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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,{2., 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.

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,{2., 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.

Functional central limit theorem for super α-stable processes

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Science China mathematics 2004年第6期47卷 874-881页

作者： HONG Wenmingdepartment of mathematics, beijing normal university,{2., China department of mathematics Beijing Normal University Beijing China

A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α 2. (0 2., the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2. and higher dimensions d 2., the limiting process is Brownian motion.

关键词： super α-stable processes occupation time central limit theorem evolution equation

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,{2., China.) 北京师范大学北京 100875

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.

The Principal Eigenvalue for Jump Processes

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Acta Mathematica Sinica,English Series 2000年第3期16卷 361-368页

作者： Mufa Chen department of mathematics,beijing {2. university,beijing 100875,P.R.China department of mathematics Beijing Normal University Beijing 100875 P. R. China

A variational formula for the lower bound of the principal eigenvalue of general Markov jump processes is *** result is complete in the sense that the condition is fulfilled and the resulting bound is sharp for Markov... 详细信息

关键词： Principal eigenvalue Jump processes Variational formula for Dirichlet form

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,{2., China 2. Institute of Applied Physics and Computational mathematics, beijing 100080, China department of mathematics Beijing Normal University Beijing China Institute of Applied Physics and Computational mathematics Beijing 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.

On asymptotics of t-type regression estimation in multiple linear model

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Science China mathematics 2004年第4期47卷 628-639页

作者： GUI Hengjiandepartment of mathematics, beijing normal university,{2., China department of mathematics Beijing Normal University Beijing China

We consider a robust estimator (t-type regression estimator) of multiple linear regression model by maximizing marginal likelihood of a scaled t-type error *** marginal likelihood can also be applied to the de-correlated response when the withinsubject correlation can be consistently estimated from an initial estimate of the model based on the independent working assumption. This paper shows that such a t-type estimator is consistent.

关键词： t-type regression estimator, M-estimator, one-step estimate, consistency, asymptotic normality.

THE HAUSDORFF MEASURE FOR THE SAMPLE PATH OF THE WESTWATER PROCESS

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Chinese Annals of mathematics,Series B 1996年第3期17卷 375-388页

作者： ZHOU XIANYIN(Depatment of mathematics, beijing normal university{2., China) department of mathematics Beijing Normal University Beijing 100875 China

It is proved that φ(s) = s2.log |logs| is the correct function to give the Hausdorff measureof a sample path of the Westwater process.

关键词： Hausdorff measure Wiener process Westwater process Sojourn time

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,{2., China department of mathematics Beijing Normal University Beijing 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 34C2. 58F14