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LONG DOMINATING CYCLES IN GRAPHS

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Systems Science and Mathematical Sciences 1998年第4期11卷 314-320页

作者： SUN Zhiren(department Of Mathematics, nanjing normal university, nanjing 210097,Institute of Systems Science, Academia Silica, Beijing 100080, China)

Let G be a connected graph of order n, and NC2(G) denote min{|N(u)U(v) |:dist(u,v) = 2}, where dist(u,v) is the distance between u and v in G. A cycle C in Gis called a dominatiny cycle, if V(G)\V(C) is an independent set in G. In this paper, weprove that if G contains a domillating cycle and 2, then G contains a dominating cycleof length at least min{n, 2NC2(G) - 2}, which proves partially a conjecture of R. Shenand F. Tian. And we give a class of graphs that show the result is shrpg.

关键词： Dominating cycle neighborhood union

Local and non-local sources of airborne particulate pollution at Beijing——The ratio of Mg/Al as an element tracer for estimating the contributions of mineral aerosols from outside Beijing

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Science China Chemistry 2005年第3期48卷 253-264页

作者： HAN Lihui1, ZHUANG Guoshun1,2,3. SUN Yele1 & WANG Zifa3.1. The Center for Atmospheric Environmental Study, department of Chemistry, Beijing normal university, Beijing 100875, China 2. Center for Atmospheric Chemistry Study, department of Environmental Science & Engineering, Fudan university, Shanghai 20043., China 3. LAPC/NZC, Institute of Atmospheric physics, CAS, Beijing 100029, China 1. The Center for Atmospheric Environmental Study Department of Chemistry Beijing Normal University 100875 Beijing China 2. Center for Atmospheric Chemistry Study Department of Environmental Science & Engineering Fudan University 200433 Shanghai China 3. Institute of Atmospheric physics CAS LAPC/NZC 100029 Beijing China

A new element tracer technique has firstly been established to estimate the contri-butions of mineral aerosols from both inside and outside Beijing. The ratio of Mg/Al in aerosol is a feasible element tracer to distinguish between the sources of inside and outside Beijing. Mineral aerosol, inorganic pollution aerosol mainly as sulfate and nitrate, and organic aerosol are the major components of airborne particulates in Beijing, of which mineral aerosol accounted for 3.%―67% of total suspended particles （TSP）, 10%―70% of fine particles （PM2.5）, and as high as 74% and 90% of TSP and PM2.5, respectively, in dust storm. The sources from outside Beijing contributed 62% （3.%―86%） of the total mineral aerosols in TSP, 69% （52%―90%） in PM10, and 76% （59%―93.） in PM2.5 in spring, and 69% （52%―83.）, 79% （52%―93.）, and 45% （7%―79%） in TSP, PM10, and PM2.5, respectively, in winter, while only20% in summer and autumn. The sources from outside Beijing contributed as high as 97% during dust storm and were the dominant source of airborne particulates in Beijing. The contributions from outside Bei-jing in spring and winter are higher than those in summer, indicating clearly that it was related to the various meteorological factors.

关键词： mineral aerosol local sources non-local sources dust storm re-suspended dust element tracer technique.

Differential Polynomials and normal Families

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Acta Mathematica Sinica,English Series 1994年第2期10卷 215-217页

作者： Xu Wansong department of Mathematics, physics and Mechanics nanjing{3. of Aeronautics and Astronautics nanjing, 210016 China 1. department of Mathematics Physics and Mechanics Nanjing University of Aeronautics and Astronautics 210016 Nanjing China

This paper continues the researches of Yang Lo and others, and gives a further generalization of Gu’s criterion for the normality of a family of meromorphic functions.

关键词： Math net Differential Polynomials and normal Families 任下

Observational constraints on the early dark energy model

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Research in Astronomy and Astrophysics 2011年第7期11卷 751-758页

作者： Lei Feng Yu-Peng Yang department of physics Nanjing University Nanjing 210093 ChinaJoint Center for Particle Nuclear Physics and Cosmology Nanjing University - Purple MountainObservatory Nanjing 210093 China

Dark energy can be studied by its influence on the expansion of the *** investigate current constraints on early dark energy（EDE） achievable by the combined observational data from type Ia supernovae（557）,baryon acoustic oscillations,the current cosmic microwave background and the observed Hubble *** find that combining these data sets provides powerful constraints on early dark energy and the best fit values of the parameters in 68% and 95% confidence-level regions are：Ωm0=0.2897 ＋0.0149＋0.0207 -0.013.-0.0194,Ωe=0.0129 ＋0.0272＋0.03.1 -0.0129-0.0129,w0= -1.0415＋0.0891＋0.1182 -0.109-0.1604,and h=0.6988＋0.0059＋0.0083.-0.0058-0.0081.

关键词： cosmology—dark energy—cosmological parameters

Uniform blow-up profiles and boundary layer for a parabolic system with localized nonlinear reaction terms

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Science China Mathematics 2005年第2期48卷 185-197页

作者： LI Huiling & WANG Mingxin department of Mathematics, Southeast university, nanjing 210018, China department of Mathematics, Xuzhou normal university, Xuzhou 221116, China 1. department of Mathematics Southeast University 210018 Nanjing China 2. department of Mathematics Xuzhou Normal University 221116 Xuzhou China

This paper deals with the blow-up properties of the solution to a semilinear parabolic system with localized nonlinear reaction terms, subject to the null Dirichlet boundary condition. We first give sufficient conditions for that the classical solution blows up in the finite time, secondly give necessary conditions and a sufficient condition for that two components blow up simultaneously, and then obtain the uniform blow-up profiles in the interior. Finally we describe the asymptotic behavior of the blow-up solution in the boundary layer.

