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Asymptotic behavior of the divergence on loop spaces over a compact Riemannian manifold

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chinese Science Bulletin 1998年第4期43卷 272-274页

作者： LI Xiangdong probability laboratory, Institute of {2. mathematics, chinese academy of sciences, beijing 100080, china probability laboratory Institute of Applied Mathematics Chinese Academy of Sciences Beijing China

The asymptotic behavior of the divergence on loop space is studied over a compact Riemannian manifold via quasi_sure analysis. A Sobolev estimate plays a crucial role.

关键词： divergence exponential integrability Sobolev estimate.

GLIVENKO-CANTELLI TYPE THEOREMS ANDTHEIR APPLICATIONS

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Acta Mathematica Scientia 1997年第3期17卷 309-318页

作者：朱力行 ACAD SINICA INST APPL MATHPROBABIL LABBEIJING 100080PEOPLES R CHINA

In this paper, we present a sufficient condition for uniform convergence of means to their expectations over the classes of real functions. Our proof is very simple via connecting this convergence to uniform convergence over the class of indicator functions. Furthermore, we obtain a convergent result concerning a non=VC class with an application to variable transformation for fitting regression model.

关键词： uniform convergence non-VC class of functions variable transformation method

Empirical likelihood confidence regions of the parameters in a partially linear single-index model

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Science china mathematics 2005年第10期48卷 1333-1348页

作者： XUE Liugen~1 & ZHU Lixing~2.1. College of applied sciences,{2. University of Technology,{2. 10002.,china 2. Department of mathematics,Hong Kong Baptist University,Hong Kong,china 1. College of applied sciences Beijing University of Technology 100022 Beijing China 2. Department of mathematics Hong Kong Baptist University Hong Kong China

In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method.

关键词： partially linear single-index model, empirical likelihood, confidence region, chi-square distribution, coverage probability.

A tentative study for the prediction of the CME related geomagnetic storm intensity and its transit time

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Science china(Technological sciences) 2005年第6期48卷 648-668页

作者： ZHAO Xinhua1,2.& FENG Xueshang1,3 1. SIGMA Weather Group, Key laboratory of Space Weather, Center for Space Science and applied Re-search,{2., beijing 100080, china 2. Graduate School of the{2., beijing 100039, china 3. School of Geophysics and Geoinformation Systems, china University of Geosciences, beijing 100083, china 1. SIGMA Weather Group Key Laboratory of Space Weather Center for Space Science and Applied Research Chinese Academy of Sciences 100080 Beijing China 2. Graduate School of the chinese academy of sciences 100039 Beijing China 3. School of Geophysics and Geoinformation Systems China University of Geosciences 100083 Beijing China

Using 80 CME-ICME events during 1997.1―2.02.9, based on the eruptive source locations of CMEs and solar magnetic field observation at the photosphere, a current sheet magnetic coordinate (CMC) system is established in order to study the propagation of CME and its geoeffectiveness. In context of this coordinate system, the effect of the eruptive source location and the form of heliospheric current sheet (HCS) at the eruptive time of CME on the geomagnetic storm intensity caused by CME and the CME’s transit time at the Earth is investigated in detail. Our preliminary conclusions are: 1) The geomagnetic disturbances caused by CMEs tend to have the so-called “same side-opposite side effect”, i.e. CMEs erupt from the same side of the HCS as the earth would be more likely to arrive at the earth and the geomagnetic disturbances associated with them tend to be of larger magnitude, while CMEs erupting from the opposite side would arrive at the earth with less probability and the corresponding geomagnetic disturbance magnitudes would be relatively weaker. 2. The angular separation between the earth and the HCS affect the corresponding disturbance intensity. That is, when our earth is located near the HCS, adverse space weather events occur most probably. 3) The erupting location of the CME and its nearby form of HCS will also affect its arrival time at the earth. According to these conclusions, in this context of CMC coordinate we arrive at new prediction method for estimating the geomagnetic storm intensity (Dstmin) caused by CMEs and their transit times. The application of the empirical model for 80 CME-ICME events shows that the relative error of Dst is within 30% for 59% events with Dstmin≤?50 nT, while the averaged absolute error of transit time is lower than 10 h for all events.

关键词： coronal mass ejections, current sheet magnetic coordinate system, geomagnetic storm intensity, transit time, prediction method.

