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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.
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.
Fletcher, Alastair, Wu, Jang-Mei
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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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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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Non-Differentiable Solution of Nonlinear Biological Population Model on Cantor Sets
Fractal and Fractional, 2020 The main objective of this study is to apply the local fractional homotopy analysis method (LFHAM) to obtain the non-differentiable solution of two nonlinear partial differential equations of the biological population model on Cantor sets. The derivative
Djelloul Ziane +3 more
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Fractal Stochastic Processes on Thin Cantor-Like Sets
Mathematics, 2021 We review the basics of fractal calculus, define fractal Fourier transformation on thin Cantor-like sets and introduce fractal versions of Brownian motion and fractional Brownian motion. Fractional Brownian motion on thin Cantor-like sets is defined with
Alireza Khalili Golmankhaneh +1 more
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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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