Hierarchies and semistability of relatively hyperbolic groups

A finitely presented group is semistable if all proper rays in the Cayley 2-complex are properly homotopic. A long standing open question asks whether all finitely presented groups are semistable. In this article, we prove semistability of groups that are hyperbolic relative to polycyclic subgroups. Key tools in the proof are a result of Mihalik-Swenson on semistability of `atomic' relatively hyperbolic groups, a combination theorem of Mihalik-Tschantz, and a hierarchical accessibility theorem of Louder-Touikan. We analyze an example that illustrates why an understanding of hierarchies is necessary for the proof of semistability in this context.Comment: 10 pages, 2 figure

A Study of Time and Labour Use on Irish Suckler Beef Farms

End of project reportLabour is one of the four factors of production and an increasingly costly and scarce input on farms. The attractiveness of non-farming employment, the nature of farm work and the price received for farm outputs are resulting in falling levels of hired and family labour

Hyperbolic groups and local connectivity

The goal of this paper is to give an exposition of some results of Bestvina-Mess on local connectivity of the boundary of a one-ended word hyperbolic group. We also give elementary proofs that all hyperbolic groups are semistable at infinity and their boundaries are linearly connected in the one-ended case. Geoghegan first observed that semistability at infinity is a consequence of local connectivity using ideas from shape theory, and Bonk-Kleiner proved linear connectivity using analytical methods. The methods in this paper are closely based on the original ideas of Bestvina-Mess.Comment: Dedicated to Mike Mihalik on his 70th birthday. 14 page

Review of high-contrast imaging systems for current and future ground- and space-based telescopes I: coronagraph design methods and optical performance metrics

The Optimal Optical Coronagraph (OOC) Workshop at the Lorentz Center in September 2017 in Leiden, the Netherlands gathered a diverse group of 25 researchers working on exoplanet instrumentation to stimulate the emergence and sharing of new ideas. In this first installment of a series of three papers summarizing the outcomes of the OOC workshop, we present an overview of design methods and optical performance metrics developed for coronagraph instruments. The design and optimization of coronagraphs for future telescopes has progressed rapidly over the past several years in the context of space mission studies for Exo-C, WFIRST, HabEx, and LUVOIR as well as ground-based telescopes. Design tools have been developed at several institutions to optimize a variety of coronagraph mask types. We aim to give a broad overview of the approaches used, examples of their utility, and provide the optimization tools to the community. Though it is clear that the basic function of coronagraphs is to suppress starlight while maintaining light from off-axis sources, our community lacks a general set of standard performance metrics that apply to both detecting and characterizing exoplanets. The attendees of the OOC workshop agreed that it would benefit our community to clearly define quantities for comparing the performance of coronagraph designs and systems. Therefore, we also present a set of metrics that may be applied to theoretical designs, testbeds, and deployed instruments. We show how these quantities may be used to easily relate the basic properties of the optical instrument to the detection significance of the given point source in the presence of realistic noise

Dynamic Leadership: Toolbox for the Values-Based Entrepreneur

Four entrepreneurship models are proposed which lend guidance in the development of a business, from birth to exit, each examining ways to maintain the business founder’s initial vision and to continue to infuse values and ethical decision-making at each stage of development

Labour efficiency on-farm

End of project reportImprovements in milking efficiency have a greater influence than any other aspect of the dairy farmers work on overall farm labour inputs (Whipp, 1992). In order to facilitate the examination of milking process labour inputs, the milking process may be divided into the following three components: herding pre and post milking (transfer of cows to and from the milking parlour); milking (milking tasks / work routines within the parlour); and washing (washing of milking machine and yard). Meanwhile, within milking specifically, the number of cows milked per operator per hour is the best measure of both the performance of the operator and the milking installation (Clough, 1978). This is affected by the following three factors: the milking times of the cows, the number and arrangement of the milking units, and the operator’s work routine (Whipp, 1992). The addition of extra milking units will only increase milking performance if the operator has idle time during milking (Hansen, 1999)

A Study of Labour Use on Irish Grassland Farms Specialising in Suckler Production

Important structural changes have taken place within the agricultural workforce in recent years. There has been a persistent decline in the proportion of the total workforce engaged in agriculture. Demand for labour by farmers has become a major issue, and if this shortage continues it will have a significant impact on the development of Irish farms in future (Ruane et al., 2001)