Extremal projectors for contragredient Lie (super)symmetries (short review)

A brief review of the extremal projectors for contragredient Lie (super)symmetries (finite-dimensional simple Lie algebras, basic classical Lie superalgebras, infinite-dimensional affine Kac-Moody algebras and superalgebras, as well as their quantum $q$-analogs) is given. Some bibliographic comments on the applications of extremal projectors are presented.Comment: 21 pages, LaTeX; typos corrected, references adde

Astrometry with MCAO: HST-GeMS proper motions in the globular cluster NGC 6681

Aims: for the first time the astrometric capabilities of the Multi-Conjugate Adaptive Optics (MCAO) facility GeMS with the GSAOI camera on Gemini-South are tested to quantify the accuracy in determining stellar proper motions in the Galactic globular cluster NGC 6681. Methods: proper motions from HST/ACS for a sample of its stars are already available, and this allows us to construct a distortion-free reference at the epoch of GeMS observations that is used to measure and correct the temporally changing distortions for each GeMS exposure. In this way, we are able to compare the corrected GeMS images with a first-epoch of HST/ACS images to recover the relative proper motion of the Sagittarius dwarf spheroidal galaxy with respect to NGC 6681. Results: we find this to be (\mu_{\alpha}cos\delta, \mu_{\delta}) = (4.09,-3.41) mas/yr, which matches previous HST/ACS measurements with a very good accuracy of 0.03 mas/yr and with a comparable precision (r.m.s of 0.43 mas/yr). Conclusions: this study successfully demonstrates that high-quality proper motions can be measured for quite large fields of view (85 arcsec X 85 arcsec) with MCAO-assisted, ground-based cameras and provides a first, successful test of the performances of GeMS on multi-epoch data.Comment: 5 pages, 4 figures. Accepted for publication by A&A Letter

Q-power function over Q-commuting variables and deformed XXX, XXZ chains

We find certain functional identities for the Gauss q-power function of a sum of q-commuting variables. Then we use these identities to obtain two-parameter twists of the quantum affine algebra U_q (\hat{sl}_2) and of the Yangian Y(sl_2). We determine the corresponding deformed trigonometric and rational quantum R-matrices, which then are used in the computation of deformed XXX and XXZ Hamiltonians.Comment: LaTeX, 12 page

M13 multiple stellar populations seen with the eyes of Stromgren photometry

We present a photometric study of M13 multiple stellar populations over a wide field of view, covering approximately 6.5 half-light radii, using archival Isaac Newton Telescope observations to build an accurate multiband Strömgren catalogue. The use of the Strömgren index cy permits us to separate the multiple populations of M13 on the basis of their position on the red giant branch. The comparison with medium and high resolution spectroscopic analysis confirms the robustness of our selection criterion. To determine the radial distribution of stars in M13, we complemented our data set with Hubble Space Telescope observations of the cluster core, to compensate for the effect of incompleteness affecting the most crowded regions. From the analysis of the radial distributions, we do not find any significant evidence of spatial segregation. Some residuals may be present in the external regions where we observe only a small number of stars. This finding is compatible with the short dynamical time-scale of M13 and represents, to date, one of the few examples of fully spatially mixed multiple populations in a massive globular cluster

The power of teaming up HST and Gaia:The first proper motion measurement of the distant cluster NGC 2419

Aims: We present the first measurement of the proper motion and orbit of the very distant and intriguing globular cluster NCG 2419. Methods: We have combined data from HST and Gaia DR1 to derive the relative proper motions of stars in the direction to the cluster. To tie to an absolute reference frame we have used a background galaxy located in the field. Results: We find the absolute proper motion of NGC 2419 to be $(\mu_{\alpha}\cos(\delta)$, $\mu_{\delta}$)=($-0.17\pm0.26,-0.49\pm0.17$) mas/yr. We have integrated the orbit of the cluster in a Galactic potential and found it to oscillate between $\sim$53 kpc and $\sim$98 kpc on a nearly polar orbit. This makes it very likely that NGC 2419 is a former cluster of the Sagittarius dwarf spheroidal galaxy, also because it shares the same sense of rotation around the Milky Way.Comment: 5 pages, 4 figures, accepted for publication by A&A Letter

