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Squeezing functions and Cantor sets [PDF]

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2020
We construct "large" Cantor sets whose complements resemble the unit disk arbitrarily well from the point of view of the squeezing function, and we construct "large" Cantor sets whose complements do not resemble the unit disk from the point of view of the squeezing function.
Arosio, L, Fornaess, JE, Shcherbina, N, Wold, EF   +3 more
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Solving Fokker-Planck Equations on Cantor Sets Using Local Fractional Decomposition Method

Abstract and Applied Analysis, 2014
The local fractional decomposition method is applied to approximate the solutions for Fokker-Planck equations on Cantor sets with local fractional derivative.
Shao-Hong Yan, Xiao-Hong Chen, Gong-Nan Xie, Carlo Cattani, Xiao-Jun Yang   +4 more
doaj   +1 more source

Lebesgue Constants for Cantor Sets

Experimental Mathematics
We evaluate the values of the Lebesgue constants in polynomial interpolation for three types of Cantor sets. In all cases, the sequences of Lebesgue constants are not bounded. This disproves the statement by Mergelyan.
Alexander Goncharov, Yaman Paksoy
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Remainders, Singular Sets and the Cantor Set

Rocky Mountain Journal of Mathematics, 1994
The authors characterize when, for nonlocally compact \(X\), there is a compactification \(\alpha X\) of \(X\) for which the closure of \(\alpha X\smallsetminus X\) is homeomorphic to the Cantor set \(2^ \omega\).
Hatzenbuhler, James P., Mattson, Don A.
openaire   +3 more sources

An orthonormal system on the construction of the generalized cantor set

International Journal of Mathematics and Mathematical Sciences, 1993
This paper presents a new complete orthonormal system of functions defined on the interval [0,1] and whose supports shrink to nothing. This system related to the construction of the Cantor ternary set.
Raafat Riad Rizkalla
doaj   +1 more source

Genus of a Cantor Set

Rocky Mountain Journal of Mathematics, 2005
A defining sequence for a Cantor set, \(X\), in 3-space, is a sequence of compact 3-manifolds, \((M_i)\) with boundary, each consisting of disjoint cubes with handles, \(M_{i+1}\subset\text{Int}\,M_i\) and \(X=\bigcap M_i\). If \(A\subset X\), \(g_A(X;(M_i))\) is the maximum genus of those components of the \(M_i\) which intersect \(A\).
openaire   +3 more sources

On the Visibility of Homogeneous Cantor Sets

Fractal and Fractional
The 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
doaj   +1 more source

Cantorvals as sets of subsums for a series connected with trigonometric functions

Pracì Mìžnarodnogo Geometričnogo Centru, 2023
We study properties of the set of subsums for convergent series k1 sin x + ... + km sin x + ... + k1 sin x[(n-1)/m+1] + ... + km sin x[(n-1)/m+1] + ...
Mykola Pratsiovytyi, Dmytro Karvatskyi
doaj   +1 more source

Characterization of the macro-Cantor set up to coarse equivalence

Karpatsʹkì Matematičnì Publìkacìï, 2013
We characterize metric spaces that are coarsely equivalent to the macro-Cantor set $2^{<\mathbb N}$.
I. M. Zarichnyi
doaj   +1 more source

Performing a Multi-Stage Mathematical and Informational Task "Dynamics of Iteration of Piecewise Linear Functions" as a Means of Developing Students' Creativity

Современные информационные технологии и IT-образование, 2020
A multistage mathematical-informational task "Piecewise linear functions iterating dynamics" aimed at students' creativity development is examined in this paper.
Valeriy Sekovanov, Vladimir Ivkov, Alexey Piguzov, Larisa Rybina   +3 more
doaj   +1 more source