A sum-product theorem in function fields

Let $A$ be a finite subset of \ffield, the field of Laurent series in $1/t$ over a finite field $\mathbb{F}_q$. We show that for any $\epsilon>0$ there exists a constant $C$ dependent only on $\epsilon$ and $q$ such that $\max\{|A+A|,|AA|\}\geq C |A|^{6/5-\epsilon}$. In particular such a result is obtained for the rational function field $\mathbb{F}_q(t)$. Identical results are also obtained for finite subsets of the $p$-adic field $\mathbb{Q}_p$ for any prime $p$.Comment: Simplification of argument and note that methods also work for the p-adic

Comment on "Nucleon elastic form factors and local duality"

We comment on the papers "Nucleon elastic form factors and local duality" [Phys. Rev. {\bf D62}, 073008 (2000)] and "Experimental verification of quark-hadron duality" [Phys. Rev. Lett. {\bf 85}, 1186 (2000)]. Our main comment is that the reconstruction of the proton magnetic form factor, claimed to be obtained from the inelastic scaling curve thanks to parton-hadron local duality, is affected by an artifact.Comment: to appear in Phys. Rev.

Dust and dark Gamma-Ray Bursts: mutual implications

In a cosmological context dust has been always poorly understood. That is true also for the statistic of GRBs so that we started a program to understand its role both in relation to GRBs and in function of z. This paper presents a composite model in this direction. The model considers a rather generic distribution of dust in a spiral galaxy and considers the effect of changing some of the parameters characterizing the dust grains, size in particular. We first simulated 500 GRBs distributed as the host galaxy mass distribution, using as model the Milky Way. If we consider dust with the same properties as that we observe in the Milky Way, we find that due to absorption we miss about 10% of the afterglows assuming we observe the event within about 1 hour or even within 100s. In our second set of simulations we placed GRBs randomly inside giants molecular clouds, considering different kinds of dust inside and outside the host cloud and the effect of dust sublimation caused by the GRB inside the clouds. In this case absorption is mainly due to the host cloud and the physical properties of dust play a strong role. Computations from this model agree with the hypothesis of host galaxies with extinction curve similar to that of the Small Magellanic Cloud, whereas the host cloud could be also characterized by dust with larger grains. To confirm our findings we need a set of homogeneous infrared observations. The use of coming dedicated infrared telescopes, like REM, will provide a wealth of cases of new afterglow observations.Comment: 16 pages, 8 figures, accepted by A&

Multi-color Optical and NIR Light Curves of 64 Stripped-Envelope Core-Collapse Supernovae

We present a densely-sampled, homogeneous set of light curves of 64 low redshift (z < 0.05) stripped-envelope supernovae (SN of type IIb, Ib, Ic and Ic-bl). These data were obtained between 2001 and 2009 at the Fred L. Whipple Observatory (FLWO) on Mt. Hopkins in Arizona, with the optical FLWO 1.2-m and the near-infrared PAIRITEL 1.3-m telescopes. Our dataset consists of 4543 optical photometric measurements on 61 SN, including a combination of UBVRI, UBVr'i', and u'BVr'i', and 2142 JHKs near-infrared measurements on 25 SN. This sample constitutes the most extensive multi-color data set of stripped-envelope SN to date. Our photometry is based on template-subtracted images to eliminate any potential host galaxy light contamination. This work presents these photometric data, compares them with data in the literature, and estimates basic statistical quantities: date of maximum, color, and photometric properties. We identify promising color trends that may permit the identification of stripped-envelope SN subtypes from their photometry alone. Many of these SN were observed spectroscopically by the CfA SN group, and the spectra are presented in a companion paper (Modjaz et al. 2014). A thorough exploration that combines the CfA photometry and spectroscopy of stripped-envelope core-collapse SN will be presented in a follow-up paper.Comment: 26 pages, 17 figures, 8 tables. Revised version resubmitted to ApJ Supplements after referee report. Additional online material is available through http://cosmo.nyu.edu/SNYU

Hints of the existence of Axion-Like-Particles from the gamma-ray spectra of cosmological sources

