Collars and partitions of hyperbolic cone-surfaces

For compact Riemann surfaces, the collar theorem and Bers’ partition theorem are major tools for working with simple closed geodesics. The main goal of this article is to prove similar theorems for hyperbolic cone-surfaces. Hyperbolic two-dimensional orbifolds are a particular case of such surfaces. We consider all cone angles to be strictly less than π to be able to consider partitions. Emily B. Dryden—partially supported by the US National Science Foundation grant DMS-0306752. Hugo Parlier—supported by the Swiss National Science Foundation grants 21-57251.99 and 20-68181.02.     

Continuous families of Hölder functions that are not of bounded variation

This paper deals with three classes of functions of great importance in analysis and its applications. We construct a family of Hölder functions in the closed unit interval having two continuous parameters. Those functions are not of bounded variation for any pair of values of the Hölder constant and exponent. The construction depends on a change of variables given by a Lipschitz function with constant equal to 1. Several questions related to the concepts of genericity, surjectivity and deformability are posed at the end.     

Un processus effectif de détermination des systoles pour les surfaces hyperboliques

We give an effective process to discribe explicitly the systols of an hyperbolic surface depending on his Fenchel-Nielsen coordinates.      

Zum Nachweis des Furfurols

Ohne Zusammenfassung     

Ultraviolet Absorption Induces Hydrogen‐Atom Transfer in G⋅C Watson–Crick DNA Base Pairs in Solution

Ultrafast deactivation pathways bestow photostability on nucleobases and hence preserve the structural integrity of DNA following absorption of ultraviolet (UV) radiation. One controversial recovery mechanism proposed to account for this photostability involves electron‐driven proton transfer (EDPT) in Watson–Crick base pairs. The first direct observation is reported of the EDPT process after UV excitation of individual guanine–cytosine (G?C) Watson–Crick base pairs by ultrafast time‐resolved UV/visible and mid‐infrared spectroscopy. The formation of an intermediate biradical species (G[?H]?C[+H]) with a lifetime of 2.9 ps was tracked. The majority of these biradicals return to the original G?C Watson–Crick pairs, but up to 10 % of the initially excited molecules instead form a stable photoproduct G*?C* that has undergone double hydrogen‐atom transfer. The observation of these sequential EDPT mechanisms across intermolecular hydrogen bonds confirms an important and long debated pathway for the deactivation of photoexcited base pairs, with possible implications for the UV photochemistry of DNA.