Contragredient representations and characterizing the local Langlands correspondence

We consider the question: what is the contragredient in terms of L-homomorphisms? We conjecture that it corresponds to the Chevalley automorphism of the L-group, and prove this in the case of real groups. The proof uses a characterization of the local Langlands correspondence over R. We also consider the related notion of Hermitian dual, in the case of GL(n,R)

Novel Routes to High Purity Oxides

Advances in the applications of ceramic material presently being introduced require products with chemical and physical properties tailored to the particular application. To attain the high standards necessary, a number of new methods of producing ceramics have been developed. One of these, organo-sol-gel processing, is the subject of the work described here. Silica is produced by the hydrolysis of tetraethylorthosilicate and the properties of the product are related to the reaction conditions leading to its production. Because the reaction is catalysed by both acid and base, the results are significantly different in each case, the two systems are dealt with separately. Under base catalysis the product morphology may be of interest as a support for metal catalysts so a third section deals with the incorporation of nickel compounds within the silica. The first section of the thesis deals with reactions prepared under neutral or acidic conditions. These conditions lead to the formation of clear rigid gels. The material was studied both during and after completion of the reaction by x-ray diffraction, infrared spectroscopy, thermogravimetric analysis, microanalysis, transmission electron microscopy and electron diffraction. The x-ray diffraction results were those of amorphous material and did not alter significantly on alteration of the reaction composition. Similarly the microanalysis and TGA results were not sensitive to alterations in the reaction conditions. The infrared spectra suffered from a similar problem giving the spectra of silica with little difference, but in a few cases peaks corresponding to carbonyl groups appear and may indicate the catalytic activity of the silica. TEM and electron diffraction were the most useful techniques. A number of sample preparation methods were used including dispersion in water or organic solvents, preparation of films, freeze drying, thin sectioning, removal of small areas by contact and staining with uranyl acetate. These all gave similar results where the product appeared to be small particles which form chains and 3D networks or material which forms plate-like areas of sample which appeared layered in nature. A number of these areas, especially the latter type, appeared crystalline when examined by electron diffraction but the patterns do not correspond to any known form of silica; this may indicate the formation of a crystalline hydrated silica. However it is not possible to determine the extent to which the preparation method influenced the observed morphology. The second section deals with the production of silica when the reaction is carried out under basic conditions. The reaction produced three distinct types of product; weak gels, colloidal dispersions and precipitates. The material was studied both during and after completion of the reaction by techniques including infrared spectroscopy, transmission and scanning electron microscopy. The product morphologies included small particles which aggregate to form 3D networks thus forming a gel, large particles of irregular shape which precipitate out of the reaction, and particles of spherical or near spherical shape with diameters up to 400nm. The size of these particles altered depending on the reaction conditions used to form them. Comparison of the size variation and particle growth rates with variations predicted from possible effects of the concentration changes on the rates of reaction and solvent properties indicate a possible nucleation and growth mechanism. The effect of including an ionic salt or polymer in the reaction support the growth mechanism proposed. Reactions employing tetrabutylorthosilicate in place of the tetraethylorthosilicate produced particles of diameter up to 1.2mum. The alteration with size, both within the tetrabutylorthosilicate reactions and in comparison with the tetraethylorthosilicate reactions, again supports the proposed mechanism. The observations also included SEM which indicated the solids formed by settling of spheres correspond to the structure of natural opal providing a dense solid with an iridescent sheen. The third section deals with the deposition of nickel complexes within the silica spheres as they grow. The original method was to deposit nickel bis(dimethylglyoximate) formed from the reaction of diacetyl, hydroxylamine and a nickel salt. However the presence of the ionic nickel salt altered the morphology of the silica and a nickel hydroxylamine chloride complex was precipitated, thus leading to the formation of particles including nickel hydroxylamine complex and silica

The Assault of Jamie Leigh Jones: How One Woman\u27s Horror Story is Changing Arbitration in America

This article examines Jones v. Halliburton Co., the Al Franken Amendment to the 2010 U.S. Defense Department Budget (Franken Amendment) that was created in response to Jones, and the impact that both could have on mandatory arbitration clauses in employment contracts in the future. Part II recounts the troubling events that led to Jones and the inclusion of the Franken Amendment in the 2010 Defense Department Budget. Part III details the arguments made for and against the inclusion of the Franken Amendment. Part IV analyzes the impact that the Franken Amendment could have on mandatory arbitration clauses in contacts in the future. Part V concludes this article

Modelling the process of reading: A social psychological study of the use children make of fairy tales

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis tries to answer the question "what does it mean to read?". I have tried to write it from the standpoint of how the work developed; the problems encountered and the solutions that were found form the stylistic theme. Consequently, it is not a neat piece of work delineated into chapters on particular academic areas of the disciplines used, rather topics are discussed as they are relevant to the problems that I had to face. If the thesis is about comprehension, then it is in itself a good example of the processes involved - it is as it were my 'reading' of the question mentioned above

The Real Chevalley Involution

We consider the Chevalley involution in the context of real reductive groups. We show that if G(R) is the real points of a connected reductive group, there is an involution, unique up to conjugacy by G(R), taking any semisimple element to a conjugate of its inverse. As applications we give a condition for every irreducible representation of G(R) to be self-dual, and to the Frobenius Schur indicator for such groups