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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 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

ENERGY FLOWS IN COMPLEX ECOLOGICAL SYSTEMS:A REVIEW

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Journal of Systems science & Complexity 2009年第3期22卷 345-359页

作者： Jiang ZHANG Department of Systems science,School of Management,beijing normal university,beijing 100875,china. Department of Systems science School of Management Beijing Normal University

Energy flow drives the complex systems to *** allometric scaling as the universalenergy flow pattern has been found in different scales of ecological *** reflects the generalpower law relationship between flow and *** underlying mechanisms of energy flow patterns areexplained as the branching transportation networks which can be regarded as the result of systematicoptimization of a biological target under *** flows in the ecological system may bemodelled by the food web model and population dynamics on the *** paper reviews thelatest progress on the energy flow patterns,explanatory models for the allometric scaling and modellingapproach of flow and network evolution dynamics in ***,the possibility of generalizingthese flow patterns,modelling approaches to other complex systems is discussed.

关键词： Allometric scaling energy flow flows in complex systems food web.

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 School of mathematical sciences Beijing Normal University Beijing 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

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 School of mathematical sciences Beijing Normal University Beijing 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 School of mathematical sciences Beijing Normal University Beijing 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

Multipliers and Herz type spaces

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science china Mathematics 2008年第10期51卷 1919-1936页

作者： LU ShanZhen School of mathematical sciences, beijing normal university, beijing 100875, china School of mathematical sciences Beijing Normal University Beijing China

Hrmander condition for boundedness of multiplier operators will be replaced by a weaker condition described by certain weighted or non-weighted Herz spaces. Some results on boundedness of multiplier operators are then established. As direct corollaries of main theorems in this paper, several celebrated results on boundedness of multiplier operators will be improved or deduced.

关键词： multiplier Herz space Herz type Hardy space 42B15 42B30 42B35

Hausdorff measures of the image, graph and level set of bifractional Brownian motion

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science china Mathematics 2010年第11期53卷 2973-2992页

作者： LUAN NaNa School of mathematical sciences, beijing normal university, beijing 100875, china School of mathematical sciences Beijing Normal University

Let BH,K = {BH,K(t), t ∈ R+} be a bifractional Brownian motion in Rd. This process is a selfsimilar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brownian motion (which is obtained for K = 1). The exact Hausdorff measures of the image, graph and the level set of BH,K are investigated. The results extend the corresponding results proved by Talagrand and Xiao for fractional Brownian motion.

关键词： bifractional Brownian motion self-similar Gaussian processes image graph level set local time Hausdorff dimension Hausdorff measure

Entropy number and non-linear approximations on multivariate Besov space by manifolds of finite pseudo-dimension

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Progress in Natural science:Materials International 2006年第3期16卷 260-265页

作者： LONG Jingfan and FANG Gensun (School of mathematical sciences, beijing normal university, beijing 100875, china Department of Computer science, Information Technology Institute, beijing 100101, china) School of mathematical sciences Beijing Normal University Beijing 100875 China Department of Computer science Information Technology Institute Beijing 100101 China

We determine the asymptotic order of entropy number and optimal non -linear approximations of anisotropic periodic Besov class of Bpθr(Td') (1≤p≤∞,1≤0≤∞) by manifolds of finite pseudo-dimension in the metric Lq... 详细信息

关键词： Pseudo-dimension anisotropic Besov class of functions entropy number nonlinear width.

Functional central limit theorem for super α-stable processes

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science china Mathematics 2004年第6期47卷 874-881页

作者： HONG WenmingDepartment of Mathematics, beijing normal university, beijing 100875, china Department of Mathematics Beijing Normal University Beijing China

A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α 2α (0 2), the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2α and higher dimensions d 2α, the limiting process is Brownian motion.

关键词： super α-stable processes occupation time central limit theorem evolution equation