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.     

Binomial Determinant Evaluations

By means of matrix decomposition and the partial fraction method, we establish several determinant evaluation formulas, which can be considered as generalizations of the Vandermonde and Cauchy determinants. Received February 24, 2005     

Regiospecific synthesis of polyfluorinated heterocycles

A series of 10 heterocycles was obtained from the reaction of 1,1,1-trifluoro-4,4-diethoxy-3-buten-2-one and 1,1,1,2,2-pentafluoro-4,4-diethoxy-3-penten-2-one with different dinucleofiles (hydrazine, methyl hydrazine, hydroxylamine and sodium cyanide). The pyrazoles, 4,5-dihydroisoxazoles and pyrrolidinones polyfluoroalkyl substituted were obtained in moderate to good yields under mild conditions.