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Reaction-diffusion processes

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Chinese Science Bulletin 1998年第17期43卷 1409-1420页

作者： CHEN Mufa beijing normal university beijing 100875, china beijing normal university Beijing China

The main progress made in the past dozen years or more in the study of reaction-diffusion (abbrev. RD) processes is surveyed. The processes are motivated from some typical models in the modern non-equilibrium statistical physics and consist of an important class of interacting particle systems which is currently an active research field in probability and mathematical physics. The models are concrete but as a part of the infinite-dimensional mathematics, the topic is quite hard. It is explained how new problems arise, and how some new ideas and new mathematical tools are introduced. Surprisingly, the mathematical tools produced from the study on the simple models then turn to have a lot of powerful applications not only in probability theory but also in other branches of mathematics. Nevertheless, the story is still far from finished, and some important open problems are proposed for further study.

关键词： Reaction-diffusion process ergodicity phase transitions coupling.

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

Progress in the study of molecular organized assemblies by dielectric relaxation spectroscopy

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Progress in Natural Science:Materials International 2006年第3期16卷 221-230页

作者： ZHAO Kongshuang, HE Kejuan and WEI Suxiang (department of Chemistry, beijing normal university, beijing 100875, china department of Chemistry, South china normal university, Guangzhou 510631, china) [a]department of Chemistry Beijing Normal University Beijing China [b]department of Chemistry South China Normal University Guangzhou China

Because dielectric spectroscopy covers a great many problems in physical and chemical systems occurring in an extremely wide frequency range, the study of this method plays an important role in physical chemistry. As an effective tool to detect inner properties of substance systems, the dielectric spectroscopy method is widely used in chemical systems and has been dramatically developed in recent decade. This review paper describes the applications of the dielectric spectroscopy in the chemical field, and main concentrations are focused on the micelle, microemulsion and other so-called molecular organized assemblies. Some dielectric principles and models proposed for these systems are introduced. In addition, recent technical developments in dielectric spectroscopy and developing trend of this method in other chemical systems are reviewed.

关键词： dielectric relaxation micelle microemulsion vesicle relaxation time.

Optimal Markovian Couplings and Applications

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Acta Mathematica Sinica,English Series 1994年第3期10卷 260-275页

作者： Chen Mufa department of Mathematics beijing normal university beijing,100875 china 1. department of Mathematics Beijing Normal University 100875 Beijing China

This paper is devoted to studying a new topic:optimal Markovian couplings,mainly for time-continuous Markov *** study emphasizes the analysis of the coupling opera- tors rather than the *** constructions of optimal Markovian couplings for Markov chains and diffusions are presented,which are often ***,the results are applied to study the L^2-convergence for Markov chains and for a diffusion on compact *** estimate of the convergent rate provided by this method can be sharp.

关键词： Chen Optimal Markovian Couplings and Applications OMC

Boundedness of Multilinear Operators in Herz-type Hardy Space

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Acta Mathematica Sinica,English Series 2000年第2期16卷 295-306页

作者： Lin Tang Dachun Yang department of Mathematics,beijing normal university,beijing 100875,P.R.china department of Mathematics Beijing Normal University Beijing 100875 P. R. China

Let k ∈ *** prove that the lnultilinear operators of finite sums of products of singular integrals on Rn are bounded from H Kqlαl·pl（Rn）×…×HKqkαk,pk（Rn）into HKqα,p（Rn）if they have vanishing moments up to a certain order dictated by the target *** conditions on vanishing moments satisfied by the multilinear operators are also necessary when αj（?）0 and the singular integrals considered here include the Calderón-Zygmund singular integrals and the fractional integrals of any orders.

关键词： Multilinear operator Calderón-Zygmund operator Fractional integral Multiplier Herz space Hardy space Atom

Estimate of Exponential Convergence Rate in Total Variation by Spectral Gap

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Acta Mathematica Sinica,English Series 1998年第1期14卷 9-16页

作者： Chen Mufa department of Mathematics, beijing normal university, beijing 100875, china 北京师范大学数学系北京

This note is devoted to study the exponential convergence rate in the total variation for reversible Markov processes by comparing it with the spectral gap. It is proved that in a quite general setup, with a suitable restriction on the initial distributions, the rate is bounded from below by the spectral gap. Furthemore, in the compact case or for birth-death processes or half-line diffosions, the rate is shown to be equal to the spectral gap.

