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Infinite-dimensional Hamiltonian Lie superalgebras

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Science china mathematics 2010年第6期53卷 1625-1634页

作者： MU Qiang1,2 & ZHANG YongZheng1,1school of mathematics and statistics,Northeast Normal university,Changchun 130024.{4. 2school of mathematics,Harbin Normal university,Harbin 150025,{4. 1. school of mathematics and statistics Northeast Normal University Changchun 130024 China2. School of Mathematics Harbin Normal University Harbin 150025 China

The natural filtration of the infinite-dimensional Hamiltonian Lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent *** are thereby able to obtain an intrinsic characterization of the Hamiltonian Lie superalgebra and establish a property of the automorphisms of the Lie superalgebra.

关键词： Hamiltonian superalgebra filtration automorphism

Hierarchical linear regression models for conditional quantiles

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Science china mathematics 2006年第12期49卷 1800-1815页

作者： TIAN Maozai & CHEN Gemai school of statistics, Renmin university of china, Beijing 100872, china and Center for Applied statistics, Renmin university of china, Beijing 100872, china Department of mathematics and statistics, university of Calgary, Canada school of statistics Renmin University of China Beijing 100872 China Department of mathematics statistics University of Calgary Canada Center for Applied statistics Renmin University of China Beijing 100872 China

The quantile regression has several useful features and therefore is gradually developing into a comprehensive approach to the statistical analysis of linear and nonlinear response models,but it cannot deal effectively with the data with a hierarchical *** practice,the existence of such data hierarchies is neither accidental nor ignorable,it is a common *** ignore this hierarchical data structure risks overlooking the importance of group effects,and may also render many of the traditional statistical analysis techniques used for studying data relationships *** the other hand,the hierarchical models take a hierarchical data structure into account and have also many applications in statistics,ranging from overdispersion to constructing min-max ***,the hierarchical models are virtually the mean regression,therefore,they cannot be used to characterize the entire conditional distribution of a dependent variable given high-dimensional ***,the estimated coefficient vector (marginal effects)is sensitive to an outlier observation on the dependent *** this article,a new approach,which is based on the Gauss-Seidel iteration and taking a full advantage of the quantile regression and hierarchical models,is *** the theoretical front,we also consider the asymptotic properties of the new method,obtaining the simple conditions for an n1/2-convergence and an asymptotic *** also illustrate the use of the technique with the real educational data which is hierarchical and how the results can be explained.

关键词： hierarchical quantile regression models,EQ algorithm,fixed effects,random effects,regression quantile.

Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models

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Science china mathematics 2006年第2期49卷 145-157页

作者： YIN Changming, ZHAO Lincheng & WEI Chengdong school of mathematics and Information Science, Guangxi university, Manning 530004. china Department of {4. and finance, university of Science and Technology of china, Hefei 230026, china Department of mathematics, Guangxi Teacher College, Manning 530001, china 1. school of mathematics and Information Science Guangxi University Nanning 530004 China 2. Department of statistics and finance University of Science and Technology of China Hefei 230026 China 3. Department of mathematics Guangxi Teacher College Nanning 530001 China

In a generalized linear model with q x 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ZiZ'i,the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.

关键词： generalized linear models quasi-likelihood estimates asymptotic normality strong consistency.

Efficient estimation for additive hazards regression with bivariate current status data

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Science china mathematics 2012年第4期55卷 763-774页

作者： TONG XingWei 1,,HU Tao 2 & SUN JianGuo 3,4.1 school of Mathematical Sciences,Beijing Normal university,Beijing 100875,china 2 school of Mathematical Sciences,Capital Normal university,Beijing 10004.,china 3 school of mathematics,Jilin university,Changchun 130012,china 4.Department of statistics,university of Missouri,Columbia,MO 65211,USA 1. school of Mathematical Sciences Beijing Normal University Beijing 100875 China2. School of Mathematical Sciences Capital Normal University Beijing 100048 China3. School of Mathematics Jilin University Changchun 130012 China4. Department of Statistics University of Missouri Columbia MO 65211 USA

This paper discusses efficient estimation for the additive hazards regression model when only bivariate current status data are available. Current status data occur in many fields including demographical studies and tumorigenicity experiments （Keiding, 1991; Sun, 2006） and several approaches have been proposed for the additive hazards model with univariate current status data （Linet M., 1998; Martinussen and Scheike, 2002）. For bivariate data, in addition to facing the same problems as those with univariate data, one needs to deal with the association or correlation between two related failure time variables of interest. For this, we employ the copula model and an efficient estimation procedure is developed for inference. Simulation studies are performed to evaluate the proposed estimates and suggest that the approach works well in practical situations. An illustrative example is provided.

