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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

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 {4. of Science, beijing Institute of Education, beijing 100011, china 3 {4. 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

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

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 4.B15 4.B30 4.B35

The crustal structure under Sanjiang and its dynamic implications:Revealed by seismic reflection/refraction profile between Zhefang and Binchuan,Yunnan

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Science china Earth sciences 2005年第9期48卷 1329-1336页

作者： ZHANG Zhongjie1, BAI Zhiming1, WANG Chunyong2, TENG Jiwen1, Lü Qingtian3, LI Jiliang1, LIU Yifeng1 & LIU Zhenkuan4.1. Institute of Geology and Geophysics, Chinese Academy of sciences, beijing 100029, china 2. Institute of Geophysics, china Seismological Bureau, beijing 100085, china 3. Institute of Deposition Resource, Chinese Academy of Geosciences, beijing 100037, china 4. school of Exploration and Information, china University of Geosciences, beijing 100083, china 1. Institute of Geology and Geophysics Chinese Academy of Sciences 100029 Beijing China 2. Institute of Geophysics China Seismological Bureau 100085 Beijing China 3. Institute of Deposition Resource Chinese Academy of Geosciences 100037 Beijing China 4. school of Exploration and Information China University of Geosciences 100083 Beijing China

The fault belts in Sanjiang mainly include Jinshajiang-Honghe fault, Lancangjiang fault and Nujiang fault (called Sanjiang faults) in western Yunnan Province, china. By interpreting the wide-angle seismic reflection/refraction profile between Zhefang and Binchuan, which crosses Tengchong and Baoshan blocks in Dianxi (western Yunnan) tectonic zone, we recon- struct the crustal structure with seismic traveltime tomography for crustal P-wave velocity and the seismic scattering image for crustal seismic reflection structure. In this paper, we firstly present the crustal structure images of P-wave velocity and seismic reflection under the wide-angle seismic profile. These results demonstrate that, the crustal velocity structure and seismic reflec- tion structure along the profile can be divided into 3 segments, and there is an obvious difference of crustal structure among the eastern, the western and the middle segment. Generally, crustal P-wave velocities in the Baoshan segment are 0.1―0.2 km/s slower and seismic reflection am- plitudes from Moho discontinuity are stronger than the other 2 segments. In the studied area, crustal thickness is about 4. km, and shows the thickening tendency from west to east along the profile. Additionally, it can be seen that there is one strong-amplitude seismic reflection event as bright points at the depths of 8―10 km, along the segment of 80―115 km of the profile (south- ward of Tengchong); and seismic reflection wave-field from Moho discontinuity varies obviously along the lateral direction. Finally, we make some discussions on the crustal thickening pattern in the Sanjiang fault belt, structural environment of earthquake development and the contact rela- tionship between the Tengchong block, Banshan block and Luxi trough.

关键词： Sanjiang area wide-angle seismic profile crustal structure.

Spatial heterogeneity of the driving forces of cropland change in china

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Science china Earth sciences 2005年第12期48卷 2231-2240页

作者： LIU Xuhua1,2, WANG Jinfeng1, LIU Mingliang4.1 & MENG Bin1,2,3 1. Institute of Geographic sciences and Natural Resources Research, Chinese Academy of sciences, beijing 100101, china 2. Graduate {4. of the Chinese Academy of sciences, beijing 100039, china 3. College of Arts and sciences of beijing Union University, beijing 100083, china 4. {4. of Forestry and Wildlife sciences, Auburn University, Auburn, Alabama, AL3684., USA 1. Institute of Geographic sciences and Natural Resources Research Chinese Academy of Sciences 100101 Beijing China 2. Graduate school of the Chinese Academy of sciences 100039 Beijing China 3. school of Forestry and Wildlife sciences Auburn University Auburn AL36849 Alabama USA 4. College of Arts and sciences of beijing Union University 100083 Beijing China

By using digital satellite remote sensing data acquired in 1987―1989 and 1999―2000 and GIS combined with the natural and socio-economic data, this paper drew an integrated zonation of the cropland change and its driving forces in china. The results indicated that the cropland change in the study period was constrained by geographical factors and driven by cli-mate change as well as socio-economic system. Moreover, the regional differences of the drivers for cropland change were significant. In the midwest of china, natural condition changes and geographical background were the main constraints and drivers, while in Eastern china, social and economic changes and economic policies were the main driving forces. The cropland loss was nationwide. The dominant factors to cause this decrease included buildup of developing area to attract foreign capital and technologies, changes of industry structure due to urban in-fluence, the change of employment notions thanks to living standard improvement, rapid ur-banization due to the expansion of cities and towns, the diminished farming net income partly because of the global warming effects, and the rapid economic growth stimulated by the con-venient transportation system. These factors interact and interdepend with each other to cause the cropland loss in china recently. The reasons for the increase of cropland were primarily the cultivation and deforestation by the farmers who want to increase income. This study on the mechnism of LUCC relied on the cropland change integrated classification considering the natural or human factors both inside and outside the region, which provides a new approach to study the integrated regionalization and LUCC mechanism.

