Every plane graph of maximum degree 8 has an edge-face 9-colouring

An edge-face colouring of a plane graph with edge set $E$ and face set $F$ is a colouring of the elements of $E \cup F$ such that adjacent or incident elements receive different colours. Borodin proved that every plane graph of maximum degree $\Delta\ge10$ can be edge-face coloured with $\Delta+1$ colours. Borodin's bound was recently extended to the case where $\Delta=9$. In this paper, we extend it to the case $\Delta=8$.Comment: 29 pages, 1 figure; v2 corrects a contraction error in v1; to appear in SIDM

Traveling waves and pattern formation for spatially discrete bistable reaction-diffusion equations (survey)

Analysis and Stochastic

Entropy based statistical inference for methane emissions released from wetland

We concentrate on the paradigm question how much stochasticity and how much chaos are present in the methane emission model. In particular we analyze the residua from the process of methane emissions from wetlands in the sedge-grass marsh, in South Bohemia, Czech Republic. Relation to entropy and a specific version of Kullback–Leibler divergence will be given. A graphical tool to assess the amount of entropy in the system is developed and illustrated on real data from the sedge-grass marsh methane emission

Sub-ps laser damage resistance of Magnetron Sputtered dielectric coatings for reflective components

International audienceWe investigate laser-induced damage thresholds of magnetron sputtered coatings in sub-ps regime. Particularly we study intrinsic LIDT of the films at 1µm, and Laser-induced contamination at high repetition rate