7 papers
Assouad-like dimensions of random Moran measures
Kathryn E. Hare, Franklin Mendivil
In this paper, we determine the almost sure values of the -dimensions of random measures supported on random Moran sets that satisfy a uniform separation condition. The -dime…
Extreme compression of grayscale images
Franklin Mendivil, Örjan Stenflo
Given an grayscale digital image, and a positive integer , how well can we store the image at a compression ratio of ? In this paper we address the above question in extrem…
Measures with specified support and arbitrary Assouad dimensions
Kathryn E. Hare, Franklin Mendivil, Leandro Zuberman
We show that if the upper Assouad dimension of the compact set is positive, then given any there is a measure with support and upper Assou…
Almost sure Assouad-like Dimensions of Complementary sets
Ignacio García, Kathryn E. Hare, Franklin Mendivil
Given a non-negative, decreasing sequence with sum , we consider all the closed subsets of such that the lengths of their complementary open intervals are given by t…
Intermediate Assouad-like dimensions
Ignacio García, Kathryn Hare, Franklin Mendivil
We introduce and study bi-Lipschitz-invariant dimensions that range between the box and Assouad dimensions. The quasi-Assouad dimensions and -spectrum are other special examples…
Assouad dimensions of complementary sets
Ignacio Garcia, Kathryn Hare, Franklin Mendivil
Given a positive, decreasing sequence whose sum is , we consider all the closed subsets of such that the lengths of their complementary open intervals are in one to…