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An asymptotic result of super-Brownian motion on hyperbolic space

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Chinese Science Bulletin 1997年第15期42卷 1240-1244页

作者： TANG JiashanDepartment of mathematics, Beijing Normal university, Beijing 100875, china institute of mathematics, shantou university, shantou 515063, china Department of mathematics Beijing Normal University Beijing China institute of mathematics Shantou University Shantou China

SUPERPROCESS is one kind of measure-valued branching Markov processes. In the recentdecades many results of superprocesses on Euclidean spaces and on general abstract spaces havebeen obtained, but there is only little work on Riemannian manifold. In this note, wewill consider the super-Brownian motions on the hyperbolic space of dimension d and give anasymptotic result of this process (see Corollary 1 below). Iscoe investigated a similar prob-

关键词： hyperbolic space radial super-Brownian motion hitting probability asymptotic.

Central limit theorem for the occupation time of catalyticsuper-Brownian motion

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Chinese Science Bulletin 1998年第24期43卷 2035-2040页

作者： HONG Wenming Department of mathematics, Beijing Normal university, Beijing 100875, china Corresponding address: institute of mathematics, shantou university, shantou 515063, china Department of mathematics Beijing Normal University Beijing China

The catalytic super_Brownian motion has been considered. If both the catalytic medium process Q and CSBM started with Lebesgue measure λ, the central limit theorem for occupation time of CSBM has been obtained in dim... 详细信息

关键词： branching rate functional Brownian collision local time catalytic super_Brownian motion occupation time central limit theorem.

Joint density of hitting time and point to an ellipse for Brownian motion

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Chinese Science Bulletin 1997年第24期42卷 2054-2058页

作者： YIN Chuancun ZHAO Xuelei Department of mathematics, Qufu Normal university, Qufu 273165, china 2. institute of mathematics, shantou university, shantou 515063, china Department of mathematics Qufu Normal University Qufu 273165 China

IT is well known that the distribution of hitting time, hitting point, last exiting time, and lastexiting point for Brownian motion to balls has been extensively studied. A similar investi-gation of rectangles or cubes has also been well done. However, analogous questions for Brow-nian motion to ellipsoid are rarely concerned. Bai and Cai obtained the distribution of

关键词： Brownian motion hitting time hitting point ellipse.

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

The Eigen Functions of the Complex Projective Space

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Acta Mathematica Sinica,English Series 1998年第1期14卷 1-8页

作者： Lu Qikeng institute of mathematics, Academia Sinica, Beijing 100080, china institute of mathematics, shantou university, shantou 515063, china

In the complex n-dimensional projective space CP^n. let λ_p(=4p(p+n)) be the eigen vaiue of the Laplace-Beltrami operator and H_p be the space of all eigen functions of eigen value λ_p. The reproducing kernel h_p(z, w) of H_p is constructed explicitly in this paper. and a system of complete orthogohal functions of H_p is construncted from h_p(z, w)(p=1,2…).

关键词： Complex projective space Reproducing kernel of eigen function

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,shantou university,shantou 515063,china 2 School of Mathematical Sciences,Suzhou university,Suzhou 215006,china institute of mathematics Shantou University Shantou 515063 China School of Mathematical Sciences Suzhou University Suzhou 215006 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 54H20

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,shantou university,shantou 515063,china ~2 College of mathematics and Information Sciences,Guangxi university,Nanning 530004,china 1. institute of mathematics Shantou University Shantou 515063 China 2. College of mathematics and Information Sciences Guangxi University Nanning 530004 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

A LIMIT THEOREM FOR INTERACTING MEASURE-VALUED BRANCHING PROCESSES

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Acta Mathematica Scientia 1997年第3期17卷 241-249页

作者：赵学雷杨敏 shantou UNIV MATH INSTSHANTOU 515063PEOPLES R CHINA STATE INFORMAT CTR BEIJING 100045PEOPLES R CHINA

It is well known that Fleming-Viot superprocesses can be obtained from the Dawson-Watanabe superprocesses by conditioning the latter to have constant total mass. The same question is investigated for measure-valued branching processes with interacting intensity independent of the geographical position. It is showed that a sequence of conditioned probability laws of this kind of interacting measure-valued branching processes also approximates to the probability law of Fleming-Viot superprocesses.

关键词： interacting measure-valued Branching processes DW-superprocesses FV-superprocesses conditioned probability law

A GEOMETRIC FEATURE FOR FINITE ELEMENT SCHEMES

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Analysis in Theory and Applications 1994年第2期10卷 83-91页

作者： Zhan Yinwei Beijing Normal university, china Permanent address: Dr. Zhan Yinwei institute of mathematics shantou university, shantou 515063 Guangdong, china 1. Beijing Normal university China

In this note we characterize the geometric facture of a (μ, r, k) - FES. Namely, for a C~μ triangular in- terpolation schcme with C^r vertex data, any angle of the macrotriangle must be divided into at least (μ + 1... 详细信息

关键词： FES Math A GEOMETRIC FEATURE FOR FINITE ELEMENT SCHEMES IIC Wang