinant interpolation parallel algorithm

Dual Hierarchies of a Multi-Component Camassa–Holm system

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Communications in Theoretical Physics 2015年第10期64卷 372-378页

作者：李红敏李玉奇陈勇 shanghai key laboratory of Trustworthy computing East China Normal University

In this paper, we derive the bi-Hamiltonian structure of a multi-component Camassa–Holm system, which associates with the multi-component AKNS hierarchy and multi-component KN hierarchy via the tri-Hamiltonian dualit... 详细信息

关键词： bi-Hamiltonian structure dual hierarchies Camasssa