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Wuhan University Journal of Natural Sciences 2023年第5期28卷 411-420页

作者： SHI Jiamin LU Zhongshu ZHANG Luyi LU Sunjia CHENG Yao School of Mathematical Sciences Suzhou University of Science and TechnologySuzhou 215009JiangsuChina

This paper concerns a discontinuous Galerkin(DG)method for a one-dimensional singularly perturbed problem which possesses essential characteristic of second order convection-diffusion problem after some simple *** derive an optimal convergence of the DG method for eight layer-adapted meshes in a general *** convergence rate is valid independent of the small ***,we establish a sharper L^(2)-error estimate if the true solution has a special regular *** experiments are also given.

关键词： layer-adapted meshes singularly perturbed problem uniform convergence discontinuous Galerkin method

uniform convergence AND SEQUENCE OF MAPS ON A COMPACT METRIC SPACE WITH SOME CHAOTIC PROPERTIES

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Analysis in Theory and Applications 2010年第1期26卷 53-58页

作者： Indranil Bhaumik Binayak S. Choudhury Bengal Engineering and Science University India

Recently, C. Tain and G. Chen introduced a new concept of sequence of time invariant function. In this paper we try to investigate the chaotic behavior of the uniform limit function f ： X →X of a sequence of continuous topologically transitive （in strongly successive way） functions fn ： X →X, where X is a compact interval. Surprisingly, we find that the uniform limit function is chaotic in the sense of Devaney. Lastly, we give an example to show that the denseness property of Devaney＇s definition is lost on the limit function.

关键词： uniform convergence chaos in the sense of Devaney topological transitivity in strongly successive way

Pointwise convergence and uniform convergence of Wavelet Frame Series

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Acta Mathematica Sinica,English Series 2006年第3期22卷 653-658页

作者： Zhi Hua ZHANG Department of Mathematics University of California

Pointwise convergence and uniform convergence for wavelet frame series is a new topic. With the help of band-limited dual wavelet frames, this topic is first researched.

关键词： Wavelet frame series Wavelet orthonormal basis uniform convergence Pointwise convergence

uniform convergence for Finite Volume Element Method for Non-selfadjoint and Indefinite Elliptic Problems

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Northeastern Mathematical Journal 2005年第1期21卷 32-38页

作者：龙晓瀚毕春加 School of Mathematics and System Science Shandong University Jinan 250100 Department of MathematicsYantai University Yantai Shandong Province 264005

In this paper, we prove the existence, uniqueness and uniform convergence of the solution of finite volume element method based on the P1 conforming element for non-selfadjoint and indefinite elliptic problems under m... 详细信息

关键词： finite volume element method P1 conforming element uniform convergence non-selfadjoint and indefinite problem

uniform convergence of Multigrid V-Cycle on Adaptively Refined Finite Element Meshes for Elliptic Problems with Discontinuous Coefficients

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Communications in Mathematical Research 2023年第3期39卷 437-475页

作者： Haijun Wu Weiying Zheng Department of Mathematics Nanjing UniversityJiangsu 210093P.R.China LSEC Institute of Computational MathematicsAcademy of Mathematics and System Sciences Chinese Academy of SciencesBeijing 100190P.R.China

The multigrid V-cycle methods for adaptive finite element discretizations of two-dimensional elliptic problems with discontinuous coefficients are *** the conditions that the coefficient is quasi-monotone up to a constant and the meshes are locally refined by using the newest vertex bisection algorithm,some uniform convergence results are proved for the standard multigrid V-cycle algorithm with Gauss-Seidel relaxations performed only on new nodes and their immediate *** multigrid V-cycle algorithm uses O(N)operations per iteration and is optimal.

