A limiting distribution for maxima of discrete stationary triangular arrays with an application to risk due to avalanches

In this paper, we generalize earlier work dealing with maxima of discrete random variables. We show that row-wise stationary block maxima of a triangular array of integer valued random variables converge to a Gumbel extreme value distribution if row-wise variances grow sufficiently fast as the row-size increases. As a by-product, we derive analytical expressions of normalising constants for most classical unbounded discrete distributions. A brief simulation illustrates our theoretical result. Also, we highlight its usefulness in practice with a real risk assessment problem, namely the evaluation of extreme avalanche occurrence numbers in the French Alps.     

Vinyl nosylates as partner in copper and silver co-catalyzed Sonogashira cross-coupling reactions

Vinyl nosylates, readily obtained from β-dicarbonyl derivatives, could be efficiently engaged in Sonogashira cross-coupling reactions, either cocatalyzed by copper or silver salts. The para-nitrobenzenesulfonate (nosylate) group allows this coupling to be performed under very mild conditions (room temperature). These new leaving group and mild conditions could be applied to the synthesis of acetylenic coumarinyl derivatives and to the total synthesis of an acetylenic monoterpene natural product, named cleviolide.     

Holonomy and contact geometry

On a Riemannian manifold, any parallel form is preserved by the flow of any Killing vector field with constant magnitude. As a consequence, on a 2n+1-dimensional K-contact manifold, there are no nontrivial parallel forms except of degrees 0 and 2n+1. Flat contact metrics on 3-manifolds are characterized by reducible holonomy.     

Performance of a silicon monochromator under high heat load

The performance of a cryogenically cooled double‐crystal silicon monochromator was studied under high‐heat‐load conditions with total absorbed powers and power densities ranging from 8 to 780 W and from 8 to 240 W mm^?2, respectively. When the temperature of the first crystal is maintained close to the temperature of zero thermal expansion of silicon, the monochromator shows nearly ideal performance with a thermal slope error of 0.6 µrad. By tuning the size of the first slit, the regime of the ideal performance can be maintained over a wide range of heat loads, i.e. from power densities of 110 W mm^?2 (at total absorbed power of 510 W) to 240 W mm^?2 (at total absorbed power of 240 W).