Carlota Simões

Mathematics and interdisciplinarity : outreach activities at the University of Coimbra

It is well known that informal learning may and should supplement formal learning. They are both known to help each other. Based on our experience of outreach activities at the University of Coimbra, we discuss the deep connection of mathematics with astronomy, physics and art. We show with some examples how these connections may facilitate the bridge between mathematics and the public, in particular young people, raising the public awareness of mathematics.

Mathematical Aspects in the Second Viennese School of Music

Mathematics and Music seem nowadays independent areas of knowledge. Nevertheless, strong connections exist between them since ancient times. Twentieth-century music is no exception, since in many aspects it admits an obvious mathematical formalization. In this article some twelve-tone music rules, as created by Schoenberg, are presented and translated into mathematics. The representation obtained is used as a tool in the analysis of some compositions by Schoenberg, Berg, Webern (the Second Viennese School) and also by Milton Babbitt (a contemporary composer born in 1916).

Stabilization and Linear Factorization of Implicit Discrete-Time Nonlinear Scalar Systems

Abstract We consider the problems of stability and stabilization of implicit discretetime nonlinear scalar systems. Linear factorization is defined and results on local stability in terms of this concept are given. Special attention is given to polynomial systems. Necessary and sufficient conditions for stability of polynomial autonomous systems and for stabilizability of polynomial control systems are obtained.