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

On the Inheritance of Orbifold Substructures

In a previous article, we defined a very flexible notion of suborbifold and characterized those suborbifolds which can arise as the images of orbifold embeddings. In particular, suborbifolds are images of orbifold embeddings precisely when they are saturated and split. This article addresses the problem of orbifold structure inheritance for three orbifolds $\mathcal{Q}\subset\mathcal{P}\subset\mathcal{O}$. We identify an appealing but ultimately inadequate notion of an inherited canonical orbifold substructure. In particular, we give a concrete example where the orbifold structure of $\mathcal{Q}$ is canonically inherited from $\mathcal{P}$, and the orbifold structure of $\mathcal{P}$ is canonically inherited from $\mathcal{O}$, but the orbifold structure of $\mathcal{Q}$ is not canonically inherited from $\mathcal{O}$. On the other hand, it is easy to see that when $\mathcal{Q}$ is embedded in $\mathcal{P}$, and $\mathcal{P}$ is embedded in $\mathcal{O}$, all of the canonical inherited orbifold substructures will agree. We also investigate the property of saturation in this context, and give an example of a suborbifold with the canonical orbifold substructure that is not saturated.Comment: 7 page

Fire and rescue service community safety initiatives: measuring impact

Purpose - The purpose of this paper is to discuss methods of capturing the impact of fire and rescue service (FRS) community safety work which directly aims to reduce the occurrence of specific incidents. Design/methodology/approach - The impact assessment method described focuses on addressing one of the major problems with regards to attributing outcomes to FRS community safety work; the influence of external factors. This paper looked to assess the incident trends within a case study UK FRS within the context of the following external data sets: first, incident trends within other UK FRSs; second, demographic trends; and third, incident data from other public services. Findings - There were instances, either across the whole region served by the case study FRS, or within specific districts, where evidence suggested a strong likelihood of the community safety work of the case study FRS contributing towards an observed reduction in incidents. These findings were established through filtering the impact of widespread external factors, which could impact upon incident figures. Research limitations/implications - The utility of this impact assessment relies upon FRS consistently recording the specific aims and focus of individual community safety activity, so that any positive outcomes can be attributed to a particular group of community safety initiatives. Originality/value - This paper discusses how an evaluation process, to deter mine the likelihood of community safety impacting upon incident numbers, can be practically applied to a FRS

Managing stress in the fire and rescue service: a UK informed global perspective

Fire and rescue service personnel can experience high levels of exposure to both occupational and post-traumatic stress, with the interplay between these generating a range of complex stress responses. The nature and cultural context of fire service work can, in turn, impact the take up and effectiveness of stress interventions. The development of appropriate processes for the prevention of, and responses to, stress exposure is therefore a crucial managerial issue. A consideration of such issues is presented, alongside an evaluation of the likely success of various stress interventions

Stress in trade union officials: an issue for managerial concern?

This study examines stress levels in, and a range of stressors experienced by, officials from a trade union within the fire and rescue service (n = 85). Findings indicate dissatisfaction with aspects of the work of union officials. Additionally, respondents exhibited excessive levels of stress resulting from the service’s organisational structure and their role within it. The benefits of the union role to the service are noted; and it is suggested that consideration be given to effecting change in organisational structure, climate, and practice in the fire and rescue service, and to improving support for union officials

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 $m_{\rm F275W}=25.39 \pm 0.10$ and $m_{\rm F336W}=25.88 \pm 0.13$ 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 $19,000 < T_{\rm eff} < 22,000$ K and $\log (L_{\rm bol}/L_{\odot})=3.92 \pm 0.14$. A BPASS v2.1 binary evolution model, with primary and secondary masses of 13 M$_{\odot}$ and 9 M$_{\odot}$ 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 emergence of topographic steady state in a perpetually dynamic self-organized critical landscape

We conducted a series of four physical modeling experiments of mountain growth at differing rates of uplift and three distinct climates ranging from relatively wet to relatively dry. The spatial and temporal pattern of landscape behavior is characterized by ∼f−1 scaling in sediment discharge and power law scaling in the magnitude and frequency of ridge movement in all four experiments. We find that internally generated self-organized critical (SOC) processes generate dynamically stable catchment geometries after ∼1 relief depths of erosion: these regularly spaced catchments have an average outlet-spacing ratio of 2.16, well within the range of values reported in field studies. Once formed, large catchment bounding ridges oscillate about a critically balanced mean location, with occasional large-scale changes in catchment size. Ridge movement appears to be driven by the competition for discharge as landslides push ridges back and forth. These dynamics lead to the emergence of a complex twofold scaling in catchment dynamics that is fully established by 1.8 relief depths of erosion; at this stage, a clear threshold has emerged separating two distinct scaling regimes, where large ridge mobility is insensitive to relief and small ridge mobility is relief dependent. Overall, we demonstrate that the development of dynamically stable large-scale landforms is related to the emergence of a complex-system hierarchy in topographic dynamics. Once formed, these landscapes do not evolve; statistical properties such as average topography and discharge become stationary while topography remains highly dynamic at smaller length scales

Hybrid Class Actions, Dual Certification, and Wage Law Enforcement in the Federal Courts

Hybrid wage-and-hour class actions, which combine a Fair Labor Standards Act ( FLSA \u27) opt-in collective action and a Federal Rule of Civil Procedure Rule 23 opt-out class action in a single civil action, demonstrate the unusual interplay of opt-in and opt-out rules. The hybrid class action, and its viability as a mechanism for wage law enforcement, raises fundamental questions as to who participates in lawsuits, how we should hold employers accountable for wage-and-hour noncompliance, and the role of the federal courts in enforcing public rights. An opt-in rule tends to produce low participation rates, while an opt-out rule tends to produce high participation rates. This means that employers are typically confronted by a larger number of state claims in the Rule 23 class action than federal claims in the FLSA action. The substantive consequences of dual certification, along with related jurisdictional and policy issues, have created division within the federal courts regarding whether FLSA opt-in collective actions and Rule 23 opt-out class actions may consistently coexist. While wage laws have historically been undermined by persistent underenforcement, the hybrid class action has the potential to expand enforcement. This Article examines the relevance of the FLSA opt-in action and its opt-in rates to Rule 23 class certification and federal jurisdiction for state wage claims. This Article engages in critical evaluation of the reasons for low FLSA opt-in rates by providing a comprehensive collection of empirical data on opt-in rates, analyzing reasons for low opt-in rates, and articulating the implications for wage law enforcement. This Article argues that FLSA section 216(b) and Rule 23 are consistent procedural enforcement mechanisms, and advances approaches to Rule 23 class certification and federal jurisdiction that integrate an understanding of low opt-in rates. Ultimately, this Article proposes that dual certification of FLSA collective actions and Rule 23 class actions is an appropriate response to the unusual interplay of opt-in and opt-out rules in hybrid class actions