On a general analytical formula for U_q(su(3))-Clebsch-Gordan coefficients

We present the projection operator method in combination with the Wigner-Racah calculus of the subalgebra U_q(su(2)) for calculation of Clebsch-Gordan coefficients (CGCs) of the quantum algebra U_q(su(3)). The key formulas of the method are couplings of the tensor and projection operators and also a tensor form for the projection operator of U_q(su(3)). We obtain a very compact general analytical formula for the U_q(su(3)) CGCs in terms of the U_q(su(2)) Wigner 3nj-symbols.Comment: 9 pages, LaTeX; to be published in Yad. Fiz. (Phys. Atomic Nuclei), (2001

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

Estimating the location of baleen whale calls using dual streamers to support mitigation procedures in seismic reflection surveys

In order to mitigate against possible impacts of seismic surveys on baleen whales it is important to know as much as possible about the presence of whales within the vicinity of seismic operations. This study expands on previous work that analyzes single seismic streamer data to locate nearby calling baleen whales with a grid search method that utilizes the propagation angles and relative arrival times of received signals along the streamer. Three dimensional seismic reflection surveys use multiple towed hydrophone arrays for imaging the structure beneath the seafloor, providing an opportunity to significantly improve the uncertainty associated with streamer-generated call locations. All seismic surveys utilizing airguns conduct visual marine mammal monitoring surveys concurrent with the experiment, with powering-down of seismic source if a marine mammal is observed within the exposure zone. This study utilizes data from power-down periods of a seismic experiment conducted with two 8-km long seismic hydrophone arrays by the R/V Marcus G. Langseth near Alaska in summer 2011. Simulated and experiment data demonstrate that a single streamer can be utilized to resolve left-right ambiguity because the streamer is rarely perfectly straight in a field setting, but dual streamers provides significantly improved locations. Both methods represent a dramatic improvement over the existing Passive Acoustic Monitoring (PAM) system for detecting low frequency baleen whale calls, with ~60 calls detected utilizing the seismic streamers, zero of which were detected using the current R/V Langseth PAM system. Furthermore, this method has the potential to be utilized not only for improving mitigation processes, but also for studying baleen whale behavior within the vicinity of seismic operations

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

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

Carbon and nitrogen abundances of individual stars in the Sculptor dwarf spheroidal galaxy

We present [C/Fe] and [N/Fe] abundance ratios and CH({\lambda}4300) and S({\lambda}3883) index measurements for 94 red giant branch (RGB) stars in the Sculptor dwarf spheroidal galaxy from VLT/VIMOS MOS observations at a resolving power R= 1150 at 4020 {\AA}. This is the first time that [N/Fe] abundances are derived for a large number of stars in a dwarf spheroidal. We found a trend for the [C/Fe] abundance to decrease with increasing luminosity on the RGB across the whole metallicity range, a phenomenon observed in both field and globular cluster giants, which can be interpreted in the framework of evolutionary mixing of partially processed CNO material. Both our measurements of [C/Fe] and [N/Fe] are in good agreement with the theoretical predictions for stars at similar luminosity and metallicity. We detected a dispersion in the carbon abundance at a given [Fe/H], which cannot be ascribed to measurement uncertainties alone. We interpret this observational evidence as the result of the contribution of different nucleosynthesis sources over time to a not well-mixed interstellar medium. We report the discovery of two new carbon-enhanced, metal-poor stars. These are likely the result of pollution from material enriched by asymptotic giant branch stars, as indicated by our estimates of [Ba/Fe]> +1. We also attempted a search for dissolved globular clusters in the field of the galaxy by looking for the distinctive C-N pattern of second population globular clusters stars in a previously detected, very metal-poor, chemodynamical substructure. We do not detect chemical anomalies among this group of stars. However, small number statistics and limited spatial coverage do not allow us to exclude the hypotheses that this substructure forms part of a tidally shredded globular cluster.Comment: 18 pages, 14 figures, 3 tables. Accepted to A&