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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 {2., Chinese Academy of Sciences, Beijing 100080,{2. 2. department of {2., shantou university, Guangdong 515063,{2. 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.

lipschitz spaces and Q_K type spaces

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Science china mathematics 2010年第3期53卷 771-778页

作者： li Hao 1 , WULAN Hasi 1, & ZHOU JiZhen 1,2.1},{2., {2. 515063, china 2.School of Sciences, Anhui university of Science and Technology, Huainan 2.2.01, china 1. department of mathematics Shantou University Shantou 515063 China2. School of Sciences Anhui University of Science and Technology Huainan 232001 China

If f(z) =Σ∞ n=0 anzn and g(z) =Σ∞n=0bnzn for functions f, g are analytic in the unit disc, the Hadamard products of f and g is defined by f * g = ∞ n=0 a n b n z n . In this paper, the lipschitz spaces Λ(s, α) ... 详细信息

关键词： Q K type spaces lipschitz spaces Hadamard products

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,{2.,{2. 515041, china 2. department of Physics,{2., {2. 515063, china department of Physics and IT Medical College Shantou University Shantou 515041 China department of Physics Shantou University Shantou 515063 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 {2.,shantou university,shantou515063,china 2.Institute of {2.,Chinese Academy of Sci-ences,Beijing100080,china) shantou Univ Dept Math Shantou 515063 Peoples R China Chinese Acad Sci Inst Math Beijing 100080 Peoples R 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

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, shantou university, {2. 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

CMC surfaces in the hyperbolic 3-space

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Chinese Science Bulletin 1998年第7期43卷 547-550页

作者： YU Zuhuan 1, 2.and li Zhenqi 1, 3 1. Institute of mathematics, Fudan {2., Shanghai 2.0433,{2. 2. department of mathematics,Sichuan Union {2., Chengdu 610064,{2. 3. department of mathematics, Nanchang {2., Nanchang 33 nstitute of Mathemalics Fudan University Shanghai China department of mathematics Sichuan Union University Chengdu China department of mathematics Nanchang University Nanchang China

CMC-H surfaces satisfying H≥1 are studied. It is proved that these surfaces possess a natural representation which is a generalization of the Bryant’s result.

关键词： hyperbolic space CMC surface Weierstrass representation.

A class of compactly supported symmetric/antisymmetric B-spline wavelets

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Progress in Natural Science:Materials International 2005年第2期15卷 31-36页

作者： yang shouzhi* and LOU Zengjian({2. of mathematics, shantou university, shantou 515063, china) department of mathematics Shantou University Shantou 515063 China

An algorithm for constructing a class of compactly supported symmetric/antisymmetric B-spline wavelets is presented. For any mth order and kth order cardinal B-spline Nm(x), Nk(x), if m+k is an even integer, the corresponding mth order B-spline wavelets ψkm(x) can be constructed, which are compactly supported symmetric/antisymmetric. In addition, if ψkm(x), m>1 is mth B-spline wavelet associated with two spline functions Nm(x) and Nk(x), then (ψkm(x))′(x) is m-1th B-spline wavelet associated with N m-1(x) and N k+1(x), i.e. (ψkm(x))′(x)=2.ψ k+1 m-1(x). Similarly, ∫x0ψkm(t)dt, k>1 is m+1th B-spline wavelet associated with N m+1(x) and N k-1(x). Using this method, we recovered Chui and Wang’s spline wavelets. Since a class of B-spline wavelets are symmetric/antisymmetric, their linear phase property is assured. Several examples are also presented.

关键词： compactly supported B-spline function B-spline wavelet symmetric antisymmetric

Fuzzy controllers based on some fuzzy implication operators and their response functions

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Progress in Natural Science:Materials International 2004年第1期14卷 16-21页

作者： li Hongxing 1*, YOU Fei 1 and PENG Jiayin 2.1. department of {2., Beijing Normal {2., Beijing 100875, china 2. department of {2., Neijiang Teacher's College, Neijiang 641112. china) Beijing Normal Univ Dept Math Beijing 100875 Peoples R China

The fuzzy controllers constructed by 2. fuzzy implication operators based on CRI algorithm and their response functions are discussed. The conclusions show that the fuzzy controllers constructed by 9 fuzzy implication operators are universal approximators to continuous functions and can be used in practical fuzzy control systems. And these 9 fuzzy implication operators except for Einstein operator intersection are all the adjoint pairs of some fuzzy implication operators. Besides, there are 3 other fuzzy controllers formed by fuzzy implication operators being regarded approximately as fitted functions.

关键词： fuzzy implication operators CRI algorithm fuzzy controllers response functions universal approximators

A three level linearized compact difference scheme for the Cahn-Hilliard equation

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Science china mathematics 2012年第4期55卷 805-826页

作者： li Juan 1,2.,SUN ZhiZhong 1,& ZHAO Xuan 1 1 department of mathematics,Southeast {2.,Nanjing 2.0096,{2. 2.Yingtian College,Nanjing 2.0046,{2. 1. department of mathematics Southeast University Nanjing 210096 China2. Yingtian College Nanjing 210046 China

This article is devoted to the study of high order accuracy difference methods tor the Cahn-rnmara equation. A three level linearized compact difference scheme is derived. The u^ique solvability and uaconditional convergence of the difference solution are proved. The convergence order is O（T2.h4） in the maximum norm. The mass conservation and the non-increase of the total energy are also verified. Some numerical examples are given to demonstrate the theoretical results.

关键词： Cahn-Hilliard equation compact difference scheme convergence solvability conservation energynon-increase