The Brightness Distribution of Bursting Sources in Relativistic Cosmologies

We present analytical solutions for the integral distribution of arbitrary bursting or steady source counts as a function of peak photon count rate within Friedmann cosmological models. We discuss both the standard candle and truncated power-law luminosity function cases with a power-law density evolution. While the analysis is quite general, the specific example discussed here is that of a cosmological gamma-ray burst distribution. These solutions show quantitatively the degree of dependence of the counts on the density and luminosity function parameters, as well as the the weak dependence on the closure parameter and the maximum redshift. An approximate comparison with the publicly available Compton Gamma Ray Observatory data gives an estimate of the maximum source luminosity and an upper limit to the minimum luminosity. We discuss possible ways of further constraining the various parameters.Comment: 16 pages plus one figure, uuencoded postscript file. to appear in Ap.J

Cosmological Brightness Distribution Fits of Gamma Ray Burst Sources

We discuss detailed fits of the BATSE and PVO gamma-ray burst peak-flux distributions with Friedman models taking into account possible density evolution and standard candle or power law luminosity functions. A chi-square analysis is used to estimate the goodness of the fits and we derive the significance level of limits on the density evolution and luminosity function parameters. Cosmological models provide a good fit over a range of parameter space which is physically reasonable.Comment: Ap.J. in press, uuencoded .ps file, 9 pages manuscript plus 5 figure

On Linkedness of Cartesian Product of Graphs

We study linkedness of Cartesian product of graphs and prove that the product of an $a$-linked and a $b$-linked graphs is $(a+b-1)$-linked if the graphs are sufficiently large. Further bounds in terms of connectivity are shown. We determine linkedness of product of paths and product of cycles

Origin of Gamma Ray Bursters

The successful discovery of X-ray, optical and radio afterglows of GRB has made possible the identification of host galaxies at cosmological distances. The energy release inferred in these outbursts place them among the most energetic and violent events in the Universe. They are thought to be the outcome of a cataclysmic stellar collapse or compact stellar merger, leading to a relativistically expanding fireball, in which particles are accelerated at shocks and produce nonthermal radiation. The substantial agreement between observations and the theoretical predictions of the fireball shock model provide confirmation of the basic aspects of this scenario. Among recent issues are the collimation of the outflow and its implications for the energetics, the production of prompt bright flashes at wavelenghts much longer than gamma-rays, the time structure of the afterglow, its dependence on the central engine or progenitor system behavior, and the role of the environment on the afterglow.Comment: Expanded version of a review to appear in Prog.Theor.Phys. S.136 (1999), "Black Holes and Gravitational Waves - New Eyes in the 21st Century", Yukawa International Seminar'99, eds. T. Nakamura et al. Uses ptpsty.tex, ptp-text.sty (included), 21 pages, 6 figure