Axion Like Particles (ALPs) are predicted to couple with photons in the presence of magnetic fields. This effect may lead to a significant change in the observed spectra of gamma-ray sources such as AGNs. Here we carry out a detailed study that for the first time simultaneously considers in the same framework both the photon/axion mixing that takes place in the gamma-ray source and that one expected to occur in the intergalactic magnetic fields. An efficient photon/axion mixing in the source always means an attenuation in the photon flux, whereas the mixing in the intergalactic medium may result in a decrement and/or enhancement of the photon flux, depending on the distance of the source and the energy considered. Interestingly, we find that decreasing the value of the intergalactic magnetic field strength, which decreases the probability for photon/axion mixing, could result in an increase of the expected photon flux at Earth if the source is far enough. We also find a 30% attenuation in the intensity spectrum of distant sources, which occurs at an energy that only depends on the properties of the ALPs and the intensity of the intergalactic magnetic field, and thus independent of the AGN source being observed. Moreover, we show that this mechanism can easily explain recent puzzles in the spectra of distant gamma-ray sources... [ABRIDGED] The consequences that come from this work are testable with the current generation of gamma-ray instruments, namely Fermi (formerly known as GLAST) and imaging atmospheric Cherenkov telescopes like CANGAROO, HESS, MAGIC and VERITAS.Comment: 16 pages, 7 figures. Replaced to match the published version in Phys. Rev. D. Minor changes with respect to v

The afterglows of gamma-ray bursts

Gamma-ray burst astronomy has undergone a revolution in the last three years, spurred by the discovery of fading long-wavelength counterparts. We now know that at least the long duration GRBs lie at cosmological distances with estimated electromagnetic energy release of 10^51–10^53 erg, making these the brightest explosions in the Universe. In this article we review the current observational state, beginning with the statistics of X-ray, optical, and radio afterglow detections. We then discuss the insights these observations have given to the progenitor population, the energetics of the GRB events, and the physics of the afterglow emission. We focus particular attention on the evidence linking GRBs to the explosion of massive stars. Throughout, we identify remaining puzzles and uncertainties, and emphasize promising observational tools for addressing them. The imminent launch of HETE-2 and the increasingly sophisticated and coordinated ground-based and space-based observations have primed this field for fantastic growth

The afterglows of gamma-ray bursts

Gamma-ray burst astronomy has undergone a revolution in the last three years, spurred by the discovery of fading long-wavelength counterparts. We now know that at least the long-duration GRBs lie at cosmological distances with estimated electromagnetic energy release of 10^51–10^53 erg, making these the brightest explosions in the Universe. In this article we review the current observational state, beginning with the statistics of X-ray, optical, and radio afterglow detections. We then discuss the insights these observations have given to the progenitor population, the energetics of the GRB events, and the physics of the afterglow emission. We focus particular attention on the evidence linking GRBs to the explosion of massive stars. Throughout, we identify remaining puzzles and uncertainties, and emphasize promising observational tools for addressing them. The imminent launch of HETE-2 and the increasingly sophisticated and coordinated ground-based and space-based observations have primed this field for fantastic growth

The afterglows of gamma-ray bursts

Gamma-ray burst astronomy has undergone a revolution in the last three years, spurred by the discovery of fading long-wavelength counterparts. We now know that at least the long duration GRBs lie at cosmological distances with estimated electromagnetic energy release of 10^51–10^53 erg, making these the brightest explosions in the Universe. In this article we review the current observational state, beginning with the statistics of X-ray, optical, and radio afterglow detections. We then discuss the insights these observations have given to the progenitor population, the energetics of the GRB events, and the physics of the afterglow emission. We focus particular attention on the evidence linking GRBs to the explosion of massive stars. Throughout, we identify remaining puzzles and uncertainties, and emphasize promising observational tools for addressing them. The imminent launch of HETE-2 and the increasingly sophisticated and coordinated ground-based and space-based observations have primed this field for fantastic growth. This overview is a combined write-up of talks given at this conference and in NASA's Goddard Space Flight Center