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A Probabilistic Approach to the First Dirichlet Eigenvalue on Non-compact Riemannian Manifold

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Acta Mathematica Sinica,English Series 1997年第1期13卷 116-126页

作者： wang Fengyu (department of mathematics,beijing {4. university,beijing 100875,China) department of mathematics Beijing Normal University 100875 Beijing China

By using diffusion process with absorbing boundary,some lower bounds are obtained for the first Dirichlet eigenvalue of operator Δ+▽h on a non-compact complete Riemannian manifold. The resulting estimates contain McKean’s estimate for ▽h=***,the first Dirichlet eigen- value for elliptic operators on R^d and the first mixed eigenvalue are also *** examples show that our estimates can be sharp even for ▽h≠0.

关键词： Dirichlet eigenvalue Diffusion process Mixed eigenvalue

Information flow and controlling in regularization inversion of quantitative remote sensing

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Science China Earth Sciences 2005年第1期48卷 74-83页

作者： YANG Hua, XU wangli, ZHAO Hongrui, CHEN Xue & wang Jindi Research Center for Remote Sensing and GIS, School of Geography, beijing normal {4., State Key Laboratory of Remote Sensing Science, beijing Key Laboratory for Remote Sensing of Environment and Digital Cities, beijing 100875, China department of mathematics, beijing normal {4., beijing 100875, China 1. Research Center for Remote Sensing and GIS School of Geography Beijing Normal University State Key Laboratory of Remote Sensing Science Beijing Key Laboratory for Remote Sensing of Environment and Digital Cities 100875 Beijing China 2. department of mathematics Beijing Normal University 100875 Beijing China

In order to minimize uncertainty of the inversed parameters to the largest extent by making full use of the limited information in remote sensing data, it is necessary to understand what the information flow in quantitative remote sensing model inversion is, thus control the information flow. Aiming at this, the paper takes the linear kernel-driven model inversion as an example. At first, the information flow in different inversion methods is calculated and analyzed, then the effect of information flow controlled by multi-stage inversion strategy is studied, finally, an information matrix based on USM is defined to control information flow in inversion. It shows that using Shannon entropy decrease of the inversed parameters can express information flow more properly. Changing the weight of a priori knowledge in inversion or fixing parameters and partitioning datasets in multi-stage inversion strategy can control information flow. In regularization inversion of remote sensing, information matrix based on USM may be a better tool for quantitatively controlling information flow.

关键词： regularization inversion, information flow, Shannon entropy decrease, information matrix.

METAMORPHIC EVOLUTION OF COESITE ECLOGITE FROM XINXIAN, HENAN PROVINCE

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Scientia Geologica Sinica 1996年第4期 483-496页

作者： wang Xiaoyan(department of Geography, capital normal university, beijing 100037)

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Test of magnetic susceptibility and grain-size age models of loess

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Progress in Natural Science:Materials International 2007年第11期17卷 1312-1317页

作者： Chen Yimeng1,2,3, Feng Zhaodong4.and Gong Huili1,2(1. MOE and Key Laboratory of Resources Environment and GIS of beijing, beijing 100037, China 2. Key Laboratory of 3D information Acquisition and Application, The capital normal university, beijing 100037, China 3. {4. of Economics & Management of Huizhou university, Huizhou 516007, China 4. Key Laboratory of Western China’s Environmental Systems, Ministry of Education, Lanzhou university, Lanzhou 730000, China) MOE and Key Laboratory of Resources Environment and GIS of beijing Beijing 100037 China Key Laboratory of 3D information Acquisition and Application The Capital Normal University Beijing 100037 China department of Economics & Management of Huizhou university Huizhou 516007 China Key Laboratory of Western China’s Environmental Systems Ministry of Education Lanzhou University Lanzhou 730000 China

Ages of the stratigraphic boundary MIS1/2 and MIS3/4.of the Yuanbu loess section in Linxia are used as the basis of the nodal control age. The age of MIS1/2 and MIS3/4.are obtained from the latest international research result—the climatic events recorded in the stalagmite in the Hulu Cave in Nanjing, that MIS1/2 is 11.5 kaB.P. and MIS3/4.is 59.8 kaB.P.. The ages of the two climatic events contain three nodal age control models (Model 1: 0 kaB.P.—59.8 kaB.P.; Model 2: 0 kaB.P.—11.5 kaB.P. and 11.5 kaB.P.—59.8 kaB.P.; Model 3: 11.5 kaB.P.—59.8 kaB.P.), which are used as the nodal control age separately. The deposition times of various stratigraphic horizons are calculated by using the magnetic susceptibility age model and grain-size age model, and then compared with each other. In addition, the AMS14. age, OSL age and the ages of YD and H events are compared with the ages of the corresponding horizons calculated by the three models of nodal control ages. From the analyses of lithologic characters and climatic stages it has been found that both the magnetic susceptibility age model and the grain-size age model have some defects. Because the accurate control ages are selected as the nodal points of the glacial period or interglacial period, the stratigraphic deposition times determined by the high resolution of magnetic susceptibility age model and grain-size age model approximate to the actual ages. As for the relative accuracy of the two age models, the magnetic susceptibility age model is more accurate than the grain-size age model.

