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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.

Self-talk of Reflection Hologram During its construction

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Chinese Journal of Lasers 1996年第4期B5卷 334-340页

作者： LIU Dahe ZHOU Jing(department of Physics, beijing normal university,beijing100875, china) beijing normal Univ Beijing China

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关键词： reflection hologram hologram grating self-talk

From the Green's Function in Tight-Binding Representation to Interatomic Many-body Potentials

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Journal of Materials Science & Technology 1999年第4期15卷 315-319页

作者： Shaojun LIU(department of physics, beijing normal university, beijing 100875, china)Xiaobo WEI(department of Physics, Liuzhou College of Education, Liuzhou 545005, china)Zhaodou CHEN Jun CAI and Benkun MA(department of Physics, beijing normal university, department of Physics Beijing Normal University Beijing 100875 China department of Physics Liuzhou College of Education Liuzhou 545005 China

In this paper, we deduce the analytical form of many-body interatomic potentials based on the Green's function in tight-binding representation. The many-body potentials are expressed as the functions of the hopping integrals which are the physical origin of cohesion of atoms. For thesimple case of s-valent system, the inversion of the many-body potentials are discussed in detail by using the lattice inversion method.

关键词： Rev Li Chen From the Green’s Function in Tight-Binding Representation to Interatomic Many-body Potentials body

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, beijing 100875, 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 department 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, beijing 100875, 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.

Theoretical studies on the mechanism of the thermal decarboxylation and decarbonylation of a number of α-keto-acids

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Chinese Journal of Chemistry 1995年第6期13卷 487-492页

作者： CHEN,Li-Tao CHEN,Guang-Ju FU,Xiao-YuanChemistry department,beijing normal university,beijing 100875,china Chemistry department Beijing Normal University Beijing 100875 China

Both processes of decarboxylation and decarbonylation of a number of acids including RCOCO2H,R=H,CH3,CH2F,CF3,CH=CH2,Ph,OH have been studied by semi-empirical MO theory AMI method to verify the reaction mechanism of each process and the effect of different substituents on *** calculated results are consistent with the experimental reports and can be summed up as follows:(1) The decarboxylation of these acids to form aldehydes and carbon dioxide is concerted and takes place through a 4-membered ring transition state in which a partial negative charge develops on the carbon of the α-carbonyl group,so that the inductive effect of some substituents is favourable for this process.(2) Their decarbonylation into carboxylic acids and carbon monoxide however is the attack of the OH on the carbon of the alkyl portion of the acid,forming a 3-membered ring transition state.(3) The activation energy of decarbonylation is lower than that of decarboxylation,since oxygen is more nucleophilic than hydrogen and also the strong OH bond need not to be broken.

关键词： Decarboxylation decarbonylation a-keto-acid

AVERAGE σ-K WIDTH OF CLASS OF L_p(R^n) IN L_q (R^n)

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Chinese Annals of Mathematics,Series B 1995年第3期16卷 351-360页

作者： LIU YONGPING(department of Mathematics, beijing normal university, Beliing 100875, china.) beijing normal UNIV DEPT MATHBEIJING 100875PEOPLES R CHINA

The average σ-K width of the Sobolev-Wiener class in Lq(Rn) is studied for and the asymptotic behaviour of this quantity is determined. The exact value of average σ-K width of some class of smooth functions in L2(Rn... 详细信息

关键词： Average σ-K width Optimal subspace,Sobolev-Wiener class,Riesz potential.