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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, academy of {3. 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, academy of {3. and systems science, chinese academy of sciences, Beijing 100080, china. Institute of systems science, academy of {3. 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

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 systems {3., 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 systems {3., 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

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

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science china mathematics 2008年第9期51卷 1644-1650页

作者： ZHANG Xiao Institute of mathematics, academy of mathematics and {3. 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 53.27 53.50 83.60

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 sciences,Beijing 100080,china {3.,chinese academy of sciences,Beijing 100080,china 3.Graduate University of chinese academy of sciences,Beijing 100080,china Institute of Computing Technology Chinese Academy of Sciences Beijing China Graduate University of chinese academy of sciences Beijing China academy of mathematics and systems {3. Chinese Academy of Sciences Beijing 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

Relations between Lipschitz functions and convex functions

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science china mathematics 2005年第5期48卷 703-710页

作者： RUAN Yingbin Department of mathematics, Fujian Normal University, Fuzhou 3.0007, china academy of mathematics and systems science, chinese academy of sciences, Beijing 100080, china Department of mathematics Fujian Normal University Fuzhou China academy of mathematics and systems {3. 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.

A note on noncommutative moment problems

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science china mathematics 2005年第8期48卷 1144-1151页

作者： MA Xiujuan School of sciences, Hebei University of Technology, Tianjin 3.013., china mathematics Institute, {3. of mathematics and systems science, chinese academy of sciences, Beijing 100080, china School of sciences Hebei University of Technology Tianjin China mathematics Institute Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Noncommutative moment problems for C*-algebras are studied. We generalize a result of Hadwin on tracial states to nontracial case. Our results are applied to obtain simple solutions to moment problems on the square and the circle as well as extend the positive unital functionals from a (discrete) complex group algebra to states on the group C*-algebra.

关键词： moment, free product, state, group C*-algebra.

CONSTRUCTION OF A PRECONDITIONER FOR DOMAIN DECOMPOSITION METHODS WITH POLYNOMIAL LAGRANGIAN MULTIPLIERS

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Journal of Computational mathematics 2001年第2期19卷 213-224页

作者： Qi-ya Hu (Institute of Computational mathematics, academy of mathematics and {3. sciences, chinese academy of sciences, Beijing 100080, china) Guo-ping Liang Jin-zhao Liu (Institute of mathematics, academy of mathematics and {3. sciences, {13. 中科院计算数学与工程计算数学所北京 100080 中科院数学所北京 100080

In this paper we consider domain decomposition methods with polynomial Lagrangian multipliers to two-dimentional elliptic problems, and construct a kind of simple preconditioners for the corresponding interface equation. It will be shown that condition number of the resulting preconditioned interface matrix is almost optimal (namelys it has only logarithmic growth with dimension of the local interface space).

关键词： Domain Decomposition Non-matching grids Lagrangian multipliers Preconditioner Condition number.