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Measures and dimensions of fractal sets in local fields

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Progress in Natural Science:Materials International 2006年第12期16卷 1260-1268页

作者： QIU Hua** and SU Weiyi(Department of Mathematics, nanjing University, nanjing 210093, China) Department of Mathematics Nanjing University Nanjing 210093 China

The study of fractal analysis over the local fields as underline spaces is very important since it can motivate new approaches and new ideas, and discover new techniques in the study of fractals. To study fractal sets in a local field K, in this paper, we define several kinds of fractal measures and dimensions of subsets in K. Some typical fractal sets in K are constructed. We also give out the Hausdorff dimensions and measures, Box-counting dimensions and Packing dimensions, and stress that there exist differences between fractal analysis on local fields and Euclidean spaces. Consequently, the theoretical foundation of fractal analysis on local fields is established.

关键词： local field p-series field Hausdorff measure and dimension Boxcounting dimension Packing measure and dimension Cantor type set.

Precession of the Orbital Plane of Binary Pulsars and Significant Variabilities

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Chinese Journal of Astronomy and Astrophysics 2005年第4期5卷 379-398页

作者： Bi-Ping Gong Department of Astronomy, nanjing University, nanjing 210093 bpgong@*** Department of Astronomy Nanjing University Nanjing 210093

There are two ways of expressing the precession of orbital plane of a binary pulsar system, given by Barker ＆ O＇Connell, Apostolatos et al. and Kidder, respectively. We point out that these two ways actually come from the same Lagrangian under different degrees of freedom. Damour ＆ Schaefer and Wex Kopeikin applied Barker ＆ O＇Connell＇s orbital precession velocity in pulsar timing measurement. This paper applies Apostolatos et al.＇s and Kidder＇s orbital precession velocity. We show that Damour ＆ Schaefer＇s treatment corresponds to negligible Spin-Orbit induced precession of periastron, while Wex ＆ Kopeikin and this paper both found significant （but not equivalent） effects. The observational data of two typical binary pulsars, PSR J2051-0827 and PSR J1713＋0747, apparently support a significant Spin-Orbit coupling effect. Specific binary pulsars with orbital plane nearly edge on could discriminate between Wex ＆ Kopeikin and this paper： if the orbital period derivative of the double-pulsar system PSRs J0737-3039 A and B, with orbital inclination angle i=87.7-29^＋17 deg, is much larger than that of the gravitational radiation induced one, then the expression in this paper is supported, otherwise Wex ＆= Kopeikin＇s is supported.

关键词： pulsars: binary pulsars - geodetic precession: individual (PSR J2051-0827 PSR J1713+0747 PSRs J0737-3039 A and B)

Effect of Conversion Efficiency on Gamma-Ray Burst Energy

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Chinese Journal of Astronomy and Astrophysics 2004年第3期4卷 267-274页

作者： Lei Xu Zi-Gao Dai Department of Astronomy nanjing University nanjing 210093 Department of Astronomy Nanjing University Nanjing 210093

Beaming effect makes it possible that gamma-ray bursts have a standardenergy, but the gamma-ray energy release is sensitive to some parameters. Our attention is focusedon the effect of the gamma ray conversion efficiency (η_γ), which may range between 0.01 and 0.9,and which probably has a random value for different GRBs under certain conditions. Making use of theafterglow data from the literature, we carried out a complete correction to the conical openingangle formula. Within the framework of the conical jet model, we ran a simple Monte Carlo simulationfor random values of η_γ, and found that the gamma-ray energy release is narrowly clustered,whether we use a constant value of η_γ or random values for different gamma-ray bursts.

关键词： gamma rays: bursts ISM: jets

EIT waves and coronal magnetic field diagnostics

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Science China(Physics,Mechanics & Astronomy) 2009年第11期52卷 1785-1789页

作者： CHEN PengFei Department of Astronomy, nanjing University, nanjing 210093, China Department of Astronomy Nanjing University Nanjing China

Magnetic field in the solar lower atmosphere can be measured by the use of the Zeeman and Hanle effects. By contrast, the coronal magnetic field well above the solar surface, which directly controls various eruptive phenomena, can not be precisely measured with the traditional techniques. Several attempts are being made to probe the coronal magnetic field, such as force-free extrapolation based on the photospheric magnetograms, gyroresonance radio emissions, and coronal seismology based on MHD waves in the corona. Compared to the waves trapped in the localized coronal loops, EIT waves are the only global-scale wave phenomenon, and thus are the ideal tool for the coronal global seismology. In this paper, we review the observations and modelings of EIT waves, and illustrate how they can be applied to probe the global magnetic field in the corona.

