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Dynamical understanding of loop soliton solution for several nonlinear wave equations

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science china {2. 2007年第6期50卷 773-785页

作者： Ji-bin li department of {2., zhejiang normal University, jinhua 32.004, china kunming University of science and technology, kunming 650093, china department of mathematics Zhejiang Normal University Jinhua 321004 China kunming University of science technology Kunming 650093 China

It has been found that some nonlinear wave equations have one-loop soliton solutions. What is the dynamical behavior of the so-called one-loop soliton solution? To answer this question, the travelling wave solutions for four nonlinear wave equations are discussed. Exact explicit parametric representations of some special travelling wave solutions are given. The results of this paper show that a loop solution consists of three different breaking travelling wave solutions. It is not one real loop soliton travelling wave solution.

关键词： planar dynamical system homoclinic orbit solitary wave solution one-loop soliton solution periodic wave solution bifurcation nonlinear wave equation 34C37 34C2. 74J30 58Z05

Exact traveling wave solutions and dynamical behavior for the (n+1)-dimensional multiple sine-Gordon equation

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science china {2. 2007年第2期50卷 153-164页

Using the methods of dynamical systems for the (n + 1)-dimensional multiple sine-Gordon equation, the existences of uncountably infinite many periodic wave solutions and breaking bounded wave solutions are obtained. For the double sine-Gordon equation, the exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.

关键词： nonlinear wave bifurcation exact explicit traveling wave solution double sine-Gordon equation multiple sine-Gordon equation 35B10 35L70 35Q51

Fuzzy controllers based on some fuzzy implication operators and their response functions

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Progress in Natural science:Materials International 2004年第1期14卷 16-21页

作者： li Hongxing 1*, YOU Fei 1 and PENG Jiayin 2.1. {2. of mathematics, Beijing normal University, Beijing 100875, china 2. {2. of mathematics, Neijiang Teacher's College, Neijiang 641112. china) Beijing normal Univ Dept Math Beijing 100875 Peoples R China

The fuzzy controllers constructed by 2. fuzzy implication operators based on CRI algorithm and their response functions are discussed. The conclusions show that the fuzzy controllers constructed by 9 fuzzy implication operators are universal approximators to continuous functions and can be used in practical fuzzy control systems. And these 9 fuzzy implication operators except for Einstein operator intersection are all the adjoint pairs of some fuzzy implication operators. Besides, there are 3 other fuzzy controllers formed by fuzzy implication operators being regarded approximately as fitted functions.

关键词： fuzzy implication operators CRI algorithm fuzzy controllers response functions universal approximators

Strong uniqueness of best approximations in spaces of bounded linear operators

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science china {2. 2004年第3期47卷 339-351页

作者： li Chong HE Jinsu department of {2., zhejiang University Hangzhou 31002., china department of {2., zhejiang normal University jinhua 32.004, china 1. department of mathematics Zhejiang University 310027 Hangzhou China 2. department of mathematics Zhejiang Normal University 321004 Jinhua China

The present paper is concerned with problems of the strong uniqueness of the best approximation and the characterization of a uniqueness element in operator *** results on the strong uniqueness of the best approximation operatorfrom RS-sets are proved and the uniqueness element of a sun in the compactoperator space from c0 to c0 is characterized by the strict Kolmogorov's *** recent results due to Lewicki and others are extended and improved.

关键词： best approximation operator, RS-set, sun, strong uniqueness, uniqueness element.

Nonlinear ergodic theorem for semitopological semigroups of non-lipschitzian mappings in Banach spaces

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Chinese science Bulletin 1997年第1期42卷 8-11页

作者： li Gang and MA Jipu1. department of {2., Yangzhou normal College, Yangzhou 2.5002. china 2. department of {2., Nanjing University, Nanjing 2.0093, china department of mathematics Yangzhou Normal College Yangzhou China department of mathematics Nanjing University Nanjing China

LET G be a semitopological semigroup, i. e. G is a semigroup with a Hausdorff topology such that for each s∈G the mapping s|→s·t and s|→t·s from G to G are continuous. G is called right reversible if any two closed left ideals of G have non-void intersection. In this case, (G,≤) is a directed system when the binary relation '≤' on G is defined by a≤b if and only if Let E be the uniformly convex Banach space

关键词： nonlinear semigroup ergodic theorem non-lipschitzian mapping.

