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Two-dimensional Riemann problems of simplified Euler equation

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Chinese Science Bulletin 1998年第6期43卷 441-444页

作者： YANG Xiaozhou 1,2.and HUANG Feimin+1 1. institute of Applied mathematics, Chinese Academy of Sciences, Beijing 100080, China 2. Department of mathematics, shantou University, Guangdong 515063, China institute of Applied mathematics Chinese Academy of Sciences Beijing China Department of mathematics Shantou University Guangdong China

The two-dimensional Riemann problem of simplifed Euler equation is discussed, in which initial value contains two different constant states that are separated by a smooth curve. This problem is a natural description of realistic phenomena, but it is hard to study by conventional idea. So a new approach is proposed. Some new properties about two-dimensional rarefaction wave, shock wave and intermediate state of solutions are disclosed.

关键词： D Riemann problem implicit functions cylindrical surface pencil of cylindrical surface.

Necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property

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Chinese Science Bulletin 1997年第3期42卷 259-260页

作者： MAI Jiehua and GU Rongbao1.institute of mathematics, {2. University, shantou 515063, China 2. Department of mathematics, Anhui University, Hefei 2.0039, China institute of mathematics Shantou University Shantou China Department of mathematics Anhui University Hefei China

IN this letter we discuss the necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property. According to ref. [1], on a closed surface, every minimal set of a C^r(r≥2. flow is trivial, but it is possible for a C^0 flow to contain non-trivial minimal sets. Thus C^0 flows on closed surfaces are more complicated than C^r(r≥2. flows.

关键词： Necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property

Anisotropic effect on the vibronic reduction factors

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Chinese Science Bulletin 2006年第21期51卷 2553-2558页

作者： QIU Qing-chun1,2.& QIAO Fen1,2.1. Department of Physics and IT, Medical College, shantou University,shantou 515041, China 2. Department of Physics, shantou University, shantou 515063, China Department of Physics and IT Medical College Shantou University Shantou China Department of Physics Shantou University Shantou China

The reduction factors p and q defined by Ham in the Ee JT system and their relation 2.-p=1 have been well accepted and the concept of reduction factors is widely used in the studies of vibronic coupling. However, when the system is under the anisotropic conditions, the reduction factors and their relation will change accordingly. The first-order reduction factors p and q of Ee system were further studied using the method of unitary transformation here. The relation between p and q proposed by Ham was investigated under both conditions of the linear coupling and the anisotropic effects. The result demonstrated that the relation of 2.-p=1 was only correct for the linear vibronic coupling, but not correct when the anisotropic effect was considered. This result suggested that the anisotropic effect influence considerably the reduction factors, and hence the physical properties of materials. Our method could be also applied to other JT systems, especially the highly symmetric JT systems involving C60 molecules.

关键词：电子振动耦合声子交迭 Jahn-Teller效应各向异性

Global smooth solution of multi-dimensional non-homogeneous conservation laws

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Progress in Natural Science:Materials International 2004年第10期14卷 15-22页

作者： YANG Xiaozhou 1 and ZHANG Tong 2. (1.Department of mathematics,shantou University,shantou515063,China 2.institute of mathematics,Chinese Academy of Sci-ences,Beijing100080,China) Dept. of Math. Shantou Univ. Shantou 515063 China Inst. of Math. Chinese Acad. of Sci. Beijing 100080 China

The initial value problem of multi-dimensional non-homogeneous conservation laws is studied and a sufficient condition of the existence of its global smooth solution is ***,three equivalent propositions of the existence of global smooth solution for multi-dimensional homogeneous scalar conservation laws are also *** global smooth solution is uniquely expressed by the global implicit function that is determined by a scalar equation,not by a system as usual methods do.

