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RADIAL BASIS FUNCTION INTERPOLATION IN SOBOLEV SPACES AND ITS APPLICATIONS

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Journal of Computational Mathematics 2007年第2期25卷 201-210页

作者： Manping Zhang (School of Mathematical sciences,Fudan university,Shanghai 200433,china Institute of Computational Mathematics,chinese academy of sciences,beijing 100080,china School of Mathematical sciences Fudan university Shanghai 200433

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space H^k（Ω）（k 〉 1）. With a special kind of radial basis function, we construct a basis in H^k（Ω） and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density.

关键词： Sobolev space Radial basis function Global data density Meshless method

Confirmation of a natural hybrid species in Petrocosmea(Gesneriaceae) based on molecular and morphological evidence

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Journal of Systematics and Evolution 2011年第5期49卷 449-463页

作者： 1,3~Zhi-Jing QIU 2~Zu-Li YUAN 1~Zhen-Yu LI 1~Yin-Zheng WANG 1(State Key Laboratory of Systematic and Evolutionary Botany,Institute of Botany,chinese academy of sciences,beijing 100093,china) 2(Henan Agricultural university,Zhengzhou 45002,china) 3.graduate School of the chinese academy of sciences,beijing 1.0049,china) (State Key Laboratory of Systematic and Evolutionary Botany Institute of Botany Chinese Academy of Sciences Beijing 100093 China) (graduate School of the chinese academy of sciences Beijing 100049 China) (Henan Agricultural university Zhengzhou 45002 China)

A natural hybrid species in Petrocosmea named Longianthera in Yanshan County,Yunnan Province is confirmed for the first time based on molecular and morphological *** character count procedure of the variable characters show that Longianthera populations are characteristic of the intermediate morphological traits between its putative parents Yanshan and Petrocosmea *** nuclear ribosomal internal transcribed spacer region and three chloroplast regions of matK,trnL-F,and trnT-L are sequenced in the putative hybrid and the related *** alignment of DNA sequences and the phylogenetic trees could exclude all the other species in Petrocosmea as the parental species except for Yanshan and *** haplotypes in the 31 internal transcribed spacer sequences and six haplotypes in 42 cpDNA sequences were found from 14 individuals of Longianthera *** analyses of DNA sequences,haplotypes,and phylogenetic trees indicate that Longianthera is likely a hybrid species between its putative parents Yanshan and ***,in which Yanshan might be the most possible maternal *** factors may contribute to the natural hybridization between these two parental species in Petrocosmea,such as the overlapped geographic distribution,habitats,flowering periods,and shared ***,the new species of Yanshan and the natural hybrid species of Longianthera are described.

关键词： chloroplast DNA Gesneriaceae ITS morphology natural hybridization Petrocosmea.

Convergence analysis of the adaptive finite element method with the red-green refinement

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Science china Mathematics 2010年第2期53卷 499-512页

作者： ZHAO XuYing 1, 3 , HU Jun 2,? & SHI ZhongCi 1 1 State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, academy of Mathematics and Systems Science, chinese academy of sciences, beijing 100190, china 2 Key Laboratory of Mathematics and Applied Mathematics (Peking university), Ministry of Education and School of Mathematical sciences, Peking university, beijing 100871, china 3.graduate university of chinese academy of sciences, beijing 100190, china State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China graduate university of chinese academy of sciences Beijing China Key Laboratory of Mathematics and Applied Mathematics (Peking university) Ministry of Education and School of Mathematical Sciences Peking University Beijing China

In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B).

关键词： red-green refinement adaptive finite element method convergence non-nested local refinement

Relationship between Surface Pollen and Modern Vegetation in Southwestern china

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Journal of Mountain Science 2010年第2期7卷 176-186页

作者： PAN Tao DAI Erfu and WU Shaohong Institute of Geographic sciences and Natural Resources Research Chinese Academy of Sciences Beijing 100101 China graduate university of chinese academy of sciences BeO'ing 100049 China Institute of Tibetan Plateau Research Chinese Academy of Sciences Beijing 100085 China

