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A Generalized Algebraic Method for Constructing a Series of Explicit Exact Solutions of a(1+1)-Dimensional Dispersive Long Wave Equation

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Communications in Theoretical Physics 2004年第9期 329-334页

作者： CHEN Yong~(1,2,3) WANG Qi~(2,3) LI Biao~(2,3)1 department of Physics,Shanghai Jiao Tong University,Shanghai 200030,china2 department of Applied mathematics,Dalian University of Technology,Dalian 116024,china3 Key Laboratory of mathematics and Mechanization,the Chinese Academy of Sciences,Beijing 100080,china

Making use of a new and more general ansatz,we present the generalized algebraic method to uniformlyconstruct a series of new and general travelling wave solution for nonlinear partial differential *** an applicationof the method,we choose a(1+1)-dimensional dispersive long wave equation to illustrate the *** a result,wecan successfully obtain the solutions found by the method proposed by Fan [***,***.153(2003)17]and find other new and more general solutions at the same time,which include polynomial solutions,exponentialsolutions,rational solutions,triangular periodic wave solutions,hyperbolic and soliton solutions,Jacobi and Weierstrassdoubly periodic wave solutions.

关键词： generalized algebraic method symbolic computation solitary wave solution Weierstrass and Jacobi elliptic functions periodic solution

The Interaction Programming Problem

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Journal of Systems Science and Systems Engineering 2001年第2期13卷 173-184页

作者： LI Rong-sheng 1, CHENG Ying 21.Institute of Operations Research, Qufu Normal University, Qufu 273165,china2.mathematics department, Heze Teachers College, Heze 274015, china Institute of Operations Research Qufu Normal UniversityQufu 273165 China mathematics department Heze Teachers CollegeHeze 274015 China

Based upon the research to the economic equilibrium problems,we present a kind of new mathematical programming problem——interaction programming problem (abbreviated by IPP). The IPP is composed of two or multiple parametric programming problems which is interrelated with each other. The IPP reflects the equality and mutual benefit relationship between two (or among multiple) economic planners in an economic system. In essence, the IPP is similar to the generalized Nash equilibria (GNE) game which has been given several names in the literature: social equilibria games, pseudo-Nash equilibria games, and equilibrium programming problems. In this paper, we establish the mathematical model and some basic concepts to the IPP. We investigate the structure and the properties of the *** also give a necessary and sufficient conditions for the existence of the equilibrium points to a kind of linear IPP.

关键词： Interaction programming problem equilibrium points partial solutions optimal solutions

A class of root-finding methods free from second derivative

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A class of root-finding methods free from second derivative

Weighted Profile Least Squares Estimation for a Panel Data Varying-Coefficient Partially Linear Model

2011 World Congress on Engineering and Technology(CET 2011)

作者： Xiuhua Wang department of mathematics Xiaogan University Xiaogan 432100 Hubei china Jisheng Kou department of mathematics Shanghai University Shanghai 200444 china

In this paper, we propose a class of root-finding methods free from second derivative for the non-linear equations. Each iteration of the new methods requires three evaluations of the function and one evaluation of its first derivative. The order of convergence of the new methods is six. So the efficiency index is higher than the ones of Newton’s irrational method, Chebyshev- Halley methods and Newton’s ***, based on the new methods, a new multistep iteration scheme is developed.

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Chinese Annals of mathematics,Series B 2010年第2期31卷 247-272页

作者： Bin ZHOU Jinhong YOU Qinfeng XU Gemai CHEN School of Finance and Statistics East China Normal University Shanghai 200241 China. department of Statistics Shanghai University of Finance and Economics Shanghai 200433 China. Corresponding Author. School of Management Fudan University Shanghai 200433 China. department of mathematics and Statistics University of Calgary Calgary Alberta T2N 1N4 Canada.

This paper is concerned with inference of panel data varying-coefficient partially linear models with a one-way error structure. The model is a natural extension of the well-known panel data linear model （due to Baltagi 1995） to the setting of semiparametric regressions. The authors propose a weighted profile least squares estimator （WPLSE） and a weighted local polynomial estimator （WLPE） for the parametric and nonparametric components, respectively. It is shown that the WPLSE is asymptotically more efficient than the usual profile least squares estimator （PLSE）, and that the WLPE is also asymptotically more efficient than the usual local polynomial estimator （LPE）. The latter is an interesting result. According to Ruckstuhl, Welsh and Carroll （2000） and Lin and Carroll （2000）, ignoring the correlation structure entirely and ＂pretending＂ that the data are really independent will result in more efficient estimators when estimating nonparametric regression with longitudinal or panel data. The result in this paper shows that this is not true when the design points of the nonparametric component have a closeness property within groups. The asymptotic properties of the proposed weighted estimators are derived. In addition, a block bootstrap test is proposed for the goodness of fit of models, which can accommodate the correlations within groups illustrate the finite sample performances of the Some simulation studies are conducted to proposed procedures.

