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A Stochastic Growth Model of Multi Macro-economic System

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A Stochastic Growth Model of Multi Macro-economic System

The Critical Phenomenon and Phase Transition for the Degree Sequences of Random Web Graph Processes

第七届中国不确定系统年会

作者： Gao-Rong Ning~(1*) Xian-Yuan Wu~1 Kai-Yuan Cai~2 Tao Liang~3 1 school of mathematical sciences,capital normal university,beijing,100037,china 2 Department of Automatic Control,beijing university of Aeronautics and Astronautics,beijing,100083,china 3 Information Engineering College,beijing capital normal university,beijing,100037,china

＜正＞In this paper we propose a simple model of multi-organizations to analyze the dynamic behaviors of macro-economic *** this model,three mechanisms are included:1) congeneric firms are mainly competition against each other,and inhomogeneous firms are mainly synergic with each other;2) the Gibrat’s Law of Proportionate Effect is followed, that is,the expected value of the growth rate of a business firm is proportional to its current size in its own industry and 3) new firms continually enter the *** find that the firm size distribution in its own industry displays heavy tails or power-law,where the power is determined by the quotient of demand factor and supply factor of this *** contrasts the Gaussian distribution predicted by Gibrat’s law of proportionate effect.

关键词： Gibrat’s law power law firms size distribution demand factor dynamical economic systems

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The Critical Phenomenon and Phase Transition for the Degree ...

Coexistence of unbounded solutions and periodic solutions of Liénard equations with asymmetric nonlinearities at resonance

第七届中国不确定系统年会

作者： Xian-Yuan Wu~1,Zhao Dong~2,Ke Liu~2,Kai-Yuan Cai~3 1 school of mathematical sciences,capital normal university,beijing,100037,china. 2 Academy of Mathematics and System sciences,Chinese Academy of sciences,beijing,100190,china. 2 Academy of Mathematics and System sciences,Chinese Academy of sciences,beijing,100190,china. 3 Department of Automatic Control,beijing university of Aeronautics and Astronautics beijing,100083,china,

＜正＞In this paper,we introduce some random web graph processes,and reveal that their degree distributions may exhibit critical phenomenon and phase transition.

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Science china Mathematics 2007年第8期50卷 1205-1216页

作者： Zai-hong WANG school of mathematical sciences,capital normal university,beijing 100037,china 1. school of mathematical sciences Capital Normal University Beijing 100037 China

In this paper, we deal with the existence of unbounded orbits of the mapping $$\left\{ \begin{gathered} \theta _1 = \theta + 2n\pi + \frac{1}{\rho }\mu (\theta ) + o(\rho ^{ - 1} ), \hfill \\ \rho _1 = \rho + c - \mu '(\theta ) + o(1), \rho \to \infty \hfill \\ \end{gathered} \right.$$ , where n is a positive integer, c is a constant and μ(θ) is a 2π-periodic function. We prove that if c > 0 and μ(θ) ≠ 0, θ, ∈ [0, 2?], then every orbit of the given mapping goes to infinity in the future for ρ large enough; if c < 0 and μ(θ) ≠ 0, θ ∈ [0, 2π], then every orbit of the given mapping goes to infinity in the past for ρ large enough. By using this result, we prove that the equation x″+f(x)x′+ax +?bx ?+?(x)=p(t) has unbounded solutions provided that a, b satisfy $1/\sqrt a + 1/\sqrt b = 2/n$ and ?(x) satisfies some limit conditions. At the same time, we obtain the existence of 2π-periodic solutions of this equation.

