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Diffusion on Middle-ΞΎ 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.
Alireza Khalili Golmankhaneh +3 more
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Fat Cantor sets and their skinny companions [PDF]
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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Using cantor sets for error detection [PDF]
PeerJ Computer Science, 2019 Error detection is a fundamental need in most computer networks and communication systems in order to combat the effect of noise. Error detection techniques have also been incorporated with lossless data compression algorithms for transmission across ...
Nithin Nagaraj
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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.
Alastair Fletcher +2 more
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Random Variables and Stable Distributions on Fractal Cantor Sets
Fractal and Fractional, 2019 In this paper, we introduce the concept of fractal random variables and their related distribution functions and statistical properties. Fractal calculus is a generalisation of standard calculus which includes function with fractal support.
Alireza Khalili Golmankhaneh +1 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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On the Visibility of Homogeneous Cantor Sets
Fractal and FractionalThe problems associated with the visible set have been explored by various scholars. In this paper, we investigate the Hausdorff dimension and the topological properties of the visible set in relation to the products of homogeneous Cantor sets.
Yi Cai, Yufei Chen
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Cantor-winning sets and their applications
Advances in Mathematics, 2017 40 pages; 08/05/15 improvements to introduction and various typos corrected. 10/09/15 conversion of notation in Theorems 11 & 12 to match Schmidt's original. Various typos and readability improvements elsewhere.
Dzmitry Badziahin, Stephen Harrap
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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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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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