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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 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, {3. 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 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 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 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 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 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

Local and non-local sources of airborne particulate pollution at beijing——The ratio of Mg/Al as an element tracer for estimating the contributions of mineral aerosols from outside beijing

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Science china Chemistry 2005年第3期48卷 253-264页

作者： HAN Lihui1, ZHUANG Guoshun1,2,3. SUN Yele1 & WANG Zifa3.1. The Center for Atmospheric Environmental Study, Department of Chemistry, beijing Normal University, beijing 100875, china 2. Center for Atmospheric Chemistry Study, Department of Environmental Science & Engineering, Fudan University, Shanghai 20043., china 3. LAPC/NZC, Institute of Atmospheric Physics, CAS, beijing 100029, china The Center for Atmospheric Environmental Study Department of Chemistry Beijing Normal University Beijing China Center for Atmospheric Chemistry Study Department of Environmental Science & Engineering Fudan University Shanghai China Institute of Atmospheric Physics CAS LAPC/NZC Beijing China

A new element tracer technique has firstly been established to estimate the contri-butions of mineral aerosols from both inside and outside beijing. The ratio of Mg/Al in aerosol is a feasible element tracer to distinguish between the sources of inside and outside beijing. Mineral aerosol, inorganic pollution aerosol mainly as sulfate and nitrate, and organic aerosol are the major components of airborne particulates in beijing, of which mineral aerosol accounted for 3.%―67% of total suspended particles （TSP）, 10%―70% of fine particles （PM2.5）, and as high as 74% and 90% of TSP and PM2.5, respectively, in dust storm. The sources from outside beijing contributed 62% （3.%―86%） of the total mineral aerosols in TSP, 69% （52%―90%） in PM10, and 76% （59%―93.） in PM2.5 in spring, and 69% （52%―83.）, 79% （52%―93.）, and 45% （7%―79%） in TSP, PM10, and PM2.5, respectively, in winter, while only20% in summer and autumn. The sources from outside beijing contributed as high as 97% during dust storm and were the dominant source of airborne particulates in beijing. The contributions from outside Bei-jing in spring and winter are higher than those in summer, indicating clearly that it was related to the various meteorological factors.

关键词： mineral aerosol local sources non-local sources dust storm re-suspended dust element tracer technique.

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

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 school of mathematical sciences Beijing Normal University Beijing China school of mathematical sciences Capital Normal University Beijing China school of Mathematics Jilin University Changchun China Department of Statistics University of Missouri Columbia 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

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 {3. of mathematical sciences, beijing Normal University, beijing 100875, china Department of Mathematics Beijing Institute of Technology Beijing China school of mathematical sciences Beijing Normal University Beijing 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.