共查询到19条相似文献,搜索用时 46 毫秒
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本文引入了概率赋范线性空间上线性算子的一致收敛和可完全刻划这种收敛的算子间的概率距离概念,并利用这些概念获得了算子连续和算子列一致收敛的本质特征,及其连续性和全连续性对于一致收敛极限运算的封闭性. 相似文献
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判别函数列一致收敛的方法有函数列一致收敛定义、Cauchy一致收敛准则、limn→∞supx∈D|fn(x)-f(x)|=0及Dini定理,本文由函数列的等度连续性,可得出几个有界闭区间上连续函数列一致收敛的充要条件,推广了Dini定理. 相似文献
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冀占江 《数学的实践与认识》2018,(11)
结合紧致度量空间中拓扑弱混合和轻度混合能够被强一致收敛所遗传.首先,仿造度量空间中强一致收敛的定义,给出了度量G-空间中G-强一致收敛的概念;其次,证明了在紧致度量G-空间中,G-弱混合性、G-轻度混合性和G-混合性能够被G-强一致收敛所遗传. 相似文献
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关于无穷级数逐项积分和逐项求导的一个注记 总被引:1,自引:0,他引:1
无穷级数的逐项积分或逐项求导一般要求原级数或未导后所成级数是一致收敛的,若此条件不满足,而逐项积分或逐项求导后的级数收敛,则它是否收敛到原级数和的积分或导数呢?这是个有趣的问题,其结论是不一定。下面举例说明之。例1考察级数1°容易验证(1)收敛但非一致收敛:.这说明(1)并非一致收敛到0.2”级数(l)逐项积分后所成级数收敛;3”显然IS(王川X学1,即逐项积分后的级数并非收敛到原级数和的积分。例2考察级数l”容易验证(2)收敛但非一致收敛:说明(2)并非一致收敛到0.2”级数(2)逐项积分后是收敛的:3”显然DS… 相似文献
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全变差有界函数列的一致(R)可积性 总被引:4,自引:0,他引:4
给出了一致有界单调函数列一致可积性定理 ,由此得出全变差序列有界的收敛函数列的一致可积性 .说明了该结论可判断一些非一致收敛函数列的逐项积分性质 . 相似文献
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本文研究了i.i.d情况下非参数回归的误差密度估计的一致收敛和均方收敛,给出了一定条件下误差密度的估计量f^n(x)的一致收敛速度和均方收敛速度。 相似文献
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给出了收敛的一致(R)可积函数列的一致有界性定理,并指出一致有界是收敛的(R)可积函数列一致(R)可积的必要条件,但不是充分条件. 相似文献
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利用函数列的极限理论方法,研究函数列积分极限中积分和极限可交换次序的问题.对一致收敛的可积函数列给出积分的极限定理,对一致有界局部一致收敛函数列给出积分控制收敛定理,通过大量实例表明该理论的意义所在. 相似文献
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本文根据定义的密度函数的估计式,得到了其一致收敛速度,并由此得到了危险率函数的强一致收敛速度. 相似文献
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In this paper the Pareto efficiency of a uniformly convergent multiobjective optimization sequence is studied. We obtain some relation between the Pareto efficient solutions of a given multiobjective optimization problem and those of its uniformly convergent optimization sequence and also some relation between the weak Pareto efficient solutions of the same optimization problem and those of its uniformly convergent optimization sequence. Besides, under a compact convex assumption for constraints set and a certain convex assumption for both objective and constraint functions, we also get some sufficient and necessary conditions that the limit of solutions of a uniformly convergent multiobjective optimization sequence is the solution of a given multiobjective optimization problem. 相似文献
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本文讨论基于整体误差一致展开式的一致收敛离散方法解的一致高阶精度外推.将该方法应用于非自共轭问题的Il'in-Allen-Southwell格式,我们得到了二阶一致收敛的外推解,并用数值计算说明该结论. 相似文献
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An alternating direction scheme on a nonuniform mesh for reaction-diffusion parabolic problems 总被引:1,自引:0,他引:1
Clavero C; Jorge JC; Lisbona F; Shishkin={paragraph} GI 《IMA Journal of Numerical Analysis》2000,20(2):263-280
In this paper we develop a numerical method for two-dimensionaltime-dependent reaction-diffusion problems. This method, whichcan immediately be generalized to higher dimensions, is shownto be uniformly convergent with respect to the diffusion problems.This method, which can immediately be generalized to higherdimensions, is shown to be uniformly convergent with respectto the diffusion parameter. 相似文献
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本文研究了右半平面内解析的Dirichlet级数的增长性,利用凸函数和一致收敛数的性质和几个引理,证明了连带级数的奇异点与原级数的增长性有关,并得到该连带级数的一些性质. 相似文献
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This paper proposes a uniformly convergent algorithm for the joint transform of the first passage time and the first passage
number of steps for general Markov renewal processes with any initial state probability vector. The uniformly convergent algorithm
with arbitrarily prescribed error can be efficiently applied to compute busy periods, busy cycles, waiting times, sojourn
times, and relevant indices of various generic queueing systems and queueing networks. This paper also conducts a numerical
experiment to implement the proposed algorithm. 相似文献
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We consider the problem of convergence of Fourier series when we make a change of variable. Under a certain reasonable hypothesis, we give a necessary and sufficient condition for a homeomorphism of the circle to transform absolutely convergent Fourier series into uniformly convergent Fourier series.
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The axisymmetric irrotational Stokes' flow for a spherical shell is analysed by means of the recently developed Fokas method via the use of global relations. Alternative series and new integral representations concerning a system of concentric spheres, yielding, by a limiting procedure, the Dirichlet or Neumann problems for the interior and the exterior of a sphere, are presented. The boundary value problems considered can be classically solved using either the finite Gegenbauer transform or the Mellin transform. Application of the Gegenbauer transform yields a series representation which is uniformly convergent at the boundary, but not convenient for many applications. The Mellin transform, on the other hand, furnishes an integral representation which is not uniformly convergent at the boundary. Here, by algebraic manipulations of the global relation: (i) a Gegenbauer series representation is derived in a simpler manner, instead of solving ODEs and (ii) an alternative integral representation, different from the Mellin transform representation is derived which is uniformly convergent at the boundary. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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M. Thamban Nair 《Numerical Functional Analysis & Optimization》2013,34(1-2):69-73
Schock (1985) has considered the convergence properties of various Galerkin-like methods for the approximate solution of the operator equation of the second kind x - Tx = y, where T is a bounded linear operator on a Banach space X, and x and y belong to X, and proved that the classical Galerkin method and in certain cases, the iterated Galerkin method are arbitrarily slowly convergent whereas the Kantororich method studied by him is uniformly convergent. It is the purpose of this paper to introduce a general class of approximations methods for x - Tx = y which includes the well-known methods of projection and the quadrature methods, and to characterize its uniform convergence, so that an arbitrarily slowly convergent method can be modified to obtain a uniformly convergent method. 相似文献