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The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation

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Acta Mathematica Sinica,English Series 2013年第4期29卷 757-776页

作者： Shao Yong LAI Nan LI Jian ZHANG department of mathematics Southwestern University of Finance and Economics department of mathematics Sichuan Normal University

A fully nonlinear generalization of the Camassa-Holm equation is investigated. Using the 3 pseudoparabolic regularization technique, its local well-posedness in Sobolev space Hs（R） with s 〉 is established via a limiting procedure. Provided that the initial momentum （1 - 02）u0 satisfies the sign condition,the existence and uniqueness of global solutionsfor the equation are shown to be true in the space C.

关键词： Existence of global solutions Camassa-Holm type equation Pseudoparabolic regulariza-tion method

Uniform partition extensions,a generating functions perspective

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Science China mathematics 2015年第12期58卷 2655-2670页

作者： LI ShanHai MA Jun YEH YeongNan School of mathematics and Quantitative economics Shandong University of Finance and Economics department of mathematics Shanghai Jiao Tong University Institute of mathematics Academia Sinica

In this paper, a bivariate generating function CF(x, y) =f(x)-yf(xy)1-yis investigated, where f(x)= n 0fnxnis a generating function satisfying the functional equation f(x) = 1 + r j=1 m i=j-1aij xif(x)*** particular, we study lattice paths in which their end points are on the line y = 1. Rooted lattice paths are defined. It is proved that the function CF(x, y) is a generating function defined on some rooted lattice paths with end point on y = 1. So, by a simple and unified method, from the view of lattice paths, we obtain two combinatorial interpretations of this bivariate function and derive two uniform partitions on these rooted lattice paths.

关键词： Chung-Feller theorem Dyck path Motzkin path Schr¨oder path

Nonempty intersection theorems in topological spaces with applications

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Applied mathematics and Mechanics(English Edition) 2009年第7期30卷 905-914页

作者：方敏黄南京 department of Economic mathematics South Western University of Finance and Economics department of mathematics Sichuan University

In this paper, we establish some new nonempty intersection theorems for generalized L-KKM mappings and prove some new fixed point theorems for set-valued mappings under suitable conditions in topological spaces. As applications, an existence theorem for an equilibrium problem with lower and upper bounds and two existence theorems for a quasi-equilibrium problem with lower and upper bounds are obtained in topological spaces. Our results generalize some known results in the literature.

关键词： generalized L-KKM/napping L-diagonally quasi-subspace transfer compactly closed-valued fixed point quasi-equilibrium problem

Maximization of the sum of the trace ratio on the Stiefel manifold, II: Computation

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Science China mathematics 2015年第7期58卷 1549-1566页

作者： ZHANG LeiHong LI RenCang department of Applied mathematics Shanghai University of Finance and Economics department of mathematics University of Texas at Arlington

The necessary condition established in Part I of this paper for the global maximizers of the maximization problem max V tr（VTAV）/tr（VTBV）＋tr（VTCV）over the Stiefel manifold{V∈Rm×l ｜VTV=Il}（l〈m）,naturally leads to a self-consistent-field（SCF）iteration for computing a *** this part,we analyze the global and local convergence of the SCF iteration,and show that the necessary condition for the global maximizers is fulfilled at any convergent point of the sequences of approximations generated by the SCF *** is one of the advantages of the SCF iteration over optimization-based *** numerical tests are reported and show that the SCF iteration is very efficient by comparing with some manifold-based optimization methods.

关键词： trace ratio Rayleigh quotient Stiefel manifold nonlinear eigenvalue problem optimality condi-tion self-consistent-field iteration eigenspace

Algebraic Structure on Dirichlet Spaces

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Acta Mathematica Sinica,English Series 2006年第3期22卷 723-728页

作者： Xing FANG Ping HE Jian Gang YING department of mathematics Zhejiang University department of Applied mathematics Shanghai University of Finance and Economics Institute of mathematics Fudan University

In this short note, we shall give a few equivalent conditions for a closed form to be Markovian, and prove that the closure of a sub-algebra of bounded functions in a Dirichlet space must be Markovian. We also study t... 详细信息

关键词： Dirichlet form Markovian property Algebra

Solvability of a class of second-order quasilinear boundary value problems

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Applied mathematics and Mechanics(English Edition) 2009年第8期30卷 1055-1062页

作者：姚庆六 department of Applied mathematics Nanjing University of Finance and Economics

The second-order quasilinear boundary value problems are considered when the nonlinear term is singular and the limit growth function at the infinite exists. With the introduction of the height function of the nonlinear term on a bounded set and the consideration of the integration of the height function, the existence of the solution is proven. The existence theorem shows that the problem has a solution if the integration of the limit growth function has an appropriate value.

关键词： quasilinear ordinary differential equation two-point boundary value problem solvability Lebesgue dominated convergence theorem

Application of Homotopy Analysis Method to Solve Relativistic Toda Lattice System

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Communications in Theoretical Physics 2010年第6期53卷 1111-1116页

作者：王琪 department of Applied mathematics Shanghai University of Finance and Economics

In this letter, the homotopy analysis method is successfully applied to solve the Relativistic Toda lattice system. Comparisons are made between the results of the proposed method and exact solutions. Analysis results show that homotopy analysis method is a powerful and easy-to-use analytic tool to solve systems of differential-difference equations.

关键词： Jhomotopy analysis method relativistic Toda lattice system

Empirical Likelihood Approach for Treatment Effect in Pretest-Posttest Trial

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Chinese Annals of mathematics,Series B 2012年第6期33卷 941-948页

作者： Qixiang HE department of Applied mathematics Shanghai University of Finance and Economics

The empirical likelihood approach is suggested to the pretest-posttest trial based on the constrains, which we construct to summarize all the given information. The author obtains a log-empirical likelihood ratio test statistic that has a standard chi-squared limiting distribution. Thus, in making inferences, there is no need to estimate variance explicitly, and inferential procedures are easier to implement. Simulation results show that the approach of this paper is more efficient compared with ANCOVA II due to the sufficient and appropriate use of information.

关键词： Empirical likelihood Pretest-posttest trial Treatment effect

Triple Positive Periodic Solutions of Nonlinear Singular Second-order Boundary Value Problems

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Acta Mathematica Sinica,English Series 2014年第2期30卷 361-370页

作者： Qing Liu YAO department of Applied mathematics Nanjing University of Finance and Economics

This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem u″（t）＋ λ（t）u（t） = f（t,u（t））,a.e.t ∈ [0,2π],u（0） = u（2π）,u′（0） = u′（2π）,where f（t,u） is a local Carath′eodory *** shows that the problem is singular with respect to both the time variable t and space variable *** applying the Leggett-Williams and Krasnosel＇skii fixed point theorems on cones,an existence theorem of triple positive solutions is *** order to use these theorems,the exact a priori estimations for the bound of solution are given,and some proper height functions are introduced by the estimations.

关键词： Periodic boundary value problem singular nonlinearity triple positive solutions fixedpoint theorem