Flat connections and Wigner-Yanase-Dyson metrics

On the manifold of positive definite matrices, we investigate the existence of pairs of flat affine connections, dual with respect to a given monotone metric. The connections are defined either using the $\alpha$-embeddings and finding the duals with respect to the metric, or by means of contrast functionals. We show that in both cases, the existence of such a pair of connections is possible if and only if the metric is given by the Wigner-Yanase-Dyson skew information.Comment: 17 page

On an iterative procedure for solving a routing problem with constraints

The generalized precedence constrained traveling salesman problem is considered in the case when travel costs depend explicitly on the list of tasks that have not been performed (by the time of the travel). The original routing problem with dependent variables is represented in terms of an equivalent extremal problem with independent variables. An iterative method based on this representation is proposed for solving the original problem. The algorithm based on this method is implemented as a computer program. © 2013 Pleiades Publishing, Ltd

Congruent families and invariant tensors

Classical results of Chentsov and Campbell state that -- up to constant multiples -- the only $2$-tensor field of a statistical model which is invariant under congruent Markov morphisms is the Fisher metric and the only invariant $3$-tensor field is the Amari-Chentsov tensor. We generalize this result for arbitrary degree $n$, showing that any family of $n$-tensors which is invariant under congruent Markov morphisms is algebraically generated by the canonical tensor fields defined in an earlier paper

The Inhomogeneous Wind of the LBV Candidate CygOB2-No.12

We present the results of high-resolution spectroscopy of the extremely luminous star CygOB2-No.12. We identified about 200 spectral features in the range 4552-7939 AA, including the interstellar NaI, KI lines and numerous very strong DIBs, along with the HeI, CII, and SiII lines. An MK spectral type we derived for the object is B4.5Ia+. Our analysis of the radial velocity data shows the presence of a gradient in the stellar atmosphere, caused by both atmospheric expansion and matter infall onto the star. The Halpha emission displays broad Thompson wings, a slightly blue-shifted PCyg type absorption component and a time-variable core absorption. We conclude that the wind is variable in time.Comment: 3 pages, 2 figures, IAU Symposium No.272 "Active OB stars: structure, evolution, mass loss and critical limits", 201

Optical spectrum of the IR-source IRC+10420 in 1992-1996

To understand the evolutionary stage of the peculiar supergiant IRC+10420, we have been taking spectra for several years at the 6m telescope. The optical spectrum of IRC+10420 of the years from 1992 through 1996 points to the increase in the temperature: spectral class A5 instead of the former F8, as was pointed out by Humpreys et al., (1973). Now it resembles the spectra of late-type B[e] stars. The spectrum contains absorptions (mainly of ions) formed in the photosphere, apparently stationary with respect to the star center of mass, and emissions too, which can be formed in the fossil expanding envelope as well as partly in its compressing region. Using our spectra and spectral data obtained by Oudmaijer (1995) we estimated the atmospheric parameters Teff=8500 K, logg=1.0, Vt=12km/s and concluded that metallicity of IRC+10420 is solar: the average value [(V,Cr,Fe)/H]=-0.03. Combination of results allows us to consider IRC+10420 as a massive supergiant evolving to the WR-stage.Comment: 14 pages, Latex, 4 ps figures, uses supertab.sty. Accepted for publication in the MNRA