Results 11 to 20 of about 6,429 (238)
ON SUMS OF SEMIBOUNDED CANTOR SETS
Rocky Mountain Journal of Mathematics, 2023 18 ...
Fillman, Jake, Tidwell, Sara H.
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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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The American Mathematical Monthly, 2019 Provisionally accepted by the American Mathematical ...
Jayadev S. Athreya +2 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. 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
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On intersections of Cantor sets: Hausdorff measure [PDF]
Opuscula Mathematica, 2013 We establish formulas for bounds on the Haudorff measure of the intersection of certain Cantor sets with their translates. As a consequence we obtain a formula for the Hausdorff dimensions of these intersections.
Steen Pedersen, Jason D. Phillips
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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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Assouad and Lower Dimensions of Some Homogeneous Cantor Sets
Journal of Mathematics, 2022 We compute the Assouad dimensions and the lower dimensions of a class of homogeneous Cantor sets without the condition that the smallest compression ratio C⋆>0 and find that the lower dimension of a homogeneous Cantor set E may be any a number in the ...
Xiao JiaQing
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A Survey on Newhouse Thickness, Fractal Intersections and Patterns
Mathematical and Computational Applications, 2022 In this article, we introduce a notion of size for sets, called the thickness, that can be used to guarantee that two Cantor sets intersect (the Gap Lemma) and show a connection among thickness, Schmidt games and patterns. We work mostly in the real line,
Alexia Yavicoli
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Visible and Invisible Cantor Sets [PDF]
, 2012 In this article we study for which Cantor sets there exists a gauge-function h, such that the h-Hausdorff-measure is positive and finite. We show that the collection of sets for which this is true is dense in the set of all compact subsets of a Polish space X.
Cabrelli, Carlos +2 more
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