Halogen atom transfer radical addition of α-polychloroesters to olefins promoted by Fe filings

The Kharasch addition of methyl 2,2-dichlorocarboxylates or trichloro acetic acid derivatives to alkenes, affording the corresponding 1:1 adducts, is promoted by the iron filings/N,N-dimethylformamide system.     

Poincaré Polynomial of Moduli Spaces of Framed Sheaves on (Stacky) Hirzebruch Surfaces

We perform a study of the moduli space of framed torsion-free sheaves on Hirzebruch surfaces by using localization techniques. We discuss some general properties of this moduli space by studying it in the framework of Huybrechts-Lehn theory of framed modules. We classify the fixed points under a toric action on the moduli space, and use this to compute the Poincaré polynomial of the latter. This will imply that the moduli spaces we are considering are irreducible. We also consider fractional first Chern classes, which means that we are extending our computation to a stacky deformation of a Hirzebruch surface. From the physical viewpoint, our results provide the mathematical framework for the counting of D4-D2-D0 branes bound states on total spaces of the bundles O_{\mathbb P¹}(-p){\mathcal {O}_{\mathbb {P}^1}(-p)} .     

Holomorphic Cartan geometry on manifolds with numerically effective tangent bundle

Let X be a compact connected Kähler manifold such that the holomorphic tangent bundle TX is numerically effective. A theorem of Demailly et al. (1994) [11] says that there is a finite unramified Galois covering M→X, a complex torus T, and a holomorphic surjective submersion f:M→T, such that the fibers of f are Fano manifolds with numerically effective tangent bundle. A conjecture of Campana and Peternell says that the fibers of f are rational and homogeneous. Assume that X admits a holomorphic Cartan geometry. We prove that the fibers of f are rational homogeneous varieties. We also prove that the holomorphic principal G-bundle over T given by f, where G is the group of all holomorphic automorphisms of a fiber, admits a flat holomorphic connection.     

Nanoelectrode ensembles for the direct voltammetric determination of trace iodide in water

Procedures for the preparation and characterisation of ensembles of gold nanodisk electrodes (NEE) of 30 nm diameter are presented, in particular focusing on improvements in the signal/background current ratios and detection limits with respect to the electrochemical oxidation of iodide and its analytical determination in water samples. At NEEs iodide undergoes a quasi-reversible diffusion controlled oxidation with a slight shift in E _1/2 values and slightly higher peak to peak separation with respect to conventional gold disk electrodes. The double layer charging current at the NEE is significantly lower than at conventional electrodes so that the detection limit (DL) by cyclic voltammetry with NEEs in tap water is significantly lower than DL at the Au-disk millimetre-sized electrode (DL 0.3 µM at NEE vs. 4 µM for Au-disk). Finally, it is shown that NEEs in combination with square wave voltammetry can be applied for the direct determination of iodide in water samples from the lagoon of Venice, with a detection limit of 0.10 µM.     

Isotopic finger-printing of active pharmaceutical ingredients by 13C NMR and polarization transfer techniques as a tool to fight against counterfeiting

The robustness of adiabatic polarization transfer methods has been evaluated for determining the carbon isotopic finger-printing of active pharmaceutical ingredients. The short time stabilities of the adiabatic DEPT and INEPT sequences are very close to that observed with the one pulse sequence, but the DEPT long time stability is not sufficient for isotopic measurements at natural abundance or low enrichment. Using the INEPT sequence for ¹³C isotopic measurements induces a dramatic reduction in the experimental time without deterioration in short time or long time stability. It appears, therefore, to be a method of choice for obtaining the isotopic finger-print of different ibuprofen samples in a minimum time. The results obtained on 13 commercial ibuprofen samples from different origins show that this strategy can be used effectively to determine ¹³C distribution within a given molecule and to compare accurately differences in the isotopic distribution between different samples of the given molecule. The present methodology is proposed as a suitable tool to fight against counterfeiting.     

Binary choices in small and large groups: A unified model

Two different ways to model the diffusion of alternative choices within a population of individuals in the presence of social externalities are known in the literature. While Galam’s model of rumors spreading considers a majority rule for interactions in several groups, Schelling considers individuals interacting in one large group, with payoff functions that describe how collective choices influence individual preferences. We incorporate these two approaches into a unified general discrete-time dynamic model for studying individual interactions in variously sized groups. We first illustrate how the two original models can be obtained as particular cases of the more general model we propose, then we show how several other situations can be analyzed. The model we propose goes beyond a theoretical exercise as it allows modeling situations which are relevant in economic and social systems. We consider also other aspects such as the propensity to switch choices and the behavioral momentum, and show how they may affect the dynamics of the whole population.