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Plus cupping degrees do not form an ideal

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Science in china(Series F) 2004年第5期47卷 635-654页

作者： LI Angsheng1,2.& ZHAO Yicheng1 1. Institute of Software,Chinese Academy of sciences,beijing 100080,{2. 2. school of information sciences,beijing normal university,beijing 1.0871.china 1. Institute of Software Chinese Academy of Sciences 100080 Beijing China 2. school of information sciences Beijing Normal University 100871 Beijing China

A computably enumerable (c.e.,for short)degree a is called plus cupping,if every c.e. degree x with 0 详细信息

A computably enumerable (c.e.,for short)degree a is called plus cupping,if every c.e. degree x with 0

关键词： computably enumerable set Turing degree definability.

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, {2. 100875, china 2.school of Science, {2. Institute of Education, {2. 100011, china 3 school of Mathematical sciences, beijing normal university, {2. 100875, china 4 College of information Science and Technology, beijing normal university, {2. 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―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

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, {2., beijing 100875, china Department of Computer Science, information Technology Institute, beijing 100101, china) [a]school of Mathematical sciences Beijing Normal University Beijing China [b]Department of Computer Science Information Technology Institute Beijing 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.

Calculating soil moisture by remote sensing and analyzing hydrologic cycle process in the Yellow River basin

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Science china(Technological sciences) 2004年第z1期47卷 1-13页

作者： YANG Shengtian1 & LIU Changming1, 2.1. school of Environmental sciences, {2., beijing 100875, china 2. Institute of Geographic Science and Natural Resources Research, beijing 100101, china beijing normal Univ Sch Environm Sci Beijing 100875 Peoples R China Inst Geog Sci & Nat Resources Beijing 100101 Peoples R China

Based on the AVHRR pathfinder remote sensing data, soil moisture, precipitation and evaporation during the period of 1982.1998, soil moisture of all layers of soil-profile (0—1 m) in the Yellow River basin over the 17 years are calculated by the remote sensing model of calculating soil water. The Yellow River basin is divided into seven subcatchments as control sections at the location of six hydrologic stations (Lanzhou, Toudaoguai, Longmen, Sanmenxia, Huayuankou and Lijin). After calculating soil moisture and obtaining runoff data and precipitation data, the dynamical features of hydrological cycle in the Yellow River basin are analyzed for the period from 1982.to 1988 using water balance method. The conclusions are as follows: It is feasible to calculate the soil water on the macro-scale, in the soil profile with temporal continuity by means of remote sensing and survey in land. Some values of the key water cycle factors in the Yellow River are obtained, which include the annual precipitation of 4000 km3, the evapotranspiration of 3000-3500 km3, and the soil moisture transformation of ?500- 500 km3. Consequently, we analyzed the process of the water cycle in the Yellow River over the 17 years, and the results show that the segment upstream of Lanzhou city is a relatively humid region, and the area of internal waters and the reaches of Shanshan is the most desiccated region. Therefore, the runoff in the depth process is intensive and the runoff-generating process is weak in more arid regions.

关键词： the Yellow River, soil moisture, remote sensing, hydrologic cycle.

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 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

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 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

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 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

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 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

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 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 42.15 42.30 42.35