This article highlights a connection between Diophantine approximation and the lower Assouad dimension by using information about the latter to show that the Hausdorff dimension of the set of badly approximable points that lie in certain non-conformal fractals, known as self-affine sponges, is bounded below by the dynamical dimension of these fractals. The results, which are the first to advance beyond the conformal setting, encompass both the case of Sierpiński sponges/carpets (also known as Bedford–McMullen sponges/carpets) and the case of Barański carpets.

Article discussing projecting on polynomial solutions of second order partial differential operators.

In this paper, the authors adapt Axler and Ramey's method of constructing the harmonic part of a homogeneous polynomial to the Fischer decomposition associated to Dirac operators acting on polynomial spinors.

This article gives results of numerical calculations of asymptotic behavior of critical points of a Ginzburg-Landau functional.