Further Results on Geometric Properties of a Family of Relative Entropies

This paper extends some geometric properties of a one-parameter family of relative entropies. These arise as redundancies when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the Kullback-Leibler divergence. They satisfy the Pythagorean property and behave like squared distances. This property, which was known for finite alphabet spaces, is now extended for general measure spaces. Existence of projections onto convex and certain closed sets is also established. Our results may have applications in the R\'enyi entropy maximization rule of statistical physics.Comment: 7 pages, Prop. 5 modified, in Proceedings of the 2011 IEEE International Symposium on Information Theor

Near infra-red spectroscopy of V838 Monocerotis

Near IR, multi-epoch, spectroscopic and photometric observations of the enigmatic, eruptive variable V838 Mon in JHK bands are reported. One of the unusual features is the detection of several strong neutral TiI lines in emission in the K band. From the strength of these lines, the mass of the ejected envelope is estimated to be in the range 10e-7 to 10e-5 M(sun). The spectra also show the strong presence of the first and second overtones of 12CO bands seen in the K and H bands. The CO bands show a complex evolution. Deep water bands at 1.4 and 1.9 micron are also seen later in the object's evolution. Blackbody fits to the JHK photometric data show that V838 Mon has evolved to temperatures between 2400 - 2600 K by approximately 130 days after outburst. The spectra at this stage have the general characteristics of a very cool M giant.Comment: 7 pages, 5 figures, to appear in Astronomy and Astrophysic