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Holomorphic invariant forms of a bounded domain

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science China mathematics 2008年第11期51卷 1945-1964页

作者： LU QiKeng institute of mathematics, {2., {3., beijing 100190, China institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

Given a complete ortho-normal system ? = (?0,?1,?2.…) of L 2.H( $ \mathcal{D} $ ), the space of holomorphic and absolutely square integrable functions in the bounded domain $ \mathcal{D} $ of ? n , we construct a holomorphic imbedding $ \iota _\phi :\mathcal{D} \to \mathfrak{F}(n,\infty ) $ , the complex infinite dimensional Grassmann manifold of rank n. It is known that in $ \mathfrak{F}(n,\infty ) $ there are n closed (μ, μ)-forms τμ (μ = 1,…,n) which are invariant under the holomorphic isometric automorphism of $ \mathfrak{F}(n,\infty ) $ and generate algebraically all the harmonic differential forms of $ \mathfrak{F}(n,\infty ) $ . So we obtain in $ \mathcal{D} $ a set of (μ, μ)-forms ι ? * τμ (μ = 1,…, n), which are independent of the system ? chosen and are invariant under the bi-holomorphic transformations of $ \mathcal{D} $ . Especially the differential metric ds 2.1 associated to the K?hler form ι ? * τ1 is a K?hler metric which differs from the Bergman metric ds 2.of $ \mathcal{D} $ in general, but in case that the Bergman metric is an Einstein metric, ds 1 2.differs from ds 2.only by a positive constant factor.

关键词： complete ortho-normal system holomorphic invariant forms 3.0}3. 3.0}65

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, {2., {3., beijing 100080, China Department of mathematics, University of science and Technology of China, Hefei 2.002., 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.

Modeling and verifying Web services driven by requirements:An ontology-based approach

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science in China(Series F) 2006年第6期49卷 792-820页

作者： HOU Lishan1,3.JIN ZHi1,2.& WU Budan1,4 1. academy of mathematics and systems science, chinese academy of sciences, {2., China 2. {3. of Computing Technology, chinese academy of sciences, {2., China 3. {3. of Software, chinese academy of sciences, {2., China 4. Graduate University of chinese academy of sciences, beijing 100049, China 1. academy of mathematics and systems science Chinese Academy of Sciences Beijing 100080 China 3. institute of Software Chinese Academy of Sciences Beijing 100080 China 2. institute of Computing Technology Chinese Academy of Sciences Bejing 100080 China 4. Graduate University of chinese academy of sciences Beijing 100049 China

Automatic discovery and composition of Web services is an important research area in Web service technology, in which the specification of Web services is a key issue. This paper presents a Web service capability description framework based on the environment ontology. This framework depicts Web services capability in two aspects： the operable environment and the environment changes resulting from behaviors of the Web service. On the basis of the framework, a requirement-driven Web service composition model has been constructed. This paper brings forward the formalization of Web service interactions with π calculus. And an automatic mechanism converting conceptual capability description to the formal process expression has been built. This kind of formal specification assists in verifying whether the composite Web service model matches the requirement.

关键词： Web service environment ontology automatic composition π calculus formal verification.

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,{2.,China 2.{3.,chinese academy of sciences,{2.,China 3.Graduate University of chinese academy of sciences,{2.,China institute of Computing Technology Chinese Academy of Sciences Beijing 100080 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

FOURIER-LEGENDRE PSEUDOSPECTRAL METHOD FOR THE NAVIER-STOKES EQUATIONS

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Journal of Computational mathematics 2000年第3期18卷 225-238页

作者： Jian Li (LSEC, institute of Computational mathematics and Scientific/Engineering Computing, {2. of mathematics and System sciences, chinese academy of sciences, beijing, 100080, China) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京 100080

Constructs a Fourier-Legendre pseudospectral scheme for Navier-Stokes equations with semi-periodic boundary condition. Equation of the scheme; Estimation of errors; Numerical results.

关键词： Navier-Stokes equations Fourier-Legendre pseudospectral method error estimation

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, {2., {3., China 1. Department of mathematics Fujian Normal University 350007 Fuzhou China 2. academy of mathematics and systems science Chinese Academy of Sciences 100080 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.

ON THE CENTRAL RELAXING SCHEMES I:SINGLE CONSERVATION LAWS

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Journal of Computational mathematics 2000年第3期18卷 313-324页

作者： Hua-zhong Tang (LSEC, institute of Computational mathematics and Scientific /Engineering Computing, {2. of mathematics and System sciences, chinese academy of sciences, beijing, 100080, China) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京 100080

Presents a central relaxing scheme for scalar conservation laws. Details on the preliminary equations; Properties of the relaxed schemes; Conclusions.

关键词： hyperbolic conservation laws the relaxing scheme TVD cell entropy inequality

ON DISCRETE PROJECTION AND NUMERICAL BOUNDARY CONDITIONS FOR THE NUMERICAL SOLUTION OF THE UNSTEADY INCOMPRESSIBLE NAVIER-STOKESEQUATIONS

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Journal of Computational mathematics 2002年第1期20卷 35-56页

作者： Lan Chieh Huang (ICMSEC, academy of mathematics and System {2., {3., beijing 100080, China) ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences 北京 100080

Focuses on a study on the fully implicit Crank Nicholson (CN) schemes and three projection methods for approximate preservation of component-consistency under projection. Transformation from incompressible Navier-Stokes equations to differential algebraic equations CN schemes; Local errors of CN projection methods; Numerical boundary conditions.

关键词： differential algebraic equations discrete projection numerical boundary conditions

THE L^2.NORM ERROR ESTIMATE OF NONCONFORMING FINITE ELEMENT METHOD FOR THE 2.D ORDER ELLIPTIC PROBLEM WITH THE LOWEST REGULARITY

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Journal of Computational mathematics 2000年第3期18卷 277-282页

作者： Lie-heng Wang (LSEC, institute of Computational mathematics and Scientific/Engineering Computing, {2. of mathematics and System sciences, chinese academy of sciences, beijing, 100080, China) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京 100080

Presents the abstract L...-norm error estimate of nonconforming finite element method. Use of the Aubin Nitsche Lemma in estimating nonconforming finite element methods; Details on the equations.

关键词： L-2.norm error estimate nonconforming f.e.m. lowest regularity