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Convergence of the Vlasov-Poisson-Fokker-Planck system to the incompressible Euler equations

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science China mathematics 2006年第2期49卷 255-266页

作者： XIAO Ling, LI Fucai & WANG Shu academy of mathematics and systems science, {4., beijing 100080, China Department of mathematics, Nanjing University, Nanjing 210093, China College of Applied sciences, beijing University of Technology, beijing 100022, China 1. academy of mathematics and systems science Chinese Academy of Sciences Beijing 100080 China 2. Department of mathematics Nanjing University Nanjing 210093 China 3. College of Applied sciences Beijing University of Technology Beijing 100022 China

We establish the convergence of the Vlasov-Poisson-Fokker-Planck system to the incompressible Euler equations in this paper. The convergence is rigorously proved on the time interval where the smooth solution to the incompressible Euler equations exists. The proof relies on the compactness argument and the so-called relative-entropy method.

关键词： Vlasov-Poisson-Fokker-Planck system incompressible Euler equations relative-entropy method.

Wandering domains in the transcendental dynamics

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chinese science Bulletin 2001年第1期46卷 34-35页

作者： WANG YuefeiInstitute of mathematics, chinese academy of sciences, beijing 100080, China Institute of mathematics Chinese Academy of Sciences Beijing China

It is shown that new classes of non-critically finite entire functions do not have wandering domains.

关键词： iteration Fatou set Julia set wandering domains.

PARALLEL CHAOTIC MULTISPLITTING ITERATIVE METHODS FOR THE LARGE SPARSE LINEAR COMPLEMENTARITY PROBLEM

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Journal of Computational mathematics 2001年第3期19卷 281-292页

作者： Zhong-zhi Bai (State Key Laboratory of Scientific/Engineering Competing Institute of Computational mathematics and Scientific/Engineering Computing, academy of mathematics and systems {4., chinese academy of sciences, beijing 100080, China) 中科院计算数学与工程计算数学所科学与工程计算国家重点实验室北京 100080

Focuses on a study which presented a parallel chaotic multisplitting method for solving the large sparse linear complementarity problem. Preliminaries of the study; Equations of the parallel chaotic multisplitting met... 详细信息

关键词： linear complementarity problem matrix multisplitting chaotic iteration relaxed method convergence property

Bifurcations and Chaos in a Discrete Predator-prey System with Holling Type-IV Functional Response

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Acta Mathematicae Applicatae Sinica 2005年第1期21卷 157-176页

作者： Ji-cai Huang Department of Applied mathematics, College of science, China Agriculture University academy of mathematics and {4. science, chinese academy of sciences, beijing 100080, China Department of Applied mathematics College of Science China Agriculture University academy of mathematics and systems science Chinese Academy of Sciences Beijing 100080 China

A discrete predator-prey system with Holling type-IV functional responseobtained by the Euler method is first investigated. The conditions of existence for foldbifurcation, flip bifurcation and Hopf bifurcation are derived by using the center manifold theoremand bifurcation theory. Furthermore, we give the condition for the occurrence of codimension-twobifurcation called the Bogdanov-Takens bifurcation for fixed points and present approximateexpressions for saddle-node, Hopf and homoclinic bifurcation sets near the Bogdanov-Takensbifurcation point. We also show the existence of degenerated fixed point with codimension three atleast. The numerical simulations, including bifurcation diagrams, phase portraits, and computationof maximum Lyapunov exponents, not only show the consistence with the theoretical analysis but alsoexhibit the rich and complex dynamical behaviors such as the attracting invariant circle,period-doubling bifurcation from period-2,3,4.orbits, interior crisis, intermittency mechanic, andsudden disappearance of chaotic dynamic.

关键词： predator-prey system bifurcations Bogdanov-Takens bifurcation chaos

A global solution of the Ein-stein-Yang-Mills equation on the conformal space

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chinese science Bulletin 2001年第6期46卷 460-461页

作者： LU QikengInstitute of mathematics, chinese academy of sciences, beijing 100080, China Institute of mathematics Chinese Academy of Sciences Beijing China

A global solution of the Einstein-Yang-Mills (EYM) equation on the conformal space is constructed. This solution is conformal invariant under the conformal group.