关键词： bivariate current status data copula model counting processes efficient estimation joint survivalfunction

Existence of unbiased estimate of regression parameters in simple linear EV models

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Science china mathematics 2005年第7期48卷 915-928页

作者： LIU Jixue & CHEN Xiru Department of statistics and finance, university of Science and Technology of china, Hefei 230026, china Department of mathematics, Graduate school of Chinese Academy of Sciences, Beijing 10004., china Department of statistics and finance University of Science and Technology of China Hefei 230026 China Department of mathematics Graduate School Chinese Academy of Sciences Beijing 100049 China

It is well known that for one-dimensional normal EV regression model X = x+ u,Y =α+βx+e, where x, u, e are mutually independent normal variables and Eu=Ee=0, the regression parameters a and β are not identifiable without some restriction imposed on the parameters. This paper discusses the problem of existence of unbiased estimate for a and β under some restrictions commonly used in practice. It is proved that the unbiased estimate does not exist under many such restrictions. We also point out one important case in which the unbiased estimates of a and β exist, and the form of the MVUE of a and β are also given.

关键词： EV regression model unbiased estimate identiflability.

A general type of twisted anomaly cancellation formulas

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Science china mathematics 2010年第7期53卷 1684-1695页

作者： WANG Yong school of mathematics and statistics, Northeast Normal university, Changchun 130024. {4. 1. school of mathematics and statistics Northeast Normal University Changchun 130024 China

For even-dimensional manifolds, we prove some twisted anomaly cancellation formulas which generalize some well-known cancellation formulas. For odd dimensional manifolds, we obtain some modularly invariant characteris... 详细信息

关键词： modular invariance transgression cancellation formulas

On the Symmetry Classes of Functions

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Wuhan university Journal of Natural Sciences 2005年第5期10卷 813-816页

作者： ZHU Ping~1,2, FAN Yun~3 1. school of mathematics and statistics, Wuhan university, Wuhan 4.0072, Hubei, {4. 2. school of Science, Beijing university of Posts and Telecommunications, Beijing 100876, {4. 3. school of mathematics and statistics, Huazhong Normal university, Wuhan 4.0079, Hubei, {4. Wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Beijing university of Posts and Telecommunications School of Science Beijing China (GRID:grid.31880.32) Huazhong Normal university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.411407.7) (ISNI:***)

Let R be an integral domain of characteristic zero such that the corresponding group rings have block decompositions. We first prove that the submodule consisting of all the R-valued ξi-symmetric functions of several variables is a symmetry class, where ξi is any block character. Then we present a relationship among certain operators introduced for block character. Then we present a relationship among certain operators introduced for block characters. As a consequence, we obtain a decomposition of an arbitrary R-valued function of several variables. Finally, we describe the symmetry property of such summands and determine all the symmetry classes.

关键词： symmetry class strict symmetry class blockcharacter ξi-symmetric function block idempotent

Global Existence of Classical Solutions for Some Oldroyd-B Model via the Incompressible Limit

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Chinese Annals of mathematics,Series B 2006年第5期27卷 565-580页

作者： Zhen LEI school of Mathematical Sciences, Fudan university, Shanghai 2004.3, china school of {4. and statistics, Northeast Normal university, Changchun 130024. china. school of Mathematical Sciences Fudan University Shanghai 200433 China school of mathematics statistics Northeast Normal University Changchun 130024 China

In this paper, we prove local and global existence of classical solutions for a system of equations concerning an incompressible viscoelastic fluid of Oldroyd-B type via the incompressible limit when the initial data ... 详细信息

关键词： Incompressible limit Global existence Oldroyd model

A theorem of Fong's type for graded algebras

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Science china mathematics 2005年第5期48卷 577-582页

作者： FAN Yun & ZHU Ping school of mathematics and statistics, Central china Normal {4., Wuhan 4.0079, china school of Mathematical Science, Nankai {4., Tianjin 300071, china 1. school of mathematics and statistics Central China Normal University 430079 Wuhan China 2. school of Mathematical Science Nankai University 300071 Tianjin China

Let G be a finite p-solvable group and k be an algebraic closed field of characteristic p. It is proved that any projective indecomposable module of a G-graded k-algebra is an induced module of a module of the subalgebra graded by a Hall p′-subgroup. A necessary and sufficient condition for the indecomposability of an induced module from a Hall p′-subgroup is obtained.

关键词： group graded algebra indecomposable induced module primitive idempotent.