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Vaught's Conjecture on Unitary Relations

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Acta Mathematica Sinica,English Series 1998年第2期14卷 277-284页

作者： Luo Libo (department of mathematics,beijing normal university,beijing 100875,china) department of mathematics Bejing Normal University

We confirm the Vaught’s conjecture and obtain a complete classification for the theories of unitary relations.

关键词： Vaught’s conjecture Unitary relation

SINGLE BIRTH PROCESSES

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Chinese Annals of mathematics,Series B 1999年第1期20卷 77-82页

作者： CHEN MUFA(department of mathematics,beijing normal university,beijing 100875,china) beijing normal Univ Dept Math Beijing 100875 Peoples R China

The single birth process is a Markov chain, either time-continuous or time-discrete, valuedin the non-negative integers: the system jumps with positive rate from k to k + 1 but not tok +j for all j 2 (this explains the meaning of 'single birth') . However, there is no restrictionfor the jumps from k to k - j(1 j< k). This note mainly deals with the uniqueness problemfor the time-continuous processes with an extension: the jumps from k to k + 1 may also beforbidden for at most finite number of k. In both cases (time-continuous or -discrete), thehitting probability and the first moment of the hitting time are also studied

关键词： Markov chains Single birth process Uniqueness criterion

Recovery of functions via their irregular sampling values

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Chinese Science Bulletin 1998年第4期43卷 268-271页

作者： FANG Gensun department of mathematics, beijing normal university, beijing 100875, china department of mathematics Lkijing Normal University Beijing China

It is proved that if a function can be completely reconstructed by tempered splines which satisfy the real Kiesz basis condition as the degree of spline goes to infinity, then the function is band limited.

关键词： band limited function cardinal splines irregular sampling.

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Saturated models

Chinese Science Bulletin 1998年第7期43卷 562-564页

作者： CHEN Guolong department of mathematics, beijing normal university, beijing 100875, china department of mathematics Beijing Normal University Beijing China

An equivalent description of saturated models is given, and some properties of countable saturated models, almost saturated models and full models are discussed. New proofs of two important theorems of the related doc... 详细信息

关键词： almost saturated model full model power type.

Strongly Singular Convo1ution Operators on the Weighted Herz-Type Hardy Spaces

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Acta Mathematica Sinica,English Series 1998年第1期14卷 67-76页

作者： Li Xiaochun Lu Shanzhen department of mathematics, beijing normal university, beijing 100875, china department of mathematics Beijing Normal University

Let 01, w2 ∈A1 （Muckenhoupt-class）. In this paper the authors prove that the strongly singular convolution operators are bounded from the homogeneous weighted Herz-type Hardy spaces HKqα,p（w1; w2） to the homogeneous weighted Herz spaces Kqα,p（w1;w2）, provided α=n（1--1/q）. Moreover, the boundedness of these operators on the non-homogeneous weighted Herz-type Hardy spaces HKqα,p（w1, w2） is also investigated.

关键词： Strongly singular convolution operator Hardy space

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.

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.

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.