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A New Multisoliton Solution to (2.1)-Dimensional KdV Equation

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Communications in Theoretical Physics 2004年第5期41卷 669-670页

作者： PENG Yan-Ze~(1,2. 1 department of mathematics,Huazhong university of Science and Technology,Wuhan 430074,China2.department of mathematics and Physics,Henan university of Science and Technology,Luoyang 471003,China department of mathematics Huazhong University of Science and Technology Wuhan 430074 China department of mathematics and Physics Henan University of Science and Technology Luoyang 471003 China

A new multisoliton solution to the(2.1)-dimensional KdV equation is obtained by means of the truncatedPainleve expansion method and a direct ansatz *** new exact solution is periodic in the propagating directionx and exponentially decaying in y and thus it is called periodic solitons.A typical spatial structure of it is illustrated bythe figures.

关键词： (2.1)-dimensional KdV equation periodic solitons truncated Painleve expansion method

Y_CΩ_(2.)are easy terms

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Chinese Science Bulletin 1998年第20期43卷 1707-1709页

作者： ZHAO Xishun 1 and WANG Ju 2.1. department of mathematics, Nanjing university, Nanjing 2.0093, China 2. Institute of Software, Chinese Academy of Sciences, Beijing 100080, China department of mathematics Nanjing University Nanjing China Institute of Software Chinese Academy of Sciences Beijing China

For any natural number n≥1, Y CΩ 2. is an easy term; that is, for any λ term M, λβ+Y\-CΩ 2. =M is consistent, where Y C is Curry fixed point combinator, Ω 2. ≡ω 2. ω 2. and ω 2. ≡λ***...x (there are 2. occurrences of x after λx ). This result is a partial solution to Jacopini’s conjecture: Y CΩ n is an easy term for any natural number n≥2.

关键词： λβ-calculus Kuper’s theorem easy term.

Moment bounds for IID sequences under sublinear expectations

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Science China mathematics 2011年第10期54卷 2155-2160页

作者： HU Feng1,2.1department of mathematics,Qufu Normal university,Qufu 2.3165,China 2.chool of {2.,Shandong university,Jinan 2.0100,China department of mathematics Qufu Normal University Qufu China School of mathematics Shandong University Jinan China

With the notion of independent identically distributed(IID) random variables under sublinear expectations introduced by Peng,we investigate moment bounds for IID sequences under sublinear expectations. We obtain a moment inequality for a sequence of IID random variables under sublinear expectations. As an application of this inequality,we get the following result:For any continuous functionsatisfying the growth condition |(x) | C(1 + |x|p) for some C > 0,p 1 depending on ,the central limit theorem under sublinear expectations obtained by Peng still holds.

关键词： moment bound sublinear expectation IID random variables G-normal distribution central limit theorem

L~∞ CONVERGENCE OF TRUNC ELEMENT FOR THE BIHARMONIC EQUATION

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Journal of Computational mathematics 1997年第1期15卷 14-22页

作者： M. Wang(department of mathematics, Beijing university, Beijing, China) 北京大学数学系北京

The paper considers the L∞ convergence for TRUNC finite elements solving the boundary value problems of the biharmonic equation. The nearly optimal L∞ estimates for the error of first order derivatives are *** TRUNC plate element is proposed and developed by Argyris et al.. The numerical experiences show that the element has very good .***,[1l2.. The mathematicalproof of convergence of the TRUNC element is given by Shi Zong-ci in paper [3]. Thispaper will consider the L~∞ convergence for the TRUNC plate element.

关键词：双谐波方程边值问题收敛性有限元法

Two-dimensional simulation of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect

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Progress in Natural Science:Materials International 2007年第12期17卷 1389-1396页

作者： Hu Jun1 and Yin Xieyuan2.1. Institute of Applied Physics and Computational mathematics, Beijing 100088, China 2. department of Modern Mechanics, {2. of Science and Technology of China, Hefei 2.002., China) Institute of Applied Physics and Computational mathematics Beijing 100088 China department of Modern Mechanics University of Science and Technology of China Hefei 230027 China

Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect are directly simulated by a mixed finite element method. A temperature perturbation is used as an initial disturbed source for the basic parallel flows. The whole spatio-temporal evolution of the binary fluid flows is exhibited: initially only the disturbed mode with the wavenumber k=π is amplified while others are damped, and continuously the amplified mode grows further and the nonlinear effect becomes important; after a nonlinear evolution transition the flow system evolves finally into a periodic right traveling wave.

