Synthesis of Dibromo-Vinyl Chalcogenides

β-Bromovinyl chalcogenides were conveniently prepared in good yields by reacting alkynyl chalcogenides with bromine or by addition of organochalcogenyl bromide to bromoacetylenes in the presence of zinc bromide.     

Catalyst-Dependent Selective Synthesis of O/S- and S/S-Acetals from Enol Ethers

Enol ethers are reacted with mercaptanes to give the corresponding O/S- or S/S-acetals in medium to high yield. Either product can be formed selectively depending on the acid catalyst and the reaction time applied.     

Backbone-only protein solution structures with a combination of classical and paramagnetism-based constraints: a method that can be scaled to large molecules.

Herein, it is shown that a medium-resolution solution structure of a protein can be obtained with the sole assignment of the protein backbone and backbone-related constriants if a derivative with a firmly bound paramagnetic metal is available. The proof-of-concept is provided on calbindin D9k, a calcium binding protein in which one of the two calcium ions can be selectively substituted by a paramagnetic lanthanide ion. The constraints used are HN (and Ha) nuclear Overhauser effects (NOEs), hydrogen bonds, dihedral angle constriants from chemical shifts, and the following paramagnetism-based constraints: 1) pseudocontact shifts, acquired by substituting one (or more) lanthanide(s) in the C-terminal calcium binding site; 2) N-HN residual dipolar couplings due to self-orientation induced by the paramagnetic lanthanide(s); 3) cross-correlations between the Curie and internuclear dipole-dipole interactions; and 4) paramagnetism-induced relaxation rate enhancements. An upper distance limit for internuclear distances between any two backbone atoms was also given according to the molecular weight of the protein. For this purpose, the paramagnetism-based constraints were collectively implemented in the program CYANA for solution structure determinations, similarly to what was previously done for the program DYANA. The method is intrinsically suitable for large molecular weight proteins.     

Combined finite element and spectral approximation of the Navier-Stokes equations

Summary We present a method for the numerical approximation of Navier-Stokes equations with one direction of periodicity. In this direction a Fourier pseudospectral method is used, in the two others a standard F.E.M. is applied. We prove optimal rate of convergence where the two parameters of discretization intervene independently.

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Approximation des équations de Navier-Stokes par une méthode éléments finis-spectrale Fourier

Resumé On présente une méthode d'approximation numérique des équations de Navier-Stokes possédant une direction de périodicité. Dans cette direction une méthode pseudospectrale basée sur des développements en série de Fourier est utilisée, dans les deux autres on applique une méthode d'éléments finis standard. On montre que la convergence est optimale et que les deux paramètres de discrétisation peuvent être choisis de façon indépendante.

     

Large deviation approach to non equilibrium processes in stochastic lattice gases

We present a review of recent work on the statistical mechanics of non equilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and can be studied rigorously providing a source of challenging mathematical problems. In this way, some principles of wide validity have been obtained leading to interesting physical consequences.     

Zero-dimensional subschemes of ruled varieties

Here we study zero-dimensional subschemes of ruled varieties, mainly Hirzebruch surfaces and rational normal scrolls, by applying the Horace method and the Terracini method This research is part of the T.A.S.C.A. project of I.N.d.A.M., supported by P.A.T. (Trento) and M.I.U.R. (Italy)     

Fast deprotection of phenoxy benzyl ethers in transfer hydrogenation assisted by microwave

Phenoxy benzyl ethers are easily and quickly deprotected in the presence of ammonium formate and microencapsulated Pd(0)EnCat with the assistance of microwave irradiation. This procedure can be applied in the presence of other functional groups as well. The described protocol is particularly convenient for the preparation in a parallel and automatic fashion of libraries of compounds possessing a phenol type moiety.     

On the numerical evaluation of Cauchy transforms

In this paper we consider simple methods for the reconstruction of the Cauchy transform over a curve when an explicit parametrization of the latter is not provided. The methods consist of replacing the parametrization of the curve by piecewise polynomial interpolation followed by the use of Newton-Cotes type formulae for the integration. The order of convergence of the resulting quadrature is higher than would be expected on the basis of considerations involving just interpolation theory, provided that the Cauchy transform is evaluated at known nodes on the curve. These results allow the calculation of the Cauchy transform at other points with the same accuracy if this scheme is followed by an interpolatory formula of sufficiently high accuracy.