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The midpoint set of a cantor set [PDF]
International Journal of Mathematics and Mathematical Sciences, 1978 A non-endpoint of the Cantor ternary set is any Cantor point which is not an endpoint of one of the remaining closed intervals obtained in the usual construction process of the Cantor ternary set in the unit interval. It is shown that the set of points in the unit interval which are not midway between two distinct Cantor ternary points is precisely the
Ken W. Lee
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Fat Cantor sets and their skinny companions
Heliyon, 2023 The terms fat and skinny in the title are vernacular references to Cantor sets of positive and zero measure respectively. The paper demonstrates that a fat Cantor subset of [0,L], L>0, possesses a skinny companion that forms a Cantor subset of [0,G ...
David R Dellwo
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Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set. [PDF]
Entropy (Basel), 2021 In this paper, we have modified the Detrended Fluctuation Analysis (DFA) using the ternary Cantor set. We propose a modification of the DFA algorithm, Cantor DFA (CDFA), which uses the Cantor set theory of base 3 as a scale for segment sizes in the DFA ...
Mariani MC +4 more
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Diffusion on Middle-ξ Cantor Sets [PDF]
Entropy, 2018 In this paper, we study Cζ-calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions. Functions with fractal support are not differentiable or integrable in terms of standard calculus, so we must involve local fractional derivatives.
Alireza Khalili Golmankhaneh +3 more
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Dimensions of subsets of cantor‐type sets [PDF]
International Journal of Mathematics and Mathematical Sciences, 2006 We define the Cantor‐type set E first, and then the Besicovitch subset Bp of E. We mainly show the dimensions of subsets of Cantor‐type set E in compatible case and incompatible case.
Fang-Xiong Zhen
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Advances in Mathematics, 2022 We introduce a topological object, called hairy Cantor set, which in many ways enjoys the universal features of objects like Jordan curve, Cantor set, Cantor bouquet, hairy Jordan curve, etc. We give an axiomatic characterisation of hairy Cantor sets, and prove that any two such objects in the plane are ambiently homeomorphic.
Cheraghi, D, Pedramfar, M
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ON SUMS OF SEMIBOUNDED CANTOR SETS
Rocky Mountain Journal of Mathematics, 2023 18 ...
Fillman, Jake, Tidwell, Sara H.
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On the Mean Residual Life of Cantor-Type Distributions: Properties and Economic Applications
Austrian Journal of Statistics, 2021 In this paper, we consider the mean residual life (MRL) function of the Cantor distribution and study its properties. We show that the MRL function is continuous at all points, locally decreasing at all points outside the Cantor set and has a unique ...
Stefanos Leonardos, Costis Melolidaksi
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Dimension of the intersection of certain Cantor sets in the plane [PDF]
Opuscula Mathematica, 2021 In this paper we consider a retained digits Cantor set \(T\) based on digit expansions with Gaussian integer base. Let \(F\) be the set all \(x\) such that the intersection of \(T\) with its translate by \(x\) is non-empty and let \(F_{\beta}\) be the ...
Steen Pedersen, Vincent T. Shaw
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The American Mathematical Monthly, 2019 Provisionally accepted by the American Mathematical ...
Jayadev S. Athreya +2 more
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