On the scalar curvature of constant mean curvature hypersurfaces in space forms

In this paper we study the behavior of the scalar curvature $S$ of a complete hypersurface immersed with constant mean curvature into a Riemannian space form of constant curvature, deriving a sharp estimate for the infimum of $S$. Our results will be an application of a weak Omori-Yau maximum principle due to Pigola, Rigoli and Setti \cite{PRS}.Comment: Final version (August 2009). To appear in Journal of Mathematical Analysis and Applications. Dedicated to Professor Marcos Dajczer on the occasion of his 60th birthda

Integrability and Quantum Phase Transitions in Interacting Boson Models

The exact solution of the boson pairing hamiltonian given by Richardson in the sixties is used to study the phenomena of level crossings and quantum phase transitions in the integrable regions of the sd and sdg interacting boson models.Comment: 5 pages, 5 fig. Erice Conferenc

Direct determination of the crystal field parameters of Dy, Er and Yb impurities in the skutterudite compound CeFe4_{4}P12_{12} by Electron Spin Resonance

Despite extensive research on the skutterudites for the last decade, their electric crystalline field ground state is still a matter of controversy. We show that Electron Spin Resonance (ESR) measurements can determine the full set of crystal field parameters (CFPs) for the Th cubic symmetry (Im3) of the Ce$_{1-x}$R$_{x}$Fe$_{4}$P$_{12}$ (R = Dy, Er, Yb, $x\lesssim 0.003$) skutterudite compounds. From the analysis of the ESR data the three CFPs, B4c, B6c and B6t were determined for each of these rare-earths at the Ce$^{3+}$ site. The field and temperature dependence of the measured magnetization for the doped crystals are in excellent agreement with the one predicted by the CFPs Bnm derived from ESR.Comment: 7 pages, 5 figures, to appear in PR