关键词： parabolic system, localized nonlinear reaction terms, blow-up profiles, boundary layer size.

The dynamical properties of Rydberg hydrogen atom near a metal surface

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Science China(physics,Mechanics & Astronomy) 2005年第6期48卷 667-675页

作者： GE Meihua1, ZHANG Yanhui1, WANG Dehua2, DU Mengli3.& LIN Shenglu1 1. College of physics and Electronics, Shandong normal university, Jinan 250014, China 2.{3. of Mathematics and physics, Shandong Institute of Architecture and Engineering, Jinan 250014, China 3. Institute of Theoretical physics, Chinese Academy of Sciences, Beijing 100080, China 1. College of physics and Electronics Shandong Normal University 250014 Jinan China 2. department of Mathematics and physics Shandong Institute of Architecture and Engineering 250014 Jinan China 3. Institute of Theoretical physics Chinese Academy of Sciences 100080 Beijing China

The dynamical properties of Rydberg hydrogen atom near a metal surface are presented by using the methods of phase space analysis and closed orbit theory. Transforming the coordinates of the Hamiltonian, we find that the phase space of the system is divided into vibrational and rotational region. Both the Poincaré surface of section and the closed orbit theory verify the same conclusion clearly. In this paper we choose the atomic principal quantum number as n = 20. The dynamical character of the exited hydrogen atom depends sensitively on the atom-surface distance d. When d is sufficiently large, the atom-surface potential can be expressed by the traditional van der Waals force and the system is integrable. When d becomes smaller, there exists a critical value dc. For d > dc, the system is near-integrable and the motion is regular. While chaotic motion appears for d < dc, and the system tends to be non-integrable. The trajectories become unstable and the electron might be captured onto the metal surface.

关键词： Rydberg hydrogen atom, van der Waals interaction, Poincaré surface of section, closed orbit theory, chaos.

Structural properties of GaN(0001) epitaxial layers revealed by high resolution X-ray diffraction

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Science China(physics,Mechanics & Astronomy) 2010年第1期53卷 68-71页

作者： XIE ZiLi 1,2,3. ZHOU YuanJun 1 , SONG LiHong 1,2 , LIU Bin 1 , HUA XueMei 1,2 , Xiu XiangQian 1 , ZHANG Rong 1,2,3.& ZHENG YouDou 1,2,3.1 JiangSu Provincial Key Laboratory of Advanced Photonic and Electronic Materials and department of physics, nanjing{3., nanjing 210093. China 2 nanjing National Laboratory of Microstructures, nanjing 210093. China 3.NJU-Yangzhou Institute of Opto-electronics, Yangzhou, 225001, China 1. JiangSu Provincial Key Laboratory of Advanced Photonic and Electronic Materials and department of physics Nanjing University Nanjing 210093 China2. Nanjing National Laboratory of Microstructures Nanjing 210093 China3. NJU-Yangzhou Institute of Opto-electronics Yangzhou 225001 China

High-resolution X-ray diffraction has been used to analyze GaN(0001) epitaxial layers on sapphire substrates. Several structural properties of GaN, including the lattice constants, strains, and dislocation densities are revealed by the technique of X-ray dffraction (XRD). Lattice constants calculated from the omega/2theta scan are c=0.5185 nm and a=0.3.57 nm. Also, the in-plane strain is -1.003., while out of the plane, the epitaxial film is almost relaxed. Several methods are used to deduce the mosaicity and dislocation density of GaN, showing that the edge type dislocations are the overwhelming majority.

关键词： GaN XRD dislocation epitaxial

Nonlinear elastic waves in a monatomic chain with nonlinear interaction

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原子与分子物理学报 2002年第1期19卷 79-82页

作者： PAN Liu-xian 1, ZHOU Guang-hui 2, LI Shu-shen 3.1.department of physics, Yiyang Teacher's College, Yiyang 413.49 2. department of physics, Hunan normal university, Changsha 410081 3. National Laboratory for Supperlattice and Microstructure, Chinese department of physics Yiyang Teacher's College Yiyang 413049 department of physics Hunan Normal University Changsha 410081 中科院半导体所 National Laboratory for Supperlattice and Microstructure 北京 100083

Nonlinear wave equation for a one-dimensional anharmonic crystal lattice in terms of its microscopic parameters is obtained by means of a continuum approximation. Using a small time scale transformation, the nonlinear wave equation is reduced to a combined KdV equation and its single soliton solution yields the supersonic kink form of nonlinear elastic waves for the system.

关键词： Monatomic chain Continuum approximation Nonlinear elastic wave

Quasi-periodic solutions with prescribed frequency in a nonlinear Schrdinger equation

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Science China Mathematics 2010年第12期53卷 3067-3084页

作者： REN Xiu-Fang department of Mathematics, nanjing university, nanjing 210093. China 1. department of Mathematics Nanjing University Nanjing 210093 China

In this paper, one-dimensional (1D) nonlinear Schrdinger equation iut-uxx + Mσ u + f ( | u | 2 )u = 0, t, x ∈ R , subject to periodic boundary conditions is considered, where the nonlinearity f is a real analytic function near u = 0 with f (0) = 0, f (0) = 0, and the Floquet multiplier Mσ is defined as Mσe inx = σne inx , with σn = σ, when n 0, otherwise, σn = 0. It is proved that for each given 0 1, the above equation admits a Whitney smooth family of small-amplitude quasi-periodic solutions with b-dimensional Diophantine frequencies, corresponding to b-dimensional invariant tori of an associated infinite-dimensional Hamiltonian system. Moreover, these b-dimensional Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proof is based on a partial Birkhoff normal form reduction and an improved KAM method.

关键词： Schrdinger equation Hamiltonian system Birkhoff normal form quasi-periodic solution