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Weierstrass形椭圆曲线上的快速点乘公式

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武汉大学学报（理学版） 2008年第5期54卷 530-534页

作者：冯荣权吴宏锋王子龙北京大学数学科学学院北京100871 中国科学院数学与系统科学研究院北京100080

研究了y2=x3+ax2+2atx+at2和y2=x3+ax2+bx这两类椭圆曲线的点乘,得到了快速的三倍乘和倍乘公式,运算花费分别为6M+6S+4C和2M+5S+3C,其中M,S,C分别为有限域中的乘法,平方,常数乘法运算;对于特殊的参数选取,运算花费分别为6M+6S和2M+5S.

关键词：椭圆曲线点乘有效算法倍乘三倍乘

PROBABILISTIC NUMERICAL APPROACH FOR PDE AND ITS APPLICATION IN THE VALUATION OF EUROPEAN OPTIONS

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Journal of Computational mathematics 2001年第6期19卷 591-600页

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

Presents a probabilistic numerical approach for a class of probabilistic differential equation. Application of the Brownian motion and Monte-Carlo method; Application in the valuation of European Options.

关键词： Brownian motion probabilistic numerical solution European Options

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 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

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 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 systems 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

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

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 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 53C27 53C50 83C60

Fiducial inference in the pivotal family of distributions

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science china mathematics 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 systems 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.

A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING THE ADVECTION-DIFFUSION EQUATIONS

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Journal of Computational mathematics 2002年第1期20卷 57-64页

作者： Huo-yuan Duan (Institute of mathematics, academy of mathematics and System sciences, chinese academy of sciences, beijing 100080, china) Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 北京 100080

Focuses on a study on the development of a stabilized finite element method for solving the advection-diffusion equations with a zero Dirichlet boundary condition. Problem formulation; Error analysis.

关键词： advection-diffusion equation stabilized finite element method