Given a finite set S of places of a number field, we prove that the field of totally S-adic algebraic numbers is not Hilbertian. The field of totally real algebraic numbers Qtr, the field of totally p-adic algebraic numbers Qtot,p, and, more generally, fields of totally S-adic algebraic numbers Qtot,S, where S is a finite set of places of Q, play an important role in number theory and Galois th...

Let M ,N be two totally real and real analytic submanifolds in Cn . We say that M and N are biholomorphically equivalent if there is a biholomorphic mapping F defined in a neighborhood of M such that F (M ) = N . As a standard fact of complexification, one knows that all totally real and real analytic embeddings of M in C n are biholomorphically equivalent if M is of maximal dimension n . Howev...

Different approaches to the decomposition of a nonsingular totally positive matrix as a product of bidiagonal matrices are studied. Special attention is paid to the interpretation of the factorization in terms of the Neville elimination process of the matrix and in terms of corner cutting algorithms of Computer Aided Geometric Design. Conditions of uniqueness for the decomposition are also given.

The aim of this paper is to give insight into the behaviour of inequivalent representations of 3{connected matroids. An element x of a matroid M is xed if there is no extension M 0 of M by an element x 0 such that fx;x 0 g is independent and M 0 is unaltered by swapping the labels on x and x 0. When x is xed, a representation of M nx extends in at most one way to a representation of M. A 3{conn...

Several investigations have been devoted towards understanding the coating process in fluidized beds. Most of these studies focused on spraying liquid droplets over the bed. However, due to the complexity of these systems, more investigations are still required to quantify the effect of operating conditions on the coating criteria. The present work aims at fundamentally understanding and pr...