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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 shantou 515063,{2..) 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

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 2.3165, china 2. {2., shantou University, shantou 515063, china Department of mathematics Qufu Normal University Qufu China institute of mathematics Shantou University Shantou 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.

OCCUPATION TIME PROCESSES OF FLEMING-VIOT PROCESSES

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Chinese Annals of mathematics,Series B 1995年第1期16卷 51-62页

作者： XUELEI (institute of mathematics, shantou University,{2., Guangdong, china.) 汕头大学数学所广东汕头 515063

Suppose that Xt is the Fleming-Viot process associated with fractional power Laplacian operator -(-△)α/2.0 < α≥ 2. and Yt= f_0￣t *** is the so-called occupation time *** this paper) the asymptotic behavior at a ... 详细信息

Suppose that Xt is the Fleming-Viot process associated with fractional power Laplacian operator -(-△)α/2.0 2. and Yt= f_0￣t *** is the so-called occupation time *** this paper) the asymptotic behavior at a large time and the absolute continuity of Yt are investigated.

关键词： Fleming-Viot superprocesss Occupation time process Asymptotic behavior Absolute continuity.

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., 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

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,{2. 2. Department of mathematics, 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.

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

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 {2., 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.

Continuous maps with the whole space being a scrambled set

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Chinese Science Bulletin 1997年第19期42卷 1603-1606页

作者： MAI Jiehuainstitute of mathematics, shantou University,{2., china institute of mathematics Shantou University Shantou China

1 A problem or scrambled setCHAOTIC behavior is a manifestation of complexity of nonlinear dynamical systems. Since theobjects, methods, aims, or emphases of study are distinct, there are some variant definitionsof chaos given by different authors, or given by the same author in his different works. Thefollowing definition mainly stems from Li and Yorke.

关键词： scrambled set expansive map analytic homeomorphism.

Smale horseshoe maps by 5-adic fractions

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Chinese Science Bulletin 1997年第10期42卷 799-803页

作者： MAI Jiehuainstitute of mathematics, shantou University,{2., china institute of mathematics Shantou University Shantou China

SMALE established a famous horseshoe model,which shows that there exists a phe-nomenon of chaos in some self-homeomorphisms of discs on the plane although these homeo-morphisms are not very complex.A main conclusion o... 详细信息

关键词： Smale horseshoe symbolic space shift map S-adic fraction topological coqjugacy.