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.     

Synthesis of 4-aryl-4,7,8,9-tetrahydro-6H-pyrazolo[3,4-b]quinolin-5-ones

Reaction of 5-amino-3-methyl-1-phenylpyrazole ( 1a ) and 5-amino-3-(4-chlorophenyl)-1H-pyrazole ( 1b ) with dimedone ( 2 ) and p-susbstituted benzaldehydes 3 in ethanol, afforded in all cases tricyclic linear 4-aryl-7,7-dimethyl-4,7,8,9-tetrahydro-6H-pyrazolo[3,4-b]quinolin-5-ones ( 4a-j ) in good yields. The linear structures and hence the regiospecificity of the reaction were established by nmr measurements.     

Classification of all irreducible unitary representations of the stabilizer of the horicycles of a tree

In this paper we describe all irreducible unitary representations of the stabilizer of the horicycles associated with an end of a homogeneous tree. This work is partially supported by G.N.A.F.A. of the C.N.R., Italy.