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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 {2., 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],[2.] and [2.], 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

Boundedness of solutions and existence of invariant tori for generalized pendulum type equation

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Chinese Science Bulletin 1997年第20期42卷 1673-1675页

作者： HUANG Hai and YUAN Rong1. Institute of Mathematics, Chinese Academy of Sciences, beijing 100080, china 2. {2. of Mathematics, beijing normal university, beijing 100875, china Institute of Mathematics Chinese Academy of Sciences Beijing China department of Mathematics Beijing Normal University Beijing China

MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2. and references cited therein ) have recently studied the existence of periodicsolutions and other properties for the following differential equation:

关键词： boundeduess of solutions invariant tori quasiperlodic solutions Moser’s small twist theorem.

Bell States and Two-Qubit Logic Gate with Superconducting Charge Qubits Coupling to a Nanomechanical Resonator

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Communications in Theoretical physics 2007年第12期48卷 999-1002页

作者： LIAO Jie-Qiao~1 and WANG Xin-Wen~(2.3)~1 department of physics,Hunan {2. university,Changsha 410081,china~2.department of physics,beijing {2. university,beijing 100875,china~3 department of Electronic Engineering and physics,Hunan university of Science and Engineering,Yongzhou 42.100,china department of physics Hunan Normal University Changsha 410081 China department of physics Beijing Normal University Beijing 100875 China department of Electronic Engineering and physics Hunan University of Science and Engineering Yongzhou 425100 China

We propose a scheme for generating Bell states involving two SQUID-based charge qubits by coupling themto a nanomechanical *** also show that it is possible to implement a two-qubit logic gate between the twocharge qu... 详细信息

关键词： Bell states superconducting charge qubit two-qubit logic gate nanomechanical resonator

Effects of enhancing p2.^(waf1) on proliferation and expression of G1 cyclins and CDKs in human breast cancer cells

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Chinese Science Bulletin 1999年第16期44卷 1489-1493页

作者： SANG Jianli, WANG Yongchao and YE Yingjiang1. Laboratory of Cell Biology , department of Biology , beijing normal university ,{2. , china 2. The Second Hospital, beijing Medical university, beijing 100044, china Laboratory of Cell Biology Department of Biology Beging Normal University Beijing China The Second Hospital Beijing Medical University Beijing China

The cyclin-dependent kinase inhibitor p2.( waf1/cip1/sdi1) is an important negative regulator in control of cell cycle. Its functions of inhibiting cancer cell growth and its effects on expression of Gl phase cyclins and related CDKs are a worthy topic for study. The plasmid expressing p2. with high level was transformed to human breast cancer cells, and the expression of p2. in cells was enhanced, then the cell growth rate, anchorage-independent growth and tu-morigenecity were tested, at the same time the expression levels of cyclinD1, CDK4,

关键词： p2.waf1 breast cancer cell cyclin CDK.

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,{2., 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, beijing normal university, beijing 100875, china department of Mathematics Beijing Institute of Technology Beijing China School of Mathematical Sciences Beijing Normal University Beijing 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.

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,{2., china) department of Biology Beijing Normal University Beijing China

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).

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 {2. 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.

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,{2., china department of Mathematics Beijing Normal University Beijing 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.