25 research outputs found
Volumes of polytopes in spaces of constant curvature
We overview the volume calculations for polyhedra in Euclidean, spherical and
hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary
tetrahedron in and . We also present some results, which provide a
solution for Seidel problem on the volume of non-Euclidean tetrahedron.
Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle,
horocycle or one branch of equidistant curve. This is a natural hyperbolic
analog of the cyclic quadrilateral in the Euclidean plane. We find a few
versions of the Brahmagupta formula for the area of such quadrilateral. We also
present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference
Spectroscopic target selection for the Sloan Digital Sky Survey: The luminous red galaxy sample
We describe the target selection and resulting properties of a spectroscopic sample of luminous red galaxies (LRGs) from the imaging data of the Sloan Digital Sky Survey (SDSS). These galaxies are selected on the basis of color and magnitude to yield a sample of luminous intrinsically red galaxies that extends fainter and farther than the main flux-limited portion of the SDSS galaxy spectroscopic sample. The sample is designed to impose a passively evolving luminosity and rest-frame color cut to a redshift of 0.38. Additional, yet more luminous red galaxies are included to a redshift of âŒ0.5. Approximately 12 of these galaxies per square degree are targeted for spectroscopy, so the sample will number over 100,000 with the full survey. SDSS commissioning data indicate that the algorithm efficiently selects luminous (M*g â - 21.4) red galaxies, that the spectroscopic success rate is very high, and that the resulting set of galaxies is approximately volume limited out to z = 0.38. When the SDSS is complete, the LRG spectroscopic sample will fill over 1 h-3 Gpc3 with an approximately homogeneous population of galaxies and will therefore be well suited to studies of large-scale structure and clusters out to z = 0.5
Optical Light Curves of Supernovae
Photometry is the most easily acquired information about supernovae. The
light curves constructed from regular imaging provide signatures not only for
the energy input, the radiation escape, the local environment and the
progenitor stars, but also for the intervening dust. They are the main tool for
the use of supernovae as distance indicators through the determination of the
luminosity. The light curve of SN 1987A still is the richest and longest
observed example for a core-collapse supernova. Despite the peculiar nature of
this object, as explosion of a blue supergiant, it displayed all the
characteristics of Type II supernovae. The light curves of Type Ib/c supernovae
are more homogeneous, but still display the signatures of explosions in massive
stars, among them early interaction with their circumstellar material. Wrinkles
in the near-uniform appearance of thermonuclear (Type Ia) supernovae have
emerged during the past decade. Subtle differences have been observed
especially at near-infrared wavelengths. Interestingly, the light curve shapes
appear to correlate with a variety of other characteristics of these
supernovae. The construction of bolometric light curves provides the most
direct link to theoretical predictions and can yield sorely needed constraints
for the models. First steps in this direction have been already made.Comment: To be published in:"Supernovae and Gamma Ray Bursters", Lecture Notes
in Physics (http://link.springer.de/series/lnpp