Astrometric orbits of SB9 stars

Hipparcos Intermediate Astrometric Data (IAD) have been used to derive astrometric orbital elements for spectroscopic binaries from the newly released Ninth Catalogue of Spectroscopic Binary Orbits (SB9). Among the 1374 binaries from SB9 which have an HIP entry, 282 have detectable orbital astrometric motion (at the 5% significance level). Among those, only 70 have astrometric orbital elements that are reliably determined (according to specific statistical tests discussed in the paper), and for the first time for 20 systems, representing a 10% increase relative to the 235 DMSA/O systems already present in the Hipparcos Double and Multiple Systems Annex. The detection of the astrometric orbital motion when the Hipparcos IAD are supplemented by the spectroscopic orbital elements is close to 100% for binaries with only one visible component, provided that the period is in the 50 - 1000 d range and the parallax is larger than 5 mas. This result is an interesting testbed to guide the choice of algorithms and statistical tests to be used in the search for astrometric binaries during the forthcoming ESA Gaia mission. Finally, orbital inclinations provided by the present analysis have been used to derive several astrophysical quantities. For instance, 29 among the 70 systems with reliable astrometric orbital elements involve main sequence stars for which the companion mass could be derived. Some interesting conclusions may be drawn from this new set of stellar masses, like the enigmatic nature of the companion to the Hyades F dwarf HIP 20935. This system has a mass ratio of 0.98 but the companion remains elusive.Comment: Astronomy & Astrophysics, in press (16 pages, 12 figures); also available at http://www.astro.ulb.ac.be/Html/ps.html#Astrometr

88th Commencement Class Speaker\u27s Address

Kristin Griffin tells the soon-to-be-graduates, We are so fortunate to have built up this kind of support for ourselves as we face something we can’t quite see, and those who make that possible — our friends, our professors, our families — should know today that they have made the difference in each of our lives

Energy Gap Contributes to Adolescent Obesity

Summarizes findings on the gap between the calories American children and adolescents consume and the calories needed for normal growth, physical activity, and body function. Compares the overall gap with that of overweight adolescents over ten years

Rigorous Density Functional Theory for Inhomogeneous Bose-Condensed Fluids

The density functional theory originally developed by Hohenberg, Kohn and Sham provides a rigorous conceptual framework for dealing with inhomogeneous interacting Fermi systems. We extend this approach to deal with inhomogeneous interacting Bose-condensed systems, limiting this presentation to setting up the formalism to deal with ground state $(T=0)$ properties. The key new feature is that one must deal with energy functionals of both the local density $n({\bf r})$ and the local complex macroscopic wavefunction $\Phi ({\bf r})$ associated with the Bose broken-symmetry (the local condensate density is $n_{c}({\bf r}) = \vert \Phi ({\bf r}) \vert ^{2}$). Implementing the Kohn-Sham scheme, we reduce the problem to a gas of weakly-interacting Bosons moving in self-consistent diagonal and off-diagonal one-body potentials. Our formalism should provide the basis for studies of the surface properties of liquid $^4$He as well as the properties of Bose-condensed atomic gases trapped in external potentials.Comment: 20 page

Operadic comodules and (co)homology theories

An operad describes a category of algebras and a (co)homology theory for these algebras may be formulated using the homological algebra of operads. A morphism of operads $f:\mathcal{O}\rightarrow\mathcal{P}$ describes a functor allowing a $\mathcal{P}$-algebra to be viewed as an $\mathcal{O}$-algebra. We show that the $\mathcal{O}$-algebra (co)homology of a $\mathcal{P}$-algebra may be represented by a certain operadic comodule. Thus filtrations of this comodule result in spectral sequences computing the (co)homology. As a demonstration we study operads with a filtered distributive law; for the associative operad we obtain a new proof of the Hodge decomposition of the Hochschild cohomology of a commutative algebra. This generalises to many other operads and as an illustration we compute the post-Lie cohomology of a Lie algebra.Comment: 32 page