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The Average Widths and Non-linear Widths of the Classes of Multivariate Functions with Bounded Moduli of Smoothness

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 663-674页

作者： Yong-ping Liu, Gui-qiao Xudepartment of Mathematics, beijing normal university, beijing 100875, china department of Mathematics, Tianjin normal Univesity, Tianjin 300074. china department of Mathematics Beijing Normal University Beijing 100875 China department of Mathematics Tianjin Normal Univesity Tianjin 300074 China

The classes of the multivariate functions with bounded moduli on Rd and Td are given and their average σ-widths and non-linear n-widths are discussed. The weak asymptotic behaviors are established for the correspondi... 详细信息

关键词： Multivariate function classes average width non-linear width

Estimates for eigenvalues of Laplacian operator with any order

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Science china Mathematics 2007年第8期50卷 1078-1086页

作者： Fa-en WU~(1+) Lin-fen CAO~2 1 department of Mathematics,beijing Jiaotong university,beijing 100044,china 2 department of Mathematics,Henan normal university,Xinxiang 453007,china department of Mathematics Beijing Jiaotong University Beijing 100044 China department of Mathematics Henan Normal University Xinxiang 453007 China

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 < \lambda _1 \leqslant \lambda _2 \leqslant \cdots \leqslant \lambda _k \leqslant \cdots $$ are the eigenvalues of the Dirichlet Laplacian operator with any order l: $$\left\{ \begin{gathered} ( - \vartriangle )^l u = \lambda u, in D \hfill \\ u = \frac{{\partial u}}{{\partial \vec n}} = \cdots = \frac{{\partial ^{l - 1} u}}{{\partial \vec n^{l - 1} }} = 0, on \partial D \hfill \\ \end{gathered} \right.$$ . Then we obtain an upper bound of the (k+1)-th eigenvalue λ k+1 in terms of the first k eigenvalues. $$\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )} \leqslant \frac{1}{n}[4l(n + 2l - 2)]^{\tfrac{1}{2}} \left\{ {\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{{l - 1}}{l}} \sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{1}{l}} } } } \right\}^{\tfrac{1}{2}} $$ . This ineguality is independent of the domain D. Furthermore, for any l ? 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang.

关键词： Dirichlet problem eigenvalue estimate Laplacian operator 35P15 58G25

THE ESTIMATE AND TEST IN THE SYMMETRICAUXILIARY INFORMATION

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Systems Science and Mathematical Sciences 1998年第2期11卷 117-124页

作者： CUI Hengjian YUAN Xiujiu(department of Mathematics, beijing normal university, beijing 100875, china) 北京师范大学数学系北京

This paper gives an estimate of a symmetric population distribution function Fand a modified K. Pearson statistic in the symmetric auxiliary information. Asymptoticalproperties show that they dominate the usual statistics. The asymptotic distribution ofthe modified K. Pearson statistic under the null hypothesis is derived. The approximateBahadur slope and asymptotic power function of a test based on the modified K. Pearsonstatistic are given. Numerical results show the modified K. Pearson statistic is better thanK. Pearson statistic.

关键词： Empirical likelihood K. Pearson statistic approximate Bahadur slope powerfunction.

Principle and application of three-band gradient difference vegetation index

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Science china Earth Sciences 2005年第2期48卷 241-249页

作者： TANG Shihao, ZHU Qijiang, WANG Jindi, ZHOU Yuyu & ZHAO Feng Research Center for Remote Sensing and GIS, department of Geography, beijing normal university, beijing 100875, china National Satellite Meteorological Center, china Meteorological Administration, beijing 100081, china 1. Research Center for Remote Sensing and GIS Department of Geography Beijing Normal University 100875 Beijing China 2. National Satellite Meteorological Center China Meteorological Administration 100081 Beijing China

Vegetation index is a simple, effective and experiential measurement of terrestrial vegetation activity, and plays a very important role in qualitative and quantitative remote sensing. Aiming at shortages of current vegetation indices, and starting from the analysis of vegetation spectral characteristics, we put forward a new vegetation index, the three-band gradient difference vegetation index (TGDVI), and established algorithms to inverse crown cover fraction and leaf area index (LAI) from it. Theoretical analysis and model simulation show that TGDVI has high saturation point and the ability to remove the influence of background to some degree, and the explicit functional relation with crown cover fraction and LAI can be established. Moreover, study shows that TGDVI also has the ability to partly remove the influence of thin cloud. Experiment in the Shunyi District, beijing, china shows that reasonable result can be reached using the vegetation index to retrieve LAI. We also theoretically analyzed the reason why the normalized difference vegetation index (NDVI) owns the low saturation point, and show that it is determined by the definition of NDVI and the characteristic of vegetation spectra, and is unavoidable to some degree. Meanwhile, through model simulation, we also indicate that the relationship between simple ratio vegetation index (SR) and LAI closes to a piecewise linear one instead of a linear one, which is mainly caused by the influence of background and different change rates of reflectance in red and infrared bands with LAI increasing.

关键词： vegetation index, remote sensing, LAI, crown cover fraction, remote sensing inversion.

