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Strong uniqueness of best approximations in spaces of bounded linear operators

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Science china mathematics 2004年第3期47卷 339-351页

作者： LI Chong HE Jinsu department of mathematics, zhejiang university Hangzhou 310027, china department of mathematics, zhejiang normal university jinhua 321004, china department of mathematics Zhejiang University Hangzhou China department of mathematics Zhejiang Normal University 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.

A lower bound on the total signed domination numbers of graphs

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Science china mathematics 2007年第8期50卷 1157-1162页

作者： Xin-zhong LU department of mathematics,zhejiang normal university,jinhua 321004,china department of mathematics Zhejiang Normal University Jinhua China

Let G be a finite connected simple graph with a vertex set V (G) and an edge set E(G). A total signed domination function of G is a function f : V (G) ∪ E(G) → {?1, 1}. The weight of f is w(f) = Σ x∈V(G)∪E(G) f(x). For an element x ∈ V (G) ∪ E(G), we define $f[x] = \sum\nolimits_{y \in N_T [x]} {f(y)} $ . A total signed domination function of G is a function f : V (G) ∪ E(G) → {?1, 1} such that f[x] ? 1 for all x ∈ V (G) ∪ E(G). The total signed domination number γ s * (G) of G is the minimum weight of a total signed domination function on G.In this paper, we obtain some lower bounds for the total signed domination number of a graph G and compute the exact values of γ s * (G) when G is C n and P n .

关键词： total signed domination function total signed domination number 26A33

Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips

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Science china mathematics 2005年第2期48卷 248-260页

作者： SHUI Shuliang & ZHU Deming College of mathematics and Physics, zhejiang normal university, jinhua 321004, china department of mathematics, East china normal university, Shanghai 200062, china College of mathematics and Physics Zhejiang Normal University Jinhua China department of mathematics East China Normal University Shanghai China

Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take inclination flip. The existence, nonexistence, and uniqueness of the 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold 1-periodic orbit and three-fold 1 -periodic orbit are also obtained. It is indicated that the number of periodic orbits bifurcated from this kind of homoclinic orbits depends heavily on the strength of the inclination flip.

关键词： bifurcation, homoclinic orbit, non-resonance, inclination flip, 1-periodic orbit.

Schwarz-Pick estimates for positive real part holomorphic functions on unit ball and polydisc

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Science china mathematics 2010年第4期53卷 1017-1024页

作者： LIU Yang 1,& CHEN ZhiHua 2 1 department of mathematics,zhejiang normal university,jinhua 321004,china 2 department of mathematics,Tongji university,Shanghai 200092,china department of mathematics Zhejiang Normal University Jinhua China department of mathematics Tongji University Shanghai China

We give higher order derivatives Schwarz-Pick estimates for all positive real part holomorphic functions on Bn and D n,and generalize early work on Schwarz-Pick estimate of higher order derivatives for holomorphic fun... 详细信息

关键词： Schwarz-Pick estimate holomorphic function Taylor expansion

Bifurcations of travelling wave solutions for two generalized Boussinesq systems

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Science china mathematics 2008年第9期51卷 1577-1592页

作者： LI JiBin1,2 1 department of mathematics, zhejiang normal university, jinhua 321004, china 2 department of mathematics, Kunming university of Science and Technology, Kunming 650093, china department of mathematics Zhejiang Normal University Jinhua China department of mathematics Kunming University of Science and Technology Kunming China

Using the methods of dynamical systems for two generalized Boussinesq systems, the existence of all possible solitary wave solutions and many uncountably infinite periodic wave solutions is obtained. Exact explicit parametric representations of the travelling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.

关键词： nonlinear wave bifurcation solitary wave exact explicit solution generalized Boussinesq system 34C37 34C23 74J30 58Z05

Dynamical understanding of loop soliton solution for several nonlinear wave equations

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Science china mathematics 2007年第6期50卷 773-785页

作者： Ji-bin LI department of mathematics, zhejiang normal university, jinhua 321004, china Kunming university of Science and Technology, Kunming 650093, china department of mathematics Zhejiang Normal University Jinhua China Kunming university of Science and Technology Kunming 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 34C23 74J30 58Z05

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

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Science china mathematics 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

Variable Separation Solution for(1+1)-Dimensional Nonlinear Models Related to Schrdinger Equation

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Communications in Theoretical Physics 2004年第10期42卷 568-572页

作者： XU Chang-Zhi~(1,2) ZHANG Jie-Fang~11 Institute of Nonlinear Physics,zhejiang normal university,jinhua 321004,china2 department of Physics and mathematics,jinhua Educational College,jinhua 321000,china Institute of Nonlinear Physics Zhejiang Normal University Jinhua 321004 China department of Physics and mathematics Jinhua Educational College Jinhua 321000 China

A variable separation approach is proposed and successfully extended to the(1+1)-dimensional *** new exact solution of(1+1)-dimensional nonlinear models related to Schr(?)dinger equation by the entranceof three arbitrary functions is *** special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution,oscillating soliton solution,and periodic soliton solutions are discussed by selecting thearbitrary functions appropriately.

关键词： variable separation approach (1+1)-dimensional nonlinear models solution of soliton

CODIMENSION 3 BIFURCATIONS OFHOMOCLINIC ORBITS WITH ORBITFLIPS AND INCLINATION FLIPS

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Chinese Annals of mathematics,Series B 2004年第4期25卷 555-566页

作者： SHUISHULIANG ZHUDEMING CollegeofmathematicsandPhysics ZhejiangNormalUniversityJinhua321004ZhejiangChina. departmentofmathematics EastChinaNormalUniversityShanghai200062China.

The homoclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near the homoclinic orbit. This homoclinic orbit is nonprincipal in the meanings that its positive semi-orbit takes orbit flip and its unstable foliation takes inclination flip. The existence, nonexistence, uniqueness and coexistence of the 1-homoclinic orbit and the 1-periodic orbit are studied. The existence of the twofold periodic orbit and three-fold periodic orbit are also obtained.

关键词： Bifurcation Homoclinic orbit Orbit flip Inclination flip Periodic orbit