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数学进展 2010年第6期39卷 741-746页

作者：王勇东北师范大学数学与统计学院长春吉林130024

在这个注记中,通过研究一些示性式的模不变性,得到了一个关于陈-Connes特征的消去公式.

关键词：模不变性陈-Connes特征消去公式

Adaptive quasi-likelihood estimate in generalized linear models

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Science china.mathematics 2005年第6期48卷 829-846页

作者： CHEN Xia & CHEN Xiru school of mathematics and statistics, Wuhan university, Wuhan 430072, china.Graduate school, Chinese Academy of Science, Beijing 100049, china school of mathematics and statistics Wuhan University Wuhan China Graduate school Chinese Academy of Science Beijing China

This paper gives a thorough theoretical treatment on the adaptive quasilikelihood estimate of the parameters in the generalized linear models. The unknown covariance matrix of the response variable is estimated by the sample. It is shown that the adaptive estimator defined in this paper is asymptotically most efficient in the sense that it is asymptotic normal, and the covariance matrix of the limit distribution coincides with the one for the quasi-likelihood estimator for the case that the covariance matrix of the response variable is completely known.

关键词： generalized linear models, quasi likelihood estimate, adaptive estimate.

WEAK REGULARIZATION FOR A CLASS OF ILL-POSED CAUCHY PROBLEMS

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Acta Mathematica Scientia 2006年第3期26卷 483-490页

作者：黄永忠郑权 Department of mathematics Huazhong university of Science and Technology Wuhan 430074China school of mathematics and statistics Huazhong Normal UniversityWuhan 430079China Department of Mathematics Huazhong University of Science and TechnologyWuhan 430074China

This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibilky method and regularized semigroups. Finally, an example is given.

关键词： Ill-posed Cauchy problem quasi-reversibility family of weakly regularizing operators fractional power regularized semigroup

Optimization Problem of a Predator-prey System with Holling Ⅱ Functional Response

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Optimization Problem of a Predator-prey System with Holling ...

Criteria for Regularity of Elliptic Diffusion Processes and It’s Application

第二十九届中国控制会议

作者： ZENG Zhijun school of mathematics and statistics,KLAC,KLVE,northeast normal university,changchun,130024,P.R.china

This paper deals with an optimal control problem of a predator-prey system with Holling Ⅱ functional *** model under consideration incorporates a refuge protecting（1-u）x of the prey and leaves ux of the prey available to the predator,where u∈[0,1].By utilizing Pontryagin’s maximal principle,we study the optimal control problem regarding u as a control function.

关键词： Optimal control Holling Ⅱ functional response Prey-refuge Predator-prey

来源： cnki会议评论

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Wuhan university Journal of Natural Sciences 2005年第2期10卷 347-350页

作者： LI Bo 1,2 , ZHANG Xiao-min 3 1.school of mathematics and statistics,Huazhong normal university,Wuhan 430079,Hubei,china.2.school of mathematics and statistics, Wuhan university, Wuhan 430072, Hubei, china.3.Faculty of Science,Ningbo university,Ningbo 315211,Zhejiang, china school of mathematics and statistics Huazhong Normal University Wuhan Hubei China school of mathematics and statistics Wuhan University Wuhan Hubei China Faculty of Science Ningbo University Ningbo Zhejiang China

The cone condition for x to be tegular for B under the elliptic diffusionprocess was proved. We also gave a necessary and sufficient condition for 0 to be regular for thornunder the elliptic diffusion process.

关键词： regular capacity thorn diffusion process

CONVERGENCE THEOREMS AND MAXIMAL INEQUALITIES FOR MARTINGALE ERGODIC PROCESSES

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Acta Mathematica Scientia 2010年第4期30卷 1269-1279页

作者：罗光洲马璇刘培德 school of mathematics and statistics Hubei Normal University College of Sciences Huazhong Agricultural University school of mathematics and statistics Wuhan University

In this article, we study two types of martingale ergodic processes. We prove that a.e. convergence and L^p convergence as well as maximal inequalities, which are established both in ergodic theory and martingale setting, also hold well for these new sequences of random variables. Moreover, the corresponding theorems in the former two areas turn out to be degenerate cases of the martingale ergodic theorems proved here.

关键词： Ergodic theory martingale convergence maximal inequalities

扭化Dirac算子的特征值估计和常值长度的调和1-形式(英文)

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数学进展 2011年第2期40卷 200-204页

作者：王勇东北师范大学数学与统计学院长春吉林130024

对带有非平凡常值长度调和1-形式的紧致旋流形,本文证明了扭化Dirac算子的第一个正特征值的下界.

关键词：扭化Dirac算子特征值调和1-形式

On the Markov equivalence of maximal ancestral graphs

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Science china.mathematics 2005年第4期48卷 548-562页

作者： ZHAO Hui, ZHENG Zhongguo & LIU Baijun school of Mathematical Sciences, Peking university, Beijing 100871, china.Department of statistics, Central china.normal university, Wuhan 430079, china school of Mathematical Sciences Peking University Beijing China

Necessary and sufficient conditions for a maximal ancestral graph (MAnG)to be Markov equivalent to another MAnG and to a DAG are provided respectively. Also a polynomial-time algorithm for converting a MAnG into its e... 详细信息

关键词： maximal ancestral graph, Markov equivalence, minimal collider path, m-separation.

THE MINIMAL OPERATOR AND WEIGHTED INEQUALITIES FOR MARTINGALES

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Acta Mathematica Scientia 2006年第1期26卷 31-40页

作者：左红亮刘培德 College of mathematics and statistics Wuhan university

In this article the authors introduce the minimal operator on martingale spaces, discuss some one-weight and two-weight inequalities for the minimal operator and characterize the conditions which make the inequalities... 详细信息

关键词： Minimal operator weight martingale inequality

An efficient algorithm for finding the largest chain graph according to a given chain graph

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Science china.mathematics 2005年第11期48卷 1517-1530页

作者： LIU Baijun,ZHENG Zhongguo & ZHAO Hui school of Mathematical Sciences, Peking university, Beijing 100871, china.Department of statistics, Central china.normal university, Wuhan 430079, china school of Mathematical Sciences Peking University Beijing China Department of statistics Central China Normal University Wuhan China

Chain graph (CG) is a general model of graphical Markov models. Some different chain graphs may describe the same conditional independence structure, then we say that these CGs are Markov equivalent. In 1990 Frydenberg showed that every class of Markov equivalent CGs has a CG which is called the largest chain graph with the greatest number of lines. This paper presents an efficient algorithm for finding the largest chain graph of the corresponding Markov equivalent class of a given CG. The computational complexity of the algorithm is O(n3). It is more efficient than the complexity O(n!) of the present algorithms. Also a more intuitive graphical characterization of the largest chain graph is provided based on the algorithm in this paper.

关键词： graphical Markov model,chain graph,largest chain graph,protected arrows,efficient algorithm