The metric anomaly of analytic torsion at the boundary of an even dimensional cone

The formula for analytic torsion of a cone in even dimensions is composed of three terms. The first two terms are well understood and given by an algebraic combination of the Betti numbers and the analytic torsion of the cone base. The third “singular” contribution is an intricate spectral invariant of the cone base. We identify the third term as the metric anomaly of the analytic torsion coming from the non-product structure of the cone at its regular boundary. Hereby we filter out the actual contribution of the concial singularity and identify the analytic torsion of an even-dimensional cone purely in terms of the Betti numbers and the analytic torsion of the cone base.     

Vinylation of cellulose in superbase catalytic systems: towards new biodegradable polymer materials

Diverse celluloses including non-mercerized and mercerized ones have been successfully vinylated with acetylene in the superbase catalytic systems MOH/DMSO and MOH/THF (M = Na, K) at 85–140 °C. Depending on the reaction conditions, degree of substitution of the hydroxyl groups by highly reactive polymerazable vinyloxy groups ranges 0.11–1.22, the yields of vinylated celluloses (insoluble in water, but soluble in DMSO) being 41–89 %. Vinylated celluloses are easily decomposed under the action of white rot fungi: Phanerochaete chrysosporium, Trametes versicolor and Trametes hirsutus, and can constitute a basis for the preparation of biodegradable polymer materials (due to polymerization or polyaddition at the vinyloxy group).     

Site‐Resolved Two‐Step Relaxation Process in an Asymmetric Dy2 Single‐Molecule Magnet

Elaborate chemical design is of utmost importance in order to slow down the relaxation dynamics in single‐molecule magnets (SMMs) and hence improve their potential applications. Much interest was devoted to the study of distinct relaxation processes related to the different crystal fields of crystallographically independent lanthanide ions. However, the assignment of the relaxation processes to specific metal sites remains a challenging task. To address this challenge, a new asymmetric Dy₂ SMM displaying a well‐separated two‐step relaxation process with the anisotropic centers in fine‐tuned local environments was elaborately designed. For the first time a one‐to‐one relationship between the metal sites and the relaxation processes was evidenced. This work sheds light on complex multiple relaxation and may direct the rational design of lanthanide SMMs with enhanced magnetic properties.