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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,{3. normal university,{3. 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, {3. 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 3.J60 3.B3.

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, {3. 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 3.S05 47G3.

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, {3. 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 42B3. 42B3.

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, {3. 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

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 {3., beijing 100875, china 2 school of Science, beijing Institute of Education, beijing 100011, china 3.school of mathematical sciences, beijing normal {3., beijing 100875, china 4 College of Information Science and Technology, beijing normal {3., 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

Efficient estimation for additive hazards regression with bivariate current status data

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Science china Mathematics 2012年第4期55卷 763-774页

作者： TONG XingWei 1,,HU Tao 2 & SUN JianGuo 3.4 1 school of mathematical sciences,{3. normal university,{3. 100875,china 2 school of mathematical sciences,Capital normal university,{3. 100048,china 3.school of Mathematics,Jilin university,Changchun 13.012,china 4 Department of Statistics,university of Missouri,Columbia,MO 65211,USA 1. school of mathematical sciences Beijing Normal University Beijing 100875 China2. School of Mathematical Sciences Capital Normal University Beijing 100048 China3. School of Mathematics Jilin University Changchun 130012 China4. Department of Statistics University of Missouri Columbia MO 65211 USA

This paper discusses efficient estimation for the additive hazards regression model when only bivariate current status data are available. Current status data occur in many fields including demographical studies and tumorigenicity experiments （Keiding, 1991; Sun, 2006） and several approaches have been proposed for the additive hazards model with univariate current status data （Linet M., 1998; Martinussen and Scheike, 2002）. For bivariate data, in addition to facing the same problems as those with univariate data, one needs to deal with the association or correlation between two related failure time variables of interest. For this, we employ the copula model and an efficient estimation procedure is developed for inference. Simulation studies are performed to evaluate the proposed estimates and suggest that the approach works well in practical situations. An illustrative example is provided.

关键词： bivariate current status data copula model counting processes efficient estimation joint survivalfunction

TRANSPORTATION INEQUALITIES FOR WEAKLY DEPENDENT SEQUENCES

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Acta Mathematica Scientia 2011年第4期31卷 1494-1502页

作者：马宇韬 school of mathematical sciences Beijing Normal University

In [3., they gave necessary and sufficient condition for T 1 C and then as applications T 1 C for weakly dependent sequences was established. In this note, based on Gozlan-L′eonard characterization for W 1 H -inequal... 详细信息

关键词： W 1 H inequality T p (C)-inequality weakly dependent sequences tensorization

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS FOR A NONLINEAR ELLIPTIC EQUATION ARISING IN ASTROPHYSICS

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Acta Mathematica Scientia 2006年第2期26卷 229-245页

作者：唐仲伟 school of mathematical sciences {3. normal university Beijing 100875China

The author first analyzes the existence of ground state solutions and cylindrically symmetric solutions and then the asymptotic behavior of the ground state solution of the equation -△u =φ（r）u^p-1, u 〉 0 in R^N, u ∈ D^1,2（R^N）, where N ≥ 3. x = （x^1,z） ∈ R^K×R^N-K,2 ≤ K ≤ N,r = ｜x′｜. It is proved that for 2（N-s）/（N-2）〈 p 〈 2^＊ = 2N/（N - 2）, 0 〈 s 〈 2, the above equation has a ground state solution and a cylindrically symmetric solution. For p = 2^＊, the above equation does not have a ground state solution but a cylindrically ***, and when p close to 2^＊, the ground state solutions are not cylindrically symmetric. On the other hand, it is proved that as p close to 2＊, the ground state solution Up has a unique maximum point xp = （x′p, Zp） and as p → 2^＊, ｜x′p｜ → r0 which attains the maximum of φ on R^N. The asymptotic behavior of ground state solution Up is also given, which also deduces that the ground state solution is not cylindrically symmetric as p goes to 2^＊.

关键词： Cylindrical symmetry asymptotic behavior ground state solution