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ON NON-ISOTROPIC JACOBI PSEUDOSPECTRAL METHOD

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Journal of Computational mathematics 2008年第4期26卷 511-535页

作者： Benyu Guo Keji Zhang department of mathematics,shanghai normal university,shanghai 200234,china Scientific Computing Key Laboratory of shanghai Universities Division of Computational Science of E-Institute of shanghai Universities department of mathematics Shanghai Normal University Shanghai 200234

In this paper, a non-isotropic Jacobi pseudospectral method is proposed and its appli- cations are considered. Some results on the multi-dimensional Jacobi-Gauss type interpolation and the related Bernstein-Jackson type inequalities are established, which play an important role in pseudospectral method. The pseudospectral method is applied to a twodimensional singular problem and a problem on axisymmetric domain. The convergence of proposed schemes is established. Numerical results demonstrate the efficiency of the proposed method.

关键词： Jacobi pseudospectral method in multiple dimensions Jacobi-Gauss type inter-polation Bernstein-Jackson type inequalities Singular problem Problem on axisymmetricdomain.

A lumped mass finite element method for vibration analysis of elastic plate-plate structures

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Science china mathematics 2010年第6期53卷 1453-1474页

作者： LAI JunJiang1,HUANG JianGuo2,3,& SHI ZhongCi4 1department of mathematics,Minjiang university,Fuzhou 350108,china 2department of mathematics,shanghai Jiao Tong university,shanghai 200240,china 3Division of Computational Science,E-Institute of shanghai Universities,shanghai normal university,shanghai 200234,china 4Institute of Computational mathematics,Academy of mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,china 1. department of mathematics Minjiang University Fuzhou 350108 China2. Department of Mathematics Shanghai Jiao Tong University Shanghai 200240 China3. Division of Computational Science E-Institute of Shanghai Universities Shanghai Normal University Shanghai 200234 China4. Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

The fully discrete lumped mass finite element method is proposed for vibration analysis of elastic plate-plate *** the space directions,the longitudinal displacements on plates are discretized by conforming linear elements,and the transverse displacements are discretized by the Morley *** means of the second order central difference for discretizing the time derivative and the technique of lumped masses,a fully discrete lumped mass finite element method is obtained,and two approaches to choosing the initial functions are also *** error analysis for the method in the energy norm is established,and some numerical examples are included to validate the theoretical analysis.

关键词： vibration analysis plate-plate structures lumped mass FEM error analysis

On quasi-convex mappings of order α in the unit ball of a complex Banach space

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Science china mathematics 2006年第11期49卷 1451-1457页

作者： LIU Taishun & XU Qinghua department of mathematics, Huzhou Teachers College, Huzhou, 313000, china department of mathematics, Jiangxi normal university, Nanchang, 330022, china department of mathematics Huzhou Teachers College Huzhou 313000 China department of mathematics Jiangxi Normal University Nanchang 330022 China

In this paper, a class of biholomorphic mappings named quasi-convex mapping of order a in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings. Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space X. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order a defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively.

关键词： coefficient estimation the homogeneous expansion quasi-convex mapping quasi-convex mapping of order a.

ON THE EXISTENCE OF FIXED POINTS FOR LIPSCHITZIAN SEMIGROUPS IN BANACH SPACES

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Chinese Annals of mathematics,Series B 2001年第3期22卷 397-404页

作者： ZENG LUCHUAN, YANG YALI department of Matematics, shanghai normal university, shanghai 200234, china. department of mathematics Shanghai Normal Univeristy Shanghai 200234 China

Let C be a nonempty bounded subset of a p-uniformly convex Banach space X, and T = {T(t): t S} be a Lipschitzian semigroup on C with lim inf |||T(t)||| < Np, where Np is n→ t s the normal structure coefficient of X. ... 详细信息

Let C be a nonempty bounded subset of a p-uniformly convex Banach space X, and T = {T(t): t S} be a Lipschitzian semigroup on C with lim inf |||T(t)||| normal structure coefficient of X. Suppose also there exists a nonempty bounded closed convex subset E of C with the following properties: (P1)x: E implies ωω(χ) C E; (P2)T is asymptotically regular on E. The authors prove that there exists a z E such that T(s)z = z for all s S. Fruther, under the similar condition, the existence of fixed points of Lipschitzian semigroups in a uniformly convex Banach space is discussed.

