29,665 research outputs found
Luminous Supernovae
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
Multiplicity estimates, analytic cycles and Newton polytopes
We consider the problem of estimating the multiplicity of a polynomial when
restricted to the smooth analytic trajectory of a (possibly singular)
polynomial vector field at a given point or points, under an assumption known
as the D-property. Nesterenko has developed an elimination theoretic approach
to this problem which has been widely used in transcendental number theory.
We propose an alternative approach to this problem based on more local
analytic considerations. In particular we obtain simpler proofs to many of the
best known estimates, and give more general formulations in terms of Newton
polytopes, analogous to the Bernstein-Kushnirenko theorem. We also improve the
estimate's dependence on the ambient dimension from doubly-exponential to an
essentially optimal single-exponential.Comment: Some editorial modifications to improve readability; No essential
mathematical change
MESON2016 -- Concluding Remarks
Several topics presented and discussed at MESON2016 are highlighted,
including pentaquarks, dibaryons and meson-nuclear bound states.Comment: concluding plenary talk given at MESON2016 -- the 14th International
Workshop on Meson Production, Properties and Interaction, 2nd-7th June 2016,
Krak\'ow, Poland, to appear in the EPJ Web of Conferences, v2 -- references
update
Semantics, Modelling, and the Problem of Representation of Meaning -- a Brief Survey of Recent Literature
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
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
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