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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 {2. 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

Quasi-likelihood estimation of average treatment effects based on model information

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science china {2. 2007年第1期50卷 1-12页

作者： Zhi-hua SUN academy of mathematics and {2. science, chinese academy of science, beijing 100080, china academy of mathematics and {2. science Chinese Academy of Science Beijing China

In this paper, the estimation of average treatment effects is considered when we have the model information of the conditional mean and conditional variance for the responses given the covariates. The quasi-likelihood method adapted to treatment effects data is developed to estimate the parameters in the conditional mean and conditional variance models. Based on the model information, we define three estimators by imputation, regression and inverse probability weighted methods. All the estimators are shown asymptotically normal. Our simulation results show that by using the model information, the substantial efficiency gains are obtained which are comparable with the existing estimators.

关键词： average treatment effects inverse probability weighted quasi-likelihood unconfounded assignment treatment model information 62.18

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 {2. of sciences, beijing 100080, china. Institute of systems science, {2. of mathematics and systems science, chinese {2. 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

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

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

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

Fiducial inference in the pivotal family of distributions

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science china {2. 2006年第3期49卷 410-432页

作者： XU Xingzhong & LI Guoying Department of mathematics, beijing Institute of Technology, beijing 100081, china academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china Department of mathematics Beijing Institute of Technology Beijing China academy of mathematics and {2. science Chinese Academy of Sciences Beijing China

In this paper a family, called the pivotal family, of distributions is considered.A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is *** method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.

关键词： confidence bounds, fiducial distributions, fiducial model, frequentist prop-erty, generalized pivotal model, pivotal family of distributions, testing hypotheses.

Relations between Lipschitz functions and convex functions

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science china {2. 2005年第5期48卷 703-710页

作者： RUAN Yingbin Department of mathematics, Fujian Normal University, Fuzhou 350007, china {2. of mathematics and systems science, chinese {2. of sciences, beijing 100080, china Department of mathematics Fujian Normal University Fuzhou China academy of mathematics and {2. science Chinese Academy of Sciences Beijing China

We discuss the relationship between Lipschitz functions and convex functions. By these relations, we give a sufficient condition for the set of points where Lipschitz functions on a Hilbert space is Frechet differenti... 详细信息

关键词： Lipschitz functions convex functions the Frechet differentiability.

Review on the study of entanglement in quantum computation speedup

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chinese science Bulletin 2007年第16期52卷 2161-2166页

作者： DING ShengChao1,3 & JIN Zhi1,2.1 Institute of Computing Technology,chinese academy of {2.s,beijing 100080,china 2.academy of mathematics and systems science,chinese academy of {2.s,beijing 100080,china 3 Graduate University of chinese academy of {2.s,beijing 100080,china Institute of Computing Technology Chinese Academy of Sciences Beijing 100080 China Graduate University of chinese academy of {2.s Beijing 100080 China academy of mathematics and {2. science Chinese Academy of Sciences Beijing 100080 China

The role the quantum entanglement plays in quantum computation speedup has been widely disputed. Some believe that quantum computation's speedup over classical computation is impossible if entan-glement is absent,while others claim that the presence of entanglement is not a necessary condition for some quantum algorithms. This paper discusses this problem systematically. Simulating quantum computation with classical resources is analyzed and entanglement in known algorithms is reviewed. It is concluded that the presence of entanglement is a necessary but not sufficient condition in the pure state or pseudo-pure state quantum computation speedup. The case with the mixed state remains open. Further work on quantum computation will benefit from the presented results.

关键词：量子论量子纠缠量子计算加速模拟