关键词： land use change, driving force, integrated classification, spatial statistics, cropland, china.

Split-plot designs with general minimum lower-order confounding

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Science china Mathematics 2010年第4期53卷 939-952页

作者： WEI JiaLin 1,4.YANG JianFeng 1,LI Peng 3 & ZHANG RunChu 1,2,1 school of mathematical sciences and LPMC,Nankai University,Tianjin 300071,china 2 KLAS and school of Mathematics and Statistics,Northeast Normal University,Changchun 130024.china 3 school of mathematical sciences,Capital Normal University,beijing 100037,china 4.school of sciences,Tianjin University of Commerce,Tianjin 300134.china 1. school of mathematical sciences and LPMC Nankai University Tianjin 300071 China4. School of Sciences Tianjin University of Commerce Tianjin 300134 China3. School of Mathematical Sciences Capital Normal University Beijing 100037 China2. KLAS and School of Mathematics and Statistics Northeast Normal University Changchun 130024 China

Split-plot designs have been widely used in industrial *** to now,most methods for choosing this kind of designs are based on the minimum aberration (MA) ***,by introducing a new pattern,called aliased effect-number pattern (AENP),Zhang et *** a general minimum lowerorder confounding (denoted by GMC for short) criterion and established a general minimum confounding (also denoted by GMC for saving notations) *** is proved that,the GMC criterion selects optimal designs in a more elaborate manner than the existing ones,and when an experimenter has a prior about the importance ordering of factors in experiments the GMC designs are better than other optimal *** this paper we extend the GMC criterion to the split-plot design case and give a GMC-FFSP criterion for ranking split-plot *** comparisons of the new criterion with the MA-MSA-FFSP criterion are given,and the optimal 32-run split-plot designs up to 14.factors under the two criteria are tabulated for comparison and application.

关键词： fractional factorial design GMC criterion minimum aberration split-plot

Fluorescence dynamics of interactions between polyamide PyPyPyβDp and DNA

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Science china Chemistry 2006年第1期49卷 75-80页

作者： ZHANG Huijuan1,2, WANG Jin3, WU Yishi1, YUAN Gu3, AI Xicheng1, WANG Li4.& ZHANG Jianping1 1. State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of sciences, beijing 100080, china 2. school of Life Science and Technology, beijing Institute of Technology, beijing 100081, china 3. College of Chemistry and Molecular Engineering, peking University, beijing 100080, china 4. Center for Condensed Matter Physics, Institute of Physics, Chinese Academy of sciences, beijing 100080, china Correspondence should be addressed to Ai Xicheng and Zhang Jianping 1. State Key Laboratory for Structural Chemistry of Unstable and Stable Species Institute of Chemistry Chinese Academy of Sciences Beijing 100080 China 2. school of Life Science and Technology Beijing Institute of Technology Beijing 100081 China 3. College of Chemistry and Molecular Engineering Peking University Beijing 100080 China 4. Center for Condensed Matter Physics Institute of Physics Chinese Academy of Sciences Beijing 100080 China

The photophysical properties of the polyamide PyPyPyβDp (PPP) were investigated by means of steady-state absorption and fluorescence spectroscopies, as well as time-resolved fluo-rescence spectroscopy. It was found that the excited-state properties of PPP are very sensitive to solvents. In TKMC buffer PPP exhibited weak fluorescence with a decay time constant of 16 ps, while with the decrease of the solvent polarity PPP showed the blue-shifted peak position, increased inten-sity and lengthened life-time for its fluorescence behavior. In the presence of calf thymus DNA, it was observed that the fluorescence intensity was enhanced and the fluorescence lifetime increased from 16 to 32 ps for PPP, which verified that PPP bound into the minor groove of DNA duplex.

关键词： polyamide (PPP), calf thymus DNA (ctDNA), time-resolved fluorescence spectroscopy, recognition dynamics.

|m| Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

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Science china(Physics,Mechanics & Astronomy) 2004年第6期47卷 676-684页

作者： WANG Jing & ZENG Jinyan Department of Physics,Tsinghua University,beijing 100084.china school of Physics,peking University,beijing 100871,china Department of Physics Tsinghua University Beijing 100084 China school of Physics Peking University Beijing 100871 China

The symmetry and |m| partial-wave analysis for two-dimensional (2D) Coulomb-scattering is investigated. As a function of energyE, the |m| partial-wave scattering amplitudef |m|(θ) is analytically continuated to the, negativeE (complexk) plane, and it is found that the bound state energy eigenvalues (E<0) are just located at the poles off |m|(θ) on the positive imaginaryk axis as is expected. In addition, as a function of |m|,f |m|(θ) is analytically continuated to the complex |m| plane, the bound state energy eigenvalues are just located at the poles off |m|(θ) on the positive real |m| axis.

关键词： two-dimensional Coulomb scattering, |m| partial-wave, Regge pole.