Results 11 to 20 of about 69,620 (237)
Two measures on Cantor sets [PDF]
Journal of Approximation Theory, 2014 We give an example of Cantor type set for which its equilibrium measure and the corresponding Hausdorff measure are mutually absolutely continuous. Also we show that these two measures are regular in Stahl-Totik sense.
Alpan G., Goncharov, A.
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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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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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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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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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The American Mathematical Monthly, 2019 Provisionally accepted by the American Mathematical ...
Jayadev S. Athreya +2 more
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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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Distinguishing Bing-Whitehead Cantor sets [PDF]
Transactions of the American Mathematical Society, 2011 Bing-Whitehead Cantor sets were introduced by DeGryse and Osborne in dimension three and greater to produce examples of Cantor sets that were non standard (wild), but still had simply connected complement. In contrast to an earlier example of Kirkor, the construction techniques could be generalized to dimensions bigger than three. These Cantor sets in $
Garity, Dennis +3 more
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Classifying Cantor Sets by their Fractal Dimensions [PDF]
, 2010 In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovitch and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-Packing measures, for the family of dimension functions h, and characterize this
Cabrelli, Carlos A. +2 more
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Data block decomposition and intelligent secure acquisition of microdata
Scientific Reports, 2023 P-sets (P stands for Packet) is a set model with dynamic characteristics, which is obtained by introducing dynamic characteristics into Cantor set and improving Cantor set. According to the fact that the characteristics of class I big data are completely
Xiuquan Zhang, Lin Shen, Kaiquan Shi
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