On the Prym map of cyclic coverings

We work out the cases in which the Prym map is dominant and generically finite for étale or totally ramified cyclic coverings.     

Time-Resolved Spectroscopy and High-Efficiency Light-Driven Hydrogen Evolution of a {Mo3S4}-Containing Polyoxometalate-Based System

Polyoxothiometalate ions (ThioPOM) are active hydrogen-evolution reaction (HER) catalysts based on modular assembly built from electrophilic clusters {MoS_x} and vacant polyoxotungstates. Herein, the dumbbell-like anion [{(PW₁₁O₃₉)Mo₃S₄(H₂O)₃(OH)}₂]⁸⁻ exhibits very high light-driven HER activity, while the active cores {Mo₃S₄} do not contain any exposed disulfido ligands, which were suspected to be the origin of the HER activity. Moreover, in the catalyst architecture, the two central {Mo₃S₄} cores are sandwiched by two {PW₁₁O₃₉}⁷⁻ subunits that act as oxidant-resistant protecting groups and behave as electron-collecting units. A detailed photophysical study was carried out confirming the reductive quenching mechanism of the photosensitizer [Ir(ppy)₂(dtbbpy)]⁺ by the sacrificial donor triethanolamine (TEOA) and highlighting the very high rate constant of the electron transfer from the reduced photosensitizer to the ThioPOM catalyst. Such results provide new insights into the field of molecular catalytic systems able to promote high HER activity.     

Planar Chiral Phosphoramidites with a Paracyclophane Scaffold: Synthesis,Gold(I) Complexes,and Enantioselective Cycloisomerization of Dienynes

The key structural feature of the new phosphoramidites is a paracyclophane scaffold in which two aryl rings are tethered by both a 1,8‐biphenylene unit and a O?P?O bridge. Suitable aryl substituents generate planar chirality. The corresponding gold(I) complexes promote the cycloisomerization of prochiral nitrogen‐tethered dienynes. These reactions afford bicyclo[4.1.0]heptene derivatives displaying three contiguous stereogenic centers, with very high diastereoselectivity and up to 95 % ee.     

Single Fusion Events at Polarized Liquid–Liquid Interfaces

A new electrochemical framework for tracking individual soft particles in solution and monitoring their fusion with polarized liquid–liquid interfaces is reported. The physicochemical principle lies in the interfacial transfer of an ionic probe confined in the particles dispersed in solution and that is released upon their collision and fusion with the fluid interface. As a proof-of-concept, spike-like transients of a stochastic nature are reported in the current–time response of 1,2-dichloroethane(DCE)|water(W) submilli-interfaces after injection of DCE-in-W emulsions. The sign and potential dependence of the spikes reflect the charge and lipophilicity of the ionic load of the droplets. A comparison with dynamic light scattering measurements indicates that each spike is associated with the collision of a single sub-picoliter droplet. This opens a new framework for the study of single fusion events at the micro- and nanoscale and of ion transport across biomimetic soft interfaces.     

LIMIT CYCLES FOR A CLASS OF SECOND ORDER DIFFERENTIAL EQUATIONS AND DUFFING EQUATIONS

By the averaging method of frst order, we study in this work the limit cycles for a class of second order diferential equations and Dufng diferential equations which can be seen as a particular perturbation of the harmonic oscillator.