关键词： Fixed points Lipschitzian semigroups Asymptotic regularity normal structure coefficient Asymptotic center

Approximate solutions to infinite dimensional LQ problems over infinite time horizon

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Science china mathematics 2006年第7期49卷 865-876页

作者： PAN Liping, ZHANG Xu & CHEN Qihong School of Mathematical Sciences, Fudan university, shanghai 200433, china School of mathematics, Sichuan university, Chengdu 610064, china department of Applied mathematics, shanghai university of Finance & Economics, shanghai 200433, china School of Mathematical Sciences Fudan University Shanghai 200433 China School of mathematics Sichuan University Chengdu 610064 China department of Applied mathematics Shanghai University of Finance & Economics Shanghai 200433 China

This paper is addressed to develop an approximate method to solve a class of infinite dimensional LQ optimal regulator problems over infinite time horizon. Our algorithm is based on a construction of approximate solutions which solve some finite dimensional LQ optimal regulator problems over finite time horizon, and it is shown that these approximate solutions converge strongly to the desired solution in the double limit sense.

关键词： approximate solution LQ problem infinite dimensional infinite time hori-

Littlewood-Paley operators with variable kernels

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Science china mathematics 2006年第5期49卷 639-650页

作者： CHEN Jiecheng, DING Yong & FAN Dashan department of mathematics, Zhejiang university (Xixi Campus), Hangzhou 310028, china School of Mathematical Sciences, Beijing normal university, Beijing 100875, china department of mathematics, university of Wisconsin-Milwaukee, Milwaukee WI 53201, USA department of mathematics, Central china normal university, Wuhan 430074, china department of mathematics Zhejiang University [Xixi Campus] Hangzhou 310028 China School of Mathematical Sciences Beijing Normal University Beijing 100875 China department of mathematics University of Wisconsin-Milwaukee Milwaukee WI 53201 USA department of mathematics Central China Normal University Wuhan 430074 China

In this paper we study a certain directional Hilbert transform and the boundedness on some mixed norm spaces. As one of applications, we prove the Lp-boundedness of the Littlewood-Paley operators with variable kernels... 详细信息

关键词： directional Hilbert transform, Sobolev spaces, Littlewood-Paley operator,variable kernel.

SCHWARZ-PICK ESTIMATES FOR BOUNDED HOLOMORPHIC FUNCTIONS ON CLASSICAL DOMAINS

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Acta Mathematica Scientia 2011年第4期31卷 1377-1382页

作者：刘洋陈志华 department of mathematics Zhejiang Normal University department of mathematics Tongji University

In this paper, Schwarz-Pick estimates for high order Fr′echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of ... 详细信息

关键词： Schwarz-Pick estimate holomorphic functions classical domains

Fredholm operators in Toeplitz algebras associated with discrete abelian groups

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Chinese Science Bulletin 1998年第14期43卷 1175-1179页

作者： XU Qingxiang 1 and CHEN Xiaoman 2 1. department of mathematics, shanghai normal university, shanghai 200234, china 2. Laboratory of mathematics for Nonlinear Sciences and Institute of mathematics, Fudan university, shanghai 200433, china department of mathematics Shanghai Normal University Shanghai China Laboratory of mathematics for Nonlinear Sciences and Institute of mathematics Fudan University Shanghai China

The locally finite below sets are introduced and the Fredholm operators in Toeplitz algebras associated with discrete abelian groups are studied.

关键词： discrete abelian group quasi_ordered group Toeplitz operator Fredholm operator.

DOUBLE S-BREAKING CUBIC TURNING POINTS AND THEIR COMPUTATION

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Journal of Computational mathematics 1996年第1期14卷 8-22页

作者： R.S. Ye Z.H. Yang(department of mathematics, shanghai university of Science and Technology, shanghai,china) shanghai UNIV SCI & TECHNOL DEPT MATHSHANGHAI 201800PEOPLES R CHINA

In the paper we are concerned with double S-breaking cubic turning points of two-parameter nonlinear problems in the presence of Z(2)-symmetry. Three extended systems are proposed to determine double S-breaking cubic turning points. We show that there exist two kinds of singular point path passing through double S-breaking cubic turning point, One is the simple quadratic turning point path, the other is the pitchfork bifurcation point path.

关键词： DOUBLE S-BREAKING CUBIC TURNING POINTS AND THEIR COMPUTATION Pro