16,068 research outputs found

    Luminous Supernovae

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    Supernovae (SNe), the luminous explosions of stars, were observed since antiquity, with typical peak luminosity not exceeding 1.2x10^{43} erg/s (absolute magnitude >-19.5 mag). It is only in the last dozen years that numerous examples of SNe that are substantially super-luminous (>7x10^{43} erg/s; <-21 mag absolute) were well-documented. Reviewing the accumulated evidence, we define three broad classes of super-luminous SN events (SLSNe). Hydrogen-rich events (SLSN-II) radiate photons diffusing out from thick hydrogen layers where they have been deposited by strong shocks, and often show signs of interaction with circumstellar material. SLSN-R, a rare class of hydrogen-poor events, are powered by very large amounts of radioactive 56Ni and arguably result from explosions of very massive stars due to the pair instability. A third, distinct group of hydrogen-poor events emits photons from rapidly-expanding hydrogen-poor material distributed over large radii, and are not powered by radioactivity (SLSN-I). These may be the hydrogen-poor analogs of SLSN-II.Comment: This manuscript has been accepted for publication in Science (to appear August 24). This version has not undergone final editing. Please refer to the complete version of record at http://www.sciencemag.org/. The manuscript may not be reproduced or used in any manner that does not fall within the fair use provisions of the Copyright Act without the prior, written permission of AAA

    Semantics, Modelling, and the Problem of Representation of Meaning -- a Brief Survey of Recent Literature

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    Over the past 50 years many have debated what representation should be used to capture the meaning of natural language utterances. Recently new needs of such representations have been raised in research. Here I survey some of the interesting representations suggested to answer for these new needs.Comment: 15 pages, no figure

    Multiplicity Estimates: a Morse-theoretic approach

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    The problem of estimating the multiplicity of the zero of a polynomial when restricted to the trajectory of a non-singular polynomial vector field, at one or several points, has been considered by authors in several different fields. The two best (incomparable) estimates are due to Gabrielov and Nesterenko. In this paper we present a refinement of Gabrielov's method which simultaneously improves these two estimates. Moreover, we give a geometric description of the multiplicity function in terms certain naturally associated polar varieties, giving a topological explanation for an asymptotic phenomenon that was previously obtained by elimination theoretic methods in the works of Brownawell, Masser and Nesterenko. We also give estimates in terms of Newton polytopes, strongly generalizing the classical estimates.Comment: Minor revision; To appear in Duke Math. Journa