10,727 research outputs found
On the cardinality of sumsets in torsion-free groups
Let be finite subsets of a torsion-free group . We prove that for
every positive integer there is a such that if then
the inequality holds unless a left translate of is
contained in a cyclic subgroup. We obtain for arbitrary
torsion-free groups, and for groups with the unique product
property, where is an absolute constant. We give examples to show that
is at least quadratic in
Self-avoiding walks on a bilayer Bethe lattice
We propose and study a model of polymer chains in a bilayer. Each chain is
confined in one of the layers and polymer bonds on first neighbor edges in
different layers interact. We also define and comment results for a model with
interactions between monomers on first neighbor sites of different layers. The
thermodynamic properties of the model are studied in the grand-canonical
formalism and both layers are considered to be Cayley trees. In the core region
of the trees, which we may call a bilayer Bethe lattice, we find a very rich
phase diagram in the parameter space defined by the two activities of monomers
and the Boltzmann factor associated to the interlayer interaction between bonds
or monomers. Beside critical and coexistence surfaces, there are tricritical,
bicritical and critical endpoint lines, as well as higher order multicritical
points.Comment: 21 pages, 10 figures. Journal of Statistical Mechanics: Theory and
Experiment (in press
A qualitative analysis of Sport Management interns’ perceptions of rotations in internships
The sport industry, which has evolved into a multi-billion rand industry, offers an increased number of complex and varied job opportunities. University Sport Management graduates are thus likely to face greater job demands in a highly competitive work environment. Rotations in Sport Management internships have been identified as an approach to prepare students for the job market. The purpose of this study was to ascertain the perceptions of Sport Management interns of rotations in internship. A qualitative case study research approach was used in the study. Eight semi-structured focus group interviews were conducted with Sport Management interns who completed their internship. The results of the study indicated that the positive experiences associated with the internship outweighed the negative experiences. Participants reported many benefits of rotations in internship. Among these were their experiences of different aspects of a sport organisation, exposure to different leadership styles, opportunity to apply their theoretical knowledge in the workplace, social issues in the workplace and development of different competencies. The findings also identified areas in which the internship experience could be strengthened. Given the great satisfaction experienced by interns, rotations in interns appear to be an ideal replacement to the traditional implementation of internship
A Learning Framework for Morphological Operators using Counter-Harmonic Mean
We present a novel framework for learning morphological operators using
counter-harmonic mean. It combines concepts from morphology and convolutional
neural networks. A thorough experimental validation analyzes basic
morphological operators dilation and erosion, opening and closing, as well as
the much more complex top-hat transform, for which we report a real-world
application from the steel industry. Using online learning and stochastic
gradient descent, our system learns both the structuring element and the
composition of operators. It scales well to large datasets and online settings.Comment: Submitted to ISMM'1
On the evolution of the molecular line profiles induced by the propagation of C-shock waves
We present the first results of the expected variations of the molecular line
emission arising from material recently affected by C-shocks (shock
precursors). Our parametric model of the structure of C-shocks has been coupled
with a radiative transfer code to calculate the molecular excitation and line
profiles of shock tracers such as SiO, and of ion and neutral molecules such as
H13CO+ and HN13C, as the shock propagates through the unperturbed medium. Our
results show that the SiO emission arising from the early stage of the magnetic
precursor typically has very narrow line profiles slightly shifted in velocity
with respect to the ambient cloud. This narrow emission is generated in the
region where the bulk of the ion fluid has already slipped to larger velocities
in the precursor as observed toward the young L1448-mm outflow. This strongly
suggests that the detection of narrow SiO emission and of an ion enhancement in
young shocks, is produced by the magnetic precursor of C-shocks. In addition,
our model shows that the different velocity components observed toward this
outflow can be explained by the coexistence of different shocks at different