关键词： Poiseuille-Rayleigh-Bénard flow Soret effect through-flow.

A blow-up criterion for classical solutions to the compressible Navier-Stokes equations

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Science China mathematics 2010年第3期53卷 671-686页

作者： HUANG XiangDi 1 & XIN ZhouPing 2. 1 department of mathematics, university of Science and Technology of China, Hefei 2.002., China 2.department of mathematics, The Chinese university of Hong Kong, Hong Kong, China department of mathematics University of Science and Technology of China Hefei China department of mathematics The Chinese University of Hong Kong Hong Kong China

In this paper, we obtain a blow-up criterion for classical solutions to the 3-D compressible Navier-Stokes equations just in terms of the gradient of the velocity, analogous to the Beal-Kato-Majda criterion for the id... 详细信息

关键词： blow-up classical solutions compressible Navier-Stokes

On conformal measures for infinitely renormalizable quadratic polynomials

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Science China mathematics 2005年第10期48卷 1411-1420页

作者： HUANG Zhiyong~1 JIANG Yunping~(2.3) & WANG Yuefei~3 1. School of Information,Renmin university of China,Beijing 100872.China 2. department of mathematics,Queens College,City university of New York,NY 11367,USA department of mathematics,Graduate School,City university of New York,New York,NY 10016,USA 3. Academy of mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,China School of Information Renmin University of China Beijing China department of mathematics Queens College City University of New York NY USA department of mathematics Graduate School City University of New York New York USA Academy of mathematics and Systems Science Chinese Academy of Sciences Beijing China

We study a conformal measure for an infinitely renormalizable quadratic polynomial. We prove that the conformal measure is ergodic if the polynomial is unbranched and has complex bounds. The main technique we use in t... 详细信息

关键词： Julia set, conformal measure, three-dimensional puzzle, infinitely renormalizable quadratic polynomial.

JACOBI SPECTRAL APPROXIMATIONS TO DIFFERENTIALEQUATIONS ON THE HALF LINE

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Journal of Computational mathematics 2000年第1期18卷 95-112页

作者： Ben-yu Guo(department of mathematics, Shanghai Normal university, Shanghai 2.02.4, China)(COM2.AC, Pohang university of Science and Technology, Pohang, Korea) 上海师范大学上海 200234

Presents a study which investigated some Jacobi approximations which are used for numerical solutions of differential equations on the half line. Application of the approximations to problems on unbounded domains; Alg... 详细信息

关键词： Jacobi spectral approximations differential equations on the half line stability and convergence

Persistence of bounded solutions to degenerate Sobolev-Galpern equations

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Science China mathematics 2010年第11期53卷 2831-2846页

作者： ZHU ChangRong1 & ZHANG WeiNian2. 1School of mathematics, Chongqing university, Chongqing 400044, China 2.angtze Center of mathematics and department of mathematics, Sichuan university, Chengdu 610064, China School of mathematics Chongqing University Chongqing China Yangtze Center of mathematics and department of mathematics Sichuan University Chengdu China

In this paper the persistence of bounded solutions to degenerate evolution equations of Sobolev-Galpern type is discussed. In order to define the evolution operator well, we study the existence and uniqueness of solutions to its linear form. On this basis we discuss exponential dichotomies of the evolution operator and give the Fredholm alternative result for bounded solutions of nonhomogeneous linear degenerate equations. This result enables us to give a condition for the persistence of bounded solutions of a general degenerate nonlinear autonomous equation under a nonautonomous perturbation.

关键词： degenerate evolution equation Sobolev-Galpern type boundedness Fredholm alternative exponential dichotomy