Formalizing the LLL Basis Reduction Algorithm and the LLL Factorization Algorithm in Isabelle/HOL.

The LLL basis reduction algorithm was the first polynomial-time algorithm to compute a reduced basis of a given lattice, and hence also a short vector in the lattice. It approximates an NP-hard problem where the approximation quality solely depends on the dimension of the lattice, but not the lattice itself. The algorithm has applications in number theory, computer algebra and cryptography.

Ellipsometry with polarisation analysis at cryogenic temperatures inside a vacuum chamber.

In this paper we describe a new variant of null ellipsometry to determine thicknesses and optical properties of thin films on a substrate at cryogenic temperatures. In the PCSA arrangement of ellipsometry the polarizer and the compensator are placed before the substrate and the analyzer after it. Usually, in the null ellipsometry the polarizer and the analyzer are rotated to find the searched minimum in intensity.