We present several applications of the Assouad dimension, and the related quasi-Assouad dimension and Assouad spectrum, to the box and packing dimensions of orthogonal projections of sets. For example, we show that if the ...

We study the relationship between the size of two sets B, S ⊂ R2, when B contains either the whole boundary or the four vertices of a square with axes-parallel sides and center in every point of S. Size refers to cardinality, ...

We study a generalization of Mor´an´s sum sets, obtaining information about the h-Hausdorff and h-packing measures of these sets and certain of their subsets.

We consider the dimensions of a family of self-affine sets related to the Bedford-McMullen carpets. In particular, we fix a Bedford-McMullen system and then randomise the translation vectors with the stipulation that the ...

A statistical model is proposed for the description of the spatial structure of a packed bed of spherical-like particles in terms of one- and two-bead distribution functions. This is the first step toward the full modeling ...

Let Hh be the h-dimensional Hausdorff measure on Rd. Besicovitch showed that if a set E is null for Hh, then it is null for Hg , for some dimension g smaller than h. We prove that this is not true for packing measures. ...

Given a fixed set of identical or different-sized circular items, the problem we deal with consists on finding the smallest object within which the items can be packed. Circular, triangular, squared, rectangular and also ...

We present approximation algorithms for the three-dimensional strip packing problem, and the three-dimensional bin packing problem. We consider orthogonal packings where 90 degrees rotations are allowed. The algorithms we ...