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Superprocesses arising from interactive stochastic flows

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Science china mathematics 2006年第4期49卷 451-476页

作者： YAN Guojun & LI Zhanbing Medical School, Shantou university, Shantou 515063, china Department of mathematics, Bejing normal university, beijing 100875, china Medical School Shantou University Shantou 515063 China Department of mathematics Bejing Normal University Beijing 100875 China

In this paper, we give a unified construction for superprocesses with dependent spatial motion constructed by Dawson, Li, Wang and superprocesses of stochastic flows constructed by Ma and Xiang. Furthermore, we also g... 详细信息

关键词： superprocess, interactive stochastic flows, martingale problem, dual processes.

Commutators of pseudo-differential operators

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Science china mathematics 2008年第3期51卷 453-460页

作者： LIN Yan School of Mathematical Sciences, beijing normal university, beijing 100875, china 1. School of Mathematical Sciences Beijing Normal University Beijing 100875 China

In this paper, the boundedness of commutators generated by pseudo-differential operators and BMO functions is discussed on Lebesgue spaces.

关键词： pseudo-differential operator BMO function commutator Lebesgue space 42B20 35S05 47G30

Moderate deviations for the quenched mean of the super-Brownian motion with random immigration

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Science china mathematics 2008年第3期51卷 343-350页

作者： HONG WenMing School of Mathematical Sciences, Laboratory of mathematics and Complex Systems, Ministry of Education,beijing normal university, beijing 100875, china School of Mathematical Sciences Laboratory of Mathematics Complex Systems Ministry of Education Beijing Normal University Beijing 100875 China

Moderate deviations for the quenched mean of the super-Brownian motion with random immigration are proved for 3≤d≤6, which fills in the gap between central limit theorem(CLT)and large deviation principle(LDP).

关键词： super-Brownian motion large deviation moderate deviation random immigration Primary 60J80 Secondary 60F05

Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science china Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2 1. Department of mathematics, beijing normal university, beijing 100875, china 2. Institute of Applied Physics and Computational mathematics, beijing 100080, china 1. Department of mathematics Beijing Normal University Beijing 100875 China 2. Institute of Applied Physics and Computational mathematics Beijing 100080 China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

Ergodicity of Reversible Reaction Diffusion Processes with General Reaction Rates

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Acta Mathematica Sinica,English Series 1994年第1期10卷 99-112页

作者： Chen Mufa Ding Wanding Zhu Dongjin Department of mathematics beijing normal university beijing,100875 china Department of mathematics Animi normal university Wuhu,241000 china 1. Department of mathematics Beijing Normal University 100875 Beijing China 2. Department of mathematics Anhui Normal University 241000 Wuhu China

In this paper,a class of reaction diffusion processes with general reaction rates is studied.A necessary and sufficient condition for the reversibility of this calss of reaction diffusion processes is given,and then t... 详细信息

关键词： Ergodicity of Reversible Reaction Diffusion Processes with General Reaction Rates

The Theory of Relativity on the Finsler Spacetime

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Journal of Systems Engineering and Electronics 1995年第4期6卷 239-252页

作者： Cao ShengLin (Department of Astronomy, beijing normal university, beijing 100875, china) Department of Astronomy Beijing Normal University Beijing 100875 China

