Morse theory on spaces of braids and Lagrangian dynamics

In the first half of the paper we construct a Morse-type theory on certain spaces of braid diagrams. We define a topological invariant of closed positive braids which is correlated with the existence of invariant sets of parabolic flows defined on discretized braid spaces. Parabolic flows, a type of one-dimensional lattice dynamics, evolve singular braid diagrams in such a way as to decrease their topological complexity; algebraic lengths decrease monotonically. This topological invariant is derived from a Morse-Conley homotopy index and provides a gloablization of `lap number' techniques used in scalar parabolic PDEs. In the second half of the paper we apply this technology to second order Lagrangians via a discrete formulation of the variational problem. This culminates in a very general forcing theorem for the existence of infinitely many braid classes of closed orbits.Comment: Revised version: numerous changes in exposition. Slight modification of two proofs and one definition; 55 pages, 20 figure

Large deviations for ideal quantum systems

We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a subdomain of the container are described by a large deviation function related to the pressure of the system. That is, untypical densities occur with a probability exponentially small in the volume of the subdomain, with the coefficient in the exponent given by the appropriate thermodynamic potential. Furthermore, small fluctuations satisfy the central limit theorem.Comment: 28 pages, LaTeX 2

Pest-predator spatial relationships in winter rape: implications for integrated crop management

Douglas Warner, Les J Allen-Williams, Andrew W Ferguson, and Ingrid H Williams, 'Pest–predator spatial relationships in winter rape: implications for integrated crop management', Pest Management Science, Vol. 56 (11): 977-982, November 2000, doi: 10.1002/1526-4998(200011)56:113.0.CO;2-U. Copyright © 2000 Society of Chemical IndustryThe brassica pod midge (Dasineura brassicae) is an important and widespread pest of winter and spring oilseed rape throughout Europe. Pods infested by D brassicae larvae split prematurely, releasing seeds, and the larvae drop to the soil into which they burrow to pupate. At this stage in its lifecycle D brassicae is potentially vulnerable to predation by carabid beetles foraging on the soil surface. This is the first study in the UK to focus on carabid beetles as predators of D brassicae in the oilseed rape crop. The spatio-temporal distributions of larvae of D brassicae dropping to the soil from the crop canopy and of adult carabid beetles active on the soil surface were analysed in two consecutive years. Insect samples were collected from spatially referenced sampling points across each crop. Counts of insects were mapped and analysed, and the degree of spatial association between predator and prey determined using Spatial Analysis by Distance Indices (SADIE). Carabid species abundant and active during peak drop of first generation D brassicae larvae included Agonum dorsale, Amara similata, Harpalus rufipes and Nebria brevicollis. The larvae of D brassicae had a marked edge distribution within the crop. SADIE analysis revealed significant spatial association between larvae of D brassicae and adult H rufipes (P <0.05) in 1998, but not with adults of A dorsale, A similata or N brevicollis. In 1999, there was strong spatial association only between larvae of D brassicae and adult A dorsale (P <0.01). Aggregation of N brevicollis adults occurred in some areas of greatest D brassicae larval counts in 1999, but overall spatial association was not signi®cant. The distributions are discussed in terms of their relevance to integrated crop management (ICM) strategies and spatial targeting of insecticides.Peer reviewe

’n Verkennende studie met die oog op die identifísering en kategorisering van leerteorieë met verwysing na die prediking

An introductory study to identify and classify theories of learning with regard to the task of preachingLearning is a lifelong process in which man must be what he can be, namely a being interacting with his world in a creative problem-solving manner for the well-being of himself and others. In a similar sense the church has always seen her task in preaching, supported by all the other domains of churchlife, as that of teaching people to come to terms with the gospel of Jesus Christ in their daily existence. This article proposes to identify, categorize and integrate the acknowledged theories underlyingthe learning process, as they exist in the social sciences, into an all encompassingmodel for learning; a model from which conclusions are drawn in the hope that further studies can spell out the implications of these conclusions as they are applicable to the task of preaching within the church

Eccentrically Loaded Bolted Connections for Type 304 and 3CR12 Stainless Steel Lipped Channels

In this paper the results of a study on eccentrically loaded bolted connections in lipped channels are presented. The steels chosen for this study are AISI Type 304 and Type 3CR12 stainless steel. It is concluded in this investigation that an acceptable prediction of the strength of eccentrically loaded bolted connections of stainless steel lipped channels may be obtained through the combination between the eccentric loaded equation and the normal bolted connection equations for stainless steel

Allergic sensitisation in South Africa: Exploring regional variation in sensitisation

Background. Allergy is a common health problem in South Africa (SA), and a rational approach to allergy testing is essential to ensure cost-effective as well as optimal patient diagnosis and management.Objectives. To review allergy testing data with respect to current national testing recommendations, and to explore the regional variations in sensitisation.Methods. Retrospective data review on allergy testing from a private pathology provider in SA over a 2-year period. Data on skin-prick testing (SPT) and allergen-specific IgE testing originating from all the provinces of SA were collected and analysed with regards to allergen positivity rate and regional sensitisation patterns.Results. Among the patients (N=45 0320) tested for a suspected inhalant allergy, 46% tested positive. Only 45% of these received additional testing for the nine recommended inhalant allergens included in the current national testing protocol. Among the patients (N=6 775) who received SPT for a suspected inhalant allergy, 59% yielded one or more positive results. The most frequent sensitising allergens were house dust mite (Dermatophagoides pteronyssinus) and grass pollen. The house dust mite, Blomia tropicalis, was a significant sensitiser in coastal regions. SPT identified two other important regional allergens which are not included in the current recommendations for inhalant allergen-specific IgE testing.Conclusions. The current diagnostic recommendations include allergens that demonstrate significant sensitisation in all regions of SA. Two additional allergens that show significant regional sensitisation in the South African population were identified. These findings may aid the recommendations for the most appropriate and cost-effective approach to allergy testing of symptomatic patients in SA