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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(department of mathematics, shantou university, shantou 515063, china) Dept. of mathematics Shantou Univ. 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)=22ψ 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

GENUINE-OPTIMAL CIRCULANT PRECONDITIONERS FOR WIENER-HOPF EQUATIONS

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Journal of Computational mathematics 2001年第6期19卷 629-638页

作者： Fu-rong lin (department of mathematics, shantou university, shantou 515063,china) 汕头大学广东汕头 515063

Discusses the genuine-optimal circulant preconditioner for finite-section Wiener-Hopf equations. Definition of the genuine-optimal circulant preconditioner; Use of the preconditioned conjugate gradient method; Numeric... 详细信息

关键词： Wiener-Hopf equations circulant preconditioner preconditioned conjugate gradient method quadrature rules Hilbert-Schmidt norm

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 department of mathematics, shantou university, shantou 515063, china 2 School of Sciences, Anhui university of Science and Technology, Huainan 232001, china department of mathematics Shantou University Shantou China School of Sciences Anhui University of Science and Technology Huainan 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

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

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 2q-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 2q-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

Raising approximation order of refinable vector by increasing multiplicity

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Science china mathematics 2006年第1期49卷 86-97页

作者： yang shouzhi & PENG lizhong department of mathematics, shantou university, shantou 515063, china LMAM, School of Mathematical Sciences, Peking university, Beijing 100871, china department of mathematics Shantou University Shantou China LMAM School of Mathematical Sciences Peking University Beijing China

An algorithm is presented for raising an approximation order of any given orthogonal multiscaling function with the dilation factor a. Let φ(x) = [φ1(x),φ2(x),…,φr(x)]T be an orthogonal multiscaling function with the dilation factor a and the approximation order m. We can construct a new orthogonal multiscaling function φnew(x) = [ φT(x). f3r+1(x),φr+2(x),…,φr+s(x)}T with the approximation order m + L(L ∈ Z+). In other words, we raise the approximation order of multiscaling function φ(x) by increasing its multiplicity. In addition, we discuss an especial setting. That is, if given an orthogonal multiscaling function φ(x) = [φ1 (x), φ2(x), …, φr(x)]T is symmetric, then the new orthogonal multiscaling function φnew(x) not only raise the approximation order but also preserve symmetry. Finally, some examples are given.

关键词： orthogonal, multiscaling functions, approximation order, symmetry.

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.

Commuting double Ockham algebras

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Science china mathematics 2008年第2期51卷 185-194页

作者： FANG Jie department of mathematics,shantou university,shantou 515063,china department of mathematics Shantou University Shantou China

In this paper,we study a certain class of double Ockham algebras (L;∧,∨,f,k,0,1), namely the bounded distributive lattices (L;∧,∨,0,1) endowed with a commuting pair of unary op- erations f and k,both of which are dual *** characterize the subdirectly irreducible members,and also consider the special case when both (L;f) and (L;k) are de Morgan *** show via Priestley duality that there are precisely nine non-isomorphic subdirectly irreducible members, all of which are simple.

关键词： subdirectly irreducible double Ockham algebra Priestley duality 06D15 06D30

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, shantou 515063, china 2. department of mathematics, Anhui university, Hefei 230039, 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