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The Blowing-up of the Solutions for a Class of Nonlinear Reaction-Diffusion Equations

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Systems Science and Systems Engineering 1999年第4期9卷 9-12页

作者： YAN Gui\|qing department of Mathematics and Information Science, yantai university yantai 264005,china

In this paper, we discuss the blowing\|up of the solutions of a class of nonlinear reaction\|diffusion equations with the general (or nonlinear) boundary conditions. On some proper assumptions, we conclude that there ...

关键词： nonlinear reaction\|diffusion equation blow\|up

BAHADUR'S REPRESENTATION FOR NEAREST NEIGHBOR MEDIAN ESTIMATES: THE FIXED DESIGN CASE

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Systems Science and Mathematical Sciences 1999年第2期12卷 133-144页

作者： YANG Ying(department of Probability and Statistics, Peking university, Beijing 100871, china)WANG Bingzhang(department of Mathematics and Information Science, yantai university, yantai 264005, china) 北京大学概率统计系北京烟台大学数学系山东烟台

Consider the nonparametric regression model Yi=g(xi) +ei, i=1, 2,...,where g is an unknown function defined on the interval [0, 1], the fixed design points xi(i≥1) are known and ei’s are i.i.d. random variables with median zero. The regressor is assumed to take values in [0, 1]∈ R and the regressand to be real valued. This paper stu-dies the behavior of the nearest neighbor median estimate gnh(x)=m(Yn1(x), Yn2(x),...,Ynh(x)), where h is the number of the nearest neighbor. Under suitable conditions, Bahadur’s representation for the above-mentioned the nonparametric regression function g is obtained. Law of iterated logarithm and asymptotic normality are also established.

关键词： Nearest neighbor median estimates Bahadur’s representation asymptotic normality law of iterated logarithm.

The Initial Boundary Value Problem for a Class ofGeneralized Nonlinear Schrodinger Equations

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Systems Science and Systems Engineering 1998年第4期8卷 488-491页

作者： YAN Guiqing(department of mathematics and Information Science, yantai university, yantai 264005)

We discuss the initial boundary value problem of a class of nonlinear Schr6dinger equations with potential functions. By the theory of the group of unitary operators and the method ofthe prior estimate, we prove the global existence of the classical solutions of the nonlinear Schrodingerequations with potential functions.

关键词： Nonlinear Schrodinger equation group of unitary operators prior estimate

On the classification of compact quantum groups U_θ(2)

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Science china Mathematics 2010年第5期53卷 256-269页

作者： ZHANG XiaoXia department of Mathematics,yantai university,yantai 264005,china 1. department of Mathematics Yantai University Yantai 264005 China

In this paper,we show that the corepresentation of compact group Uθ(2) on the vector space is determined by its infinitesimal generators B0,B2,A0,A1 and A2,where θ is an irrational *** also show that B0 and B2 commute with Aj,j = 0,1,2,so B0,A0,A1 and A2 are sl(2,C) loop *** we exhibit all irreducible representations of Uθ(2),which are different from those of group U(2),and use above results to give the classification of quantum groups Uθ(2),which is analogous to that of irrational algebra Aθ.At the same time,we also give all the forms of automorphisms on quantum group Uθ(2).

关键词： compact quantum group comultiplication irreducible representation

GENERAL CAUCHY PROBLEM FOR THE LINEAR SHALLOW-WATER EQUATIONS ON AN EQUATORIAL BETA-PLANE

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Journal of Hydrodynamics 2006年第3期18卷 303-309页

作者： SHEN Chun SHI Wei-hui school of Mathematics and Information Yantai Normal University Yantai 264025 China Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China department of Mathematics Shanghai University Shanghai 200444 China

Based on the theory of stratification, the well-posedness of the initial value problem for the linear shallow-water equations on an equatorial beta-plane was discussed. The sufficient and necessary conditions of the existence and uniqueness for the local solution of the equations were presented and the existence conditions for formal solutions of the equations vere also given. For the Cauchy problem on the hyper-plane {t = O}, the local analytic solution were worked out and a special case was discussed. Finally, an example was used to explain the variety of formal solutions for the ill-posed problem.

关键词： stratification initial value problem,well-posedness shallow-water equations

The cohomology group of weak entwining structure

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Science china Mathematics 2007年第5期50卷 665-674页

作者： Ling JIA & Fang LI department of Mathematics, Ludong university, yantai 264025, china department of Mathematics, Zhejiang university, Hangzhou 310027, china 1. department of Mathematics Ludong University Yantai 264025 China 2. department of Mathematics Zhejiang University Hangzhou 310027 China

In this paper, we reveal that a weak entwining structure admits a rich cohomology theory. As an application we compute the cohomology of a weak entwining structure associated to a weak coalgebra-Galois extension.

关键词： weak entwining structure cohomology group 16W80 16W99

PACKING A TREE OF ORDER p WITH A (p,p+1)-GRAPH

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Journal of Systems Science & Complexity 2003年第1期16卷 122-132页

作者： WANGMin LIGuojun departmentofMathematics YantaiUniversityYantai264005China departmentofMathematics ShandongUniversityJinan250100China

Let G1 and G2 be two graphs of the same order,If G1 is isomorphic to a spanning subgraph of the complement of G2,then we say that G1 and G2 are packable.A graph G is called a (p,m)-graph if G has p vertices and m *** main purpose of this paper is to present a necessary and sufficient condition for a tree of order p and a (p,p+1)-graph to be packable.

关键词： Packing tree (p p+ 1)-graph.

On the classification of compact quantum groups Uθ（2）

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Science china Mathematics 2010年第5期 256-269页

作者： ZHANG XiaoXia department of Mathematics,yantai university,yantai 264005,china

关键词： compact quantum group comultiplication irreducible representation

Lie bialgebras of generalized Witt type

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Science china Mathematics 2006年第4期49卷 533-544页

作者： SONG Guang’ai & SU Yucai College of Mathematics and Information Science, Shandong Institute of Business and Technology, yantai 264005, china department of Mathematics, university of Science and Technology of china, Hefei 230026, china department of Mathematics, Shanghai Jiaotong university, Shanghai 200240, china College of Mathematics Information Science Shandong Institute of Business Technology Yantai 264005 China department of Mathematics University of Science Technology of china Hefei 230026 China department of Mathematics Shanghai Jiaotong University Shanghai 200240 China

In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W, W(?)W) is trivial.

关键词： Lie bialgebras, Yang-Baxter equation, Lie algebra of generalized Witt type.