135 research outputs found
A manifold structure for the group of orbifold diffeomorphisms of a smooth orbifold
For a compact, smooth C^r orbifold (without boundary), we show that the
topological structure of the orbifold diffeomorphism group is a Banach manifold
for finite r \ge 1 and a Frechet manifold if r=infty. In each case, the local
model is the separable Banach (Frechet) space of C^r (C^infty, resp.)
orbisections of the tangent orbibundle.Comment: 26 pages, 2 figures, final versio
On the notions of suborbifold and orbifold embedding
The purpose of this article is to investigate the relationship between
suborbifolds and orbifold embeddings. In particular, we give natural
definitions of the notion of suborbifold and orbifold embedding and provide
many examples. Surprisingly, we show that there are (topologically embedded)
smooth suborbifolds which do not arise as the image of a smooth orbifold
embedding. We are also able to characterize those suborbifolds which can arise
as the images of orbifold embeddings. As an application, we show that a
length-minimizing curve (a geodesic segment) in a Riemannian orbifold can
always be realized as the image of an orbifold embedding.Comment: 11 pages. Final Version. arXiv admin note: text overlap with
arXiv:1205.115
Elementary orbifold differential topology
Taking an elementary and straightforward approach, we develop the concept of a regular value for a smooth map f:O→P between smooth orbifolds O and P. We show that Sardʼs theorem holds and that the inverse image of a regular value is a smooth full suborbifold of O. We also study some constraints that the existence of a smooth orbifold map imposes on local isotropy groups. As an application, we prove a Borsuk no retraction theorem for compact orbifolds with boundary and some obstructions to the existence of real-valued orbifold maps from local model orbifold charts
Resilience Management: A Framework for Assessing and Improving the Resilience of Organisations
Resilient Organisations Research Report 2007/01Organisations today are increasingly aware of the need to prepare for the unexpected. High profile international events of the last decade, such as the September 11th terrorist attacks, the Indian Ocean tsunami, Hurricane Katrina and the emerging threat of a pandemic all serve to remind organisations that the unimaginable can and does happen.
Stories emerge from these events of organisations that survived or failed; at first glance there does not appear to be a particular pattern. Some survivors had excellent disaster response plans in place; others had none, surviving purely on the merits of strong leadership and the commitment and determination of staff. Many organisations that are devastated simply never reopen again; others evolve so radically that they are hard to recognise from their pre-crisis form.
This research project seeks to explore what it is that makes some organisations more able to survive a major crisis than others, and suggests a framework for both evaluating and improving the resilience of individual organisations
Ultraviolet Detection of the Binary Companion to the Type IIb SN 2001ig
We present HST/WFC3 ultraviolet imaging in the F275W and F336W bands of the
Type IIb SN 2001ig at an age of more than 14 years. A clear point source is
detected at the site of the explosion having and
mag. Despite weak constraints on both the
distance to the host galaxy NGC 7424 and the line-of-sight reddening to the
supernova, this source matches the characteristics of an early B-type main
sequence star having K and . A BPASS v2.1 binary evolution model, with
primary and secondary masses of 13 M and 9 M respectively,
is found to resemble simultaneously in the Hertzsprung-Russell diagram both the
observed location of this surviving companion, and the primary star
evolutionary endpoints for other Type IIb supernovae. This same model exhibits
highly variable late-stage mass loss, as expected from the behavior of the
radio light curves. A Gemini/GMOS optical spectrum at an age of 6 years reveals
a narrow He II emission line, indicative of continuing interaction with a dense
circumstellar medium at large radii from the progenitor. We review our findings
on SN 2001ig in the context of binary evolution channels for stripped-envelope
supernovae. Owing to the uncrowded nature of its environment in the
ultraviolet, this study of SN 2001ig represents one of the cleanest detections
to date of a surviving binary companion to a Type IIb supernova.Comment: 8 pages, 3 figures. Resubmitted to ApJ after minor changes requested
by refere
The classification of frequencies in the {\gamma} Doradus / {\delta} Scuti hybrid star HD 49434
Hybrid stars of the {\gamma} Doradus and {\delta} Scuti pulsation types have
great potential for asteroseismic analysis to explore their interior structure.
To achieve this, mode identi- fications of pulsational frequencies observed in
the stars must be made, a task which is far from simple. In this work we begin
the analysis by scrutinizing the frequencies found in the CoRoT photometric
satellite measurements and ground-based high-resolution spectroscopy of the
hybrid star HD 49434. The results show almost no consistency between the
frequencies found using the two techniques and no characteristic period
spacings or couplings were identified in either dataset. The spectroscopic data
additionally show no evidence for any long term (5 year) variation in the
dominant frequency. The 31 spectroscopic frequencies identified have standard
deviation profiles suggesting multiple modes sharing (l, m) in the {\delta}
Scuti frequency region and several skewed modes sharing the same (l, m) in the
{\gamma} Doradus frequency region. In addition, there is a clear frequency in
the {\gamma} Doradus frequency region that appears to be unrelated to the
others. We conclude HD 49434 remains a {\delta} Scuti/ {\gamma} Doradus
candidate hybrid star but more sophisticated models dealing with rotation are
sought to obtain a clear picture of the pulsational behaviour of this star.Comment: Accepted for publication in MNRAS December 201
The Stratified Structure of Spaces of Smooth Orbifold Mappings
We consider four notions of maps between smooth C^r orbifolds O, P with O
compact (without boundary). We show that one of these notions is natural and
necessary in order to uniquely define the notion of orbibundle pullback. For
the notion of complete orbifold map, we show that the corresponding set of C^r
maps between O and P with the C^r topology carries the structure of a smooth
C^\infty Banach (r finite)/Frechet (r=infty) manifold. For the notion of
complete reduced orbifold map, the corresponding set of C^r maps between O and
P with the C^r topology carries the structure of a smooth C^\infty Banach (r
finite)/Frechet (r=infty) orbifold. The remaining two notions carry a
stratified structure: The C^r orbifold maps between O and P is locally a
stratified space with strata modeled on smooth C^\infty Banach (r
finite)/Frechet (r=infty) manifolds while the set of C^r reduced orbifold maps
between O and P locally has the structure of a stratified space with strata
modeled on smooth C^\infty Banach (r finite)/Frechet (r=infty) orbifolds.
Furthermore, we give the explicit relationship between these notions of
orbifold map. Applying our results to the special case of orbifold
diffeomorphism groups, we show they inherit the structure of C^\infty Banach (r
finite)/Frechet (r=infty) manifolds. In fact, for r finite they are topological
groups, and for r=infty they are convenient Frechet Lie groups.Comment: 31 pages, 2 figures; corrected and expande
Frequency and mode identification of gamma Doradus from photometric and spectroscopic observations
The prototype star for the gamma Doradus class of pulsating variables was studied employing photometric and spectroscopic observations to determine the frequencies and modes of pulsation. The four frequencies found are self-consistent between the observation types and almost identical to those found in previous studies (1.3641 d(-1), 1.8783 d(-1), 1.4742 d(-1), and 1.3209 d(-1)). Three of the frequencies are classified as l, m = (1, 1) pulsations and the other is ambiguous between l, m = (2, 0) and (2, -2) modes. Two frequencies are shown to be stable over 20 yr since their first identification. The agreement in ground-based work makes this star an excellent calibrator between high-precision photometry and spectroscopy with the upcoming TESS observations and a potential standard for continued asteroseismic modelling
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