The wafer-level production of Fused Silica microlens arrays is limited by systematic process non-uniformities. The common molten resist-reflow process with subsequent dry-etching allows for manufacturing of microlens arrays on 200 mm wafers. A thorough pro ...
The optical performance of refractive plano-convex microlenses is mainly related to the quality of their (a)spherical surface. An efficient tolerancing of this surface is a key step towards the manufacturing of high quality microlenses. However, we demonst ...
We present a detailed study of the low-energy excitations of two existing finite-size realizations of the planar kagome Heisenberg antiferromagnet on the sphere: the cuboctahedron and the icosidodecahedron. After highlighting a number of special spectral f ...
We investigate the regularity of the free boundary for the Signorini problem in Rn+1. It is known that regular points are (n−1)-dimensional and C∞. However, even for C∞ obstacles φ, the set of non-regular (or degenerate) points could be very large—e.g. wit ...
An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is not contained in a line or a circle, then P spans at least ordinary circles. Moreover, we determine the exact minimu ...
We study the structure of planar point sets that determine a small number of distinct distances. Specifically, we show that if a set of n points determines o(n) distinct distances, then no line contains Omega(n (7/8)) points of and no circle contains Omega ...
We show that the lines of every arrangement of n lines in the plane can be colored with O(root n/log n) colors such that no face of the arrangement is monochromatic. This improves a bound of Bose et al. by a circle minus(root/log n) factor. Any further imp ...
Erd\H{o}s conjectured in 1946 that every n-point set P in convex position in the plane contains a point that determines at least floor(n/2) distinct distances to the other points of P. The best known lower bound due to Dumitrescu (2006) is 13n/36 - O(1). I ...