关键词： Total variation Spectral gap Markov processes

Implementation of a multiple round quantum dense coding using nuclear magnetic resonance

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Science china(Physics,Mechanics & astronomy) 2005年第6期48卷 706-715页

作者： ZHANG Jingfu1, XIE Jingyi2, WANG Chuan1, DENG Zhiwei3, LU Zhiheng4, & LONG Guilu1,5 1. Key Laboratory For Quantum Information and Measurements of MOE, department of Physics, Tsinghua university, beijing 100084,china 2. department of Materials Science and Engineering, beijing normal university, beijing 100875, china 3. Testing and Analytical Center, beijing normal university, beijing 100875,china 4. department of Physics, beijing normal university, beijing 100875, china 5. Key Laboratory For atomic and Molecular Nanosciences, Tsinghua university, beijing 100084,china 1. Key Laboratory For Quantum Information and Measurements of MOE Department of Physics Tsinghua University 100084 Beijing China 2. department of Materials science and Engineering Beijing Normal University 100875 Beijing China 3. Testing and Analytical Center Beijing Normal University 100875 Beijing China 4. department of Physics Beijing Normal University 100875 Beijing China 5. Key Laboratory For Atomic and Molecular Nanosciences Tsinghua University 100084 Beijing China

A multiple round quantum dense coding scheme based on the quantum phase estimation algorithm is proposed and implemented in a three qubit nuclear magnetic resonance (NMR) quantum computer. Using an m + 1 qubit system, Bob can transmit one of 2m+1 messages to Alice, through manipulating only one qubit and exchanging it between Alice and Bob for m rounds. The information capacity is enhanced to m + 1 bits as compared to m bits in a classical scheme. The scheme has been demonstrated in NMR system, and the experimental results show a good agreement between theory and experiment.

关键词： quantum dense coding, multiple round, nuclear magnetic resorance

Estimation of Spectral Gap for Markov Chains

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Acta Mathematica Sinica,English Series 1996年第4期12卷 337-360页

作者： Chen Mufa department of Mathematics beijing normal university beijing, 100875 china department of Mathematics Beijing Normal University Beijing China

The study of the convergent rate (spectra gap) in the L^2-sense is motivated from several different fields: probability statistics, mathematical physics, computer science and so on and it is now an artive research topic. Based on a new approach (the coupling technique) introduced in [7] for the estimate of the convergent rate and as a continuation of [4],[5],[7-9],[23] and [24], this paper studies the estimate of the rate for time-continuous Markov chains. Two variational formulas for the rate are presented here for the first time for birth-death processes. For diffusions, similar results are presented in an accompany paper [10]. The new formulas enable us to recover or improve the main known results. The connection between the sharp estimate and the corresponding eigenfunction is explored and illustrated by various examples. A previous result on optimal Markovian couplings is also extended in the paper.

关键词： Markov chains Spectral gap Couplings

Constraints of f(R) gravity in Palatini approach with observational Hubble data

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Science china(Physics,Mechanics & astronomy) 2011年第8期54卷 1378-1383页

作者： ZHAI ZhongXu & LIU WenBiao department of Physics, Institute of Theoretical Physics, beijing normal university, beijing 100875, china 1. department of Physics Institute of Theoretical Physics Beijing Normal University Beijing 100875 China

We use the newly released observational H(z) data (OHD), the Cosmic Microwave Background (CMB) shift parameter, and the Baryon Acoustic Oscillation (BAO) measurements data to constrain cosmological parameters of f(R) gravity in Palatini formalism in which the f(R) form is defined as f(R) = R β/Rn. Under the assumption of a spatially flat FRW universe, we get the best fitting results of the free parameters (Ωm0, n). In the calculation, we marginalize the likelihood function over H0 by integrating the probability density P ∝ e-χ2/2 to obtain the best fitting results and the confidence regions in the Ωm0-n plane. The constraints results of (Ωm0, n) = (0.33, 0.41) by OHD only and (Ωm0, n) = (0.23, 0.08) by the combination of OHD+CMB+BAO both indicate that the universe goes through three last phases, i.e., radiation dominated, matter-dominated, and late time accelerated expansion without introduction of dark energy.

关键词： f(R) gravity OHD CMB BAO accelerating expansion dark energy