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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
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