Limits of contraction groups and the Tits core

The Tits core G^+ of a totally disconnected locally compact group G is defined as the abstract subgroup generated by the closures of the contraction groups of all its elements. We show that a dense subgroup is normalised by the Tits core if and only if it contains it. It follows that every dense subnormal subgroup contains the Tits core. In particular, if G is topologically simple, then the Tits core is abstractly simple, and if G^+ is non-trivial then it is the unique minimal dense normal subgroup. The proofs are based on the fact, of independent interest, that the map which associates to an element the closure of its contraction group is continuous.Comment: 11 page

The classification and management of limestone pavements - an endangered habitat

This thesis describes an in-depth study of limestone pavements across North West England and North Wales. The aim was to combine elements of geodiversity and biodiversity in order to create a holistic limestone pavement classification to inform future management. A field-based research protocol was used to assess a stratified random sample (46 pavements), accounting for approximately 10% of the limestone pavements in the geographical area. Detailed analyses of key elements are presented, along with important issues that continue to pose threats to this Annex One Priority Habitat. This research resulted in a comprehensive classification, using TWINSPAN analysis and Nonmetric Multidimensional Scaling, identifying six distinct holistic functional groups. The prime factors driving limestone pavement morphology, and hence the classification, were established to be lithology, proximity to structural fault, altitude and human intervention, particularly in terms of grazing intensity. Three upland, open limestone pavement classes were formed. Of these, the richest in terms of geodiversity and biodiversity was the group with the thickest bedding planes and hence the deepest grikes, typically greater than 1m. The class that was most species-poor was "at the highest altitude (above 450m), formed on the thin limestones of the Yoredales. These were characterised by shallow, wide grikes. The third upland limestone pavement group had mid-range grikes, generally 0.5-1m in depth, and small clints. Two wooded classes were identified. One was a lowland 'classic' wooded limestone pavement group with deep, narrow grikes and shallow soils. Indicator species included Juniperus communis and Taxus baccata. The second wooded group was situated proximal to a major structural fault. In this group the pavement dip ranged between 10°-40° with well-runnelled clints that were heavily moss-covered. The sixth group was low altitude, proximal to the coast, characterised by low moss growth, un-vegetated clints and the presence of Ulex europaeus. Conservation management was identified as key to the quality of the limestone pavement habitat and this thesis identifies best management practises and links these to the holistic limestone pavement classification. Finally, as a sample case study, this thesis presents mollusc species and diversity from eleven of the Yorkshire limestone pavements. Analysis establishes significant links between geodiversity and mollusc populations, with key drivers for mollusc communities echoing those of plant species on limestone pavement.Funded by the Yorkshire Dales National Park and the University of Chester

Static inverters which sum a plurality of waves Patent

Describing static inverter with single or multiple phase outpu

Assessing Domestic Demand for Organic and ‘Locally Grown' Produce on An ‘Organic Island': Dominica's Dilemma

The economy of Dominica faces a unique set of challenges. As with many other Caribbean nations, Dominica has historically been dependent upon agriculture. Over the past several hundred years, the island's economy has been largely supported through the concentrated mono-cropping of a variety of export-oriented crops including coffee, limes, vanilla, and bananas (FAVACA, 2008). Today, approximately 45% of Dominica's labor force is employed in the agricultural sector (FAVACA, 2008). While neighboring countries have economically benefited from tourism, due to its lack of white sand beaches, Dominica is not a typical tourist destination. Taking advantage of its landscape, rainforests, and diversity of natural wildlife, in an effort to diversify its economy Dominica has instead catered to eco-/wellness tourists. Bridging its agricultural foundations with the ecological preservation needed to support its tourist industry, the government of Dominica has signaled its interest in transforming Dominica into an Organic Island (‘Organic Dominica') by 2015. Through this initiative, sustainable, organic agricultural production methods will be encouraged. Complementing this, a ‘Buy Organic, Locally Grown' campaign has been proposed to encourage domestic and regional consumption of Dominica's agricultural outputs and food products. As such, ‘Organic Dominica' has the potential to simultaneously address ongoing national concerns surrounding food security, foreign exchange availability, domestic un/underemployment, and environmental preservation. Before and since proposing this policy, surveys were conducted to identity the major stakeholders in (organic) agricultural production, and current and potential markets for organic production. It remains, however, to quantify Dominica's capacity to produce organic goods, the scale of the potential market, and the price premia that organic production could command. This information is critical to determining the appropriate initial level of producer support and marketing programs required to successfully promote the production and consumption of Dominica's organic outputs and propel Dominica toward the desired status of a model ‘Organic Island'.contingent valuation, willingness to pay, Caribbean, organic, locally grown, food, Agricultural and Food Policy, International Development, Marketing, O13, O54, Q01, Q13, Q18,