We prove that if A is a Borel set in the plane of equal Hausdorff and packing dimension s > 1, then the set of pinned distances {|x − y| : y ∈ A} has full Hausdorff dimension for all x outside of a set of Hausdorff dimension ...

This paper presents a novel method for localization of mobile robots in structured environments. The estimation of the position and orientation of the robot relies on the minimisation of the partial Hausdorff distance ...

We obtain new lower bounds on the Hausdorff dimension of distance sets and pinned distance sets of planar Borel sets of dimension slightly larger than 1, improving recent estimates of Keleti and Shmerkin, and of Liu in ...

We prove new bounds on the dimensions of distance sets and pinned distance sets of planar sets. Among other results, we show that if A ⊂ R2 is a Borel set of Hausdorff dimension s > 1, then its distance set has Hausdorff ...

In this note we prove that the Hausdorff distance between compact sets and the Kantorovich distance between measures, provide an adequate setting for the convergence of Muckenhoupt weights. The results which we prove on ...

Behaviour can be used to infer animal welfare states. Poultry birds tend to move less under conditions of thermal stress; hence the hypothesis of this research is that this unrest behaviour can be used as an indicator of ...