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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 university, Wuhan 430079, China school of Mathematical Science, Nankai university, Tianjin 300071, China school of mathematics and statistics Central China Normal University Wuhan China school of Mathematical Science Nankai University 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.

On the Cayley-Bacharach property and the construction of vector bundles

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Science China mathematics 2011年第9期54卷 1891-1898页

作者： SUN Hao 1,2 1 Department of mathematics and statistics,Huazhong normal university,Wuhan 430079,China 2 Department of mathematics,East China normal university,Shanghai 200241,China Department of mathematics and statistics Huazhong Normal University Department of mathematics East China Normal University

We study the Cayley-Bacharach property on complex projective smooth varieties of dimension n≥2 for zero dimensional subscheme defined by the zero set of the wedge of r-n + 1 global sections of a rank r≥n vector bund... 详细信息

关键词： Cayley-Bacharach property vector bundle reflexive sheaf k-very ample

Revisit of Sheppard corrections in linear regression

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Science China mathematics 2010年第6期53卷 1435-1451页

作者： LIU TianQing1,ZHANG BaoXue1,HU GuoRong1 & BAI ZhiDong1,2,1Key Laboratory for Applied statistics of MOE and school of mathematics and statistics,northeast normal university,Changchun 130024,China 2Department of statistics and Applied Probability,National university of Singapore,Singapore 117543,Singapore Key Laboratory for Applied statistics of MOE and school of mathematics and statistics Northeast Normal University

Dempster and Rubin(D&R) in their JRSSB paper considered the statistical error caused by data rounding in a linear regression model and compared the Sheppard correction,BRB correction and the ordinary LSE by *** asymptotic results when the rounding scale tends to 0 were also *** a previous research,we found that the ordinary sample variance of rounded data from normal populations is always inconsistent while the sample mean of rounded data is consistent if and only if the true mean is a multiple of the half rounding *** the light of these results,in this paper we further investigate the rounding errors in linear *** notice that these results form the basic reasons that the Sheppard corrections perform better than other methods in D&R examples and their conclusion in general cases is *** in which the Sheppard correction works worse than the BRB correction are also ***,we propose a new approach to estimate the parameters,called "two-stage estimator",and establish the consistency and asymptotic normality of the new estimators.

关键词： asymptotic normality consistency linear regression model rounded data two-stage estimates

Checking for normality in linear mixed models

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Science China mathematics 2012年第4期55卷 787-804页

作者： WU Ping 1,,ZHU LiXing 2,3 & FANG Yun 4 1.school of Finance and statistics,East China normal university,Shanghai 200241,China 2 school of statistics and mathematics,Yunnan university of Finance and Economics,Yunnan 650221,China 3 The Department of mathematics,Hong Kong Baptist university,Hong Kong 999077,China 4 mathematics and Science College,Shanghai normal university,Shanghai 200234,China school of Finance and statistics East China Normal University Shanghai China school of statistics and mathematics Yunnan University of Finance and Economics Yunnan China The Department of mathematics Hong Kong Baptist University Hong Kong China mathematics and Science College Shanghai Normal University Shanghai China

Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.

关键词： linear mixed models estimated best linear unbiased predictors BHEP tests conditional MonteCarlo test

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 430072, Hubei, China 2. school of Science, Beijing university of Posts and Telecommunications, Beijing 100876, China 3. school of mathematics and statistics, Huazhong normal university, Wuhan 430079, Hubei, China school of mathematics and statistics Wuhan University Wuhan Hubei China school of Science Beijing University of Posts and Telecommunications Beijing China school of mathematics and statistics Huazhong Normal University Wuhan Hubei China

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

A Principal Theorem of normal Discretization Schemes for Operator Equations of the First Kind

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Wuhan university Journal of Natural Sciences 2001年第4期6卷 767-768页

作者： Du Nai lin 1, Wang Hannah 2 1.school of mathematics and statistics, Wuhan university, Wuhan 430072, China 2. school of Foreign Languages and Literature,Wuhan university,Wuhan 430072,China school of mathematics and statistics Wuhan University Wuhan China school of Foreign Languages and Literature Wuhan University Wuhan China

The authors announce a newly-proved theorem of theirs. This theorem is of principal significance to numerical computation of operator equations of the first kind.

关键词： operator equation of the first kind normal discretization scheme pure pseudoinverse

A family of transitive modular Lie superalgebras with depth one

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Science China mathematics 2007年第10期50卷 1451-1466页

作者： Wen-de LIU~(1+) Yong-zheng ZHANG~2 ~1 Department of mathematics,Harbin normal university,Harbin 150080,China ~2 Department of mathematics,northeast normal university,Changchun 130024,China Department of mathematics Harbin Normal University Harbin China Department of mathematics Northeast Normal University Changchun China

The embedding theorem is established for Z-graded transitive modular Lie superalgebras g■■■(g-1)satisfying the conditions: (i)g0■■(g-1) and g0-module g-1 is isomorphic to the natural■(g-1)-module; (ii)dim g1=2/3n(2n^2+1),where n=1/2dim g-1. In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian *** restricted Lie superalgebras are also considered.

关键词： flag, divided power algebra, modular Lie superalgebra, embedding theorem

NONLINEAR STABILITY OF VISCOUS SHOCK WAVES FOR ONE-DIMENSIONAL NONISENTROPIC COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH A CLASS OF LARGE INITIAL PERTURBATION

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Acta Mathematica Scientia 2018年第3期38卷 973-1000页

作者： Shaojun TANG Lan ZHANG school of mathematics and statistics Wuhan university school of mathematics and statistics Wuhan University

We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous shock waves are shown to be time asymptotically stable under large initial perturbation with no restriction on the range of the adiabatic exponent provided that the strengths of the viscous shock waves are assumed to be sufficiently *** proofs are based on the nonlinear energy estimates and the crucial step is to obtain the positive lower and upper bounds of the density and the temperature which are uniformly in time and space.

关键词： One-dimensional nonisentropic compressible Navier–Stokes equations viscous shock waves nonlinear stability large initial perturbation

Isometric Immersions into Warped Product Spaces

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Acta Mathematica Sinica,English Series 2010年第12期26卷 2269-2282页

作者： Qun CHEN Cai Rong XIANG~1) school of mathematics and statistics, Wuhan university, Wuhan 430072, P.R. China school of mathematics and statistics Wuhan University Wuhan 430072 China

This paper concerns the submanifold geometry in the ambient space of warped productmanifolds F^n×σ R, this is a large family of manifolds including the usual space forms R^m, S^m and H^m. We give the fundamental theorem for isometric immersions of hypersurfaces into warped product space R^n×σ R, which extends this kind of results from the space forms and several spaces recently considered by Daniel to the cases of infinitely many ambient spaces.

关键词： Isometric immersion hypersurface warped product the fundamental theorem