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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 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

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

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

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 100875 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

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

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 1. school of mathematical Sciences Beijing Normal University Beijing 100875 China

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

On the stability of diffusion processes with state-dependent switching

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Science china Mathematics 2006年第9期49卷 1258-1274页

作者： XI Fubao & ZHAO Liqin Department of Mathematics, beijing Institute of Technology, beijing 100081, china school of mathematical Sciences, beijing normal university, beijing 100875, china Department of Mathematics Beijing Institute of Technology Beijing 100081 China school of mathematical Sciences Beijing Normal University Beijing 100875 China

In this paper we consider the stability for diffusion processes with state-dependent switching. We first prove their Feller continuity by the coupling methods. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions. Finally, we append a very brief discussion about the regularity of these processes.

关键词： Feller continuity, coupling, strong Feller continuity, exponential ergodicity,state-dependent switching.

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 Beijing 100875 China

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.

Development and application of ergodicity model with FRCM and FLAR for hydrological process

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Science china(Technological Sciences) 2009年第2期52卷 379-386页

作者： WANG HongRui1, FENG QiLei2, LIN Xin3 & ZENG WenYi4 1 College of Water Science, Key Laboratory for Water and Sediment Sciences of the Ministry of Education, beijing normal university, beijing 100875, china 2 school of Science, beijing Institute of Education, beijing 100011, china 3 school of mathematical Sciences, beijing normal university, beijing 100875, china 4 College of Information Science and Technology, beijing normal university, beijing 100875, china 1. College of Water Science Key Laboratory for Water and Sediment Sciences of the Ministry of Education Beijing Normal University Beijing 100875 China 2. school of Science Beijing Institute of Education Beijing 100011 China 3. school of mathematical Sciences Beijing Normal University Beijing 100875 China 4. College of Information Science and Technology Beijing Normal University Beijing 100875 China

In this paper, a new ergodic property analysis model of hydrological process is proposed based on fuzzy-rough c-means clustering (FRCM), autocorrelogram, and fuzzy least absolute regression (FLAR). A precipitation time series (1951―2004) from Shanghai Hydrology Station is then analyzed with the model. The results show that the precipitation time series of April, May, June, and September has er-godic property. We conclude that in the long run, the precipitation of April, May, June, and September will not keep decreasing; it will converge to its mean value in some period.

关键词： hydrological process ergodic autocorrelogram fuzzy-rough c-means clustering fuzzy least absolute regression