Frame functions in finite-dimensional Quantum Mechanics and its Hamiltonian formulation on complex projective spaces

This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of so-called frame functions, introduced by A.M. Gleason to prove his celebrated theorem. In particular, the problem of associating quantum state with positive Liouville densities is tackled from an axiomatic point of view, proving a theorem classifying all possible correspondences. A similar result is established for classical observables representing quantum ones. These correspondences turn out to be encoded in a one-parameter class and, in both cases, the classical objects representing quantum ones result to be frame functions. The requirements of $U(n)$ covariance and (convex) linearity play a central r\^ole in the proof of those theorems. A new characterization of classical observables describing quantum observables is presented, together with a geometric description of the $C^*$-algebra structure of the set of quantum observables in terms of classical ones.Comment: 32 pages, no figure, fixed some coefficients and added some comments and references, accepted for publication in Int. J. Geom. Methods. Mod. Phy

XMM-Newton detects the beginning of the X-ray decline of SN 1995N

We present the results of a new XMM-Newton observation of the interacting supernova 1995N, performed on July 27, 2003. We find that the 0.2-10.0 keV flux has dropt at a level of 1.44e-13 erg cm^-2 s^-1, about one order of magnitude lower than that of a previous ASCA observation performed on January 1998. The X-ray spectral analysis shows statistically significant evidence for the presence of two distinct components, that can be modeled with emission from optically thin, thermal plasmas at different temperatures. From these temperatures we derive that the exponent of the ejecta density distribution is n ~ 6.5.Comment: 3 pages, 2 figures. To appear in proceedings of the International Conference "1604-2004: Supernovae as Cosmological Lighthouses" (Padova, Italy, June 16-19, 2004), eds. M. Turatto, W. Shea, S. Benetti and L. Zampieri, ASP conference Serie

Iterative and Recursive Estimation in Structural Non-Adaptive Models

An inference method, called latent backfitting is proposed. It appears well suited for econometric models where the structural relationships of interest define the observed endogenous variables as a known function of unobserved state variables and unknown parameters. This nonlinear state space specification paves the way for iterative or recursive EM-like strategies. In the E-steps the state variables are forecasted given the observations and a value of the parameters. In the M-steps these forecasts are used to deduce estimators of the unknown parameters from the statistical model of latent variables. The proposed iterative/recursive estimation is particularly useful for latent regression models and for dynamic equilibrium models involving latent state variables. Practical implementation issues are discussed through the example of term structure models of interest rates. Nous proposons une méthode d'inférence appelée «latent backfitting». Cette méthode est spécialement conçue pour les modèles économétriques dans lesquels les relations structurelles d'intérêt définissent les variables endogènes observées comme une fonction connue des variables d'états non observées et des paramètres inconnus. Cette spécification espace-état non linéaire ouvre la voie à des stratégies itératives ou récursives de type EM. Dans l'étape E, les variables d'état sont prédites à partir des observations et des valeurs des paramètres. Dans l'étape M, ces prévisions sont utilisées pour déduire des estimateurs des paramètres inconnus à partir du modèle statistique des variables latentes. L'estimation itérative/récursive proposée est particulièrement utile pour les modèles avec équation de régression latente et les modèles dynamiques d'équilibre utilisant des variables d'état latentes. Les questions relatives à l'application de ces méthodes sont analysées à travers l'exemple des modèles de structure par termes des taux d'intérêt.Asset Pricing Models, Latent Variables, Estimation, Iterative or Recursive Algorithms, Modèles d'évaluation d'actifs financiers, variables latentes, estimation, algorithmes itératifs ou récursifs

Ejecta and progenitor of the low-luminosity Type IIP supernova 2003Z

The origin of low-luminosity Type IIP supernovae is unclear: they have been proposed to originate either from massive (about 25 Msun) or low-mass (about 9 Msun) stars. We wish to determine parameters of the low-luminosity Type IIP supernova 2003Z, to estimate a mass-loss rate of the presupernova, and to recover a progenitor mass. We compute the hydrodynamic models of the supernova to describe the light curves and the observed expansion velocities. The wind density of the presupernova is estimated using a thin shell model for the interaction with circumstellar matter. We estimate an ejecta mass of 14 Msun, an explosion energy of 2.45x10^50 erg, a presupernova radius of 229 Rsun, and a radioactive Ni-56 amount of 0.0063 Msun. The upper limit of the wind density parameter in the presupernova vicinity is 10^13 g/cm, and the mass lost at the red/yellow supergiant stage is less than 0.6 Msun assuming the constant mass-loss rate. The estimated progenitor mass is in the range of 14.4-17.4 Msun. The presupernova of SN 2003Z was probably a yellow supergiant at the time of the explosion. The progenitor mass of SN 2003Z is lower than those of SN 1987A and SN 1999em, normal Type IIP supernovae, but higher than the lower limit of stars undergoing a core collapse. We propose an observational test based on the circumstellar interaction to discriminate between the massive (about 25 Msun) and moderate-mass (about 16 Msun) scenarios.Comment: 8 pages, 9 figures, 3 tables, accepted for publication in Astronomy & Astrophysics; one reference remove