Exact solution of a quantum forced time-dependent harmonic oscillator

The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator

Broad band time-resolved E_{p,i}--L_{iso} correlation in GRBs

We report results of a systematic study of the broad band (2--2000 keV) time resolved prompt emission spectra of a sample of gamma-ray bursts (GRBs) detected with both Wide Field Cameras on board the \sax\ satellite and the \batse\ experiment on board CGRO. In this first paper, we study the time-resolved dependence of the intrinsic peak energy $E_{p,i}$ of the $E F(E)$ spectrum on the corresponding isotropic bolometric luminosity $L_{\rm iso}$. The $E_{p,i}$--$L_{\rm iso}$ relation or the equivalent relation between $E_{p,i}$ and the bolometric released energy $E_{iso}$, derived using the time averaged spectra of long GRBs with known redshift, is well established, but its physical origin is still a subject of discussion. In addition, some authors maintain that these relations are the result of instrumental selection effects. We find that not only a relation between the measured peak energy $E_p$ and the corresponding energy flux, but also a strong $E_{p,i}$ versus $L_{\rm iso}$ correlation are found within each burst and merging together the time resolved data points from different GRBs. We do not expect significant instrumental selection effects that can affect the obtained results, apart from the fact that the GRBs in our sample are sufficiently bright to perform a time-resolved spectroscopy and that they have known redshift. If the fundamental physical process that gives rise to the GRB phenomenon does not depend on its brightness, we conclude that the found $E_{p,i}$ versus $L_{\rm iso}$ correlation within each GRB is intrinsic to the emission process, and that the correlations discovered by Amati et al. and Yonetoku et al. are likely not the result of selection effects. We also discuss the properties of the correlations found.Comment: 27 pages,4 tables, 7 figure, accepted for publication in The Astrophysical Journa

Genera of curves on a very general surface in P3P^3

In this paper we consider the question of determining the geometric genera of irreducible curves lying on a very general surface $S$ of degree $d$ at least 5 in $\mathbb{P}^3$ (the cases $d \leqslant 4$ are well known). We introduce the set $Gaps(d)$ of all non-negative integers which are not realized as geometric genera of irreducible curves on $S$. We prove that $Gaps(d)$ is finite and, in particular, that $Gaps(5)= \{0,1,2\}$. The set $Gaps(d)$ is the union of finitely many disjoint and separated integer intervals. The first of them, according to a theorem of Xu, is $Gaps_0(d):=[0, \frac{d(d-3)}{2} - 3]$. We show that the next one is $Gaps_1(d):= [\frac{d^2-3d+4}{2}, d^2-2d-9]$ for all $d \geqslant 6$.Comment: 16 page

New BeppoSAX-WFC results on superbursts

Presently seven superbursters have been identified representing 10% of the total Galactic X-ray burster population. Four superbursters were discovered with the Wide Field Cameras (WFCs) on BeppoSAX and three with the All-Sky Monitor and Proportional Counter Array on RXTE. We discuss the properties of superbursters as derived from WFC observations. There are two interesting conclusions. First, the average recurrence time of superbursts among X-ray bursters that are more luminous than 10% of the Eddington limit is 1.5 yr per object. Second, superbursters systematically have higher alpha values and shorter ordinary bursts than most bursters that have not exhibited superbursts, indicating a higher level of stable thermonuclear helium burning. Theory predicts hitherto undetected superbursts from the most luminous neutron stars. We investigate the prospects for finding these in GX~17+2.Comment: Submitted in January 2004 for the Proceedings of the meeting 'X-Ray Timing 2003: Rossi and Beyond', eds. P. Kaaret, F. K. Lamb, & J. H. Swank (Melville, NY: American Institute of Physics

The BeppoSAX WFC X-ray source catalogue

We present the catalogue of X-ray sources detected by the two Wide Field Cameras (WFCs) in complete observations on board BeppoSAX during its 6 years of operational lifetime, between April 1996 and April 2002. The BeppoSAX WFCs were coded mask instruments sensitive in the 2-28 keV energy band with a 40x40 square degree fields of view, pointing in opposite directions and perpendicularly to the BeppoSAX Narrow Field Instruments (NFI). The WFCs were usually operated simultaneously to NFI observations, each lasting up to several days. WFCs observed thus the entire sky several times with a typical sensitivity of 2 to 10 mCrab. A systematic analysis of all WFC observations in the BeppoSAX archive has been carried out using the latest post-mission release of the WFC analysis software and calibrations. The catalogue includes 253 distinct sources, obtained from a total sample of 8253 WFC detections. We describe the basic statistical properties of the sample and present a six-year history of two celestial calibration X-ray sources.Comment: 15 pages, 11 figures, Catalogue, Accepted for publication on A&