Summability of Fourier-Laplace Series with the Method of Lacunary Arithmetical Means at Lebesgue Points

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Acta Mathematica Sinica,English Series 2001年第3期17卷 489-496页

作者： Feng DAI Kun Yang WANG department of Mathematics.beijing normal university.beijing 100875,P.R.china E-mail:wangky@bnu,*** ***

Let ∑n-1 be the unit sphere in the n-dimensional Euclidean space Rn.For a function f ∈L(∑n-1) denote by σNδ（f） the Cesàro means of order δ of the Fourier-Laplace series of *** special value λ∶=（n-2）/2 of δ is known as the critical *** the case when n is even,this paper proves the existence of the‘rare’sequence {nk} such that the summability 1/N sum from k=1 to N σnkλ（f）（x）→f（x）,N→∞ takes place at each Lebesgue point satisfying some antipole conditions.

关键词： Convergence Fourier-Laplace series Spherical harmonics Lebesgue point

Target-Scarching on Percolation

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Communications in Theoretical Physics 2005年第9期44卷 431-434页

作者： YANG Shi--Jie department of Physics, beijing normal university, beijing 100875, china

We study target-searching processes on a percolation, on which a hunter tracks a target by smelling odorsit emits. The odor intensity is supposed to be inversely proportional to the distance it propagates. The Monte Carlosimulation is performed on a 2-dimensional bond-percolation above the threshold. Having no idea of the location of thetarget, the hunter determines its moves only by random attempts in each direction. For lager percolation connectivityP0.90, it reveals a scaling law for the searching time versus the distance to the position of the target. The scalingexponent is dependent on the sensitivity of the hunter. For smaller P, the scaling law is broken and the prohability offinding out the target significantly reduces. The hunter seems trapped in the cluster of the percolation and can hardlyreach the goal.

关键词： percolation searching scaling law

Laser-field-induced magnon amplification in a magnetic semiconductor quantum well under an external magnetic field

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Journal of university of Science and Technology beijing 2003年第5期10卷 69-72页

作者： Peng FengPhysics department, university of Science and Technology beijing, beijing 100083, china Phys. Dept. Univ. of Sci. and Technol. Beijing Beijing 100083 China

The laser-field induced magnon amplification in a magnetic semiconductorquantum well under an external magnetic field was discussed, it is shown that when the laserfrequency is near to the electron cyclotron frequency, no matter how weaker the laser field is, themagnon amplification always occurs. In case of fixed laser frequency, the optical absorption ofmagnons obeys the definite selection rule to the laser field strength. The rate of change of magnonoccupation is calculated, and the amplification condition is given.

关键词： magnon amplification magnetic semiconductor quantum well laser field

Anomalous magnetotransport in LaMn_(1-x)Te_xO_3

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Science china(Physics,Mechanics & astronomy) 2009年第7期52卷 987-992页

作者： TAN GuoTai1,2, CHEN ZhengHao3 & ZHANG XiaoZhong4,5 1 Key Laboratory of Beam Technology & Materials Modification of the Ministry of Education, Institute of Low Energy Nuclear Physics, beijing normal university, beijing 100875, china 2 beijing Radiation Center, beijing 100875, china 3 Laboratory of Optical Physics, Institute of Physics, Chinese Academy of Sciences, beijing 100080, china 4 Key Laboratory of Advanced Materials of the Ministry of Education, department of Materials Science and Engineering, Tsinghua university, beijing 100084, china 5 beijing National Center for Electron Microscopy, Tsinghua university, beijing 100084, china 1. Key Laboratory of Beam Technology & Materials Modification of the Ministry of Education Institute of Low Energy Nuclear Physics Beijing Normal University Beijing 100875 China 2. beijing Radiation Center Beijing 100875 China 3. Laboratory of Optical Physics Institute of Physics Chinese Academy of Sciences Beijing 100080 China 4. Key Laboratory of Advanced Materials of the Ministry of Education Department of Materials Science and Engineering Tsinghua University Beijing 100084 China 5. beijing National Center for Electron Microscopy Tsinghua University Beijing 100084 China

The LaMn1-xTexO3+δ (x=0.1, 0.2, 0.3) were synthesized using solid-state reaction method for the first time. X-ray photoemission spectrum (XPS) shows that in the samples the Te ions have a valence of Te4+, and Mn3+ ions are partly converted into Mn2+ and Mn4+ due to the excess oxygen and Te doping. The magnetotransport associated with Mn2+, Mn3+ and Mn4+ was investigated. The experimental results show that the samples are insulator at 0 T when the amount of Mn3+ is much larger or less than the sum of Mn2+ and Mn4+; by contrast, the samples display metal to insulator transition with increasing temperature when the amount of Mn3+ is close to the sum of Mn2+ and Mn4+. These anomalous magnetotransport behaviors were analyzed in the frame of the double-exchange (DE) mechanism.

关键词： colossal magnetoresistance La-Te-Mn-O magnetotransport

Bergman kernel function on Hua construction of the fourth type

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Progress in Natural Science:Materials International 2007年第8期17卷 893-899页

作者： Yin Weiping~(**) Lin Ping (department of Mathematics,Capital normal university,beijing 100037,china) [a]department of Mathematics Capital Normal University Beijing China

This paper introduces the Hua construction and presents the holomorphic automorphism group of the Hua construction of the fourth *** the Bergman kernel function,under the condition of holomorphie automorphism and the standard complete or- thonormal system of the semi-Reinhardt domain,the infinite series form of the Bergman kernel function is *** applying the prop- erties of polynomial andΓfunctions,various identification relations of the aforementioned form are developed and the explicit formula of the Bergman kernel function for the Hua construction of the fourth type is obtained,which suggest that many of the previously-reported results are only the special cases of our findings.

关键词： Hua construction Bergman kernel function holomorphic automorphism group