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Some scaled limit theorems for an immigration super-Brownian motion

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Science China Mathematics 2008年第2期51卷 203-214页

作者： ZHANG Mei School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China School of Mathematical Sciences Beijing Normal University Beijing China

In this paper,the small time limit behaviors for an immigration super-Brownian motion are studied,where the immigration is determined by Lebesgue measure.We first prove a functional central limit theorem,and then stud... 详细信息

关键词： super-Brownian motion with immigration functional central limit theorem large deviation moderate deviation

A random walk with a branching system in random environments

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Science China Mathematics 2007年第5期50卷 698-704页

作者： Ying-qiu LI Xu LI Quan-sheng LIU School of Mathematics and Computing Sciences Changsha University of Science and TechnologyChangsha 410076China LMAM University of Bretgne-SudBP57356017 VannesPrance

We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on Z with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system.

关键词： random walks in random environments branching processes in random environments rightmost particles phase transition large deviation

THE CHUNG-SMIRNOV LAW FOR THE PRODUCT-LIMIT ESTIMATOR UNDER RANDOM CENSORSHIP

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Chinese Annals of Mathematics,Series B 1991年第1期12卷 96-105页

作者：顾鸣高 McGill University MontrealCanada.

The maximal deviation of the product limit estimator on the whole line isinvestigated.The analogue of Chung-Smirnov law of iterated logarithm is proved undervery mild conditions on censoring.An improved oonvergenoe rate is found and shown tobe best possible The result is proved by an i.***.d.representation scheme of the productlimit estimator on the whole line.Improved rates of convergence for the i.***.d.representation on compact set are also derived.

关键词： estimator deviation analogue maximal logarithm iterated proof biome apply Singh

Moderate deviations for the quenched mean of the super-Brownian motion with random immigration

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Science China Mathematics 2008年第3期51卷 343-350页

作者： HONG WenMing School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education,Beijing Normal University, Beijing 100875, China School of Mathematical Sciences Laboratory of Mathematics and Complex Systems Ministry of Education Beijing Normal University Beijing China

Moderate deviations for the quenched mean of the super-Brownian motion with random immigration are proved for 3≤d≤6, which fills in the gap between central limit theorem(CLT)and large deviation principle(LDP).

关键词： super-Brownian motion large deviation moderate deviation random immigration

EXISTENCE OF MINIMISERS FOR A CLASS OF FREE DISCONTINUITY PROBLEMS IN THE HEISENBERG GROUP H^n

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Acta Mathematica Scientia 2005年第3期25卷 455-469页

作者：宋迎清杨孝平秦姣华 Department of Mathematics & Calculation Hunan City University School of Science Nanjing University of Science & Technology

The purpose of this paper is to prove existence of minimisers of the functional where Ω is an open set of the Heisenberg group Hn, K runs over all closed sets of Hn, u varies in C_H^1(Ω\ K), α,β> 0,q≥1, g ∈ Lq(... 详细信息

关键词： SBV_H function Heisenberg group minimiser energy deviation free discontinuity problem

Approximation by randomly weighting method in censored regression model

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Science China Mathematics 2009年第3期52卷 561-576页

作者： WANG ZhanFeng WU YaoHua ZHAO LinCheng Department of Statistics and Finance University of Science and Technology of ChinaHefei 230026China

Censored regression ("Tobit") models have been in common use, and their linear hypothesis testings have been widely studied. However, the critical values of these tests are usually related to quantities of an unknown error distribution and estimators of nuisance parameters. In this paper, we propose a randomly weighting test statistic and take its conditional distribution as an approximation to null distribution of the test statistic. It is shown that, under both the null and local alternative hypotheses, conditionally asymptotic distribution of the randomly weighting test statistic is the same as the null distribution of the test statistic. Therefore, the critical values of the test statistic can be obtained by randomly weighting method without estimating the nuisance parameters. At the same time, we also achieve the weak consistency and asymptotic normality of the randomly weighting least absolute deviation estimate in censored regression model. Simulation studies illustrate that the per-formance of our proposed resampling test method is better than that of central chi-square distribution under the null hypothesis.

关键词： censored regression model least absolute deviation asymptotic normality local alternative randomly weighting method asymptotic power

X-Ray Diffraction Pattern of Graphite Oxide

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Chinese Physics Letters 2013年第9期30卷 94-96页

作者：母仕佳苏玉长肖立华刘斯东胡特汤洪波 School of Materials Science and Engineering Central South UniversityChangsha 410083

X-ray diffraction patterns of graphite oxide(GO)are theoretically simulated as a function of the displacements of carbon atoms using the Debye–Waller factor in terms of the Warren–Bodenstein equation.The results demon-strate that GO has the turbostratically stacked structure.The high order(001)peaks gradually disappear with the increase in atomic thermal vibrations along𝑑c-axis while the(ℎk0)ones weaken for the vibrations along a-axis.When the displacement deviation𝑣ua𝑏=0.015nm and𝑣𝑑uc=0.100nm the computed result is consistent with the experimental measurements.

关键词： structure. deviation displacement

Influence of Orifice Position deviations on Distribution Performance of Gravity-Type Liquid Distributor Analyzed Through Mathematical Pathway

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Transactions of Tianjin University 2018年第2期24卷 152-159页

作者： Jinsheng Sun Zhiwei Zhang Chengtian Cui Tianpei Li Sheng Fu School of Chemical Engineering and Technology Tianjin University

The distribution performance of the gravity-type liquid distributor(GTLD) significantly affects column operation efficiency and the consequent product quality. In industrial settings, maldistribution is normally considered to be caused by vertical positional or coplanarity errors stemming from deflections associated with manufacture and installation, or even by excessive weight. The lack ofestimation protocols or standards impedes the description ofthis error, which influences the corresponding outflow rates. Given this situation, the paper proposes a lumped parameter, orifice position deviation(OPD), to facilitate the calculation of the relative discharge rate error(RDRE)based on a formula derivation, which allows the systematic analysis of the influence ofa single orifice or weir OPD.The paper introduces a sensitivity factor K as a concise and unified expression in theoretical RDREs for calibrating the influence of OPD on the RDREs ofgeometrically different orifices and weirs. With respect to the GTLD, a larger K indicates the need for more strict OPD requirements. The paper verifies that the extent of GTLD outflow nonuniformity is associated with diverging tendencies regarding its morphology, especially in the orifice and weir, which can be determined using our proposed procedures.

关键词： Liquid distributor Installation Orifice position deviation Relative discharge rate error Sensitivity factor

Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails

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Science China Mathematics 2010年第6期53卷 1421-1434页

作者： LIU Li School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China School of Mathematics and Statistics Wuhan University Wuhan China

This paper studies the moderate deviations of real-valued extended negatively dependent(END) random variables with consistently varying tails.The moderate deviations of partial sums are first given.The results are then used to establish the necessary and sufficient conditions for the moderate deviations of random sums under certain circumstances.

关键词： moderate deviation extended negative dependence consistently varying tail random sum