evolutionary stages, within the same beam of the single-dish observations.Comment: 7 pages, 4 figures, accepted for publication in Ap
Solution of a model of SAW's with multiple monomers per site on the Husimi lattice
We solve a model of self-avoiding walks which allows for a site to be visited
up to two times by the walk on the Husimi lattice. This model is inspired in
the Domb-Joyce model and was proposed to describe the collapse transition of
polymers with one-site interactions only. We consider the version in which
immediate self-reversals of the walk are forbidden (RF model). The phase
diagram we obtain for the grand-canonical version of the model is similar to
the one found in the solution of the Bethe lattice, with two distinct
polymerized phases, a tricritical point and a critical endpoint.Comment: 16 pages, including 6 figure
Grand canonical and canonical solution of self-avoiding walks with up to three monomers per site on the Bethe lattice
We solve a model of polymers represented by self-avoiding walks on a lattice
which may visit the same site up to three times in the grand-canonical
formalism on the Bethe lattice. This may be a model for the collapse transition
of polymers where only interactions between monomers at the same site are
considered. The phase diagram of the model is very rich, displaying coexistence
and critical surfaces, critical, critical endpoint and tricritical lines, as
well as a multicritical point. From the grand-canonical results, we present an
argument to obtain the properties of the model in the canonical ensemble, and
compare our results with simulations in the literature. We do actually find
extended and collapsed phases, but the transition between them, composed by a
line of critical endpoints and a line of tricritical points, separated by the
multicritical point, is always continuous. This result is at variance with the
simulations for the model, which suggest that part of the line should be a
discontinuous transition. Finally, we discuss the connection of the present
model with the standard model for the collapse of polymers (self-avoiding
self-attracting walks), where the transition between the extended and collapsed
phases is a tricritical point.Comment: 34 pages, including 10 figure
Gas Kinematics and Excitation in the Filamentary IRDC G035.39-00.33
Some theories of dense molecular cloud formation involve dynamical
environments driven by converging atomic flows or collisions between
preexisting molecular clouds. The determination of the dynamics and physical
conditions of the gas in clouds at the early stages of their evolution is
essential to establish the dynamical imprints of such collisions, and to infer
the processes involved in their formation. We present multi-transition 13CO and
C18O maps toward the IRDC G035.39-00.33, believed to be at the earliest stages
of evolution. The 13CO and C18O gas is distributed in three filaments
(Filaments 1, 2 and 3), where the most massive cores are preferentially found
at the intersecting regions between them. The filaments have a similar
kinematic structure with smooth velocity gradients of ~0.4-0.8 km s-1 pc-1.
Several scenarios are proposed to explain these gradients, including cloud
rotation, gas accretion along the filaments, global gravitational collapse, and
unresolved sub-filament structures. These results are complemented by HCO+,
HNC, H13CO+ and HN13C single-pointing data to search for gas infall signatures.
The 13CO and C18O gas motions are supersonic across G035.39-00.33, with the
emission showing broader linewidths toward the edges of the IRDC. This could be
due to energy dissipation at the densest regions in the cloud. The average H2
densities are ~5000-7000 cm-3, with Filaments 2 and 3 being denser and more
massive than Filament 1. The C18O data unveils three regions with high CO
depletion factors (f_D~5-12), similar to those found in massive starless cores.Comment: 20 pages, 14 figures, 6 tables, accepted for publication in MNRA
IC 4200: a gas-rich early-type galaxy formed via a major merger
We present the result of radio and optical observations of the S0 galaxy IC
4200. We find that the galaxy hosts 8.5 billion solar masses of HI rotating on
a ~90 deg warped disk extended out to 60 kpc from the centre of the galaxy.
Optical spectroscopy reveals a simple-stellar-population-equivalent age of 1.5
Gyr in the centre of the galaxy and V- and R-band images show stellar shells.
Ionised gas is observed within the stellar body and is kinematically decoupled
from the stars and characterised by LINER-like line ratios.We interpret these
observational results as evidence for a major merger origin of IC 4200, and
date the merger back to 1-3 Gyr ago.Comment: Accepted for publication in Astronomy & Astrophysics; 18 pages, 13
figures; the tables of Appendix C can be downloaded at
http://www.astro.rug.nl/~pserra/IC420
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