Multiplication on uniform -Cantor sets
Let $ C $ be the middle-third Cantor set. Define $ C* C=\{x* y: x, y\in C\} $, where $*=+,-
,\cdot,\div $(when $*=\div $, we assume $ y\neq0 $). Steinhaus\cite {HS} proved in 1917 …
,\cdot,\div $(when $*=\div $, we assume $ y\neq0 $). Steinhaus\cite {HS} proved in 1917 …
On the sum of squares of the middle-third Cantor set
Z Wang, K Jiang, W Li, B Zhao - Journal of Number Theory, 2021 - Elsevier
On the sum of squares of the middle-third Cantor set - ScienceDirect Skip to main contentSkip
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On the measure of products from the middle-third Cantor set
L Marchese - Acta Mathematica Hungarica, 2022 - Springer
We prove upper and lower bounds for the Lebesgue measure of the set of products xy with x
and y in the middle-third Cantor set. Our method is inspired by Athreya, Reznick and Tyson …
and y in the middle-third Cantor set. Our method is inspired by Athreya, Reznick and Tyson …
Arithmetic on Moran sets
X Ren, L Tian, J Zhu, K Jiang - Fractals, 2019 - World Scientific
Let (ℳ, ck, nk) be a class of Moran sets. We assume that the convex hull of any E∈(ℳ, ck, nk)
is [0, 1]. Let A, B be two nonempty sets in ℝ. Suppose that f is a continuous function defined …
is [0, 1]. Let A, B be two nonempty sets in ℝ. Suppose that f is a continuous function defined …
Multiple representations of real numbers on self-similar sets with overlaps
X Ren, J Zhu, L Tian, K Jiang - arXiv preprint arXiv:1810.04930, 2018 - arxiv.org
Let $ K $ be the attractor of the following IFS $$\{f_1 (x)=\lambda x, f_2 (x)=\lambda x+ c-
\lambda, f_3 (x)=\lambda x+ 1-\lambda\}, $$ where $ f_1 (I)\cap f_2 (I)\neq\emptyset,(f_1 …
\lambda, f_3 (x)=\lambda x+ 1-\lambda\}, $$ where $ f_1 (I)\cap f_2 (I)\neq\emptyset,(f_1 …