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Approximation of dense-n/2-subgraph and table compression problems

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science china mathematics 2005年第9期48卷 1223-1233页

作者： XU Dachuan~1 HAN Jiye~2 & DU Dongle~3 1. College of applied sciences,beijing University of Technology,beijing 100022,china 2. institute of applied mathematics,academy of mathematics and systems science,chinese academy of sciences,beijing 100080,china 3. Faculty of Administration,University of New Brunswick,P.O.Box 4400,Fredericton,NB E3B 5A3,Canada College of applied sciences Beijing University of Technology Beijing 100022 China institute of applied mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China Faculty of Administration University of New Brunswick P.O. Box 4400 Fredericton NB E3B 5A3 Canada

We develop improved approximation algorithms for two NP-hard problems: the dense-n/2-subgraph and table *** on SDP relaxation and advanced rounding techniques,we first propose 0. 5982 and 0. 5970-approximation algorithms respec- tively for the dense-n/2-subgraph problem (DSP) and the table compression problem (TCP). Then we improve these bounds to 0. 6243 and 0. 6708 respectively for DSP and TCP by adding triangle inequalities to strengthen the SDP *** results for TCP beat the 0. 5 bound of a simple greedy algorithm on this problem,and hence answer an open question of Anderson in an affirmative way.

关键词： dense-n/2-subgraph problem(DSP) table compression problem(TCP) SDP approximation ratio

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 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 1. institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 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

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

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 systems sciences, chinese academy of sciences, beijing 100080, china) Guo-ping Liang Jin-zhao Liu (institute of mathematics, academy of mathematics and systems sciences, 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 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 1. Department of mathematics Beijing Institute of Technology Beijing 100081 China 2. academy of mathematics and systems science Chinese Academy of Sciences Beijing 100080 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 mathematics 2005年第8期48卷 1144-1151页

作者： MA Xiujuan School of sciences, Hebei University of Technology, Tianjin 300130, china mathematics institute, academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china 1. School of sciences Hebei University of Technology 300130 Tianjin China 2. mathematics institute Academy of Mathematics and Systems Science Chinese Academy of Sciences 100080 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 mathematics 2006年第3期49卷 320-329页

作者： LIU Gongxiang & YE Yu institute of mathematics, academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china Department of mathematics, University of science and Technology of china, Hefei 230026, china institute of mathematics Academy of Mathematics systems science Chinese Academy of Sciences Beijing 100080 China Department of mathematics University of Science Technology of china Hefei 230026 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.