Results 41 to 50 of about 122,847 (179)

When Cantor sets intersect thickly [PDF]

Transactions of the American Mathematical Society, 1993
The thickness of a Cantor set on the real line is a measurement of its "size". Thickness conditions have been used to guarantee that the intersection of two Cantor sets is nonempty. We present sharp conditions on the thicknesses of two Cantor sets which imply that their intersection contains a Cantor set of positive thickness.
Hunt, Brian R., Kan, Ittai, Yorke, James A.   +2 more
openaire   +2 more sources

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

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

Kakeya sets in Cantor directions [PDF]

Mathematical Research Letters, 2008
10 pages; Preliminary ...
Bateman, Michael D., Katz, Nets Hawk
openaire   +2 more sources

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

Cantor set zeros of one-dimensional Brownian motion minus Cantor function [PDF]

, 2012
It was shown by Antunovi\'{c}, Burdzy, Peres, and Ruscher that a Cantor function added to one-dimensional Brownian motion has zeros in the middle $\alpha$-Cantor set, $\alpha \in (0,1)$, with positive probability if and only if $\alpha \neq 1/2$. We give
Ruscher, Julia
core  

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

Homeomorphisms of R and the Davey Space

Applied General Topology, 2004
Up to homeomorphism, there are 9 topologies on a three point set {a, b, c}. Among the resulting topological spaces we have the so called Davey space, where the only non-trivial open set is, let us say, {a}. This is an interesting topological space to the
Sheila Carter, F.J. Craveiro de Carvalho
doaj   +1 more source

Persistence landscapes of affine fractals

Demonstratio Mathematica, 2022
We develop a method for calculating the persistence landscapes of affine fractals using the parameters of the corresponding transformations. Given an iterated function system of affine transformations that satisfies a certain compatibility condition, we ...
Catanzaro Michael J., Przybylski Lee, Weber Eric S.   +2 more
doaj   +1 more source