797 research outputs found
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 -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
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 ,
)=() mas/yr. We have integrated the
orbit of the cluster in a Galactic potential and found it to oscillate between
53 kpc and 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
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