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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,{2., 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 probability laboratory Institute of Applied Mathematics Chinese Academy of Sciences Bcijing 100080 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,Beijing University of Technology,Beijing 10002.,{2. 2. Department of mathematics,Hong Kong Baptist University,Hong Kong,{2. College of applied sciences Beijing University of Technology Beijing China 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 SIGMA Weather Group Key Laboratory of Space Weather Center for Space Science and Applied Research Chinese Academy of Sciences Beijing China Graduate School of the chinese academy of sciences Beijing China School of Geophysics and Geoinformation Systems China University of Geosciences 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.

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 institute of applied {2. Chinese Academy of Sciences Beijing 100080 China Department of probability and Statistics Peking University Beijing 100871 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

Pairwise entanglement and local polarization of Heisenberg model

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Science china(Physics,Mechanics & Astronomy) 2008年第10期51卷 1515-1522页

作者： XI XiaoQiang1,2. ZHANG Tao3, YUE RuiHong3,4 & LIU WuMing2.1 Department of applied mathematics and Physics, Xi’an {2. of Post and Telecommunications, Xi’an 710061, china 2.Beijing National laboratory for Condensed Matter Physics, {2. of Physics, chinese academy of sciences, Beijing 100080, china 3 {2. of Modern Physics, Northwest University, Xi’an 710069, china 4 Department of Physics, Ningbo University, Ningbo 3152.1, china Department of applied mathematics and Physics Xi’an Institute of Post and Telecommunications Xi’an China Beijing National laboratory for Condensed Matter Physics Institute of Physics Chinese Academy of Sciences Beijing China institute of Modern Physics Northwest University Xi’an China Department of Physics Ningbo University Ningbo China

The characteristics of pairwise entanglement and local polarization (LP) are dis-cussed by studying the ground state (states) of the Heisenberg XX model. The re-sults show that: the ground state (states) is (are) composed of the micro states with the minimal polarization (0 for even qubit and 1/2.for odd qubit); LP and the prob-ability of the micro state have an intimate relation, i.e. the stronger the LP, the smaller the probability, and the same LP corresponds to the same probability; the pairwise entanglement of the ground state is the biggest in all eigenvectors. It is found that the pairwise entanglement is decreased by the state degeneracy and the system size. The concurrence approaches a fixed value of about 0.3412.(for odd-qubit chain) or 0.3491 (for even-qubit chain) if the qubit number is large enough.

关键词： Heisenberg XX model local polarization pairwise entanglement

Some Performance Measures of Transfer Line Consisting of Two Unreliable Machines with Reprocess Rule

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Systems Science and Systems Engineering 1998年第3期8卷 27-36页

作者： LI Wei CAO Jinhua institute of applied mathematics, chinese academy of sciences,Beijing {2.

In this paper, we consider a transfer line with two unreliable machines and a single storage buffer, in which the second machine’s processing time and repair time have general distributions, and a piece processed by machine i will be reprocessed with probability q i (i=1, 2. because of uncompletely or not very well processed just before. At first, the exactly results of the reprocessed rate, the output rate and the blocked probability of machine 1, the reprocessed rate and the starved probability of machine 2. and the production rate of the system, are obtained when the first machine is reliable. And then, some approximating results of above indices are given when two machines are both unreliable.

关键词： transfer line reprocess rule blocked probability production rate.

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 {2. , chinese academy of sciences , 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.

ANALYSIS OF TWO-MACHINE CONWIP SYSTEM:MATRIX GEOMETRIC SOLUTION

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Systems Science and Mathematical sciences 2000年第4期13卷 366-375页

作者： LIU Bin, YUE Dequan, CAO Jinhua, WANG Huanqiu (institute of applied {2., chinese academy of sciences, Beijing 100080, china) institute of applied {2. Chinese Academy of Sciences Beijing 100080 China

In this paper we consider a two-machine CONWIP system. Firstly, we mathematically model the system as a QBD process. By using the matrix geometric solution technique, we obtain the equilibrium conditions of the system. Next, we derive the stationary probability distribution of the process. Finally, we give some important performance measures of the system.

关键词： CONWIP system work-in-process demand order QBD process matrix geometric solution.