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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, {2., 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

Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science china Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2.1. Department of Mathematics, beijing normal university, beijing 100875, {2. 2. Institute of Applied Physics and Computational Mathematics, beijing 100080, {2. Department of Mathematics Beijing Normal University Beijing China Institute of Applied Physics and Computational Mathematics Beijing China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

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,{2.,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

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, {2., 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

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, {2., 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 42.15 42.30 42.35

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, {2., 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 42.2. 35S05 47G30

Optimal reactions for the synthesis of superheavy nucleus ^(2.0)Hs

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Science china(Physics,Mechanics & Astronomy) 2006年第6期49卷 641-648页

作者： LIU Zuhua1,3 & BAO Jingdong1,2.1. Key Laboratory of Beam Technology and Material Modification of Ministry of Education, beijing normal university, beijing 100875, {2. 2. Physics Department, beijing normal university, beijing 100875, {2. 3. {2. Institute of Atomic Energy, beijing 102.13, {2. Key Laboratory of Beam Technology and Material Modification of Ministry of Education Beijing Normal University Beijing China china Institute of Atomic Energy Beijing China Physics Department Beijing Normal University Beijing China

The superheavy nucleus 2.0Hs is expected to be a “double-magic” deformed nucleus. We have calculated its cross sections of evaporation residue for the reactions 2.8Cm(2.Mg,4n)2.0Hs, 2.4Pu(30Si,4n)2.0Hs, 2.8U(36S,4n)2.0Hs and 2.6Ra(48Ca,4n)2.0Hs using a two-parameter Smoluchowski equation. It is found from our results that 2.6Ra(48Ca,4n)2.0Hs and 2.8U(36S,4n)2.0Hs are two optimal reactions for the synthesis of the superheavy nucleus 2.0Hs due to their large negative Q-values.

关键词： diffused fusion barrier,Smoluchowski equation,superheavy nuclei.

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, {2., beijing 100875, china School of mathematical Sciences Beijing Normal University Beijing 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

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, {2. 2.School of Science, beijing Institute of Education, beijing 100011, {2. 3 School of mathematical Sciences, beijing normal university, beijing 100875, {2. 4 College of Information Science and Technology, beijing normal university, beijing 100875, {2. College of Water Science Key Laboratory for Water and Sediment Sciences of the Ministry of Education Beijing Normal University Beijing China School of Science Beijing Institute of Education Beijing China School of mathematical Sciences Beijing Normal University Beijing China College of Information Science and Technology Beijing Normal University Beijing 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―2.04) 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