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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 {2., 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 {2., 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

Lower bounds for eigenvalues of the Dirac-Witten operator

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science china {2. 2009年第8期52卷 2459-2468页

作者： CHEN YongFa institute of mathematics,{2.,chinese academy of sciences,beijing 100190,china institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

We get optimal lower bounds for the eigenvalues of the Dirac-Witten operator of compact(with or without boundary) spacelike hypersurfaces of Lorentian manifold satisfying certain conditions,just in terms of the mean curvature and the scalar curvature and the spinor energy-momentum tensor. In the limiting case,the spacelike hypersurface is either maximal and Einstein manifold with positive scalar curvature or Ricci-flat manifold with nonzero constant mean curvature.

关键词： Dirac-Witten operator eigenvalue mean curvature scalar curvature 53C2. 53C40 53C80 83C60

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, {2., 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

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 {2., academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china. institute of systems {2., academy of mathematics and systems science, chinese academy of sciences, Be institute of systems {2. 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

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, {2.s, chinese academy of sciences, beijing 100080, china) Guo-ping Liang Jin-zhao Liu (institute of mathematics, {2.s, chinese 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.

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 {2. 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 note on noncommutative moment problems

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science china {2. 2005年第8期48卷 1144-1151页

作者： MA Xiujuan School of sciences, Hebei University of Technology, Tianjin 300130, china {2. institute, academy 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.

Monomial Hopf algebras over fields of positive characteristic

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science china {2. 2006年第3期49卷 320-329页

作者： LIU Gongxiang & YE Yu institute of mathematics, {2., chinese academy of sciences, beijing 100080, china Department of mathematics, University of science and Technology of china, Hefei 2.002., china institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Department of mathematics University of Science and Technology of China Hefei China

In this paper, we study the structures of monomial Hopf algebras over a field of positive characteristic. A necessary and sufficient condition for the monomial coalgebra Cd(n) to admit Hopf structures is given here, and if it is the case, all graded Hopf structures on Cd(n)are completely classified. Moreover, we construct a Hopf algebras filtration on Cd(n) which will help us to discuss a conjecture posed by Andruskiewitsch and Schneider. Finally combined with a theorem by Montgomery, we give the structure theorem for all monomial Hopf algebras.

关键词： monomial coalgebra, Gaussian binomial coefficient, monomial Hopf algebra.