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Nash Inequalities for General Symmetric Forms

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Acta Mathematica Sinica,English Series 1999年第3期15卷 353-370页

作者： Mufa Chen Department of Mathematics, beijing normal university, beijing 100875. P. R. china Department of Mathematics Beijing Normal University Beijing P. R. China

This paper deals with the Nash inequalities and the related ones for general symmetric forms which can be very much unbounded. Some sufficient conditions in terms of the isoperimetric inequalities and some necessary conditions for the inequalities are presented. The resulting conditions can be sharp qualitatively as illustrated by some examples. It turns out that for a probability measure, the Nash inequalities are much stronger than the Poincare and the logarithmic Sobolev inequalities in the present context.

关键词： Nash inequality Symmetric form Isoperimetric Inequality Jump process

Sufficient and Necessary Conditions for Stochastic Comparability of Jump Processes

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Acta Mathematica Sinica,English Series 2000年第1期16卷 99-102页

作者： Yuhui Zhang Department of Mathematics,beijing normal university,beijing 100875.P.R.china Department of Mathematics Beijing Normal University Beijing 100875 P.R. China

This note is devoted to the study of the stochastic comparability of jump *** the basis of[2]and[3],it is proved that two jump processes are stochastically comparable if and only if their q-pairs are ***,the result co... 详细信息

关键词： Stochastically comparable Totally stable Conservative Uniqueness

The Theory of Relativity on the Finsler Spacetime

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Journal of Systems Engineering and Electronics 1995年第4期6卷 239-252页

作者： Cao ShengLin (Department of Astronomy, beijing normal university, beijing 100875. china) Department of Astronomy Beijing Normal University Beijing 100875 China

According to some local properties of Lorentz transformation, Einstein stated: 'Vetheitiss greater than that of light have no possibility of existence.' He neglected to point out the applicable range of the special theory of relativity. In fact, it could only be applied to the subluminal-speeds. This paper shows that if ones think of the possibility of the existence of the superluminal-speeds and redescribe the special theory of relativity following Einstein's way, it could be supposed that the physical spacetime is a Finsler spacetime, characterized by the metric ds4=gijkldxidxidxkdxl. If so, a new spactime transformation could be found by invariant ds4 and the theory of relativity is discussed on this transformation it is possible that the Finsler spacetime F(x,y) may be endowed with a catastrophic nature. Based on the different properties between the ds2 and ds4, it is discussed that the flat spacetime will also have the catastrophic nature on the Finsler metric ds4. The spacetime transformations and the Physical quantities will suddenly change at the catastrophe set of the spacetime, the light cone. It will be supposed that only the dual velocity of the superluminal-speeds could be observed. If so, a particle with the superluminal-speed v> c could be regarded as its anti-particle with the dual velocity v1=c2/ v< c. On the other hand, it could be assumed that the horizon of the field of the general relativity is also a catastrophic set. If so, a particle with the superluminal-speeds could be projected near the horizon of these fields, and the particle will move on the sauce-like curves. It is very interesting that, in the Schwarzschild fields, the theoretical calculation for the sauce-like curves should be in agreement with tie data of the superluminal expansion of extragalactic radio sources observed year after year. (see Gao, 1992b).The ca- tastrophe of spacetime has some deep cosmological means. According to the some interested subjects in the Process of

关键词： Theory of relativity Finsler spacetime Superluminal-speed Subluminal-speed Catastrophe theory Superluminal expansion Extragalactic radio sources Cosmology

Calculating soil moisture by remote sensing and analyzing hydrologic cycle process in the Yellow River basin

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Science china(Technological sciences) 2004年第z1期47卷 1-13页

作者： YANG Shengtian1 & LIU Changming1, 2 1. school of Environmental sciences, beijing normal university, beijing 100875. china 2. Institute of Geographic Science and Natural Resources Research, beijing 100101, china beijing normal Univ Sch Environm Sci Beijing 100875 Peoples R China Inst Geog Sci & Nat Resources Beijing 100101 Peoples R China

Based on the AVHRR pathfinder remote sensing data, soil moisture, precipitation and evaporation during the period of 1982—1998, soil moisture of all layers of soil-profile (0—1 m) in the Yellow River basin over the 17 years are calculated by the remote sensing model of calculating soil water. The Yellow River basin is divided into seven subcatchments as control sections at the location of six hydrologic stations (Lanzhou, Toudaoguai, Longmen, Sanmenxia, Huayuankou and Lijin). After calculating soil moisture and obtaining runoff data and precipitation data, the dynamical features of hydrological cycle in the Yellow River basin are analyzed for the period from 1982 to 1988 using water balance method. The conclusions are as follows: It is feasible to calculate the soil water on the macro-scale, in the soil profile with temporal continuity by means of remote sensing and survey in land. Some values of the key water cycle factors in the Yellow River are obtained, which include the annual precipitation of 4000 km3, the evapotranspiration of 3000-3500 km3, and the soil moisture transformation of ?500- 500 km3. Consequently, we analyzed the process of the water cycle in the Yellow River over the 17 years, and the results show that the segment upstream of Lanzhou city is a relatively humid region, and the area of internal waters and the reaches of Shanshan is the most desiccated region. Therefore, the runoff in the depth process is intensive and the runoff-generating process is weak in more arid regions.

关键词： the Yellow River, soil moisture, remote sensing, hydrologic cycle.

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.china 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

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.china 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

Superprocesses arising from interactive stochastic flows

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Science china Mathematics 2006年第4期49卷 451-476页

作者： YAN Guojun & LI Zhanbing Medical school, Shantou university, Shantou 515063, china Department of Mathematics, Bejing normal university, beijing 100875. china Medical school Shantou University Shantou 515063 China Department of Mathematics Bejing Normal University Beijing 100875 China

In this paper, we give a unified construction for superprocesses with dependent spatial motion constructed by Dawson, Li, Wang and superprocesses of stochastic flows constructed by Ma and Xiang. Furthermore, we also g... 详细信息

关键词： superprocess, interactive stochastic flows, martingale problem, dual processes.

Weighted estimates for commutators of singular integral operators with non-doubling measures

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Science china Mathematics 2007年第11期50卷 1621-1641页

作者： Guo-en HU~1 Da-chun YANG~(2+) Dong-yong YANG~2 1 Department of Applied Mathematics,university of Information Engineering,Zhengzhou 450002,china 2 school of mathematical sciences,beijing normal university,beijing 100875.china Department of Applied Mathematics University of Information Engineering Zhengzhou 450002 China school of mathematical sciences Beijing Normal University Beijing 100875 China

Letμbe a nonnegative Radon measure on R^d which only satisfiesμ(B(x,r))≤C_0r^n for all x∈R^d,r>0,and some fixed constants C_0>0 and n∈(0,d].In this paper,some weighted weak type estimates with A_(p,(log L)~σ)~ρ(μ) weights are established for the commutators generated by Calder■n-Zygmund singular integral operators with RBMO(μ) functions.

关键词： non-doubling measure weight singular integral operator commutator

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