关键词： Multigrid adaptive finite elements elliptic problems discontinuous coefficients uniform convergence

RATES OF STRONG uniform convergence OF NEAREST NEIGHBOR DENSITY ESTIMATES ON ANY COMPACT SET

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Applied Mathematics and Mechanics(English Edition) 1990年第4期11卷 385-393页

作者：张涤新 Guizhou Planning College Guiyang

In this paper, we propose the concept of rates of strong uniform convergence of nearest neighbor density estimates on any compact set and obtain some better convergence rates. Hence the problem of the strong uniform c... 详细信息

关键词： Mathematical Modeling convergence Rate Industrial Mathematic Density Estimate uniform convergence

THE uniform convergence OF A DG METHOD FOR A SINGULARLY PERTURBED VOLTERRA INTEGRO-DIFFERENTIAL EQUATION

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数学物理学报:B辑英文版 2023年第5期43卷 2159-2178页

作者：陶霞谢资清 School of Mathematics Hunan Institute of Science and TechnologyYueyang 414006China Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education) School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China

The purpose of this work is to implement a discontinuous Galerkin(DG)method with a one-sided flux for a singularly perturbed Volterra integro-differential equation(VIDE)with a smooth ***,the regularity property and a decomposition of the exact solution of the singularly perturbed VIDE with the initial condition are *** the existence and uniqueness of the DG solution are *** some appropriate projection-type interpolation operators and their corresponding approximation properties are *** on the decomposition of the exact solution and the approximation properties of the projection type interpolants,the DG method achieves the uniform convergence in the L2 norm with respect to the singular perturbation parameter e when the space of polynomials with degree p is used.A numerical experiment validates the theoretical ***,an ultra-convergence order 2p+1 at the nodes for the one-sided flux,uniform with respect to the singular perturbation parameter e,is observed numerically.

关键词： singularly perturbed VIDE DG method Shishkin mesh uniform convergence

Some uniform convergence results for kernel estimators

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Science China Mathematics 2013年第9期56卷 1945-1956页

作者： MENG MeiXia AI ChunRong School of Statistics and Management Shanghai University of Finance and Economics School of Statistics and Management Key Laboratory of Mathematical EconomicsMinistry of EducationShanghai University of Finance and Economics Department of Economics University of Florida

This paper derives some uniform convergence rates for kernel regression of some index functions that may depend on infinite dimensional parameter. The rates of convergence are computed for independent, strongly mixing and weakly dependent data respectively. These results extend the existing literature and are useful for the derivation of large sample properties of the estimators in some semiparametric and nonparametric models.

关键词： uniform convergence kernel estimation convergence rate

DIFFERENCE SCHEME OF uniform convergence IN THE L~∞ NORM FOR SINGULAR PERTURBATION OF THE THIRD BVP

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Annals of Differential Equations 1997年第1期13卷 85-93页

作者：白清源谢丽聪林鹏程福州大学 350002

In the paper, the linear second order ordinary differential equations of singularly perturbed turning point problems with third boundary value conditions isconsidered. We get a priori estimate of the solution's derivatives, and constructa II'in type difference scheme with an exponential type fitted facter and obtaina uniform convergence result on the small parameter e of order one in the L∞norm.

关键词： Singular Perturbation Turning Point uniform convergence

convergence of complex martingale for a branching random walk in an independent and identically distributed environment

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Frontiers of Mathematics in China 2021年第1期16卷 187-209页

作者： Xin WANG Xingang LIANG Chunmao HUANG Department of General Education Wenzhou Business CollegeWenzhou 325035China School of Mathematics and Statistics Beijing Technology and Business UniversityBeijing 100048China Department of Mathematics Haxbin Institute of Technology(Weihai)Weihai 264209China

We consider anR^(d)-valued discrete time branching random walk in an independent and identically distributed environment indexed by time n∈*** W_(n)(z)(z∈C^(d))be the natural complex martingale of the *** show necessary and sufficient conditions for the L^(α)-convergence of W_(n)(z)forα>1,as well as its uniform convergence region.

关键词： Branching random walk random environment moments uniform convergence complex martingale L^(α)-convergence