36,385 research outputs found
Mather sets for sequences of matrices and applications to the study of joint spectral radii
The joint spectral radius of a compact set of d-times-d matrices is defined
?to be the maximum possible exponential growth rate of products of matrices
drawn from that set. In this article we investigate the ergodic-theoretic
structure of those sequences of matrices drawn from a given set whose products
grow at the maximum possible rate. This leads to a notion of Mather set for
matrix sequences which is analogous to the Mather set in Lagrangian dynamics.
We prove a structure theorem establishing the general properties of these
Mather sets and describing the extent to which they characterise matrix
sequences of maximum growth. We give applications of this theorem to the study
of joint spectral radii and to the stability theory of discrete linear
inclusions.
These results rest on some general theorems on the structure of orbits of
maximum growth for subadditive observations of dynamical systems, including an
extension of the semi-uniform subadditive ergodic theorem of Schreiber, Sturman
and Stark, and an extension of a noted lemma of Y. Peres. These theorems are
presented in the appendix
A reappraisal of parameters for the putative planet PTFO 8-8695b and its potentially precessing parent star
Published photometry of fading events in the PTFO 8-8695 system is modelled
using improved treatments of stellar geometry, surface intensities, and,
particularly, gravity darkening, with a view to testing the planetary-transit
hypothesis. Variability in the morphology of fading events can be reproduced by
adopting convective-envelope gravity darkening, but near-critical stellar
rotation is required. This leads to inconsistencies with spectroscopic
observations; the model also predicts substantial photometric variability
associated with stellar precession, contrary to observations. Furthermore, the
empirical ratio of orbital to rotational angular momenta is at odds with
physically plausible values. An exoplanet transiting a precessing,
gravity-darkened star may not be the correct explanation of periodic fading
events in this system
Emission-line stars in the LMC: the Armagh survey, and a metacatalogue
[Aims] Accurate astrometry is required to reliably cross-match 20th-century
photographic catalogues against 21st-century digital surveys. The present work
provides modern-era identifications and astrometry for the 801 emission-line
objects "of stellar appearance" in the Armagh survey (the largest of its nature
to date). [Methods] Targets have been individually identified in digital images
using the Armagh Atlas and, in most cases, unambiguously matched to entries in
the UCAC astrometric catalogues. [Results] Astrometry with sub-arcsecond
precision is now available for all the major photographic spectroscopic surveys
of the LMC. The results are used to compile an annotated metacatalogue of 1675
individual, spectroscopically identified candidate H-alpha-emission stars,
including detailed cross-matching between catalogues, and resolving many
(though not all) identification ambiguities in individual primary sources
The Competition Account of AchievementāValue
A great achievement makes oneās life go better independently of its results, but what makes an achievement great? A simple answer isāits difficulty. I defend this view against recent, pressing objections by interpreting difficulty in terms of competitiveness. Difficulty is determined not by how hard the agent
worked for the end but by how hard others would need to do in order to compete. Successfully reaching a goal is a valuable achievement because it is difficult, and it is difficult because it is competitive. Hence, both virtuosic performances and lucky successes can be valuable achievements
Improved astrometry for the Bohannan & Epps catalogue
Aims: Accurate astrometry is required to reliably cross-match 20th-century
catalogues against 21st-century surveys. The present work aims to provide such
astrometry for the 625 entries of the Bohannan & Epps (BE74) catalogue of
H emission-line stars. Methods: BE74 targets have been individually
identified in digital images and, in most cases, unambiguously matched to
entries in the UCAC4 astrometric catalogue. Results: Sub-arcsecond astrometry
is now available for almost all BE74 stars. Several identification errors in
the literature illustrate the perils of relying solely on positional
coincidences using poorer-quality astrometry.Comment: 3 pages, 1 figure. Accepted in A&
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