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ON THE MODULI NUMBER OF PLANE CURVE SINGULARITIES WITHONE CHARACTERISTIC PAIR

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Chinese Annals of Mathematics,Series B 1999年第4期20卷 407-412页

作者： CHEN HAO(department of Mathematics, zhongshan university,{2., china) zhongshan Univ Dept Math Guangzhou 510275 Peoples R China

The author gives another linear-algebraic proof of the famous result of Zariski, Delorme,Briancon- Granger- Maisonobe about the moduli number of plane curve singularities with the same topological type as Xa + Yb = 0 (i.e.,with one characteristic pair). Since the original proof depends very much on the division theorem of Briancon, it cannot be generalized to higher dimensions. It is hopeful that the proof here will be applied to the higher dimensional cases.

关键词： Moduli number Plane curve Singularity Characteristic pair

ID-WAVELETS METHOD FOR HAMMERSTEIN INTEGRAL EQUATIONS

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Journal of Computational Mathematics 1998年第6期16卷 499-508页

作者： Xian-biao Wang Wei Lin (department of Mathematics, zhongshan university,{2., china) zhongshan Univ Dept Math Canton 510275 Peoples R China

The numerical solutions to the nonlinear integral equations of Hammerstein-type y(t) = f(t) + integral(0)(1)k(t, s)g(s, y(s))ds, t is an element of [0,1] are investigated. A degenerate kernel scheme basing on ID-wavelets combined with a new collocation-type method is presented. The Daubechies interval wavelets and their main properties are briefly mentioned. The rate of approximation solution converging to the exact solution is given. Finally we also give two numerical examples.

关键词： nonlinear integral equation interval wavelets degenerate kernel

Population-size-dependent branching processes in Markovian random environments

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Chinese Science Bulletin 1998年第8期43卷 635-638页

作者： WANG Hanxing 1 and DAI Yonglong 2.1. department of Mathematics, Shanghai university, Shanghai 2.1800,{2. 2. department of Mathematics, zhongshan university, guangzhou 510275,{2. department of Mathematics Shanghai University Shanghai China department of Mathematics Zhongshan University Gunngzhou China

A branching model {Z n} n≥0is considered where the offspring distribution of the population’s evolution is not only dependent on the population size, but also controlled by a Markovian environmental process {ξ n} n≥0. For this model, asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k, θof the offspring distribution converges to m>1 as the population size k grows to ∞. In the case that {ξ n} n≥0is an irreducible positive recurrent Markov chain, certain extinction (i.e. P(Z n=0 for some n)=1) and noncertain extinction (i.e. P(Z n=0 for some n)<1) are studied.

关键词： Markov chains in random environments stochastic population models branching processes.

PREPARATION　OF　NANOCOMPOSITE　BINARY　GADOLINIUM　ALLOYS　AND　THEIR　ENHANCED　MAGNETIC　ENTROPY　CHANGE

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中国有色金属学会会刊：英文版 1996年第3期6卷 86-91页

作者： Zhang Jieli Shao Yuanzhi(department ofphysics, zhongshan university,{2.) zhongshan UNIV DEPT PHYSGUANGZHOU 510275PEOPLES R CHINA

ＰＲＥＰＡＲＡＴＩＯＮＯＦＮＡＮＯＣＯＭＰＯＳＩＴＥＢＩＮＡＲＹＧＡＤＯＬＩＮＩＵＭＡＬＬＯＹＳＡＮＤＴＨＥＩＲＥＮＨＡＮＣＥＤＭＡＧＮＥＴＩＣＥＮＴＲＯＰＹＣＨＡＮＧＥ￥ＺｈａｎｇＪｉｅｌｉ；ＳｈａｏＹｕａｎｚｈｉ... 详细信息

ＰＲＥＰＡＲＡＴＩＯＮＯＦＮＡＮＯＣＯＭＰＯＳＩＴＥＢＩＮＡＲＹＧＡＤＯＬＩＮＩＵＭＡＬＬＯＹＳＡＮＤＴＨＥＩＲＥＮＨＡＮＣＥＤＭＡＧＮＥＴＩＣＥＮＴＲＯＰＹＣＨＡＮＧＥ￥ＺｈａｎｇＪｉｅｌｉ；ＳｈａｏＹｕａｎｚｈｉ（Ｄｅｐａｒｔｍｅｎｔｏｆｐｈｙｓ...

