Results 1 to 10 of about 122,847 (179)
Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set [PDF]
Entropy, 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 ...
Maria C. Mariani +4 more
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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.
Ken W. Lee
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Proceedings of the American Mathematical Society, 2021 We show that Li–Yorke chaos ensures the existence of a scrambled Cantor set.
Miller, Benjamin +2 more
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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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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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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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Julia sets and wild Cantor sets [PDF]
Geometriae Dedicata, 2014 There exist uniformly quasiregular maps $f:\mathbb{R}^3 \to \mathbb{R}^3$ whose Julia sets are wild Cantor sets.
Fletcher, Alastair, Wu, Jang-Mei
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Cuntz–Krieger Algebras and Wavelets on Fractals [PDF]
, 2011 We consider representations of Cuntz–Krieger algebras on the Hilbert space of square integrable functions on the limit set, identified with a Cantor set in the unit interval.
Marcolli, Matilde, Paolucci, Anna Maria
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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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Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]
Demonstratio Mathematica, 2021 Cantor sets are constructed from iteratively removing sections of intervals. This process yields a cumulative distribution function (CDF), constructed from the invariant Borel probability measure associated with their iterated function systems.
Byars Allison +5 more
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