关键词： Semiparametric Panel data Local polynomial Weighted estimation Block bootstrap

Effect of Dy on Structure and Magnetic Properties of Dy_xFe_(60.5-x)Pt_(39.5) Alloys

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Journal of Wuhan University of Technology(Materials Science) 2010年第1期25卷 135-137页

作者：左卫群 department of Information of Materials Science and Engineering Guilin University of Electronic Technology

Effects of the content of Dy on structure and magnetic properties of DyxFe60.5-xPt39.5 alloys（x = 0, 0.5, 1.0, 1.5） were investigated. The results of XRD analysis proved that the phase-transitional temperature of DyxFe60.5-xPt39.5 alloys from disordered face-centered-cubic structure to ordered face-centered-tetragonal cubic structure decreases with the increase of the content of Dy（x）. Suitable content of Dy can improve the exchange coupling between soft magnetic phase and hard magnetic phase by refining grain size, while the remanence ratio and coercivity of the Fe60.5Pt39.5 alloy can be significantly improved by a small replacement of Fe by Dy, good magnetic properties were obtained in Dy0.5Fe60.0Pt39.5 alloys.

关键词： phase transformation degree of order grain size exchange coupling

Regularity properties of a class of hybrid methods

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Communications in Nonlinear Science and Numerical Simulation 2000年第1期5卷 27-30页

作者： Daxue CHEN and Aiguo XIAO department of Basic Sciences, Xiangtan College of Mechanical and Electrical Engineering, Xiangtan411101, china department of mathematics, Xiangtan University, Xiangtan 411105, china e-mail: xiaoag@xtu. edu. cn, xag@lsec. cc. ac department of Basic Sciences Xiangtan Coll. Mech. and Elec. Eng. Xiangtan 411101 China department of mathematics Xiangtan University Xiangtan 411105 China

The existence of spurious steady solutions and period-2 solutions in constant timestep is studied. The concepts of R[1]-regularity and R[2]-regularity of a class of hybrid methods for dynamical systems of ordinary differential equations are introduced and studied. Some conditions guaranteeing R[1]-regularity and R[2]-regularity of such methods applied to dynamical systems of ordinary differential equations with some important structures are given.

关键词： hybrid method dynamical system regularity spurious solution

Conservation laws of some soliton equations with self-consistent sources

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Journal of Shanghai University(English Edition) 2011年第3期15卷 157-165页

作者：李琪张大军陈登远 department of mathematics College of Sciences Shanghai University department of mathematics East China Institute of Technology

Infinitely many conservation laws for some （1＋1）-dimension soliton hierarchy with self-consistent sources are constructed from their corresponding Lax pairs directly. Three examples are given. Besides, infinitely many conservation laws for Kadomtsev-Petviashvili （KP） hierarchy with self-consistent sources are obtained from the pseudo-differential operator and the Lax pair.

关键词： Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy with self-consistent sources Kaup-Newell (KN) hierarchy with self-consistent sources Ablowitz-Ladik (AL) hierarchy with self-consistent sources Kadomtsev-Petviashvili (KP) hierarchy with self-consistent sources conservation laws

AVERAGE σ-WIDTHS OF THE UNIT BALL OF I_1~∞(R)IN I_2~∞(R)

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Analysis in Theory and Applications 1994年第2期10卷 92-104页

作者： Wu Huoxiong Beijing Normal University,.china department of mathematics Chenzhou Normal College, Hunan, 423000 P R china

In this paper we study the average σ-K width and the average σ-linear width of the unit ball of l;（R） inl;（R）. The exact values of these widths are calculated and an optimal subspace with the optimal linear oper... 详细信息

关键词： Math WIDTHS OF THE UNIT BALL OF I1 AVERAGE R)IN I2 APPI 飞飞

FEEDBACK CONTROL OF A CLASS OF FLEXIBLE SYSTEMS WITH COUPLED BENDING AND TORSIONAL VIBRATIONS

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Systems Science and Mathematical Sciences 1993年第2期6卷 120-129页

作者： YU Nairun WANG Miansen ZHU Guangtian department of Basic Courses Northwest Textile Institute,Xian 710048.china department of mathematics,Xian Jiaotong University,Xian710049,china Institute of Systems Science. Academia Sinica, Beijing 100080,china 西北纺织工学院陕西西安西安交通大学陕西西安中科院系统科学所北京

In this paper, a class of flexible systems of beams with coupled bending andtorsional vibrations, which has important applications in the dynamics of aircraft is dis-cussed. The existence and uniqueness of the solution for this class of systems are proved,where the spectral analysis method and the unconditional base theory are used, and asufficient condition for the asymptotic stability of the closed-loop system is obtained bymeans of the (D) class operators theory.

关键词： Flexible system feedback control C0-semigroup unconditional base asymptotic stability