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Harmonic maps with potential from complete manifolds

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Chinese Science Bulletin 1998年第21期43卷 1780-1786页

作者： CHEN Qun mathematics department, Central china normal university, Wuhan 430079, china Institute of mathematics, Fudan university, shanghai 200433, china mathematics department Central China Normal University Wuhan China Institute of mathematics Fudan University Shanghai China

Harmonic maps with potential from complete manifolds are considered. This is a new kind of maps more general than the usual harmonic maps relating to many interesting problems such as equilibrium system of ferromagnetic spin chain and Neumann motion. Aiming at the general properties, the author derives basic gradient estimates and then Liouville type results for these maps, which are interesting in constrast to those of the usual harmonic maps for the presence of potentials.

关键词： harmonic maps potential ferromagnetic chain gradient estimate.

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 1. School of Finance and Statistics East China Normal University Shanghai 200241 China2. School of Statistics and Mathematics Yunnan University of Finance and Economics Yunnan 650221 China3. The Department of Mathematics Hong Kong Baptist University Hong Kong 999077 China4. Mathematics and Science College Shanghai Normal University Shanghai 200234 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

A MODIFIED LEVENBERG-MARQUARDT ALGORITHM FOR SINGULAR SYSTEM OF NONLINEAR EQUATIONS

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Journal of Computational mathematics 2003年第5期21卷 625-636页

作者： Jin-yan Fan (department of mathematics, shanghai Jiaotong university, shanghai 200240, china) department of mathematics Shanghai Jiaotong University 上海 200240

Based on the work of paper [1], we propose a modified Levenberg-Marquardt algoithm for solving singular system of nonlinear equations F(x) = 0, where F(x) : Rn - Rn is continuously differentiable and F'(x) is Lipschitz continuous. The algorithm is equivalent to a trust region algorithm in some sense, and the global convergence result is given. The sequence generated by the algorithm converges to the solution quadratically, if ||F(x)||2 provides a local error bound for the system of nonlinear equations. Numerical results show that the algorithm performs well.

关键词： Singular nonlinear equations Levenberg-Marquardt method Trust region al- gorithm Quadratic convergence.

Highest weight representations of a Lie algebra of Block type

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Science china mathematics 2007年第4期50卷 549-560页

作者： Yue-zhu WU & Yu-cai SU department of mathematics, shanghai Jiaotong university, shanghai 200240, china department of mathematics, Qufu normal university, Qufu 273165, china department of mathematics, university of Science and Technology of china, Hefei 230026, china 1. department of mathematics Shanghai Jiaotong University Shanghai 200240 China 2. department of mathematics Qufu Normal University Qufu 273165 China 3. department of mathematics University of Science and Technology of China Hefei 230026 China

For a field $\mathbb{F}$ of characteristic zero and an additive subgroup G of $\mathbb{F}$ , a Lie algebra B(G) of the Block type is defined with the basis {L α,i , c | α ∈ G ?1 ≤ i ∈ ?} and the relations [L α,i , L β,j ] = ((i + 1)β ? (j + 1)α)L α+β,i+j + αδ α, ?β δ i+j,?2 c, [c, L α,i ] = 0. Given a total order ? on G compatible with its group structure, and any Λ ∈ B(G) 0 * , a Verma B(G)-module M(Λ, ?) is defined, and the irreducibility of M(Λ, ?) is completely determined. Furthermore, it is proved that an irreducible highest weight B(?)-module is quasifinite if and only if it is a proper quotient of a Verma module.

关键词： Verma modules Lie algebras of Block type irreducibility 17B10 17B65 17B68

WHEN CAN THE STABLE ALGEBRA DETERMINE THE STRUCTURE OF A C-ALGEBRA ?

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Chinese Annals of mathematics,Series B 1994年第2期15卷 153-156页

作者： WU LIANGSEN (Institute of mathematics, east normal university, shanghai 2.0062. china) 华东师范大学数学系上海 200062

Let A and B be C-algebras. Suppose that K is the algebra of all compact operators on a seperable Hilbert space, and α is an action on the stable algebra K A induced by SU(∞).It is proved that if A is α-invariant stable isomorphic to B, then there is a-isomorphism between A and B. An analogous result is obtained by considering On K A in the place of K A, where On is the Cuntz algebra (3≤ n < ∞).

关键词： C-algebra Stable algebra Cuntz algebra α-invariance.

THE STABILITY ANALYSIS OF THE θ-METHODS FOR DELAY DIFFERENTIAL EQUMIONS

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Journal of Computational mathematics 1996年第3期14卷 203-212页

作者： H.J.Tian J-X.Kuang(department of mathematics, shanghai normal university, shanghai, china) shanghai normal UNIV DEPT MATH SHANGHAI PEOPLES R CHINA

This paper deals with the stability analysis of θ-methods for the numericalsolution of delny dmerential equations (DDEs). We focus on the behavioux of suchmethods in the solution of the linear test equation y'(t) = a(t)y(t) + b(t)y(t - T),where T > o, a(t) and b(t) are functions from R to C. It is proved that the linearθ-method and the one-leg θ-method are TGP-stable if and only if θ = 1.

关键词： METHODS FOR DELAY DIFFERENTIAL EQUMIONS THE STABILITY ANALYSIS OF THE Math

On Non-Decomposable Hermitian Forms over Gaussian Domain

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Acta Mathematica Sinica,English Series 1998年第4期14卷 447-456页

作者： Zhu Fuzu, department of mathematics, east china normal university, shanghai 2.0062. china department of mathematics East China Normal University 200062 Shanghai China

Methods are presented for the construction of non-decomposable Hermitian forms over the ring of integers of an imaginary quadratic field.

关键词： Non-decomposable form Indecomposable form Odd form Even form Reduced form

Rose solutions with three petals for planar 4-body problems

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Science china mathematics 2010年第12期53卷 3085-3094页

作者： DENG ChunHua 1,2 , ZHANG ShiQing 1, & ZHOU Qing 3 1 Yangtze Center of mathematics and College of mathematics, Sichuan university, Chengdu 610064, china 2 Faculty of mathematics and Physics, Huaiyin Institute of Technology, Huai’an 223001, china 3 department of mathematics, east china normal university, shanghai 2.0062. china 1. Yangtze Center of mathematics and College of mathematics Sichuan University Chengdu 610064 China2. Faculty of Mathematics and Physics Huaiyin Institute of Technology Huai’an 223001 China3. Department of Mathematics East China Normal University Shanghai 200062 China

For planar Newtonian 4-body problems with equal masses, we use variational methods to prove the existence of a non-collision periodic choreography solution such that all bodies move on a rose-type curve with three pet... 详细信息

关键词： 4-body problems with Newtonian potentials rose solutions with three petals winding numbers variational minimization methods

Global Existence of Positive Periodic Solutions for a Distributed Delay Competition Model

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Acta Mathematicae Applicatae Sinica 2003年第3期19卷 491-498页

作者： Xian-yi Li, De-ming Zhudepartment of mathematics, east china normal university, shanghai 2.0062. china department of mathematics and Physics, Nanhua university, Hengyang 421001, china department of mathematics East China Normal University Shanghai 200062 China department of mathematics and Physics Nanhua University Hengyang 421001 China

By using the continuation theorem of Mawhin’s coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition model , where r 1 and r 2 are continuous ω-periodic functions in R + = [0,∞) with are positive continuous ω-periodic functions in R + = [0,∞), b i (i = 1, 2) is nonnegative continuous ω-periodic function in R + = [0,∞), ω and T are positive constants, and . Some known results are improved and extended.

关键词： Global existence positive periodic solution coincidence degree distributed delay model