Generalized Paraxial Ray Trace Procedure Derived from Geodesic Deviation

Paraxial ray tracing procedures have become widely accepted techniques for acoustic models in seismology and underwater acoustics. To date a generic form of these procedures including fluid motion and time dependence has not appeared in the literature. A detailed investigation of the characteristic curves of the equations of hydrodynamics allows for an immediate generalization of the procedure to be extracted from the equation form geodesic deviation. The general paraxial ray trace equations serve as an ideal supplement to ordinary ray tracing in predicting the deformation of acoustic beams in random environments. The general procedure is derived in terms of affine parameterization and in a coordinate time parameterization ideal for application to physical acoustic ray propagation. The formalism is applied to layered media, where the deviation equation reduces to a second order differential equation for a single field with a general solution in terms of a depth integral along the ray path. Some features are illustrated through special cases which lead to exact solutions in terms of either ordinary or special functions.Comment: Original; 40 pages (double spaced), 1 figure Replaced version; 36 pages single spaced, 7 figures. Expanded content; Complete derivation of the equations from the equations of hydrodynamics, introduction of an auxiliary basis for three dimensional wave-front modeling. Typos in text and equations correcte

The Chemical and Dynamical Evolution of Isolated Dwarf Galaxies

Using a suite of simulations (Governato et al. 2010) which successfully produce bulgeless (dwarf) disk galaxies, we provide an analysis of their associated cold interstellar media (ISM) and stellar chemical abundance patterns. A preliminary comparison with observations is undertaken, in order to assess whether the properties of the cold gas and chemistry of the stellar components are recovered successfully. To this end, we have extracted the radial and vertical gas density profiles, neutral hydrogen velocity dispersion, and the power spectrum of structure within the ISM. We complement this analysis of the cold gas with a brief examination of the simulations' metallicity distribution functions and the distribution of alpha-elements-to-iron.Comment: To appear in the proceedings of the JENAM 2010 Symposium "Dwarf Galaxies: Keys to Galaxy Formation and Evolution" (Lisbon, 9-10 September 2010), P. Papaderos, S. Recchi, G. Hensler (eds.), Springer Verlag (2011), in pres

Basic Twist Quantization of osp(1|2) and kappa-- Deformation of D=1 Superconformal Mechanics

The twisting function describing a nonstandard (super-Jordanian) quantum deformation of $osp(1|2)$ is given in explicite closed form. The quantum coproducts and universal R-matrix are presented. The non-uniqueness of the twisting function as well as two real forms of the deformed $osp(1|2)$ superalgebras are considered. One real quantum $osp(1|2)$ superalgebra is interpreted as describing the $\kappa$-deformation of D=1, N=1 superconformal algebra, which can be applied as a symmetry algebra of N=1 superconformal mechanics.Comment: 13 pages,LaTeX, v2. References added, typos correcte

The Stellar Populations of the Cetus Dwarf Spheroidal Galaxy

We present Hubble Space Telescope Wide Field Planetary Camera 2 photometry in the V and I passbands of the recently discovered Local Group dwarf spheroidal galaxy in Cetus. Our color-magnitude diagram extends from above the first ascent red giant branch (RGB) tip to approximately half a magnitude below the horizontal branch (HB). Adopting a reddening of E(B-V) = 0.03, the magnitude of the RGB tip yields a distance modulus of (m-M)o = 24.46 +/- 0.14. After applying the reddening and distance modulus, we have utilized the color distribution of RGB stars to determine a mean metal abundance of [Fe/H] = -1.7 on the Zinn & West scale with an intrinsic internal abundance dispersion of +/-0.2 dex. An indirect calculation of the HB morphology of Cetus based on the mean dereddened HB color yields (B-R)/(B+V+R) = -0.91 +/- 0.09, which represents an HB that is redder than what can be attributed solely to Cetus' metal abundance. As such, Cetus suffers from the `second parameter effect' in which another parameter besides metallicity is controlling the HB morphology. If we adopt the conventional `age hypothesis' explanation for the second parameter effect, then this implies that Cetus is 2-3 Gyr younger than Galactic globular clusters at its metallicity.Comment: 13 pages, 8 figures, Accepted for publication in the March 10, 2002 Ap