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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

MULTIPLICITY OF PERIODICSOLUTIONS OF DUFFING'S EQUATIONSWITH LIPSCHITZIAN CONDITIONMULTIPLICITY OF PERIODICSOLUTIONS OF DUFFING'S EQUATIONS WITH LIPSCHITZIAN CONDITION

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Chinese Annals of Mathematics,Series B 2000年第4期21卷 479-488页

作者： WANG ZAIHONG (Department of Mathematics, Capital normal university, beijing 100037, china.) Department of Mathematics Capital Normal University Beijing 100037 China

This paper deals with the existence and multiplicity of periodic solutions of Duffing equations x + g(x) = p(t). The author proves an infinity of periodic solutions to the periodically forced nonlinear Duffing equations provided that g(x) satisfies the globally lipschitzian condition and the time-mapping satisfies the weaker oscillating property.

关键词： Periodic solution Time mapping Poincare-Birkhoff twist theorem

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.

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, beijing normal Univ Dept Phys Beijing 100875 Peoples R China Liuzhou Coll Educ Dept Phys Liuzhou 545005 Peoples R 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

L~∞ CONVERGENCE OF TRUNC ELEMENT FOR THE BIHARMONIC EQUATION

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Journal of Computational Mathematics 1997年第1期15卷 14-22页

作者： M. Wang(Department of Mathematics, beijing university, beijing, china) 北京大学数学系北京

The paper considers the L∞ convergence for TRUNC finite elements solving the boundary value problems of the biharmonic equation. The nearly optimal L∞ estimates for the error of first order derivatives are *** TRUNC plate element is proposed and developed by Argyris et al.. The numerical experiences show that the element has very good .***,[1l2]. The mathematicalproof of convergence of the TRUNC element is given by Shi Zong-ci in paper [3]. Thispaper will consider the L~∞ convergence for the TRUNC plate element.

关键词： Biharmonic equations Convergent boundaries Shape functions Vertices Interpolation Weighting functions Integers

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

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

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, china 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, 0.41) 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

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