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 $H^3$ and $S^3$. 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 ∼0.5. 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 ≈ - 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