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TOEPLITZ OPERATORS AND ALGEBRAS ON DIRICHLET SPACES

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Chinese Annals of mathematics,Series B 2002年第3期23卷 385-396页

作者： CAO GUANGFU department of mathematics, Sichuan university, Chengdu 610064, china. department of mathematics Sichuan University Chengdu 610064 China

The automorphism group of the Toeplitz C^*- algebra, J(C^1), generated by Toeplitz op-erators with C^1-symbols on Dirichlet space D is discussed; the K0, K1-groups and the first cohomology group of J(C^1) are computed. In addition, the author proves that the spectra of Toeplitz operators with C^1-symbols are always connected, and discusses the algebraic prop-erties of Toeplitz *** particular, it is proved that there is no nontrivial selfadjoint Toeplitz operator on D and Tψ^* = Tψ^- if and only if Tψ is a scalar operator.

关键词： Dirichlet space Toeplitz operator Toeplitz algebra

DIMENSIONS OF SELF-AFFINE SETS WITH OVERLAPS

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Chinese Annals of mathematics,Series B 2003年第3期24卷 275-284页

作者： HUA Su department of mathematics, Tsinghua university, Beijing 100084, china. Tsing Hua Univ Dept Math Beijing 100084 Peoples R China

The authora develop an algorithm to show that a class of self-affine sets with overlaps can be viewed as sofic affine-invariant sets without overlaps,thus by using the results of [11] and [10],the hausdorff and minkow... 详细信息

关键词： self-affine set overlap hausdorff dimension minkowski dimension

CLASSICAL SOLUTION OF QUASI-STATIONARY STEFAN PROBLEM

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Chinese Annals of mathematics,Series B 1996年第2期17卷 175-186页

作者： YI FAHUAI department of mathematics, Suzhou university, Suzhou 215006, china. SUZHOU UNIV DEPT MATHSUZHOU 215006PEOPLES R CHINA

This paper considers the quasi-stationary Stefan problem:△u(x,t)=0 in space-time domain,u=0 and Vv +(?)u/(?)u=0 on the free boundary.Under the natural conditions the existence of classical solution locally in time is proved bymaking use of the property of Frechet derivative operator and fixed point theorem. For thesake of simplicity only the one-phase problem is dealt with. In fact two-phase problem can bedealt with in a similar way with more complicated calculation.

关键词： Classical solution Quasi-stationary Stefan problem Frechet derivative

ON THE APPROXIMATELY SIMILARITY OF OPERATORS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 465-472页

作者： WEI GUOQIANG (department of mathematics, East china Normal university, Shanghai 200062, china.) E china Normal Univ Dept Math Shanghai 200062 Peoples R China

The author shows that a rank-preserving *-isorporphism between separable C*-algebras with unity is approximately equivalent to the identity representation. Some applications are made for approximately similarity of n-... 详细信息

关键词： C*-algebra Rank-preserving *-isomorphism Approximately equevalent,Approximately similar n-tuples of operators

Equivalent construction of the infinitesimal time translation operator in algebraic dynamics algorithm for partial differential evolution equation

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Science china(Physics,Mechanics & Astronomy) 2010年第8期53卷 1475-1480页

作者： LIU ChengShi department of mathematics, Northeast Petroleum university, Daqing 163318, china 1. department of mathematics Northeast Petroleum University Daqing 163318 China

We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.

关键词： algebraic dynamics infinitesimal time translation operator partial differential evolution equation

NUMERICAL COMPUTATION OF BOUNDED SOLUTIONS FORA SEMILINEAR ELLIPTIC EQUATION ON AN INFINITE STRIP

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Journal of Computational mathematics 1999年第2期17卷 159-170页

作者： Fu-ming Ma(department of mathematics, Jilin ’university, Changchun 130023, china) 吉林大学数学系吉林长春

In this paper, we consider the computation of bounded solutions of a semilinear elliptic equation on an infinite strip. The dynamical system approach and reduction on center manifold are used to overcome the difficult... 详细信息

关键词： numerical method nonlinear PDE center manifold

Existence and uniqueness for BSDE with stopping time

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Chinese Science Bulletin 1998年第2期43卷 96-99页

作者： CHEN Zengjing department of mathematics, Shandong university, Jinan 250100, china department of mathematics Shandong University Jinan China

The existence and uniqueness of the solutions for a class of backward stochastic differential equations (BSDEs for short) in a random interval are discussed.

关键词： BSDE stopping time adapted solution.

A FAMILY OF HIGH-ODER PARALLEL ROOTFINDERS FOR POLYNOMIALS

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Journal of Computational mathematics 2000年第3期18卷 283-288页

作者： Shi-ming Zheng (department of mathematics, Xixi Campus,Zhejiang university, Hangzhou, 310028, china) 浙江大学浙江杭州 310028

Presents a family of parallel iterations for finding all zeros of a polynomial without evaluation of derivatives. Construction of iterations; Convergence of the iterations; Details on the numerical examples.

关键词： parallel iteration zeros of polynomial order of convergence

BIVARIATE FRACTAL INTERPOLATION FUNCTIONS ON RECTANGULAR DOMAINS

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Journal of Computational mathematics 2002年第4期20卷 349-362页

作者： Xiao-yuan Qian (department of Applied mathematics, Dalian university of Technology, Dalian 116024, china) department of Applied mathematics Dalian University of Technology Dalian 116024

Non-tensor product bivariate fractal interpolation functions defined on gridded rectangular domains are constructed. Linear spaces consisting of these functions are introduced. The relevant Lagrange interpolation problem is discussed. A negative result about the existence of affine fractal interpolation functions defined on such domains is obtained.

关键词： fractal bivariate functions interpolation