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ON THE RANGE OF RANDOM WALKS IN RANDOM ENVIRONMENT　

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Chinese Annals of mathematics,Series B 1995年第1期16卷 131-138页

作者： ZHOU XIANYIN(department of mathematics, beijing normal university, beijing 100875, china.) beijing normal UNIV DEPT MATHBEIJING 100875PEOPLES R CHINA

The range of random walk on Z￣d in symmetric random environment is investigated. As results, it is proved that the strong law of large numbers for the range of random walk on Zdin some random environments holds if d... 详细信息

关键词： Law of large numbers Ergodic theorem Range of random walk Random environment Effective resistance.

Eigenvalues, inequalities and ergodic theory

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Chinese Science Bulletin 2000年第9期45卷 769-774页

作者： chen mufadepartment of mathematics, beijing normal university, beijing 100875, china department of mathematics Beijing Normal University Beijing China

This paper surveys the main results obtained during the period 1992-1999 on three aspects mentioned in the title. The first result is a new and general variational formula for the lower bound of spectral gap (i.e. the first non-trivial eigenvalue) of elliptic operators in Euclidean space, Laplacian on Riemannian manifolds or Markov chains (?). Here, a probabilistic method -coupling method is adopted. The new formula is a dual of the classical variational formula. The last formula is actually equivalent to Poincare inequality. To which, there are closely related logarithmic Sobolev inequality, Nash inequality, Liggett inequality and so on. These inequalities are treated in a unified way by using Cheeger’s method which comes from Riemannian geometry. This consists of ?2. The results on these two aspects are mainly completed by the author joint with F. Y. Wang. Furthermore, a diagram of the inequalities and the traditional three types of ergodicity is presented (?3). The diagram extends the ergodic

关键词： eigenvalue inequality ergodic theory Markov process.

Coupling, spectral gap and related topics (Ⅱ)

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Chinese Science Bulletin 1997年第18期42卷 1409-1416页

作者： chen Muf adepartment of mathematics, beijing normal university, beijing 100875, china department of mathematics Beijing Normal University Beijing 100875 China

THIS is the second one of a series of three reviews. The ideas introduced in the last review are used to study the estimate of spectral gap and four classes of typical eigenvalue problems on manifolds. The comparison ... 详细信息

关键词： diffusions manifold Markov chains spectral gap couplings.

Quasi-critical ring of a primitive ring with nonzero socle

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Chinese Science Bulletin 1997年第3期42卷 189-192页

作者： JIANG Zimeidepartment of mathematics, beijing normal university, beijing 100875, china department of mathematics Beijing Normal University Beijing China

IN ref. [1] Jacobson proved the structure theorem for primitive rings with nonzero socles that R is a primitive ring withsocle S≠{0} if and only if there is a pair of dual vector spaces (M,M’) over a division ring Δ such that S=F(M, M’)(?) R(?)(?)(M, M’), where (?)(M, M’)-{ω∈Ω|ωM’(?)M’, Ω is the complete ring of linear transformations of M over Δ}, F(M, M’) is the set of all linear transformations of (?)(M, M’) of finite rank. After that, some people reproved this theorem by using different methods such as those in refs. [2, 3]. In

关键词： primitive ring socle conjugate space total subspace of conjugate space.

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

Linear estimation and distribution of the limit cycles bifurcated from a kind of degenerate polycycles

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Science china mathematics 2007年第3期50卷 334-344页

作者： Li-qin ZHAO department of mathematics, beijing normal university, beijing 100875, china department of mathematics Beijing Normal University Beijing 100875 China

In this paper, we investigate the number and the distribution of the limit cycles bifurcated from a kind of degenerate planar polycycles through three singular points: a saddle-node P 0, a fine saddle P 1 with finite order m ∈ N, a contractive (attracting) saddle P 2 with the hyperbolicity ratio q 2(0) ? Q. The connection between P 0 and P 1 is of hh-type and the connection between P 0 and P 2 is of hp-type. It is assumed that the connections between P 0 to P 2 and P 0 to P 1 keep unbroken. We obtain that the cyclicity of this polycycle is not more than 3m + 1, which is linearly dependent on the order of the resonant saddle P 1. We also show that the cyclicity is not more than m + 3 if q 2(0) > m, and that the nearer q 2(0) is close to 1, the more the limit cycles are bifurcated.

关键词： degenerate polycycle cyclicity finitely-smooth normal form transition map 34C05 34C23 58F14

The Goldbach 3-primes property for polynomial rings over certain infinite fields

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Chinese Science Bulletin 1998年第15期43卷 1256-1260页

作者： WANG Shiqiang department of mathematics, beijing normal university, beijing 100875, china department of mathematics Beijing Normal University Beijing China

On the basis of Effinger and Hayes’ theorem about the Goldbach 3_primes property of polynomial rings F over finite fields F , by model_theoretic method it is proved that for each characteristic k (including 0), there... 详细信息

关键词： model theory polynomial 3 primes property.

Sufficient and Necessary Conditions for Stochastic Comparability of Jump Processes

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Acta Mathematica Sinica,English Series 2000年第1期16卷 99-102页

作者： Yuhui Zhang department of mathematics,beijing normal university,beijing 100875,P.R.china department of mathematics Beijing Normal University Beijing 100875 P.R. China

This note is devoted to the study of the stochastic comparability of jump *** the basis of[2]and[3],it is proved that two jump processes are stochastically comparable if and only if their q-pairs are ***,the result co... 详细信息

关键词： Stochastically comparable Totally stable Conservative Uniqueness

Multi-parameter infinite-dimensional(r,δ)-OU process

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Chinese Science Bulletin 1999年第5期44卷 418-423页

作者： WANG ZikunInstitute of mathematics, Shantou university, Shantou 515063, china department of mathematics, beijing normal university, beijing 100875, china Institute of mathematics Shantou University Shantou China department of mathematics Beijing Normal University Beijing China

The definition of n-parameter infinite-dimensional (r, δ) -Ornstein-Uhlenbeck process {X_t (·)}((r,δ)-OUP_n~∞ for short) is given. The absolute continuity of distribution μ_t of X_t(·) and the limit of X_t(·) w... 详细信息

关键词： multi-parameter (r δ)-OUPn∞ absolute continuity in hierarchy.