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CONVERGENCE AND SUPERCONVERGENCE OF HERMITE BICUBIC ELEMENT FOR EIGENVALUE PROBLEM OF THE BIHARMONIC EQUATION

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Journal of Computational mathematics 2001年第2期19卷 139-142页

作者： Dong-sheng Wu (Institute of systems science, {2. of mathematics and systems sciences, chinese academy of sciences, beijing 100080, china ) 中科院系统科学所北京 100080

Provides information on a study which discussed the convergence and superconvergence for eigenvalue problem of the biharmonic equation using the Hermite bicubic element. Discussion on eigenvalue problem for biharmonic equation; Background on asymptotic error expansions and interpolation postprocessing; Superconvergence approximations to the eigenvalue and eigenfunction.

关键词： Hermite bicubic element biharmonic equation interpolation postprocessing eigenvalue problem

BOUNDARY FEEDBACK STABILIZATION OF NONUNIFORM TIMOSHENKO BEAM WITH A TIPLOAD

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chinese Annals of mathematics,Series B 2001年第4期22卷 485-494页

作者： YAN QINGXU, FENG DEXING Institute of systems science, {2. of mathematics and systems science, chinese academy of sciences, beijing 100080, china. Institute of systems science, {2. of mathematics and systems science, chinese academy of sciences, Be Institute of systems science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

The boundary stabilization problem of a Timoshenko beam attached with a mass at one end is studied. First, with linear boundary force feedback and moment control simultaneously at the end attached with the load, the energy corresponding to the closed loop system is proven to be exponentially convergent to zero as time t →∞. Then, some counterexamples are given to show that, in other casest the corresponding closed loop system is, in general, not stable asymtotically, let alone exponentially.

关键词： Timoshenko beam Boundary feedback control C0 semigroups Exponential stability Multiplier method

On the ratio of different norms of caloric functions and related eigenfunctions of an integral operator

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science china {2. 2012年第8期55卷 1597-1612页

作者： DING YuTao 1,2.& ZHANG LiQun 1,2.1 Institute of mathematics,academy of mathematics and systems science,chinese academy of sciences,beijing 100190,china 2.Hua Loo-Keng Key Laboratory of mathematics,chinese academy of sciences,beijing 100190,china Institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Hua Loo-Keng Key Laboratory of mathematics Chinese Academy of Sciences Beijing China

We investigate the ratio of L 1 and L 2.norms of the Cauchy problem solutions of heat equations with compact support initial *** related asymptotic behavior of the eigenvalues and eigenfunctions of certain integral op... 详细信息

关键词： integral operators eigenvalues heat equation

A CLASS OF NEW PARALLEL HYBRID ALGEBRAIC MULTILEVEL ITERATIONS

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Journal of Computational mathematics 2001年第6期19卷 651-672页

作者： Zhong-zhi Bai (LSEC ICMSEC, academy of mathematics and {2. sciences, chinese academy of sciences, beijing 100080, china) 中科院计算数学与科学工程计算所北京 100080

Presents preconditioning matrices having parallel computing function for the coefficient matrix and a class of parallel hybrid algebraic multilevel iteration methods for solving linear equations. Solution to elliptic ... 详细信息

关键词： elliptic boundary value problem system of linear equations symmetric positive definite matrix multilevel iteration parallel method

Study on the generator f of the operators I_n and I_t

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science china {2. 2010年第10期53卷 2589-2603页

作者： CHEN HanLin academy of mathematics and {2. science,chinese academy of sciences,beijing 100190,china academy of mathematics and {2. science Chinese Academy of Sciences Beijing China

Define two operators In and It,the inner product operator In(g)(x) := j∈Zs(g,f(·-j))f(x-j) and the interpolation operator It(g)(x) := j∈Zs g(j)f(x-j),where f belongs to some space and integer s *** call f the generator of the operators In and *** is well known that there are many results on operators In and *** there remain some important problems to be further *** application we first need to find the available generators (that can recover polynomials as It(p) = p or In(p) = p,p ∈Πm-1) for constructing the relative *** this paper,we focus on the available generator in the class of spline *** shall see that not all spline functions can be used to construct available ***,we do find a spline function in S,of degree m-1,where m is even and S is a class of *** for odd m the problem is still *** on spline functions in this paper are new.