关键词： nanocomposites magnetic refrigeration rare earth

The Influence of Minimal Subgroups on the Structure of Finite Groups

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Acta Mathematica Sinica,English Series 2000年第1期16卷 63-70页

作者： Yanming Wang Mathematics department,zhongshan {2.,guangzhou 510275,P.R.china Mathematics department Zhongshan University Guangzhou 510275 P.R. China

Let G be a finite *** question how the properties of its minimal subgroups influence the structure of G is of considerable interest for some *** this paper we try to use c-normal condition on minimal subgroups to char... 详细信息

关键词： c-normal subgroup Supersolvable Nilpotent Generalized Fitting subgroup

Effect of an impurity on 3-electron quantum dots in magnetic fields

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Science china(Physics,Mechanics & Astronomy) 2004年第5期47卷 521-530页

作者： LIU Yimin1,2. HUANG Gangming1 & BAO Chengguang1 1. department of Physics, zhongshan university,{2., china 2. department of Physics, Shaoguan university, Shaoguan 512.05, china 1. department of Physics Zhongshan University 510275 Guangzhou China 2. department of Physics Shaoguan University 512005 Shaoguan China

The ground-state property of a 2.dimensional 3-electron quantum dot (QD) subjected to an external magnetic fieldB and affected by an impurity is studied. The impurity is located at thez-axis by a distanced from the plane of the dot. The evolution of the angular momentumL o and the spinS o of the ground state in accordance withB andd has been calculated, and the results are summarized and plotted in a (L o,S o) diagram. The spatial distribution of the electrons (the size and the geometric features) and the optical absorption have also been investigated. The (L o S o) diagram indicates thatL o andS o may jump whend and/orB vary. It was found that, due to the constraints arising from symmetry, each symmetric geometry is accessible only to a specific group of states having specificL o andS o.

关键词： quantum dot, ground state, charged impurity, magnetic field.

The Isotone Mappings on Ockham Algebras

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Acta Mathematica Sinica,English Series 1996年第1期12卷 43-48页

作者： Fang Jie department of Mathematics zhongshan university {2., 510275 china 中山大学数学系广东广州

In this paper we shall describe some algebraic concepts of Ockham algebras. We show that, if L, M∈K1,1 then H（S（L）,S（M））≌S（H（L,M））.

关键词： Isotone (Ockham) Isomorphism

A Generalization of Hall-Higman's Reduction Theorem

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Acta Mathematica Sinica,English Series 1995年第1期11卷 74-80页

作者： Wang Yanming department of Mathematics zhongshan university {2.,510275 china harm.showa-u.ac.jp

In this paper,we generalize the Hall-Higman’s reduction theorem by dropping the restrictive hypothesis(丨G丨,丨H丨)=1 and determine the detailed structure of G.

关键词： Hall A Generalization of Hall-Higman’s Reduction Theorem

On a problem of Skiba from the Kourovka Notebook

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Science china Mathematics 2004年第1期47卷 96-103页

作者： WANG Yanming & WEI HuaquanLingnan College and School of Mathematics, zhongshan university, guangzhou 510275,{2. School of Mathematics, zhongshan university, guangzhou 510275,{2. department of Mathematics, Guangxi Teacher’s College, Nanning 530001,{2. 1. Lingnan College and School of Mathematics Zhongshan University 510275 Guangzhou China 2. School of Mathematics Zhongshan University 510275 Guangzhou China 3. department of Mathematics Guangxi Teacher’s College 530001 Nanning China

In this paper, we give a positive answer to a recent open problem of Skiba in Kourovka Notebook without using the odd order theorem and other deep theorems. Some of the techniques are improved.

关键词： supersolvable group c-supple merited subgroup complemented subgroup generalized fitting subgroup saturated formation