Random Walk on Surfaces with Hyperbolic Cusps

We consider the operator associated with a random walk on finite volume surfaces with hyperbolic cusps. We study the spectral gap (upper and lower bound) associated with this operator and deduce some rate of convergence of the iterated kernel towards its stationary distribution.     

Tetramethylammonium hydroxide thermochemolysis for the analysis of cellulose and free carbohydrates in a peat bog

We have compared TMAH thermochemolysis with the classical method using acid hydrolysis for carbohydrates analysis in a peat core. Even if TMAH thermochemolysis does not analyse hemicellulosic carbohydrates and discriminate each individual carbohydrate sensu stricto, it allows the analysis of a cellulose pool hidden to acid hydrolysis and the specific analysis of free and terminal carbohydrates. Simple direct comparisons of thermochemolysis data with data generated from acid hydrolysis cannot be done because of the different mechanisms involved in each process. TMAH thermochemolysis must be viewed and used as a pertinent and complementary method for the analysis of carbohydrates protected and trapped by the organic matter in complex environmental systems.     

Diastereoselective Access to Polyoxygenated Polycyclic Spirolactones through a Rhodium‐Catalyzed [3+2] Cycloaddition Reaction: Experimental and Theoretical Studies

The synthetic utility of γ‐alkylidenebutenolides is demonstrated as highly competent dipolarophile partners in both intra‐ and intermolecular rhodium(II)‐catalyzed 1,3‐dipolar cycloaddition reactions. The strength of this approach lies in the formation of spiro[6,4]lactone moieties with the concomitant construction of quaternary spiro stereocenters. Typically, the construction of spirolactones involves an esterification step, which has often been reported as a “biosynthetic pathway”, and often occurs either as or near to the final step of a total synthesis. Furthermore, a convergent and versatile route is reported for the formation of the (5,7) skeleton of molecules that were isolated from the Schisandra genus. Computational studies were performed to provide an overall picture of the mechanism of the intermolecular [3+2] cycloaddition between 2‐diazo‐1,3‐ketoester and protoanemonin and to rationalize the empirical observations. In particular, we have demonstrated for the first time that the rhodium center plays an important role during the cyclization step itself and reacts with the dipolarophile as a complex with the ylide.     

Analyzing excited-state processes and optical signatures of a ratiomeric fluorine anion sensor: a quantum look

Recently, the spectroscopic signatures of a benzoselenadiazole derivative have been investigated in the framework of designing a new ratiometric fluoride sensor(Saravanan et al., Org Lett, 2014, 16: 354–357). It was suggested that this sensor is undergoing excited-state intramolecular proton transfer. In this work, we provide a new look at these experimental data, using a state-of-the-art time-dependent density functional theory approach to mimic the spectroscopic signatures. New insights about the nature of the excited-state processes are obtained.     

Mathematical working space and paradigms as an analysis tool for the teaching and learning of analysis

ZDM – Mathematics Education - Mathematical working space (MWS) is a model that is used in research in mathematics education, particularly in the field of geometry. Some MWS elements are...