关键词： Einstein-Yang-Mills equation $12(2)-connection confor- mal space.

Exponential inequalities for associated random variables and strong laws of large numbers

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science China mathematics 2007年第5期50卷 705-714页

作者： Shan-chao YANG & Min CHEN Deptartment of mathematics, Guangxi Normal University, Guilin 54.004. China academy of mathematics and systems {4., chinese academy of sciences, beijing 100080, China 1. Deptartment of mathematics Guangxi Normal University Guilin 541004 China 2. academy of mathematics and systems science Chinese Academy of Sciences Beijing 100080 China

Some exponential inequalities for partial sums of associated random variables are established. These inequalities improve the corresponding results obtained by Ioannides and Roussas (1999), and Oliveira (2005). As application, some strong laws of large numbers are given. For the case of geometrically decreasing covariances, we obtain the rate of convergence n-1/2(log log n)1/2(logn) which is close to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Ioannides and Roussas (1999), and Oliveira (2005) only got n-1/3(logn)2/3 and n-1/3(logn)5/3, separately.

关键词： associated random variable exponential inequality strong law of large numbers rate of convergence 60E15 60F15

Wavelet Analysis of the Schwabe Cycle Properties in Solar Activity

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chinese Journal of Astronomy and Astrophysics 2004年第6期4卷 578-582页

作者： Gui-Ming LeNational Astronomical Observatories, chinese academy of sciences, beijing 100012 Center for Space science and Applied Research Center, chinese academy of sciences, {4. National Astronomical Observatories Chinese Academy of Sciences Beijing 100012 []Center for Space Science and Applied Research Center Chinese Academy of Sciences Beijing 100080

Properties of the Schwabe cycles in solar activity are investigated by using wavelet transform. We study the main range of the Schwabe cycles of the solar activity recorded by relative sunspot numbers, and find that the main range of the Schwabe cycles is the periodic span from 8-year to 14.year. We make the comparison of 11-year’s phase between relative sunspot numbers and sunspot group numbers. The results show that there is some difference between two phases for the interval from 1710 to 1810, while the two phases are almost the same for the interval from 1810 to 1990.

关键词： sun sunspot sun activity method data analysis

On factorizable solution of the differential equation(f')~2-a_0(z)(f-a)1(z))~2f

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chinese science Bulletin 1997年第21期42卷 1779-1782页

作者： YUAN Wenjun and HE YuzanInstitute of mathematics, chinese academy of sciences, beijing 100080, China Institute of mathematics Chinese Academy of Sciences Beijing 100080 China

If the coefficients are transcendental, Bergweiler et al. proved that in all possible non-trivialfactorization f(z)=h(g(z)), the growth of the right factor g(z) can be controlled by thegrowth of the coefficients. In ref. [2], He and Laine proved a similar conclusion for two othertypical kinds of nonlinear differential equations. But for the following equation:

关键词： factorization growth order meromorphic function ordinary differential equation.

MULTI-AGENT TRACKING OF A HIGH-DIMENSIONAL ACTIVE LEADER WITH SWITCHING TOPOLOGY

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Journal of systems science & Complexity 2009年第4期22卷 722-731页

作者： Yiguang HONG Xiaoli WANG Key Lab of systems and Control,Institute of systems science,academy of {4. and systems science,chinese academy of sciences,beijing 100190,China. Key Lab of systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

This paper considers a multi-agent tracking problem for a high-dimensional active leaderand variable interconnection topology. The state of the leader not only keeps changing but also maynot be measured. To estimate the state such a leader individually, a neighbor-based local controllertogether with a neighbor-based state-estimation rule is given for each autonomous agent. Then, theauthors prove that, with the help of a constructed common Lyapunov function (CLF), each agent cantrack the active leader with unmeasurable states. Finally, the authors explicitly construct a CLF foran active leader with unknown periodic input for illustration.

关键词： Active leader distributed algorithms multi-agent systems switching topology.