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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

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.{4. 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

Synthesis of superheavy nuclei with ^(238)U target

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Science china(physics,Mechanics & Astronomy) 2009年第10期52卷 1482-1488页

作者： LIU ZuHua1,3 & BAO JingDong2,4.1 Key Laboratory of Beam Technology and Material Modification of Ministry of Education,beijing normal university,beijing {4.china 2 department of physics,beijing normal university,beijing {4.china 3 china Institute of Atomic Energy,beijing 1024.3,china 4.Center of Theoretical Nuclear physics,National Laboratory of Heavy Ion Accelerator of Lanzhou,Lanzhou 730000,china Key Laboratory of Beam Technology and Material Modification of Ministry of Education Beijing Normal University Beijing 100875 China department of physics Beijing Normal University Beijing 100875 China china Institute of Atomic Energy Beijing 102413 China Center of Theoretical Nuclear physics National Laboratory of Heavy Ion Accelerator of Lanzhou Lanzhou 730000 China

The production of superheavy nuclei with Z=108-116 via hot fusion reactions of the neutron-rich projectiles with 238U target is systematically *** results show that the production cross sections of superheavy nuclei do not decrease monotonously as the atomic number Z *** cross sections of the superheavy nuclei at Z = 112 and 115 are enhanced as compared with the whole Z-trend in synthesis of the superheavy nuclei,which clearly illustrates that the reactions with large negative Q-value and shell correction are more favorable to synthesize superheavy nuclei.

关键词： superheavy nuclei fusion reaction cross section 238U target

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.

On the stability of diffusion processes with state-dependent switching

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Science china Mathematics 2006年第9期49卷 1258-1274页

作者： XI Fubao & ZHAO Liqin department of Mathematics, beijing Institute of Technology, beijing 100081, china School of Mathematical Sciences,{4., beijing 100875. china department of Mathematics Beijing Institute of Technology Beijing 100081 China School of Mathematical Sciences Beijing Normal University Beijing 100875 China

In this paper we consider the stability for diffusion processes with state-dependent switching. We first prove their Feller continuity by the coupling methods. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions. Finally, we append a very brief discussion about the regularity of these processes.

关键词： Feller continuity, coupling, strong Feller continuity, exponential ergodicity,state-dependent switching.

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,{4. 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.

Effect of Bcl-2 and caspase-3 on calcium distribution in apoptosis of HL-60 cells

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Cell Research 2000年第3期10卷 213-220页

作者： ZHANG MIN, HONG QING ZHANG, SHAO BAI XUE (department of Biology, beijing normal university, beijing 100875. china) departmentofBiology BeijingNormalUniversityChina.

Apoptosis manifests in two major execution programs downstream of the death signal: the caspase pathway and organelle dysfunction. An important antiapoptosis factor, Bcl-2 protein, contributes in caspase pathway of apoptosis. Calcium, an important intracellular signal element in cells, is also observed to have changes during apoptosis, which maybe affected by Bcl-2 protein. We have previously reported that in Harringtonine (HT) induced apoptosis of HL-60 cells, there’s a change of intracellular calcium distribution, moving from cytoplast especially Golgi’s apparatus to nucleus and accumulating there with the highest concentration. We report here that caspase-3 becomes activated in HT-induced apoptosis of HL-60 cells, which can be inhibited by overexpression of Bcl-2 protein. No sign of apoptosis or intracellular calcium movement from Golgi’s apparatus to nucleus in HL-60 cells overexpressing Bcl-2 or treated with Ac-DEVD-CHO, a specific inhibitor of caspase-3. The results indicate that activated caspase-3 can promote the movement of intracellular calcium from Golgi’s apparatus to nucleus, and the process is inhibited by Ac-DEVD-CHO (inhibitor of caspase-3), and that Bcl-2 can inhibit the movement and accumulation of intracellular calcium in nucleus through its inhibition on caspase3. Calcium relocalization in apoptosis seems to be irreversible, which is different from the intracellular calcium changes caused by growth factor.

关键词： Apoptosis calcium caspase-3 bcl-2 laser scanning confocal microscopy (LSCM).

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.

The Besov Space B_1^(0.1) on Domains

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Acta Mathematica Sinica,English Series 2001年第2期17卷 181-196页

作者： Yi Qing GUI Shan Zhen LU Da Chun YANG department of Mathematics. beijing normal university. beijing 100875. P. R. {4. department of Mathematics Beijing Normal University Beijing 100875 P. R. China

Let Ω be a bounded Lipschitz domain. Define B1,r0.1（Ω）={f∈L1（Ω）: there is an F∈ B10.1（Rn） such that F|Ω=f| and B1,z0.1（Ω）={f∈B10.1（Rn）: f=0 on Rn\}. In this paper, the authors establish the atomic decompositions of these spaces. As by-products, the authors obtained the regularity on these spaces of the solutions to the Dirichlet problem and the Neumann problem of the Laplace equation on R+n.

关键词： Besov space Lipschitz domain Atom Laplace equation