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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 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

On several families of elliptic curves with arbitrary large Selmer groups

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Science china Mathematics 2010年第9期53卷 2329-2340页

作者： LI Fei & QIU DeRong school of mathematical sciences,Institute of Mathematics and Interdisciplinary Science,Capital normal university,beijing 100048,china 1. school of mathematical sciences Institute of Mathematics and Interdisciplinary Science Capital Normal University Beijing 100048 China

In this paper,we calculate the ()-Selmer groups S()(E/Q) and S()(E/Q) of elliptic curves y2 = x(x + εpD)(x + εqD) via the descent *** particular,we show that the Selmer groups of several families of such ell... 详细信息

关键词： elliptic curve Selmer group Mordell-Weil group

The information entropy of a static dilaton black hole

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Science china(Physics,Mechanics & Astronomy) 2008年第2期51卷 113-125页

作者： LIU ChengZhou Institute of Theoretical Physics, Binzhou university, Binzhou 256600, china Department of Physics, beijing normal university, beijing 100875. china 1. Institute of Theoretical Physics Binzhou University Binzhou 256600 China 2. Department of Physics Beijing Normal University Beijing 100875 China

In accordance with holographic principle, by calculating the statistical entropy of the quantum field just at the event horizon of the Garfinkle-Horowitz-Strominger dilaton black hole, the information entropy of the black hole was investigated and the Bekenstein-Hawking formula was obtained. The results show that black hole entropy is identical with the statistical entropy of the quantum field at the horizon. Using the generalized uncertainty relation, the divergence of the state density near the event horizon in usual quantum field theory was removed, and the cutoffs and the little mass approximation in the heat gas method of black hole entropy were avoided. Thus, the microstates of the massive scalar field just at the event horizon of the static dilaton black hole were studied directly and a description on holograph principle was presented. By using residue theorem, the integral difficulty in the calculation was overcome, and the information entropy and the Bekenstein-Hawking formula were obtained quantitatively. Compared with the black hole entropy from the loop quantum gravity, the consistency of methods and results of calculating black hole entropy in non-commutative quantum field theory and loop quantum gravity was investigated. By this, the gravity correction constant in the generalized uncertainty relation was suggested and the sense of holographic principle was discussed.

关键词： black hole entropy holographic principle non-commutative quantum field theory event horizon loop quantum gravity

Relativist ic Corrections to the Thermal Sunyaev-Zel'dovich Power Spectrum

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Chinese Journal of Astronomy and Astrophysics 2003年第5期3卷 410-414页

作者： Hai-Ning LiNational Astronomical Observatories, Chinese Academy of sciences, beijing 100012 lhnDepartment of Astronomy, beijing normal university, beijing 100875 National Astronomical Observatories CAS NAOC Beijing 100012 China []Department of Astronomy Beijing Normal University Beijing 100875

We present a quantitative estimate of the relativistic corrections to thethermal SZ power spectrum produced by the energetic electrons in massive clusters. The correctionsare well within 10% for current experiments with working frequencies below ν 350 GHz. Moreover, the corrections appear to be slightlysmaller at higher l or smaller angular scales. We conclude that there is no need to include therelativistic corrections in the theoretical study of the SZ power spectrum especially at lowfrequencies unless the SZ power spectrum is used for precision cosmology.

关键词： cosmic microwave background cosmology: theory galaxies: clusters: general

On the number of B_(π')-characters in a nilpotent π-block

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Science china Mathematics 2008年第1期51卷 1-4页

作者： HAI JinKe~(1+) & ZHU YiXin~2 1 school of mathematical sciences, Qingdao university, Qingdao 266071, china 2 school of mathematical sciences, Capital normal university, beijing 100037, china school of mathematical sciences Qingdao University Qingdao 266071 China school of mathematical sciences Capital Normal University Beijing 100037 China

Brouéand Puig set the definition of nilpotent p-blocks, stated the existence of such blocks, and then proved that there is a unique Brauer character in a nilpotent p-block. The present paper, based on the works of Slattery and Robinson, generalizes the above idea to theπ-block theory of aπ-separable group, defines the nilpotency of aπ-block, and proves that there is a unique B_(π')-character in a nilpotentπ-block.

关键词： π-separable groups π-blocks π-subpairs nilpotentπ-blocks

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.

Effects of chronic exposure to nonylphenol on locomotor activity and social behavior in zebrafish(Danio rerio)

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Journal of Environmental sciences 2010年第9期22卷 1435-1440页

作者： Jigang Xia,Cuijuan Niu ,Xuejiao Pei Ministry of Education Key Laboratory of Biodiversity Science and Ecological Engineering,College of Life sciences,beijing normal university,100875.beijing,china. [a] Ministry of Education Key Laboratory of Biodiversity Science Ecological Engineering College of Life Sciences Beijing Normal University 100875 Beijing China

Nonylphenol （NP）, a xenoestrogen ubiquitously found in aquatic ecosystems, is of high environmental concern. The present work assessed the effects of exposure to NP on locomotor activity and social behavior in male and female zebrafish （Danio rerio）, to evaluate the possible hazard of NP to fish behavior and to pursue a potential biomarker of NP contamination. Fish were randomly divided into six groups. Five groups were receiving 0.1, 1, 10, 50 and 100 μg/L nominal concentrations of NP for 60 days, respectively. A sixth control group was given the same treatment as the other five groups, but no NP. Locomotor activity, aggressive behavior, group preference and leaving shoal were examined. NP exposure showed marked influence on locomotor activity of the male zebrafish, whereas that of the female was not significantly affected by NP. Aggressive behavior and group preference were significantly affected by NP exposure in both male and female groups. Locomotor activity and aggressive behavior of the male and group preference of both male and female zebrafish were clearly inhibited at 100 μg/L NP. No significant alteration in leaving shoal was observed under NP exposure. The results suggested that changes in locomotor activity and aggressive behavior of the male and group preference of both male and female may be used as an ecologically relevant integrative biomarker of NP contamination.

关键词： chronic toxicity nonylphenol biomarker zebrafish

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.

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. china 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