关键词： loess nodal control age magnetic susceptibility age model grain-size age model test

Structure of 〔Na(DB18C6) (CH_3OH)〕_2W_6O_(19)·(DB18C6)·(CH_3OH)

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Chinese Journal of Structural Chemistry 1997年第3期16卷 172-176页

作者： LU Xiao-Ming CHU Yi-Ming DI Jing LIU Shun-Cheng(department of Chemistry, capital normal university beijing 100037, China) department of Chemistry Capital Normal University Beijing 100037 China

Complex [(DB18C6 ) (CH3OH )]2W6O19. (DB18C6 ) - (CH3OH),Mr=2630. 4., monoclinic, space group P21/c, a=18. 699 (5), b= 19. 568 (4., c=22. 785(5) A, β= 112. 91(2)°, V=7679(7) A, Z=4. D.=2- 275 g/cm3, F(000)= 4.92, p= 92. 52 cm-1. The final R=0. 035 and Rw =0. 04. for 5689 observed reflections (I>3σ(I) ). The complex contains one hexatungstate anion and two sodiumcations. Each Na cation is inlaid in the cavity of one dibenzo-18-crown-6 (DB18C6)with six Na-O coordination bonds. In addition, it linked to O atom of CH3OH fromone side of DB18C6 and bonded to one of the terminal O atoms in hexatungstate anionfrom the other side. The two DB18C6 connected with hexatungstate symmetrically bythe long-distance interaction through the O- Na -O bonds with Na- O distances of2. 28(1)~2- 37(1 ) A W-O distances are 1. 68(2) ~2. 34.2) A. C-O distancesin methanol coordinated with cation are 1. 38 (4.) ~ 1- 4. (4. A.

关键词： dibenzo-18-crown-6 (DB18C6) polyoxotungstate anion crystal structure

A Construction of Characteristic Tilting Modules

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Acta Mathematica Sinica,English Series 2002年第1期18卷 129-136页

作者： DENG Bang Ming department of mathematics. beijing normal {4.. beijing 100875. P. H. China department of mathematics Beijing Normal University Beijing P. R. China

Associated with each finite directed quiver Q is a quasi-hereditary algebra. the so-called twisted double of the path algebra kQ. Characteristic tilting modules over this class of quasi-hereditary algebras are constructed. Their endonorphism algebras are explicitly described. It turns out that this class of quasi-hereditary algebras is closed under taking the Ringel dual.

关键词： Quasi-hereditary algebra Characteristic tilting module Ringel dual

Nash Inequalities for Markov Processes in Dimension One

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Acta Mathematica Sinica,English Series 2002年第1期18卷 147-156页

作者： MAO Yong Hua department of mathematics. beijing normal {4.. beijing 100875. P. R. China department of mathematics Beijing Normal University Beijing P. R. China

In this paper. we give characterizations of Nash inequalities for birth-death process and diffusion process on the line. As a by-product. we prove that for these processes. transience implies that the semigroups P(t) ... 详细信息

关键词： Nash inequalities Hardy type inequality Birth-death process Diffusion

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 School of Mathematical Sciences, beijing normal university, beijing 100875, China department of mathematics Beijing Institute of Technology Beijing 100081 China School of Mathematical Sciences Beijing Normal University Beijing 100875 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.

Approximation of functions on the Sobolev space with a Gaussian measure

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Science China mathematics 2010年第2期53卷 373-384页

作者： wang HePing 1, ZHANG YanWei 2 & ZHAI XueBo 1 1 School of Mathematical Sciences, capital normal university, beijing 10004., China 2 department of {4., Zaozhuang university, Zaozhuang 277160, China 1. School of Mathematical Sciences Capital Normal University Beijing 100048 China2. Department of Mathematics Zaozhuang University Zaozhuang 277160 China

We discuss the best approximation of periodic functions by trigonometric polynomials and the approximation by Fourier partial summation operators, Valle-Poussin operators, Ces`aro operators, Abel opera-tors, and Jackson operators, respectively, on the Sobolev space with a Gaussian measure and obtain the average error estimations. We show that, in the average case setting, the trigonometric polynomial subspaces are the asymptotically optimal subspaces in the L q space for 1≤q < ∞, and the Fourier partial summation operators and the Valle-Poussin operators are the asymptotically optimal linear operators and are as good as optimal nonlinear operators in the L q space for 1≤q < ∞.

关键词： average width best approximation approximation by linear operators Sobolev space Gaussian measure