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THE MINIMAL CLOSED NON-TRIVIAL IDEALS OF TOEPLITZ ALGEBRAS ON DISCRETE GROUPS

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Chinese Annals of Mathematics,Series B 2000年第3期21卷 367-374页

作者： XU QINGXIANG(Department of Mathematics, shanghai normal university, shanghai 20023{4. {{4..) E-mail:qxxu@*** Department of Mathematics Shanghai Normal University Shanghai 200234 China

Let G be a discrete group and (G, G+) an ordered group. Let (G, GF) be the minimal quasiordered group containing (G, G+). Let G+ (G) and (G) be the corresponding Toeplitz algebras, and γGF,G+ the natural C*-algebra morphism from G+ (G) to GF(G). This paper studies the connection between Ker GF,G+ and the minimal closed ideal ofTG+ (G). It is proved that if G is amenable and GF≠G+, then Ker γGF,G+ is exactly the minimal closed non-trivial ideal of G+ (G). As an application, in the last part of this paper, a character of K-groups of Toeplitz algebras on ordered groups is clarified.

关键词： Discrete group Toeplitz algebra Minimal ideal

Note on families of semistable curves over P^1 with 4.singular fibers whose Jacobian are non-compact

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Science china Mathematics 2010年第7期53卷 1710-1713页

作者： YU Fei 1, 2 1 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, china 2 Department of Mathematics, east china normal university, shanghai 200062, china Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Department of Mathematics East China Normal University Shanghai China

Let f : S → P 1 be a semistable family of curves of genus g 2. We prove that if f admits exactly 5 singular fibers and 4.of them have non-compact Jacobian, then g = 2.

关键词： singular fiber adjoint linear system non-compact Jacobian

Frequency stabilization of Nd:YVO_4.mini-laser using the third-harmonic detection

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Chinese Science Bulletin 2002年第22期47卷 1864-1866页

作者： LIU Yanghui, LI Xiaoyong, Bl Zhiyi & MA LongshengDepartment of Physics, Key Laboratory for Optics and Magnetic Resonance Spectroscopy, east china normal university, shanghai 200062, china Department of Physics Key Laboratory for Optics and Magnetic Resonance Spectroscopy East China Normal University Shanghai China

Via saturated absorption spectroscopy and thethird-harmonic detection techulque, the hyperfine spectra of127I2 near 532 nm have been observed within the tuningrange of a mini Nd: YVO4.KTP laser. The laser is frequencystabilized against one hypeffine structure (hfs) component of127I2. The analysis of error signal shows that it is possible torealize a bouency stability of 3.0 × l0-l3 at 1 s avrmge time.

关键词： Nd:YVO4.KTP laser laser frequency stabilization 3rd-harmonic detection saturated absorption.

A NONLINEAR GALERKIN METHOD WITH VARIABLEMODES FOR KURAMOTO-SIVASHINSKY EQUATION

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Journal of Computational Mathematics 1999年第3期17卷 243-256页

作者： Yu-jiang wu(Depadrtment of Mathematics, shanghai university, Jiadiap shanghai 201800, china Department of Mathematics, Lanzhou university, Lanzhou 750000, china) 上海大学数学系上海

This article proposes a kind of nonlinear Galerkin methods with variable modes for the long-term integration of Kuramoto-Sivashinsky equation. It consists of finding an appropriate or best number of modes in the correction of the method. Convergence results and error estimates are derived for this method. Numerical examples show also the efficiency and advantage of our method over the usual nonlinear Galerkin method and the classical Galerkin method.

关键词： Kuramoto-Sivaskinsky equation nonlinear Galerkin method approximation convergence

CONTACT PROCESS ON HEXAGONAL LATTICE

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Acta Mathematica Scientia 2010年第3期30卷 769-790页

作者：姚强李群昌 Department of Statistics and Actuarial Science School of Finance and Statistics East China Normal University School of Mathematical Sciences Peking University

In this article, we discuss several properties of the basic contact process on hexagonal lattice H, showing that it behaves quite similar to the process on d-dimensional lattice Zd in many aspects. Firstly, we construct a coupling between the contact process on hexagonal lattice and the oriented percolation, and prove an equivalent finite space-time condition for the survival of the process. Secondly, we show the complete convergence theorem and the polynomial growth hold for the contact process on hexagonal lattice. Finally, we prove exponential bounds in the supercritical case and exponential decay rates in the subcritical case of the process.

