共查询到20条相似文献,搜索用时 46 毫秒
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介绍数学分析课程中处处连续但处处不可导函数的教学,通过电子课件演示函数的图象,使学生理解这一类函数的局部与整体的某种相似性质,并对“分形”概念有一个初步的了解. 相似文献
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为了方便向大学生介绍处处不可导的连续函数的构造,对van derWaerden的级数构造法和Bush直接定义函数的构造法分别进行推广并给出证明. 相似文献
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对于模糊数值函数的积分原函数的可导性问题,本文构造性地给出一反例,说明存在(K)可积的模糊数值函数其积分原函数并不是几乎处处可导的。 相似文献
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该文讨论了非平稳负(正)相依序列加权和的几乎处处中心极限定理,改进并推广了相依序列几乎处处中心极限定理的相关结果. 相似文献
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<正> 求二元函数未定型极限一般是很困难的,下面介绍几种方法。1 二元函数的罗必塔法则二元函数的罗必塔法则是一元函数罗必法则的推广。为了得到此法则,首先介绍一个引理。引理(一元函数柯西中值定理的推广).若函数f(x,y)及F(x,y)在点(x_0,y_0)的某邻域内连续,且偏导 相似文献
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李祥 《数学年刊A辑(中文版)》1985,(3)
本文引入一种递归表现的能行拓补空间,研究了这种空间中按点处处非递归的性质,获得了下述结果: 在任何递归表现的拓扑空间中有处处单纯点集和处处非递归的r.e.点集。 相似文献
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该文证明了随机元序列的一个一般的几乎处处中心极限定理, 并把这一结论应用于随机变量序列的函数. 相似文献
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Stamatis Cambanis 《Journal of multivariate analysis》1973,3(4):420-434
The following path properties of real separable Gaussian processes ξ with parameter set an arbitrary interval are established. At every fixed point the paths of ξ are continuous, or differentiable, with probability zero or one. If ξ is measurable, then with probability one its paths have essentially the same points of continuity and differentiability. If ξ is measurable and not mean square continuous or differentiable at every point, then with probability one its paths are almost nowhere continuous or differentiable, respectively. If ξ harmonizable or if it is mean square continuous with stationary increments, then its paths are absolutely continuous with probability one if and only if ξ is mean square differentiable; also mean square differentiability of ξ implies path differentiability with probability one at every fixed point. If ξ is mean square differentiable and stationary, then on every interval with probability one its paths are either differentiable everywhere or nondifferentiable on countable dense subsets. Also a class of harmonizable processes is determined for which of the following are true: (i) with probability one paths are either continuous or unbounded on every interval, and (ii) mean square differentiability implies that with probability one on every interval paths are either differentiable everywhere or nondifferentiable on countable dense subsets. 相似文献
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从数学分析知函数在某区间上可微则必连续,但反之未必;本文构造一个函数,并证明了它在[0,1]连续且处处不可微. 相似文献
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Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defined. Formulas for star-shaped differential of a pointwise maximum and a pointwise minimum of a finite number of directionally differentiable functions, and a composite of two directionaUy differentiable functions are derived. Furthermore, the mean-value theorem for a directionaUy differentiable function is demonstrated. 相似文献
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Andrew J. Hetzel 《International Journal of Mathematical Education in Science & Technology》2013,44(4):488-491
This note could find classroom use in an introductory course on complex analysis. Using some of the most significant theorems from complex analysis, the main result provides a simple method for transforming many elementary functions (defined on the complex plane) into everywhere continuous functions that are differentiable only on a nowhere dense set. Accordingly, such continuous functions are termed ‘practically nowhere differentiable’. The twofold pedagogical value of this method is that (1) students can readily generate examples of everywhere continuous, practically nowhere differentiable functions that do not require any direct appeal to infinite series, and (2) the often dynamical difference between the behaviour of functions of a complex variable and functions of a real variable is showcased. 相似文献
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P. Jiménez-Rodríguez S. Maghsoudi G.A. Muñoz-Fernández 《Journal of Mathematical Analysis and Applications》2014
In 1951 V. Jarník constructed two continuous functions whose Volterra convolution is nowhere differentiable. We generalize Jarník?s results by proving that the set of such functions is maximal lineable. This would shed some light on a question posed in 1973 on the structure of the set of continuous functions whose Volterra convolution is nowhere differentiable. 相似文献
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Dr. A. Kriegl 《Monatshefte für Mathematik》1982,94(2):109-124
The aim of this paper is to characterize those locally convex spaces, which have the following properties. 1. Any curve, which is differentiable if composed with continuous linear forms, is differentiable for its own. 2. Any differentiable curve is Riemann integrable. 3. The topology is determined by the differentiable curves. 4. Linear mappings are continuous iff they are differentiable. This category of thec
-complete bornological spaces is symetrically monoidal closed and includes the LF-spaces.
Unterstützt durch das Forschungsstipendium GZ 61 622/134-14/80 des Bundesministeriums für Wissenschaft und Forschung. 相似文献
Unterstützt durch das Forschungsstipendium GZ 61 622/134-14/80 des Bundesministeriums für Wissenschaft und Forschung. 相似文献
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Andreas Fischer 《Mathematische Nachrichten》2010,283(6):828-845
The notion of Peano differentiability generalizes the differentiability in the usual sense to higher order. Peano differentiable functions have derivatives which are sometimes differentiable or continuous or not even locally bounded. We give a complete characterisation of the sets in which Peano differentiable functions which are definable in an o‐minimal expansion of a real closed field are continuously differentiable. Thereby, we also distinguish between several kinds of discontinuities (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Mark Lynch 《International Journal of Mathematical Education in Science & Technology》2013,44(4):509-511
It is well known that differentiable functions defined on R are continuous. However, this result assumes that one uses the usual topology. In this paper, an example is given of a differentiable, nowhere continuous function by changing the basic open sets at just one point. And also a characterization is given of the implication ‘differentiability implies continuity’. 相似文献
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This short note presents four examples of compactly supported symmetric refinable componentwise polynomial functions: (i) a componentwise constant interpolatory continuous refinable function and its derived symmetric tight wavelet frame; (ii) a componentwise constant continuous orthonormal and interpolatory refinable function and its associated symmetric orthonormal wavelet basis; (iii) a differentiable symmetric componentwise linear polynomial orthonormal refinable function; (iv) a symmetric refinable componentwise linear polynomial which is interpolatory and differentiable. 相似文献