关键词： generator available generator inner product operator spline interpolation operator two-closed refinable

CONVERGENCE OF NONLINEAR CONJUGATE GRADIENT METHODS

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Journal of Computational mathematics 2001年第5期19卷 539-548页

作者： Yu-hong Dai (LSEC, ICMSEC, academy of mathematics and {2. sciences, chinese academy of sciences,beijing 100080, china) 中科院计算数学与科学工程计算所北京 100080

Presents a study on methods for unconstrained optimization. Assumptions of the study; Main results; Convergence properties of the methods under simplified Armijo-type line search.

关键词： unconstrained optimization conjugate gradient (generalized) line search global convergence

Admissibilities of linear estimator in a class of linear models with a multivariate t error variable

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science china {2. 2010年第8期53卷 2011-2019页

作者： YANG GuoQing 1 & WU QiGuang 2.1 Department of mathematics,Tongji University,Shanghai 2.0092.china 2.Institute of {2. science,academy of mathematics and {2. science,chinese academy of sciences,beijing 100190,china Department of mathematics Tongji University Shanghai China Institute of systems science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

This paper discusses admissibilities of estimators in a class of linear models,which include the following common models:the univariate and multivariate linear models,the growth curve model,the extended growth curve model,the seemingly unrelated regression equations,the variance components model,and so *** is proved that admissible estimators of functions of the regression coefficient β in the class of linear models with multivariate t error terms,called as Model II,are also ones in the case that error terms have multivariate normal distribution under a strictly convex loss function or a matrix loss *** is also proved under Model II that the usual estimators of β are admissible for p 2.with a quadratic loss function,and are admissible for any p with a matrix loss function,where p is the dimension of β.

关键词： multivariate t distribution convex loss quadratic loss matrix loss admissible estimator

Holomorphic invariant forms of a bounded domain

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science china {2. 2008年第11期51卷 1945-1964页

作者： LU QiKeng Institute of mathematics, academy of mathematics and systems science, chinese academy of sciences, beijing 100190, china Institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Given a complete ortho-normal system ? = (?0,?1,?2.…) of L 2.H( $ \mathcal{D} $ ), the space of holomorphic and absolutely square integrable functions in the bounded domain $ \mathcal{D} $ of ? n , we construct a holomorphic imbedding $ \iota _\phi :\mathcal{D} \to \mathfrak{F}(n,\infty ) $ , the complex infinite dimensional Grassmann manifold of rank n. It is known that in $ \mathfrak{F}(n,\infty ) $ there are n closed (μ, μ)-forms τμ (μ = 1,…,n) which are invariant under the holomorphic isometric automorphism of $ \mathfrak{F}(n,\infty ) $ and generate algebraically all the harmonic differential forms of $ \mathfrak{F}(n,\infty ) $ . So we obtain in $ \mathcal{D} $ a set of (μ, μ)-forms ι ? * τμ (μ = 1,…, n), which are independent of the system ? chosen and are invariant under the bi-holomorphic transformations of $ \mathcal{D} $ . Especially the differential metric ds 2.1 associated to the K?hler form ι ? * τ1 is a K?hler metric which differs from the Bergman metric ds 2.of $ \mathcal{D} $ in general, but in case that the Bergman metric is an Einstein metric, ds 1 2.differs from ds 2.only by a positive constant factor.

关键词： complete ortho-normal system holomorphic invariant forms 32.36 32.65

A quasi-local mass for 2.spheres with negative Gauss curvature

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science china {2. 2008年第9期51卷 1644-1650页

作者： ZHANG Xiao Institute of mathematics, academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china Institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

We extend our previous definition of quasi-local mass to 2.spheres whose Gauss curvature is negative, and prove its positivity.

关键词： general relativity quasi-local mass positivity 53C2. 53C50 83C60