关键词： Hexagonal lattice contact process critical value complete convergence theorem rate of growth

Accurate studies on the full vibrational energy spectra and molecular dissociation energies for some electronic states of N_(2)molecule

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Science china(Physics,Mechanics & Astronomy) 2005年第4期48卷 385-398页

作者： REN Weiyi1,2, SUN Weiguo1, HOU Shilin3 & FENG Hao4.1. Institute of Physics, College of Chemical Engineering, Sichuan university, Chengdu 610065, china 2. Institute of Theoretical Physics, Xihua normal university, Nanchong 637002, china 3. Department of Physics, china Oceanography university, Qingdao 266003, china 4. College of Physics, Sichuan university, Chengdu 610065, china 1. Institute of Physics College of Chemical Engineering Sichuan University 610065 Chengdu China 2. Institute of Theoretical Physics Xihua Normal University 637002 Nanchong China 3. Department of Physics China Oceanography University 266003 Qingdao China 4. College of Physics Sichuan University 610065 Chengdu China

It is usually very difficult to directly obtain molecular dissociation energy De and all accurate high-lying vibrational energies for most diatomic electronic states using modern experimental techniques or quantum theories, and it is also very difficult to give accurate analytical expression for diatomic molecular dissociation energy. This study proposes a new analytical formula for obtaining accurate molecular dissociation energy based on the LeRoy and Bernstein’s energy expression in dissociation limit. A set of full vibrational energy spectra for some electronic states of N2 molecule are studied using the algebraic method (AM) suggested recently, and the corresponding accurate molecular dissociation energies are evaluated using the proposed new formula and high-lying AM vibrational energies. The results show that the AM spectra and the new theoretical dissociation energies agree excellently with experimental data, and thereby providing a new physical approach to generating accurate dissociation energies for electronic states of diatomic molecules.

关键词： vibrational energy, dissociation energy, nitrogen molecule, algebraic method.

An extended stochastic response surface method for random field problems

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Acta Mechanica Sinica 2007年第4期23卷 445-450页

作者： Shuping Huang Xinjian Kou shanghai Jiaotong university,shanghai 20024.,china shanghai Jiaotong university Shanghai 200240 China

An efficient and accurate uncertainty propagation methodology for mechanics problems with random fields is developed in this paper. This methodology is based on the stochastic response surface method （SRSM） which has been previously proposed for problems dealing with random variables only. This paper extends SRSM to problems involving random fields or random processes fields. The favorable property of SRSM lies in that the deterministic computational model can be treated as a black box, as in the case of commercial finite element codes. Numerical examples are used to highlight the features of this technique and to demonstrate the accuracy and efficiency of the proposed method. A comparison with Monte Carlo simulation shows that the proposed method can achieve numerical results close to those from Monte Carlo simulation while dramatically reducing the number of deterministic finite element runs.

关键词： Stochastic response surface Karhunen-Loeve expansion Polynomial chaos Random field Stochastic finite elements

Highest weight representations of a Lie algebra of Block type

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Science china Mathematics 2007年第4期50卷 549-560页

作者： Yue-zhu WU & Yu-cai SU Department of Mathematics, shanghai Jiaotong university, shanghai 20024., china Department of Mathematics, Qufu {{4. university, Qufu 273165, china Department of Mathematics, university of Science and Technology of china, Hefei 230026, china 1. Department of Mathematics Shanghai Jiaotong University Shanghai 200240 China 2. Department of Mathematics Qufu Normal University Qufu 273165 China 3. Department of Mathematics University of Science and Technology of China Hefei 230026 China

For a field $\mathbb{F}$ of characteristic zero and an additive subgroup G of $\mathbb{F}$ , a Lie algebra B(G) of the Block type is defined with the basis {L α,i , c | α ∈ G ?1 ≤ i ∈ ?} and the relations [L α,i , L β,j ] = ((i + 1)β ? (j + 1)α)L α+β,i+j + αδ α, ?β δ i+j,?2 c, [c, L α,i ] = 0. Given a total order ? on G compatible with its group structure, and any Λ ∈ B(G) 0 * , a Verma B(G)-module M(Λ, ?) is defined, and the irreducibility of M(Λ, ?) is completely determined. Furthermore, it is proved that an irreducible highest weight B(?)-module is quasifinite if and only if it is a proper quotient of a Verma module.

关键词： Verma modules Lie algebras of Block type irreducibility 17B10 17B65 17B68

JACOBI SPECTRAL METHODS FOR MULTIPLE- DIMENSIONAL SINGULAR DIFFERENTIAL EQUATIONS

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Journal of Computational Mathematics 2003年第3期21卷 325-338页

作者： Li-Han Wang Ben-yu Guo (Department of Mathematics, shanghai normal university, shanghai 20023{4. {{4.) Department of Mathematics Shanghai Normal University 上海 200234

Jacobi polynomial approximations in multiple dimensions are investigated. They are applied to numerical solutions of singular differential equations. The convergence analysis and numerical results show their advantages.

关键词： Jacobi approximations Multiple dimensions.