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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,{4. 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

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{4. 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

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

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.{4. 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

Synthesis and Crystal Structure of Co(C_6NO_2H_4._3. H_2O

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Chinese Journal of Structural chemistry 1997年第5期16卷 376-379页

作者： ZI Feng-Lan ZHOU Yin-Zhuang TU Shu-Jie LIU Shun-Cheng(department of chemistry, capital Nimal University, beijing, 100037)JIN Xiang-Lin(Institute of Physical {4., beijing University, beijing, 100871) department of chemistry Capital Normal University Beijing 100037 China Institute of Physical chemistry Beijing University Beijing 100871 China

The reaction of CoCl2. 6H2O with picolinic acid gives the title compound Co-(C6NO3H4.3. H2O at room temperature. The crystallographic data for Co(C6NO3H5)3. H2O: monoclinic, space group C2/c, a= 29. 8316(6), b= 8. 573(2),c= 13. 835(3) , β= 95. 93(3)°, Z= 16, Mr=4.3. 3, Dc= 1. 673 g/cm3, μ(MoKa)= 1. 109 mm-1, F (000) = 1808, R =0. 036, R. =0.04. for 24.7 independent observed reflections [F≥4.0σ(F)]. The Co atom is coordinated by three oxygen andthree nitrogen atoms, forming a distorted octahedral coordination geometry. In the unitcell, two kinds of isomerides are included. They are the mirror images to each other.

关键词： synthesis crystal structure cobalt complex isomer

Electrochemical Behavior of Adriamycin at Ni/GC Ion Implantation Modified Electrode

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Chinese Chemical Letters 2000年第7期11卷 601-602页

作者： Jing Bo HU Qi Long LI(department of chemistry, beijing normal University, Bejing 100875) beijing normal Univ Dept Chem Beijing 100875 Peoples R China

With a Ni/GC ion implantation modified electrode as working electrode, in 0.1 mol/L HOAc-NaOAc (pH=4.62) solution, a sensitive reductive wave of ADM was obtained by linear sweep voltammetry. The peak potential was -0.55 V (***). The peak current is proportional to the concentration of ADM with a detection limit of 6.9 X 10(-8) mol/L. The behavior of the reduction wave was studied. The experiments of AES and XPS showed that Ni was surely implanted into the surface of the GCE and the implanted Ni at the GCE improved the electrocatalytic activity.

关键词： ion implantation modified electrode electrochemical behavior adriamycin

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 100875,china 2 {4. of Physics,beijing normal University,beijing 100875,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

Asymmetric Photocatalyzed Addition of Cyclic Ammes to the Chiral 5-(l)-Menthyloxy-2(5H)-furanone

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Chinese Chemical Letters 1999年第11期10卷 889-892页

作者： Zhao Yang WANG Tian Ying JIAN Qing Hua CHEN(department of chemistry,beijing normal University, beijing 100875) department of chemistry Beijing Normal University Beijing 100875 China

The benzophenone-initiated photoaddition of N-methyl ammes 2 to the chiral synthon1 proceeds in a regiospecitlc and highlyr stereocontrolled thshion to give the C-C photoadductscontaining a ne\viy stereogenic center 3a-3c. The enantiomerically pure N-C photoadducts, aminobutenolides 5a-5c have been obtained from the enantioselective photoaddition of secondary cyclicammes 4.with the chiral synthon 1 under the same conditions.

关键词： Asymmetric photocatalysed conjugate addition enantiomerically pure C-Cphotoadducts. secondary cyclic amine enantiomerically pure N-C photoaducts.

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,{4. 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, 0.4.) 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