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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.

Nash Inequalities for Markov Processes in Dimension One

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Acta Mathematica Sinica,English Series 2002年第1期18卷 147-156页

作者： MAO Yong Hua department of Mathematics. beijing normal university. beijing 100875. P. R. {4. department of Mathematics Beijing Normal University Beijing P. R. China

In this paper. we give characterizations of Nash inequalities for birth-death process and diffusion process on the line. As a by-product. we prove that for these processes. transience implies that the semigroups P(t) ... 详细信息

关键词： Nash inequalities Hardy type inequality Birth-death process Diffusion

ENERGY FLOWS IN COMPLEX ECOLOGICAL SYSTEMS:A REVIEW

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Journal of Systems Science & Complexity 2009年第3期22卷 345-359页

作者： Jiang ZHANG department of Systems Science,School of Management,beijing normal university,beijing 100875.china. department of Systems Science School of Management Beijing Normal University Beijing 100875 China

Energy flow drives the complex systems to *** allometric scaling as the universalenergy flow pattern has been found in different scales of ecological *** reflects the generalpower law relationship between flow and *** underlying mechanisms of energy flow patterns areexplained as the branching transportation networks which can be regarded as the result of systematicoptimization of a biological target under *** flows in the ecological system may bemodelled by the food web model and population dynamics on the *** paper reviews thelatest progress on the energy flow patterns,explanatory models for the allometric scaling and modellingapproach of flow and network evolution dynamics in ***,the possibility of generalizingthese flow patterns,modelling approaches to other complex systems is discussed.

关键词： Allometric scaling energy flow flows in complex systems food web.

Variational Formulas of Poincare-Type Inequalities in Banach Spaces of Functions on the Line

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Acta Mathematica Sinica,English Series 2002年第3期18卷 417-436页

作者： Mu Fa CHEN department of Mathematics. beijing normal. university. beijing 100875. P. R. china department of Mathematics Beijing Normal University Beijing P. R. China

Motivated from the study on logarithmic Sobolev. Nash and other functional inequalities, the variational formulas for Poincare inequalities are extended to a large class of Banach (Orlicz) spaces of functions on the line. Explicit criteria for the inequalities to hold and explicit estimates for the optimal constants in the inequalities are presented. As a typical application, the logarithmic Sobolev constant is carefully examined.

关键词： Variational formula Poincare inequality Logarithmic Sobolev inequality Orliez 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.

Challenges in the theoretical investigations of lipid membrane configurations

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Chinese physics B 2013年第2期22卷 36-44页

作者：涂展春 department of physics Beijing Normal University Kavli Institute for Theoretical physics china Chinese Academy of Sciences

We report some key results in the theoretical investigations of configurations of lipid membranes and present several challenges in this field,which involve（i）the exact solutions to the shape equation of lipid vesicles,（ii）the exact solutions to the governing equations of open lipid membranes,（iii）the neck condition of two-phase vesicles in the budding state,（iv） the nonlocal theory of membrane elasticity,and（v）the relationship between the symmetry and the magnitude of the free energy.

关键词： configuration lipid membrane

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, beijing 100875. china 1. department of Mathematics Beijing Normal University 100875 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 < d < 2α (0 < α ≤ 2), the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2α and higher dimensions d < 2α, the limiting process is Brownian motion.

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

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 normal 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

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, beijing 100875. china 1. department of Mathematics Beijing Normal University 100875 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.