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Linear estimation and distribution of the limit cycles bifurcated from a kind of degenerate polycycles

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Science china Mathematics 2007年第3期50卷 334-344页

作者： Li-qin ZHAO department of Mathematics, beijing normal university, beijing 100875. china department of Mathematics Beijing Normal University Beijing 100875 China

In this paper, we investigate the number and the distribution of the limit cycles bifurcated from a kind of degenerate planar polycycles through three singular points: a saddle-node P 0, a fine saddle P 1 with finite order m ∈ N, a contractive (attracting) saddle P 2 with the hyperbolicity ratio q 2(0) ? Q. The connection between P 0 and P 1 is of hh-type and the connection between P 0 and P 2 is of hp-type. It is assumed that the connections between P 0 to P 2 and P 0 to P 1 keep unbroken. We obtain that the cyclicity of this polycycle is not more than 3m + 1, which is linearly dependent on the order of the resonant saddle P 1. We also show that the cyclicity is not more than m + 3 if q 2(0) > m, and that the nearer q 2(0) is close to 1, the more the limit cycles are bifurcated.

关键词： degenerate polycycle cyclicity finitely-smooth normal form transition map 34.05 34.23 58F14

The Goldbach 3-primes property for polynomial rings over certain infinite fields

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Chinese Science Bulletin 1998年第15期43卷 1256-1260页

作者： WANG Shiqiang department of Mathematics, beijing normal university, beijing 100875. china department of Mathematics Beijing Normal University Beijing China

On the basis of Effinger and Hayes’ theorem about the Goldbach 3_primes property of polynomial rings F over finite fields F , by model_theoretic method it is proved that for each characteristic k (including 0), there... 详细信息

关键词： model theory polynomial 3 primes property.

Quasi-critical ring of a primitive ring with nonzero socle

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Chinese Science Bulletin 1997年第3期42卷 189-192页

作者： JIANG Zimeidepartment of Mathematics, beijing normal university, beijing 100875. china department of Mathematics Beijing Normal University Beijing China

IN ref. [1] Jacobson proved the structure theorem for primitive rings with nonzero socles that R is a primitive ring withsocle S≠{0} if and only if there is a pair of dual vector spaces (M,M’) over a division ring Δ such that S=F(M, M’)(?) R(?)(?)(M, M’), where (?)(M, M’)-{ω∈Ω|ωM’(?)M’, Ω is the complete ring of linear transformations of M over Δ}, F(M, M’) is the set of all linear transformations of (?)(M, M’) of finite rank. After that, some people reproved this theorem by using different methods such as those in refs. [2, 3]. In

关键词： primitive ring socle conjugate space total subspace of conjugate space.

Constraints on Cardassian universe from Gamma ray bursts

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Science china(physics,Mechanics & Astronomy) 2010年第9期53卷 1720-1725页

作者： WANG TaiShan1 & LIANG Nan2 1 department of physics & Center for Astrophysics,Tsinghua university,{4. 100084.china 2 department of Astronomy,{4. normal university,{4. 100875.china 1. department of physics & Center for Astrophysics Tsinghua University Beijing 100084 China2. Department of Astronomy Beijing Normal University Beijing 100875 China

Constraints on the original Cardassian model and the modified polytropic Cardassian model are examined from the recently derived 4. gamma-ray bursts(GRBs) data calibrated with the method that can avoid the circularity *** results show that GRBs can be an optional observation to constrain the Cardassian *** the GRBs data with the newly de-rived size of baryonic acoustic oscillation peak from the Sloan Digital Sky Survey(SDSS),and the position of the first acoustic peak of the Cosmic Microwave Background radiation(CMB) from Wilkinson Microwave Anisotropy Probe(WMAP),we find Ωm0=0.27+0.02-0.02,n=0.06+0.07-0.08(1σ) for the original Cardassian model,and Ωm0=0.27+0.23-0.02,n=-0.09+0.23-1.91,β=0.82+2.10-0.62(1σ) for the modified polytropic Cardassian model.

关键词： Cardassian Gamma ray burst Cosmic Microwave Background baryonic acoustic oscillation

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. {4. 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

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 {4. normal university, Guangzhou 510631, {4.) [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.

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