On the Cayley-Bacharach property and the construction of vector bundles

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science china {2. 2011年第9期54卷 1891-1898页

作者： SUN Hao 1,2.1 department of mathematics and Statistics,Huazhong normal University,Wuhan 430079,{2. 2.department of mathematics,East china normal University,Shanghai 2.02.1,{2. 1. department of mathematics and Statistics Huazhong Normal University Wuhan 430079 China2. Department of Mathematics East China Normal University Shanghai 200241 China

We study the Cayley-Bacharach property on complex projective smooth varieties of dimension n≥2.for zero dimensional subscheme defined by the zero set of the wedge of r-n + 1 global sections of a rank r≥n vector bund... 详细信息

关键词： Cayley-Bacharach property vector bundle reflexive sheaf k-very ample

Complex variable method for plane elasticity of icosahedral quasicrystals and elliptic notch problem

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science china(Physics,Mechanics & Astronomy) 2008年第7期51卷 773-780页

作者： li lianHe1,2.& FAN TianYou1 1 {2. of Physics, Beijing Institute of technology, Beijing 100081, china 2.College of mathematics science, Inner Mongolia normal University, Hohhot 01002., china department of Physics Beijing Institute of Technology Beijing 100081 China College of mathematics science Inner Mongolia Normal University Hohhot 010022 China

The complex variable method for the plane elasticity theory of icosahedral quasicrystals is developed. Based on the general solution obtained previously, complex representations of stress and displacement components of phonon and phason fields in the quasicrystals are given. With the help of conformal transformation, an analytic solution for the elliptic notch problem of the material is presented. The solution of the Griffith crack problem can be observed as a special case of the results. The stress intensity factor and energy release rate of the crack are also obtained.

关键词： icosahedral quasicrystals plane elasticity elliptic notch complex variable method

The proof of FFD(L)≤11/9OPT(L) +7/9

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Chinese science Bulletin 1997年第15期42卷 1262-1265页

作者： li Rongheng, YUE Minyi1. department of {2., Hunan normal University, Changsha 410081, china 2. Institute of Applied {2., Chinese Academy of sciences, Beijing 100080, china department of mathematics Hunan Normal University Changsha 410081 China Institute of Applied mathematics Chinese Academy of Sciences Beijing 100080 China

THE one-dimensional bin-packing problem is defined as follows: for a given list L={p1, p2.…, Pn}, where 0i≤1 denotes the item and its size as well, we are to pack all the items in-to bins, each of which has a capaci... 详细信息

THE one-dimensional bin-packing problem is defined as follows: for a given list L={p1, p2./sub>,…, Pn}, where 0i≤1 denotes the item and its size as well, we are to pack all the items in-to bins, each of which has a capacity 1, and the goal is to minimize the number of bins *** first-fit-decreasing （FFD） algorithm is a famous approximate algorithm for the bin-pack-ing problem. The FFD algorithm first sorts all the list into non-increasing order and then pro-cesses the pieces in that order by placing each item into the first bin into which it fits.

关键词： bin-packing minimal counter-example weigtht-function FFD-algorithm.

Image space analysis for variational inequalities with cone constraints and applications to traffic equilibria

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science china {2. 2012年第4期55卷 851-868页

作者： li Jun 1,& HUANG NanJing 2.1 College of {2. and Information,china West normal University,Nanchong 637009,china 2.department of {2.,Sichuan University,Chengdu 610064,china 1. College of mathematics and Information China West Normal University Nanchong 637009 China2. Department of Mathematics Sichuan University Chengdu 610064 China

In this paper,the image space analysis (for short,ISA) is employed to investigate variational in- equalities (for short,VI) with cone *** separation for VI with cone constraints is characterized by using the normal cone to a regularization of the image,and saddle points of the generalized Lagrangian func- ***-type necessary and sufficient optimality conditions for VI with cone constraints are presented by using a separation *** functions and weak sharpness for VI with cone constraints are also investi- ***,the obtained results are applied to standard and time-dependent traffic equilibria introduced by Daniele,Maugeri and Oettli.

关键词： variational inequality image space analysis linear separation necessary and sufficient optimalitycondition traffic equilibrium