Based on the pollen data obtained from thirty-five surface soil samples and investigated vegetation data from seven plant quadrats,the quantitative relationship between surface soil pollen and modern vegetation are studied in the longitudinal range-gorge region (LRGR) in Southwestern china.R-values (referring to pollen assemblages) are calculated with pollen percentage and plant *** coefficients of similarity between pollen and vegetation are *** results show that the pollen assemblages on surface soil of all vegetation zones can basically represent the native vegetation,but the pollen assemblages are not fully according with the *** is due to the influencing factors including pollen preservation ability,pollen production,amount of exotic pollen and pollen *** pollen representation in surface soil is different in families and *** pollen of woody plants such as Pinus,Tsuga,Alnus,Fagus and Castanopsis are over-representative,but those of Quercus,Carpinus Myrica,Elaeocarpaceae,Ericaceae,Theaceae and Llex are underrepresentative;the pollen of herbaceous plants such as Artemisia and Rubiaceae are over-representative,while those of others including Gramineae and Araliaceae are *** R-values of the same taxon pollen in different vegetation zones are different,depending on their distances from the pollen *** coefficients of the similarity between plant communities and pollen assemblages are mostly over 70%,which indicate again that the surface soil pollen and spores assemblages can represent the *** is concluded that there is a good corresponding relationship between surface pollen assemblages and native vegetation in LRGR,and it is of great significance for reconstructing the past vegetation and paleoclimate using quantitative fossil pollen data in this region.

关键词： Longitudinal range-gorge region (LRGR) Pollen assemblage Vegetation R-value Coefficient of similarity

Taxonomic revision of Lepisorus(***.) Ching ***(Polypodiaceae) from china

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Journal of Systematics and Evolution 2009年第6期47卷 581-598页

作者： ~(1,2)Xin-Ping QI ~1Xian-Chun ZHANG~* 1(State Key Laboratory of Systematic and Evolutionary Botany,Institute of Botany,chinese academy of sciences,beijing 100093,china) 2(graduate university of chinese academy of sciences,beijing 1.0049,china) (State Key Laboratory of Systematic and Evolutionary Botany Institute of Botany Chinese Academy of Sciences Beijing 100093 China) (graduate university of chinese academy of sciences Beijing 100049 China)

The taxonomy of Lepisorus(***.) Ching *** in china was revised based on herbarium specimen examinations,field observations,and microscopic study of rhizome scales,soral paraphyses,leaf epidermis, and *** a result,nine species were recognized:Lepisorus macrosphaerus(Baker) Ching,Lepisorus asterolepis (Baker) Ching,Lepisorus marginatus Ching,Lepisorus kuchenensis(***) Ching,Lepisorus megasorus(***.) Ching,Lepisorus kawakamii(Hayata) Tagawa,Lepisorus subsessilis Ching & ***,Lepisorus affinis Ching, and Lepisorus nudus(Hook.) *** kawakamii(Hayata) Tagawa was reinstated;Lepisorus gyirongensis Ching & *** and Lepisorus longus Ching were reduced to synonyms *** and ***,respectively. The subdivision ofLepisorus macrosphaerus was not *** scales and paraphyses are the most useful characters for species delimitation as well as for infrageneric *** of the leaf epidermis and spore ornamentation are usually stable and thus of great significance in understanding the relationships among groups within the genus.

关键词： china Lepisorus Lepisorus sect.Lepisorus Polypodiaceae taxonomic revision

The red damping wing of Gunn-Peterson trough in the high redshift GRBs

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Science china(Physics,Mechanics & Astronomy) 2009年第9期52卷 1428-1433页

作者： XU Zhou1,2 & WEI DaMing1,3 1 Purple Mountain Observatory, chinese academy of sciences, Nanjing 210008, china 2 graduate university of chinese academy of sciences, beijing 100012, china 3 Joint Center for Particle Nuclear Physics and Cosmology of Purple Mountain Observatory-Nanjing university, Nanjing 210008, china Purple Mountain Observatory Chinese Academy of Sciences Nanjing China graduate university of chinese academy of sciences Beijing China Joint Center for Particle Nuclear Physics and Cosmology of Purple Mountain Observatory-Nanjing university Nanjing China

We calculate the red damping wing of Gunn-Peterson trough taking the evolution of the neutral fraction into consideration and take a clear look at the ionized region around the ionizing sources. We get the result that the damping wing flux feature is mainly determined by the neutral hydrogen outside the ionized bubble and the cut off in the damping wing would be useful to get the size of the ionized bubble. We also fit the red damping wing of the recently discovered high redshift GRB080913 and find that the ionized bubble is too small to create apparent cut off in the spectrum of this burst.