关键词： Liénard equations unbounded solutions periodic solutions 34C11 34C25

The localization of 1-cohomology of transitive Lie algebroids

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Science china Mathematics 2006年第2期49卷 277-288页

作者： CHEN Zhuo & LIU Zhangju Department of Mathematics, capital normal university, beijing 100037, china school of mathematical Science, Peking university, beijing 100871, china 1. Department of Mathematics Capital Normal University Beijing 100037 China 2. school of mathematical Science Peking University Beijing 100871 China

For a transitive Lie algebroid A on a connected manifold M and its representation on a vector bundle F, we define a morphism of cohomology groups rk: Hk(A,F) → Hk(Lx,Fx), called the localization map, where Lx is the adjoint algebra at x ∈ M. The main result in this paper is that if M is simply connected, or H (LX,FX) is trivial, then T is injective. This means that the Lie algebroid 1-cohomology is totally determined by the 1-cohomology of its adjoint Lie algebra in the above two cases.

关键词： transitive Lie algebroid representation cohomology localization.

On the number of B_(π')-characters in a nilpotent π-block

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Science china Mathematics 2008年第1期51卷 1-4页

作者： HAI JinKe~(1+) & ZHU YiXin~2 1 school of mathematical sciences, Qingdao university, Qingdao 266071, china 2 school of mathematical sciences, capital normal university, beijing 100037, china school of mathematical sciences Qingdao University Qingdao 266071 China school of mathematical sciences Capital Normal University Beijing 100037 China

Brouéand Puig set the definition of nilpotent p-blocks, stated the existence of such blocks, and then proved that there is a unique Brauer character in a nilpotent p-block. The present paper, based on the works of Slattery and Robinson, generalizes the above idea to theπ-block theory of aπ-separable group, defines the nilpotency of aπ-block, and proves that there is a unique B_(π')-character in a nilpotentπ-block.

关键词： π-separable groups π-blocks π-subpairs nilpotentπ-blocks

Some scaled limit theorems for an immigration super-Brownian motion

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Science china Mathematics 2008年第2期51卷 203-214页

作者： ZHANG Mei school of mathematical sciences,beijing normal university,beijing 100875,china 1. school of mathematical sciences Beijing Normal University Beijing 100875 China

In this paper,the small time limit behaviors for an immigration super-Brownian motion are studied,where the immigration is determined by Lebesgue *** first prove a functional central limit theorem,and then study the l... 详细信息

关键词： super-Brownian motion with immigration functional central limit theorem large deviation moderate deviation 60J80 60F05

Commutators of pseudo-differential operators

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Science china Mathematics 2008年第3期51卷 453-460页

作者： LIN Yan school of mathematical sciences, beijing normal university, beijing 100875, china 1. school of mathematical sciences Beijing Normal University Beijing 100875 China

In this paper, the boundedness of commutators generated by pseudo-differential operators and BMO functions is discussed on Lebesgue spaces.

关键词： pseudo-differential operator BMO function commutator Lebesgue space 42B20 35S05 47G30

Infinitely many radial solutions to elliptic prob-lems with critical Sobolev and Hardy terms

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Science china Mathematics 2008年第9期51卷 1609-1618页

作者： TANG ZhongWei school of mathematical sciences, beijing normal university, beijing 100875, china 1. school of mathematical sciences Beijing Normal University Beijing 100875 China

Let Ω ? ? N be a ball centered at the origin with radius R > 0 and N ? 7, 2* = $ \frac{{2N}} {{N - 2}} $ . We obtain the existence of infinitely many radial solutions for the Dirichlet problem ?Δu = $ \frac{\mu } {{|x|^2 }}u + |u|^{2^* - 2} u + \lambda u $ in Ω, u = 0 on ?Ω for suitable positive numbers μ and λ. Such solutions are characterized by the number of their nodes.

关键词： nodal solutions compactness critical Sobolev and Hardy terms 35J60 35B33

On the weak convergence of super-Brownian motion with immigration

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Science china Mathematics 2009年第9期52卷 1875-1886页

作者： ZHANG Mei school of mathematical sciences, beijing normal university, beijing 100875, china school of mathematical sciences Beijing Normal University Beijing 100875 China

We prove fluctuation limit theorems for the occupation times of super-Brownian motion with immigration. The weak convergence of the processes is established, which improves the results in references. The limiting proc... 详细信息

关键词： super-Brownian motion with immigration occupation time process central limit theorem tightness 60J80 60F05