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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

SOLVING TRUST REGION PROBLEM IN LARGE SCALEOPTIMIZATION

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Journal of Computational mathematics 2000年第1期18卷 1-12页

作者： Bing-sheng He(department of mathematics, Nanjing university, Naming 210093, China) 南京大学江苏南京 210093

Presents a study which introduced a method for solving trust region problem in scale minimization. Review of the conjugate gradient method (CG) and the projection and contraction (PC) method; Convergence behavior of t... 详细信息

关键词： trust region problem conjugate gradient method projection and contraction method

THE FUNCTION d_k(n) AT CONSECUTIVE INTEGERS

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Chinese Annals of mathematics,Series B 1999年第4期20卷 473-478页

作者： MENG ZAIZHAO(department of mathematics, Peking university, Beijing 100871, China) department of mathematics Peking University Beijing 100871 China

Let dk(n) denote the k-fold iterated divisor function (k ≥ 2). It is proved that for sufficiently large x) dk(n) = dk(n + 1) holds for >> x(log log x)-3 integers n ≤x.

关键词： Divisor function Multiplicative function Congruence

CONVERGENCE OF THE POINT VORTEX METHODS FOR EULER EQUATION ON HALF PLANE

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Journal of Computational mathematics 1996年第3期14卷 213-222页

作者： P.W. Zhang(department of mathematics, Beijing university, Beijing, China) 北京大学数学系北京

In this paper, we study the point vortex method for 2-D Euler equation of incompressible how on the half plane, and the explicit Euler's scheme is considered with the reflection method handling the boundary condition.... 详细信息

关键词： Math CONVERGENCE OF THE POINT VORTEX METHODS FOR EULER EQUATION ON HALF PLANE Zhang

THE CONVERGENCE ON A FAMILY OF ITERATIONS WITH CUBIC ORDER

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Journal of Computational mathematics 2001年第5期19卷 467-474页

作者： Dan-fu Han (department of mathematics, Zhejiang university, Hangzhou 310028, China) 浙江大学浙江杭州 310028

Establishes a convergent theorem for a family of iterations with cubic order by using general convergence hypotheses. Disadvantage of using the cubic majorizing function; Convergence of the majorizing sequence; Overvi... 详细信息

关键词： convergence majorizing method gamma-condition error estimate

GENUINE-OPTIMAL CIRCULANT PRECONDITIONERS FOR WIENER-HOPF EQUATIONS

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Journal of Computational mathematics 2001年第6期19卷 629-638页

作者： Fu-rong Lin (department of mathematics, Shantou university, Shantou 515063,China) 汕头大学广东汕头 515063

Discusses the genuine-optimal circulant preconditioner for finite-section Wiener-Hopf equations. Definition of the genuine-optimal circulant preconditioner; Use of the preconditioned conjugate gradient method; Numeric... 详细信息

关键词： Wiener-Hopf equations circulant preconditioner preconditioned conjugate gradient method quadrature rules Hilbert-Schmidt norm

On the direct path problem of s-elementary frame wavelets

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Science China mathematics 2010年第12期53卷 3187-3196页

作者： DAI XingDe 1 , DIAO YuanAn 1 & GUO XunXiang 2,1 department of mathematics and statistics, university of North Carolina at Charlotte, Charlotte, NC 28223, USA 2 department of mathematics, Southwestern university of Finance and Economics, Chengdu 611130, China department of mathematics and statistics University of North Carolina at Charlotte Charlotte USA department of mathematics Southwestern University of Finance and Economics Chengdu China

In this paper, we discuss the path-connectivity between two s-elementary normalized tight frame wavelets via the so-called direct paths. We show that the existence of such a direct path is equivalent to the non-existence of an atom of a σ-algebra defined over the defining sets of the corresponding frame wavelets, using a mapping defined by the natural translation and dilation operations between the sets. In particular, this gives an equivalent condition for the existence of a direct path between two s-elementary wavelets.

关键词： wavelets frame wavelets frame wavelet sets path-connectivity of wavelets direct path

Strong uniqueness of best approximations in spaces of bounded linear operators

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Science China mathematics 2004年第3期47卷 339-351页

作者： LI Chong HE Jinsu department of mathematics, Zhejiang university Hangzhou 310027, China department of mathematics, Zhejiang Normal university Jinhua 321004, China department of mathematics Zhejiang University Hangzhou China department of mathematics Zhejiang Normal University Jinhua China

The present paper is concerned with problems of the strong uniqueness of the best approximation and the characterization of a uniqueness element in operator *** results on the strong uniqueness of the best approximation operatorfrom RS-sets are proved and the uniqueness element of a sun in the compactoperator space from c0 to c0 is characterized by the strict Kolmogorov's *** recent results due to Lewicki and others are extended and improved.

关键词： best approximation operator, RS-set, sun, strong uniqueness, uniqueness element.

Completely regular paracompact reflection of locales

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Science China mathematics 2006年第6期49卷 820-826页

作者： HE Wei & LUO Maokang department of mathematics, Nanjing Normal university, Nanjing 210097, China department of mathematics, Sichuan university, Chengdu 610064, China department of mathematics Nanjing Normal University Nanjing China department of mathematics Sichuan University Chengdu China

We give an explicit construction of the completely regular paracompact reflection pL of a completely regular locale L described as a sublocale of the Stone-tech compactification βL of L.

关键词： completely regular paracompact locale, nucleus.