Does The Addition of a Duration Improve the L_iso - E_peak Relation For Gamma-Ray Bursts?

Firmani et al. proposed a new Gamma Ray Burst (GRB) luminosity relation that showed a significant improvement over the L_iso-E_peak relation. The new proposed relation simply modifies the E_peak value by multiplying it by a power of T_0.45, where T_0.45 is a particular measure of the GRB duration. We begin by reproducing the results of Firmani for his 19 bursts. We then test the Firmani relation for the same 19 bursts except that we use independently measured values for L_iso, T_0.45, and E_peak, and we find that the relation deteriorates substantially. We further test the relation by using 60 GRBs with measured spectroscopic redshifts, and find a relation that has a comparable scatter as the original L_iso-E_peak relation. That is, a much larger sample of bursts does not reproduce the small scatter as reported by Firmani et al. Finally, we investigate whether the Firmani relation is improved by the use of any of 32 measures of duration in place of T_0.45. The quality of each alternative duration measure is evaluated with the root mean square of the scatter between the observed and fitted logarithmic Liso values. Although we find some durations yield slightly better results than T_0.45, the differences between the duration measures are minimal. We find that the addition of a duration does not add any significant improvement to the L_iso-E_peak relation. We also present a simple and direct derivation of the Firmani relation from both the L_iso-E_peak and Amati relations. In all we conclude that the Firmani relation neither has an independent existence nor does it provide any significant improvement on previously known relations that are simpler.Comment: ApJ in press, 17 pages, 3 figures, 3 table

Micromagnetic Domain Structures in Cylindrical Nickel Dots

The magnetic domain structures of cylindrical nickel dots (diameters from 40 nm to 1700 nm) with anisotropy parallel to the cylinder axis is predicted by the ratio of the dot diameter to the stripe period of unpatterned films with the same perpendicular anisotropy. The dominant domain structure for a given ratio increases in complexity as the ratio increases. We present evidence for the full micromagnetic domain structure for the simplest cases

Orbital debris research at NASA Johnson Space Center, 1986-1988

Research on orbital debris has intensified in recent years as the number of debris objects in orbit has grown. The population of small debris has now reached the level that orbital debris has become an important design factor for the Space Station. The most active center of research in this field has been the NASA Lyndon B. Johnson Space Center. Work is being done on the measurement of orbital debris, development of models of the debris population, and development of improved shielding against hypervelocity impacts. Significant advances have been made in these areas. The purpose of this document is to summarize these results and provide references for further study

A short note on the presence of spurious states in finite basis approximations

The genesis of spurious solutions in finite basis approximations to operators which possess a continuum and a point spectrum is discussed and a simple solution for identifying these solutions is suggested

Optimal tracking for pairs of qubit states

In classical control theory, tracking refers to the ability to perform measurements and feedback on a classical system in order to enforce some desired dynamics. In this paper we investigate a simple version of quantum tracking, namely, we look at how to optimally transform the state of a single qubit into a given target state, when the system can be prepared in two different ways, and the target state depends on the choice of preparation. We propose a tracking strategy that is proved to be optimal for any input and target states. Applications in the context of state discrimination, state purification, state stabilization and state-dependent quantum cloning are presented, where existing optimality results are recovered and extended.Comment: 15 pages, 8 figures. Extensive revision of text, optimality results extended, other physical applications include

Informational Imperfections in the Capital Market and Macro-Economic Fluctuations

This paper describes the role that informational imperfections in capital markets are likely to play in business cycles. It then developes a simple illustrative model of the impact of adverse selection in the equity market and the way in which this may lead to large fluctuations in the effective cost of capital in response to relatively small demand shocks. The model also derives an expression for the cost of equity capital in the presence of adverse selection and provides informational explanations for several widely observed macro-economic phenomena.

The localization sequence for the algebraic K-theory of topological K-theory

We prove a conjecture of Rognes by establishing a localization cofiber sequence of spectra, K(Z) to K(ku) to K(KU) to Sigma K(Z), for the algebraic K-theory of topological K-theory. We deduce the existence of this sequence as a consequence of a devissage theorem identifying the K-theory of the Waldhausen category of Postnikov towers of modules over a connective A-infinity ring spectrum R with the Quillen K-theory of the abelian category of finitely generated pi_0(R)-modules.Comment: Updated final version. Small change in definition of S' construction and correction to the proof of 2.