New exact solutions for power-law inflation Friedmann models

We consider the spatially flat Friedmann model. For a(t) = t^p, especially, if p is larger or equal to 1, this is called power-law inflation. For the Lagrangian L = R^m with p = - (m - 1)(2m - 1)/(m - 2), power-law inflation is an exact solution, as it is for Einstein gravity with a minimally coupled scalar field Phi in an exponential potential V(Phi) = exp(mu Phi) and also for the higher-dimensional Einstein equation with a special Kaluza-Klein ansatz. The synchronized coordinates are not adapted to allow a closed-form solution, so we use another gauge. Finally, special solutions for the closed and open Friedmann model are found.Comment: 9 pages, LaTeX, reprinted from Astron. Nachr. 311 (1990) 16

The Parabolic Anderson Model with Acceleration and Deceleration

We describe the large-time moment asymptotics for the parabolic Anderson model where the speed of the diffusion is coupled with time, inducing an acceleration or deceleration. We find a lower critical scale, below which the mass flow gets stuck. On this scale, a new interesting variational problem arises in the description of the asymptotics. Furthermore, we find an upper critical scale above which the potential enters the asymptotics only via some average, but not via its extreme values. We make out altogether five phases, three of which can be described by results that are qualitatively similar to those from the constant-speed parabolic Anderson model in earlier work by various authors. Our proofs consist of adaptations and refinements of their methods, as well as a variational convergence method borrowed from finite elements theory.Comment: 19 page

Derivation of a Sample of Gamma-Ray Bursts from BATSE DISCLA Data

We have searched for gamma-ray bursts (GRBs) in the BATSE DISCLA data over a time period of 5.9 years. We employ a trigger requiring an excess of at least 5 sigma over background for at least two modules in the 50-300 keV range. After excluding certain geographic locations of the satellite, we are left with 4485 triggers. Based on sky positions, we exclude triggers close to the sun, to Cyg X-1, to Nova Persei 1992 and the repeater SGR 1806-20, while these sources were active. We accept 1013 triggers that correspond to GRBs in the BATSE catalog, and after visual inspection of the time profiles classify 378 triggers as cosmic GRBs. We denote the 1391 GRBs so selected as the "BD2 sample". The BD2 sample effectively represents 2.003 years of full sky coverage for a rate of 694 GRBs per year. Euclidean V/Vmax values have been derived through simulations in which each GRB is removed in distance until the detection algorithm does not produce a trigger. The BD2 sample produces a mean value = 0.334 +- 0.008.Comment: 5 pages, 3 figures, Latex with aipproc.sty, Proc. of the 5th Huntsville Gamma Ray Burst Symposium, Oct. 1999, ed. R.M. Kippen, AI

Ring extensions invariant under group action

Let $G$ be a subgroup of the automorphism group of a commutative ring with identity $T$. Let $R$ be a subring of $T$ such that $R$ is invariant under the action by $G$. We show $R^G\subset T^G$ is a minimal ring extension whenever $R\subset T$ is a minimal extension under various assumptions. Of the two types of minimal ring extensions, integral and integrally closed, both of these properties are passed from $R\subset T$ to $R^G\subset T^G$. An integrally closed minimal ring extension is a flat epimorphic extension as well as a normal pair. We show each of these properties also pass from $R\subset T$ to $R^G\subseteq T^G$ under certain group action.Comment: Revisions: minor edits and results 4.9-4.11 removed due to error in 4.9; 15 pages; comments welcom

How Historical Is Begriffsgeschichte?

This is a preprint (author's original) version of the article published in History of European Ideas 25(1-2):9-14. The final version of the article can be found at http://dx.doi.org/10.1016/S0191-6599(99)00015-7 (login required to access content). The version made available in OpenBU was supplied by the author.Author's Origina

Luminosities, Space Densities and Redshift Distributions of Gamma-Ray Bursts

We use the BD2 sample of gamma-ray bursts (GRBs) based on 5.9 years of BATSE DISCLA data with a variety of models of the luminosity function to derive characteristic GRB luminosities, space densities and redshift distributions. Previously published results for an open universe and modest density evolution of the GRBs showed characteristic peak luminosities around 5x10**51 erg/s in the 50-300 keV band if the emission is isotropic, and local space densities around 0.2 Gpc**-3 yr**-1. In this paper, we illustrate for several luminosity function models the predicted distributions of peak flux, luminosity and redshifts. We use the luminosity function models also to address the connection between supernovae and GRB. If all supernovae of Type Ib/c harbor a GRB, the beaming fraction would have to be 10**-5 - 10**-3.5. We find that GRB 980425, if correctly identified with SN 1998bw, has to be part of a population different from that of the bulk of GRBs.Comment: 5 pages, 4 figures, Latex with aipproc.sty, Proc. of the 5th Huntsville Gamma Ray Burst Symposium, Oct. 1999, ed. R.M. Kippen, AI