According to some local properties of Lorentz transformation, Einstein stated: 'Vetheitiss greater than that of light have no possibility of existence.' He neglected to point out the applicable range of the special theory of relativity. In fact, it could only be applied to the subluminal-speeds. This paper shows that if ones think of the possibility of the existence of the superluminal-speeds and redescribe the special theory of relativity following Einstein's way, it could be supposed that the physical spacetime is a Finsler spacetime, characterized by the metric ds4=gijkldxidxidxkdxl. If so, a new spactime transformation could be found by invariant ds4 and the theory of relativity is discussed on this transformation it is possible that the Finsler spacetime F(x,y) may be endowed with a catastrophic nature. Based on the different properties between the ds2 and ds4, it is discussed that the flat spacetime will also have the catastrophic nature on the Finsler metric ds4. The spacetime transformations and the Physical quantities will suddenly change at the catastrophe set of the spacetime, the light cone. It will be supposed that only the dual velocity of the superluminal-speeds could be observed. If so, a particle with the superluminal-speed v> c could be regarded as its anti-particle with the dual velocity v1=c2/ v< c. On the other hand, it could be assumed that the horizon of the field of the general relativity is also a catastrophic set. If so, a particle with the superluminal-speeds could be projected near the horizon of these fields, and the particle will move on the sauce-like curves. It is very interesting that, in the Schwarzschild fields, the theoretical calculation for the sauce-like curves should be in agreement with tie data of the superluminal expansion of extragalactic radio sources observed year after year. (see Gao, 1992b).The ca- tastrophe of spacetime has some deep cosmological means. According to the some interested subjects in the Process of

关键词： Theory of relativity Finsler spacetime Superluminal-speed Subluminal-speed Catastrophe theory Superluminal expansion Extragalactic radio sources Cosmology

Convergence rates for reversible Markov chains without the assumption of nonnegative definite matrices

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Science china mathematics 2010年第8期53卷 1979-1988页

作者： MAO Yong-Hua School of Mathematical Sciences,beijing normal university,Laboratory of mathematics and Complex Systems,Ministry of Education,beijing 100875,china 1. School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875 China

Explicit convergence rates in geometric and strong ergodicity for denumerable discrete time Markov chains with general reversible transition matrices are obtained in terms of the geometric moments or uniform moments of the hitting times to a fixed *** way by Lyapunov's drift conditions is also used to derive these convergence *** a typical example,the discrete time birth-death process(random walk) is studied and the explicit criteria for geometric ergodicity are presented.

关键词： Markov chain spectral theory convergence rate geometric ergodicity strong ergodicity Lyapunov’s condition

ASYMPTOTIC normalITY OF M-ESTIMATES IN THE EV MODEL

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Systems Science and Mathematical Sciences 1997年第3期10卷 225-236页

作者： CUI Hengjian(Department of mathematics, beijing normal university, beijing 100875, china) 北京师范大学数学系北京

The M-estimate of parameters in the errors-in-variables (EV) model Y =xτβ0+∈,X =x+u ((∈,uτ)τ is a (p+1)-dimensional spherical error, Coy[(∈, uτ)τ] =σ2Ip+1)being considered. The M-estimate βn,, of β0 under a general ρ(·) function and the estimateof σ2 are given, the strong consistency and asymptotic normality of βn as well as are obtained. The conditions for the ρ(·) function in this paper are similar to that of linearexpression of M-estimates in the linear regression model.

关键词： EV model M-estimate strong consistency asymptotic normality

△-tame quasi-hereditary algebras

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Science china mathematics 2007年第2期50卷 240-252页

作者： Yun-ge XU & Ying-bo ZHANG Faculty of mathematics and Computer Science, Hubei university, Wuhan 430062, china School of mathematics Sciences, beijing normal university, beijing 100875, china Faculty of mathematics and Computer Science Hubei University Wuhan China School of mathematics Sciences Beijing Normal University Beijing China

Let (K, M,H) be an upper triangular bimodule problem. Briistle and Hille showed that the opposite algebra A of the endomorphism algebra of a projective generator P of the matrices category of (K., M, H) is quasi-hereditary, and there is an equivalence between the category of△-good modules of A and Mat(K, M). In this note, based on the tame theorem for bimodule problems, we show that if the algebra A associated with an upper triangular bimodule problem is of△-tame representation type, then the category F(△) has the homogeneous property, i.e. almost all modules in F(△) are isomorphic to their Auslander-Reiten translations. Moreover, if (K, M,H)is an upper triangular bipartite bimodule problem, then A is of△-tame representation type if and only if F(△) is homogeneous.

关键词： bimodule problem quasi-hereditary algebra △-tameness homogeneity.