Home OALib Journal OALib PrePrints Submit Ranking News My Lib FAQ About Us Follow Us+
 Title Keywords Abstract Author All
Search Results: 1 - 10 of 100 matches for " "
 Mauro Di Nasso Mathematics , 2014, Abstract: We isolate conditions on the relative size of sets of natural numbers $A,B$ that guarantee a nonempty intersection $\Delta(A)\cap\Delta(B)\ne\emptyset$ of the corresponding sets of distances. Such conditions apply to a large class of zero density sets. We also show that a variant of Khintchine's Recurrence Theorem holds for all infinite sets $A=\{a_1  Mauro Di Nasso Mathematics , 2014, Abstract: We consider shifts of a set$A\subseteq\mathbb{N}$by elements from another set$B\subseteq\mathbb{N}$, and prove intersection properties according to the relative asymptotic size of$A$and$B$. A consequence of our main theorem is the following: If$A=\{a_n\}$is such that$a_n=o(n^{k/k-1})$, then the$k$-recurrence set$R_k(A)=\{x\mid |A\cap(A+x)|\ge k\}$contains the distance sets of arbitrarily large finite sets.  Stephen Semmes Mathematics , 2007, Abstract: The focus here is on connected fractal sets with topological dimension 1 and a lot of topological activity, and their connections with analysis.  Mathematics , 2014, Abstract: Let$E, F\subset \R^d$be two self-similar sets. Under mild conditions, we show that$F$can be$C^1$-embedded into$E$if and only if it can be affinely embedded into$E$; furthermore if$F$can not be affinely embedded into$E$, then the Hausdorff dimension of the intersection$E\cap f(F)$is strictly less than that of$F$for any$C^1$-diffeomorphism$f$on$\R^d$. Under certain circumstances, we prove the logarithmic commensurability between the contraction ratios of$E$and$F$if$F$can be affinely embedded into$E$. As an application, we show that$\dim_HE\cap f(F)<\min\{\dim_HE, \dim_HF\}$when$E$is any Cantor-$p$set and$F$any Cantor-$q$set, where$p,q\geq 2$are two integers with$\log p/\log q\not \in \Q\$. This is related to a conjecture of Furtenberg about the intersections of Cantor sets.