On notions of harmonicity for non-symmetric Dirichlet form

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Science china mathematics 2010年第6期53卷 1407-1420页

作者： MA ZhiMing1, ZHU RongChan1, & ZHU XiangChan2.1Institute of applied mathematics, {2. of mathematics and Systems Science, chinese academy of sciences, beijing 100190, china 2.chool of Mathematical sciences, Peking University, beijing 100871, china 1. Institute of applied mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China2. School of Mathematical Sciences Peking University Beijing 100871 China

In this paper, we extend the equivalence of the analytic and probabilistic notions of harmonicity in the context of Hunt processes associated with non-symmetric Dirichlet forms on locally compact separable metric spaces. Extensions to the processes associated with semi-Dirichlet forms and nearly symmetric right processes on Lusin spaces including infinite dimensional spaces are mentioned at the end of this paper.

关键词： harmonic functions uniformly integrable martingale SPV integrable non-symmetric Dirichlet forms non-symmetric Beurling-Deny decomposition Hunt processes

First passage times for multidimensional denumerable state Markov processes

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chinese Science Bulletin 1999年第11期44卷 970-980页

作者： XU Guanghui(HSU Guang-Hui) and XU DejuInstitute of applied mathematics ,{2. , beijing 100080, china Asian-Pacific Operations Research Center within CAS and APORS , beijing 100080, china Institue of applied Mathemics Chinese Academy of Sciences Beijing China Asian-Pacific Operations Research Center within CAS and APORS Beijing China

For a general multidimensional denumerable state Markov process with any initial state probability vector, the probability density function and its LS transform of the first passage time to a certain given state set are obtained and the algorithms for them are derived. It is proved that the resulting errors of the algorithms are both uniform in their respective *** numerical results are presented.

关键词： multidimensional denumerable state Markov process first passage time uniformization uniform error.

STRONG REPRESENTATIONS OF THE SURVIVAL FUNCTION ESTIMATOR ON INCREASING SETS FOR TRUNCATED AND CENSORED DATA

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Acta Mathematica Scientia 1999年第3期19卷 251-260页

作者：孙六全郑忠国 chinese Acad Sci Inst Appl Math Beijing 100080 Peoples R China Peking Univ Dept Stat & Probabil Beijing 100871 Peoples R China

In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.

关键词： truncated and censored data cumulative hazard function product-limit estimator strong representations

Necessary and sufficient conditions for the existence of equilibrium in abstract non-autonomous functional differential equations

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Science china mathematics 2010年第8期53卷 2045-2059页

作者： ZHENG ZuoHuan 1 & LI XiLiang 2.1 Institute of applied mathematics,{2. of mathematics and Systems Science,chinese {2. of sciences,beijing 100190,china 2.College of mathematics and Information sciences,Shandong Institute of Business and Technology,Yantai 2.4005,chinaAbstract In this article,we aim to establish necessary and sufficient conditions that guarantee the existence of equilibria and continuous equilibria for the continuous skew-product semiflow induced by a class of 1. Institute of applied mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China2. College of Mathematics and Information Sciences Shandong Institute of Business and Technology Yantai 264005 China

non-autonomous finite-delay functional differential equations without any monotone conditions assumed.A minimal set is constructed in terms of which necessary and sufficient conditions for a continuous equilibrium to ... 详细信息

关键词： continuous equilibrium non-autonomous functional differential equations skew-product semiflows topological dynamics

The variation in the magnetic fluctuation anisotropy across the front boundaries of magnetic clouds and its geomagnetic response

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chinese Science Bulletin 2002年第10期47卷 863-867页

作者： LIU Rui & WEI FengsiDepartment of Geophysics, Peking University, beijing 100871, china {2. for Space Weather, Center for Space Science and applied Research, chinese academy of sciences, beijing 100080, china Department of Geophysics Peking University Beijing China lab for Space Weather Center for Space Science and Applied Research Chinese Academy of Sciences Beijing China

A statistical study of magnetic fluctuations near the front boundaries of magnetic clouds is approached with the method of Minimum Variance Analysis, based on the data of ImpS and Wind spacecraft. New discoveries are that (1) fluctuation anisotropy tends to increase across the front boundaries of magnetic clouds; (2. there is a good correlation between the fluctuation anisotropy and the geomagnetic activity indices; and (3) in some cases, although there is southward field component immediately after the front boundary, Kp index descends (or Dst index ascends) with a corresponding decrease of the fluctuation anisotropy; in other cases with no distinct southward field component, Kp index ascends (or Dst index descends) with a corresponding increase of the fluctuation anisotropy. Thus we suggest that the fluctuation anisotropy might be a useful indicator in diagnosing the magnetic activities of magnetic clouds.

关键词： front boundary of magnetic clouds geomagnetic activity fluctuation anisotropy.