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L-R smash products for bimodule algebras

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Progress in Natural Science:Materials International 2006年第6期16卷 580-587页

作者： ZHANG Liangyun (department of mathematics, Nanjing Agricultural university, Nanjing 210095, china.department of mathematics, Nanjing university, Nanjing 210008, china. [a] department of mathematics Nanjing Agricultural University Nanjing China [b] department of mathematics Nanjing University Nanjing China

In this paper, we prove that the L-R smash product A(?)H is exactly the twisted smash product A * H if H is a finite dimensional cocommutative Hopf algebra, and give a sufficient and necessary condition for L-R smash products to be bialgebras (Hopf algebras) . For any finite dimensional coquasitriangular Hopf algebra (H,σ), we prove that the L-R smash product H(?)H is semisimple Artinian if H is semisimple and H * is unimodular. In particular, the L-R smash product D(H)* (?)D(H)* semisimple Artinian if the Drin-fel'd double D(H) is semisimple.

关键词： bimodule algebras L-R smash products coquasitriangular Hopf algebras Long bialgebras.

ASYMPTOTIC NORMALITY OF WAVELET ESTIMATOR IN HETEROSCEDASTIC MODEL WITH α-MIXING ERRORS

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Journal of Systems Science & Complexity 2011年第4期24卷 725-737页

作者： Hanying LIANG department of mathematics Tongji University Shanghai 200092 China.

Consider heteroscedastic regression model Yni= g（xni）＋ σniεni （1 〈 i 〈 n）, where σ2ni= f（uni）, the design points （xni, uni） are known and nonrandom, g（.） and f（.） are unknown functions defined on closed interval [0, 1], and the random errors （εni, 1 ≤i≤ n） axe assumed to have the same distribution as （ξi, 1 ≤ i ≤ n）, which is a stationary and a-mixing time series with Eξi =0. Under appropriate conditions, we study asymptotic normality of wavelet estimators of g（.） and f（.）. Finite sample behavior of the estimators is investigated via simulations, too.

关键词： α-mixing asymptotic normality heteroscedastic regression model wavelet estimator.

THE GROWTH THEOREM FOR STARLIKE MAPPINGS ON BOUNDED STARLIKE CIRCULAR DOMAINS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 401-408页

作者： LIU TAISHUN (department of mathematics, university of Science and Technology of china. Hefei 230026, china.REN GUANGBIN (department of mathematics, university of Science and Technology of china. Hefei 230026, china. Univ Sci & Technol china Dept Math Anhua 230026 Peoples R China

The authors obtain the growth and covering theorem for the class of normalized biholomorphic starlike mappings on bounded starlike circular *** type of domain discussed is rather general, since the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it. In the unit disc, it is just the famous growth and covering theorem for univalent *** theorem successfully realizes the initial idea of H. Cartan about how to extend geometric function theory from one variable to several complex variables.

关键词： Starlike mappings Growth theorem Starlike circular domains

THE GPL-STABILITY OF RUNGE-KUTTA METHODS FORDELAY DIFFERENTIAL SYSTEMS

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Journal of Computational mathematics 2000年第1期18卷 75-82页

作者： Biao Yang Lin Qiu Jiao-xun Kuang(department of mathematics, Shanghai Normal university, Shanghai 200234, china.) 上海师范大学上海 200234

Presents a study which dealt with stability of the implicit Runge-Kutta methods for the numerical solutions of the systems of delay differential equations. Stability behavior of the methods; Exponential solutions of t... 详细信息

关键词： delay differential equation implicit Runge-Kutta methods GPL-stability

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

CHARACTERIZATIONS OF JORDAN (?)-SKEW MULTIPLICATIVE MAPS ON OPERATOR ALGEBRAS OF INDEFINITE INNER PRODUCT SPACES

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Chinese Annals of mathematics,Series B 2005年第4期 82-95页

作者： AN RUNLING HOU JINCHUAN department of mathematics, Shanxi university, taiyuan 030000, china. department of mathematics, Shanxi Teachers university, Linfen 041004, Shanxi, china.

Let H and K be indefinite inner product spaces. This paper shows that a bijective map φ:B(H)→B(K) satisfies φ(AB+ + B+A) =φ(A)φ(5)+ +φ(B)+φ(A) for every pair A,B ∈B(H) if and only if either φ(A) = cU AU+ for all A or φ(A) = cUA+U+ for all A; φsatisfies φ(AB+A) = φ(A)φ(B)+φ(A) for every pair A,B ∈B(H) if and only if either φ(A) = UAV for all A or φ(A) = UA+V for all A, where A+ denotes the indefinite conjugate of A, U and V are bounded invertible linear or conjugate linear operators with U+U = c-1I and V+V = cI for some nonzero real number c.

关键词： Indefinite inner product spaces (?)-Automorphisms Jordan product

A CONSTRUCTIVE PROOF OF THE INVERSION FORMULA FOR ZONAL FUNCTIONS ON SL(2, R)

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Chinese Annals of mathematics,Series B 1996年第1期17卷 81-88页

作者： XIAO CHANGBAI ZHENG WEIXING SU WEIYI (department of mathematics, Nanjing university Nanjing 210093, china.) NANJING UNIV DEPT MATHNANJING 210093PEOPLES R CHINA

A constructive proof is given for the inversion formula for zonal functions on SL(2, R). A concretely constructed sequence of zonal drictions are proved to satisfy the inversion formula obtained by Harish-Chandra for compact supported infinitely differentiable zonal *** use of the property of this sequence somehow similar to that of approxination kernels,the authors deduce that the inversion formula is true for continuous zonal functions on SL(2, R)under some condition. The classical result can be viewed as a corollary of the results here.

关键词： Inversion formula Zonal function Approximation kernel

A MULTISTEP FINITE VOLUME METHOD WITH PENALTY FOR THERMAL CONVECTION PROBLEMS IN TWO OR THREE DIMENSIONS

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Journal of Systems Science & Complexity 2008年第1期21卷 129-143页

作者： Min YANG department of mathematics Yantai University Yantai 264005 China

The author considers a thermal convection problem with infinite Prandtl number in two or three dimensions. The mathematical model of such problem is described as an initial boundary value problem made up of three partial differential equations. One equation of the convection-dominated diffusion type for the temperature, and another two of the Stokes type for the normalized velocity and pressure. The approximate solution is obtained by a penalty finite volume method for the Stokes equation and a multistep upwind finite volume method for the convection-diffusion equation. Under suitable smoothness of the exact solution, error estimates in some discrete norms are derived.

关键词： Error estimate finite volume thermal convection problem unstructured meshes.

L~∞ CONVERGENCE OF TRUNC ELEMENT FOR THE BIHARMONIC EQUATION

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Journal of Computational mathematics 1997年第1期15卷 14-22页

作者： M. Wang(department of mathematics, Beijing university, Beijing, china. 北京大学数学系北京

The paper considers the L∞ convergence for TRUNC finite elements solving the boundary value problems of the biharmonic equation. The nearly optimal L∞ estimates for the error of first order derivatives are *** TRUNC plate element is proposed and developed by Argyris et al.. The numerical experiences show that the element has very good .***,[1l2]. The mathematicalproof of convergence of the TRUNC element is given by Shi Zong-ci in paper [3]. Thispaper will consider the L~∞ convergence for the TRUNC plate element.

关键词： Biharmonic equations Convergent boundaries Shape functions Vertices Interpolation Weighting functions Integers