1,729 research outputs found

    Bäcklund transformations for noncommutative anti-self-dual Yang-Mills equations

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    We present Bäcklund transformations for the non-commutative anti-self-dual Yang–Mills equations where the gauge group is G = GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasi-determinants and belong to a non-commutative version of the Atiyah–Ward ansatz. In the commutative limit, our results coincide with those by Corrigan, Fairlie, Yates and Goddard

    Heat Transfer Due to Unsteady Effects as Investigated in a High-Speed, Full-Scale, Fully-Cooled Turbine Vane and Rotor Stage

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    Experiments were conducted to examine the effects of film cooling on a gas turbine engine’s high‐pressure turbine section. The focus for this effort was in the tip/shroud region of a rotor stage and a high pressure turbine vane. A primary goal was to understand the unsteady flow effects. Attempts were also made to characterize the effects as caused by the fully‐cooled rotor stage. Data for this investigation was taken at the U.S. Air Force’s Turbine Research Facility (TRF), a transient blowdown facility with instrumentation fitted to a full‐scale, high‐speed, fully‐cooled vane and rotor stage of proprietary design. Measurements of pressure, temperature, and heat flux were taken at flow conditions non‐dimensionally matched to actual engine operation. From this high speed data the relevant film‐cooling parameters (heat transfer coefficients, film cooling effectiveness, and overall effectiveness) were determined over a range of operating conditions. Of specific interest were the high frequency events associated with the blade passage frequency on both the vane and shroud surfaces. It was found that tip flow and vane wake‐rotor interaction result in noticeable heat flux variations in time

    Uniform Algebras Over Complete Valued Fields

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    UNIFORM algebras have been extensively investigated because of their importance in the theory of uniform approximation and as examples of complex Banach algebras. An interesting question is whether analogous algebras exist when a complete valued field other than the complex numbers is used as the underlying field of the algebra. In the Archimedean setting, this generalisation is given by the theory of real function algebras introduced by S. H. Kulkarni and B. V. Limaye in the 1980s. This thesis establishes a broader theory accommodating any complete valued field as the underlying field by involving Galois automorphisms and using non-Archimedean analysis. The approach taken keeps close to the original definitions from the Archimedean setting. Basic function algebras are defined and generalise real function algebras to all complete valued fields. Several examples are provided. Each basic function algebra is shown to have a lattice of basic extensions related to the field structure. In the non-Archimedean setting it is shown that certain basic function algebras have residue algebras that are also basic function algebras. A representation theorem is established. Commutative unital Banach F-algebras with square preserving norm and finite basic dimension are shown to be isometrically F-isomorphic to some subalgebra of a Basic function algebra. The theory of non-commutative real function algebras was established by K. Jarosz in 2008. The possibility of their generalisation to the non-Archimedean setting is established in this thesis. In the context of complex uniform algebras, a new proof is given using transfinite induction of the Feinstein-Heath Swiss cheese "Classicalisation" theorem.Comment: PhD Thesis 2012, 113 pages, The main results were presented at The Sixth Conference on Function Spaces at SIUE USA 201

    Can contemporary art methods facilitate designers' creativity?

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    Art and industrial design share a long history, with some of the first industrial designers originating from the arts. Through the early part of the twentieth century many designers were educated and influenced by artists and on occasions they collaborated in the development of art/design movements. In recent decades this relationship has weakened with artists and industrial designers working towards different goals and paying less attention to how one another work. This research was undertaken to investigate whether contemporary artists were now using methods that may facilitate industrial design. [Continues.

    Identifying and responding to people with mild learning disabilities in the probation service

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    It has long been recognised that, like many other individuals, people with learningdisabilities find their way into the criminal justice system. This fact is not disputed. Whathas been disputed, however, is the extent to which those with learning disabilities arerepresented within the various agencies of the criminal justice system and the ways inwhich the criminal justice system (and society) should address this. Recently, social andlegislative confusion over the best way to deal with offenders with learning disabilities andmental health problems has meant that the waters have become even more muddied.Despite current government uncertainty concerning the best way to support offenders withlearning disabilities, the probation service is likely to continue to play a key role in thesupervision of such offenders. The three studies contained herein aim to clarify the extentto which those with learning disabilities are represented in the probation service, toexamine the effectiveness of probation for them and to explore some of the ways in whichprobation could be adapted to fit their needs.Study 1 and study 2 showed that around 10% of offenders on probation in Kent appearedto have an IQ below 75, putting them in the bottom 5% of the general population. Study 3was designed to assess some of the support needs of those with learning disabilities in theprobation service, finding that many of the materials used by the probation service arelikely to be too complex for those with learning disabilities to use effectively. To addressthis, a model for service provision is tentatively suggested. This is based on the findings ofthe three studies and a pragmatic assessment of what the probation service is likely to becapable of achieving in the near future
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