关键词： cosmology theory intergalactic medium gamma ray burst

SiO/CNTs:A new anode composition for lithium-ion battery

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Science china Chemistry 2009年第12期52卷 2047-2050页

作者： REN YuRong1,2,3?,QU MeiZhen1 & YU ZuoLong1 1 Chengdu Institute of Organic Chemistry,chinese academy of sciences,Chengdu 610041,china 2 College of Chemistry,Jilin Normal university,Siping 136000,china 3.graduate university of chinese academy of sciences,beijing 100039,china Chengdu Institute of Organic Chemistry Chinese Academy of Sciences Chengdu China College of Chemistry Jilin Normal University Siping China graduate university of chinese academy of sciences Beijing China

A new anode composition SiO/CNTs (carbon nanotubes) has been prepared by chemical vapor deposition (CVD) method. The results of scanning electron microscopy (SEM) confirm that CNTs deposit on small SiO particles,form a cage,and enwrap SiO particles tightly. SiO/CNTs anode composition exhibits an initial discharge and charge capacity of 1171 and 789 mAh/g,and maintains a reversible capacity of 500 mAh/g after 80 cycles. The improvement of the cyclic performance for SiO/CNTs composition is related to the maintaining of the electric network during cycling,which benefits from a tight contact between CNTs and SiO particles.

关键词： SiO/CNTs CVD composition anode Li-ion battery

Nonlinear autoregressive models with heavy-tailed innovation

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Science china Mathematics 2005年第3期48卷 333-340页

作者： JIN Yang & AN Hongzhi School of Statistics, Renmin university of china, beijing 100872, china academy of Mathematics and Systems Science, chinese academy of sciences, beijing 100080, china Sch. of Statistics Renmin Univ. of China Beijing 100872 China Acad. of Mathematics and Syst. Sci. Chinese Acad. of Sci. Beijing 100080 China

In this paper, we discuss the relationship between the stationary marginal tail probability and the innovation's tail probability of nonlinear autoregressive models. We show that under certain conditions that ensure the stationarity and ergodicity, one dimension stationary marginal distribution has the heavy-tailed probability property with the same index as that of the innovation's tail probability.

关键词： nonlinear autoregressive model, innovation, tail probability.

Validating global hydrological models by ground and space gravimetry

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chinese Science Bulletin 2009年第9期54卷 1534-1542页

作者： ZHOU JiangCun1,2,3, SUN HePing1,2 & XU JianQiao1,2 1 Institute of Geodesy and Geophysics, chinese academy of sciences, Wuhan 430077, china 2 Key Laboratory of dynamic geodesy, chinese academy of sciences, Wuhan 430077, china 3.graduate university of chinese academy of sciences, beijing 1.0049, china Institute of Geodesy and Geophysics Chinese Academy of Sciences Wuhan China Key Laboratory of dynamic geodesy Chinese Academy of Sciences Wuhan China graduate university of chinese academy of sciences Beijing China

The long-term continuous gravity observations obtained by the superconducting gravimeters (SG) at seven globally-distributed stations are comprehensively analyzed. After removing the signals related to the Earth's tides and variations in the Earth's rotation, the gravity residuals are used to describe the seasonal fluctuations in gravity field. Meanwhile, the gravity changes due to the air pressure loading are theoretically modeled from the measurements of the local air pressure, and those due to land water and nontidal ocean loading are also calculated according to the corresponding numerical models. The numerical results show that the gravity changes due to both the air pressure and land water loading are as large as 100×10-9 m s-2 in magnitude, and about 10×10-9 m s-2 for those due to the nontidal ocean loading in the coastal area. On the other hand, the monthly-averaged gravity variations over the area surrounding the stations are derived from the spherical harmonic coefficients of the GRACE-recovered gravity fields, by using Gaussian smoothing technique in which the radius is set to be 600 km. Com-pared the land water induced gravity variations, the SG observations after removal of tides, polar mo-tion effects, air pressure and nontidal ocean loading effects and the GRACE-derived gravity variations with each other, it is inferred that both the ground- and space-based gravity observations can effec-tively detect the seasonal gravity variations with a magnitude of 100×10-9 m s-2 induced by the land water loading. This implies that high precision gravimetry is an effective technique to validate the re-liabilities of the hydrological models.

关键词：重力测量水文模型模型验证和空间地面重力变化季节性波动空气压力