关键词： conservation laws global smooth solution global implicit function diffeomorphism

Non-wandering points and the depth for graph maps

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Science China mathematics 2007年第12期50卷 1818-1824页

作者： Jie-hua MAI~1 Tai-xiang SUN~(2.) ~1 institute of mathematics,{2. University,{2. 515063,China ~2.College of mathematics and Information Sciences,Guangxi University,Nanning 530004,China institute of mathematics Shantou University Shantou China College of mathematics and Information Sciences Guangxi University Nanning China

Let G be a graph and f:G→G be *** by R(f) andΩ(f) the set of recurrent points and the set of non-wandering points of f ***Ω_0(f) = G andΩ_n(f)=Ω(f|_(Ω_(n-1)(f))) for all n∈*** minimal m∈NU {∞} such thatΩ_m(f)=Ω_(m+1)(f) is called the depth of *** this paper,we show thatΩ_2.(f)=(?) and the depth of f is at most ***,we obtain some properties of non-wandering points of f.

关键词： graph map, non-wandering point, the depth of a graph map

The nonexistence of sensitive commutative group actions on graphs

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Science China mathematics 2007年第8期50卷 1197-1204页

作者： Jie-hua MAI~1 En-hui SHI~(2.) 1 institute of mathematics,{2. University,{2. 515063,China 2.School of Mathematical Sciences,Suzhou University,Suzhou 2.5006,China institute of mathematics Shantou University Shantou China School of Mathematical Sciences Suzhou University Suzhou China

In this paper,we observe a special kind of continuous functions on *** estimating the integrals of these functions,we prove that there are no sensitive commutative group actions on ***,we consider a 1-dimensional continuum composed of a spiral curve and a circle and show that there exist sensitive homeomorphisms on it,which answers negatively a question proposed by Kato in 1993.

关键词： homeomorphism commutative group action graph map sensitivity expansiveness infinite spiral curve 54H2.

Multiwavelet sampling theorem in Sobolev spaces

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Science China mathematics 2010年第12期53卷 3197-3214页

作者： LI YouFa 1,2.& YANG ShouZhi 1, 1 Department of mathematics, shantou University,{2., China 2.College of mathematics and Information Sciences, Guangxi University, Nanning 530004, China Department of mathematics Shantou University Shantou China College of mathematics and Information Sciences Guangxi University Nanning China

This paper is to establish the multiwavelet sampling theorem in Sobolev spaces. Sampling theorem plays a very important role in digital signal communication. The most classical sampling theorem is Shannon sampling theorem, which works for bandlimited signals. Recently, sampling theorems in wavelets or multiwavelets subspaces are extensively studied in the literature. In this paper, we firstly propose the concept of dual multiwavelet frames in dual Sobolev spaces (H s (R) , H-s (R)). Then we construct a special class of dual multiwavelet frames, from which the multiwavelet sampling theorem in Sobolev spaces is obtained. That is, for any f ∈ H s (R) with s > 1/2. it can be exactly recovered by its samples. Especially, the sampling theorem works for continuous signals in L 2.(R), whose Sobolev exponents are greater than 1 /2.

关键词： Sobolev spaces refinable function vectors dual multiwavelet frames delta function sampling theorem

A SPLITTING ITERATION METHOD FOR DOUBLE X_0-BREAKING BIFURCATION POINTS

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Journal of Computational mathematics 1998年第3期16卷 267-274页

作者： Rui-song Ye (institute of mathematics, {2. University, Guangdong 515063, China) institute of mathematics Shantou University Guangdong 515063 China

A splitting iteration method is proposed to compute double X0-breaking bifurcation points. The method will reduce the computational work and storage, it converges linearly with an adjustable speed. Numerical computat... 详细信息

关键词： Double X0-breaking bifurcation point splitting iteration method extended system

A REMARK ON EXTINCTION OF A CLASS OF SUPERPROCESSES

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Chinese Annals of mathematics,Series B 1996年第1期17卷 115-120页

作者： ZHAO XUELEI (institute of mathematics, Shatou University{2., China.) institute of mathematics Shantou University Shantou 515063 China

The extinction of a class of superprocesses associated with general branching characterstics and underlying Markov processes is investigated. The extinction is closely associated with the branching characteristics and... 详细信息

关键词： Superprocess Extinction Nonlinear evolution equation Branching characteristic Recurrence and transience