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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 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 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 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.

Gerbes and twisted orbifold quantum cohomology

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science china mathematics 2008年第6期51卷 995-1016页

作者： PAN JianZhong~1 RUAN YongBin~(2,3) YIN XiaoQin~(1,3+) 1 institute of mathematics,academy of mathematics and systems science,chinese academy of sciences,beijing 100080,china 2 Department of mathematics,University of Wisconsin-Madison,WI 53706,USA 3 Department of mathematics,The Hong Kong University of science and Technology,Hong Kong,china institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Department of mathematics University of Wisconsin-Madison Madison USA Department of mathematics The Hong Kong University of Science and Technology Hong Kong China

In this paper,we construct an orbifold quantum cohomology twisted by a flat gerbe. Then we compute these invariants in the case of a smooth manifold and a discrete torsion on a global quotient orbifold.

关键词： gerbe orbifold quantum cohomology 53D45

On ultraproducts of operator algebras

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science china mathematics 2005年第9期 134-145页

作者： LI Weihua institute of mathematics,academy of mathematics and systems science,chinese academy of sciences,beijing 100080,china

Some basic questions on ultraproducts of C-algebras and von Neumann al- gebras,including the relation to K-theory of C-algebras are *** specifically, we prove that under certain conditions,the K-groups of ultraproduct of C-algebras are iso- morphic to the ultraproduct of respective K-groups of *** also show that the ultraproducts of factors of type Ⅱare prime,*** isomorphic to any non-trivial tensor product.

关键词： von Neumann algebras C-algebras ultraproducts K-group double commutants

A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING THE STOKES AND NAVIER-STOKES EQUATIONS PART I. THE LINEAR CASE

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Journal of systems science & Complexity 2001年第4期14卷 278-292页

作者： DUAN Huoyuan (Department of Computer science, china University of Geo-sciences, beijing 100083, china) LIANG Guoping (institute of mathematics, academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china) 中国地质大学（北京）北京 100083 中科院数学所北京 100080

A new stabilized method is established for the Stokes equations with a zero- th term and convection. It is shown that this new methodology is stable and has an optimal error estimates for all mesh-Peclet number, allow... 详细信息

关键词： Stokes equation with zero-th term and convection stabilized finite elements.

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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 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 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

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