关键词： coronal mass ejections (CMEs) magnetic field diagnostics magnetohydrodynamics (MHD)

On critical values concerning the evolution of the long period families

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Chinese Journal of Astronomy and Astrophysics 2009年第4期9卷 494-500页

作者： Xi-Yun Hou1,21 Astronomy Department, nanjing University, nanjing 210093, China 2 Institute of Space Environment and Astronautics, nanjing University, nanjing 210093, China Astronomy Department Nanjing University Nanjing 210093 China Institute of Space Environment and Astronautics Nanjing University Nanjing 210093 China

In a previous paper, we proposed another special critical value concerning the evolution of the long period family around the equilateral equilibrium points, besides the two values given by Henrard. Are there any other special critical values？ After studying the stability curves of the long period family carefully, we gave a negative answer. During the study, we found an interesting family of periodic orbits which we called the homo family. We studied the evolution of this family following the increase of μ. With these findings, we were able to explain the origin of the four branches of periodic families emanating from L4 and the stability results of the equilateral equilibrium points.

关键词： celestial mechanics

Rank theorems of operators between Banach spaces

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Science China Mathematics 2000年第1期43卷 1-5页

作者： MA JipuDepartment of Mathematics, nanjing University, nanjing 210093, China Department of Mathematics Nanjing University Nanjing China

LetE andF be Banach spaces, andB(E,F) all of bounded linear operators onE intoF. LetT 0 ∈B( E,F) with an outer inverseT 0 # ∈B( F,E). Then a characteristic condition ofS=(I + T0 # (T-T0)-1 T0 # with T∈B(E, F) and ∥ T0 # (T - T0 ∥ < 1, being a generalized inverse ofT, is presented, and hence, a rank theorem of operators onE intoF is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis.

关键词： rank theorem generalized inverse operator-value map.

A local probability exponential inequality for the large deviation of an empirical process indexed by an unbounded class of functions and its application

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Science China Mathematics 2004年第6期47卷 821-830页

作者： ZHANG DixinDepartment of Finance, Business School, nanjing University, nanjing 210093, China Department of Finance Business School Nanjing University Nanjing China

A local probability exponential inequality for the tail of large deviation of an empirical process over an unbounded class of functions is proposed and studied. A new method of truncating the original probability space and a new symmetrization method are given. Using these methods, the local probability exponential inequalities for the tails of large deviations of empirical processes with non-i.i.d. independent samples over unbounded class of functions are established. Some applications of the inequalities are discussed. As an additional result of this paper, under the conditions of Kolmogorov theorem, the strong convergence results of Kolmogorov on sums of non-i.i.d. independent random variables are extended to the cases of empirical processes indexed by unbounded classes of functions, the local probability exponential inequalities and the laws of the logarithm for the empirical processes are obtained.

关键词： empirical process large deviation unbounded class of functions local probability exponential inequality

Integral expressions of Lyapunov exponents for autonomous ordinary differential systems

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Science China Mathematics 2009年第1期52卷 195-216页

作者： DAI XiongPing Department of Mathematics, nanjing University, nanjing 210093, China Department of Mathematics Nanjing University Nanjing China

In the paper, the author addresses the Lyapunov characteristic spectrum of an ergodic autonomous ordinary differential system on a complete riemannian manifold of finite dimension such as the d-dimensional euclidean space ? d , not necessarily compact, by Liaowise spectral theorems that give integral expressions of Lyapunov exponents. In the context of smooth linear skew-product flows with Polish driving systems, the results are still valid. This paper seems to be an interesting contribution to the stability theory of ordinary differential systems with non-compact phase spaces.

关键词： Lyapunov spectrum of differential system multiplicative ergodic theorem C 1-vector field smooth linear skew-product flow lifting of probability 34D08 37C10 60B05 37H15 28D10

Line Broadening in a Limb Flare: Derivation of Macro-turbulent Velocity Fields

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Chinese Journal of Astronomy and Astrophysics 2002年第3期2卷 277-286页

作者： Ying Liu and Ming-De DingDepartment of Astronomy, nanjing University, nanjing 210093 Department of Astronomy Nanjing University Nanjing 210093

The line profiles of Ha in a limb flare on 1998 November 11 appear to be unusually broadened. It is considered that macro-turbulence (or macroscopic mass motions) may be one of the main causes. We use an inversion technique to extract the probability distribution of the line-of-sight velocity in the flare. There exist some differences between the velocity distributions deduced from Ha and from Ca II λ8542, which may be because the two lines depend differently on the temperature and velocity. Since the loop density is high, we obtain a rather short cooling time (several tens of seconds) from the hot X-ray loops to the cool loops visible in Ha. Possible origins of the large scale motions are discussed.

关键词： Sun: flares - Sun: atmospheric motions - Line: profiles