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Neutral diorganotin compounds of the 1,3-dithiole-2-thione-4,5-dithiolate ligand have been prepared. The syntheses of Me₂Sndmit, Et₂Sndmit, Bu₂Sndmit, (C₈H₁₇)₂Sndmit, (C₁₀H₂₁)₂Sndmit and (C₁₄H₂₉)₂Sndmit are described. For the purposes of indicating the formation of different structural phases, D.S.C. powder patterns are reported for initial and recrystallised samples of Me₂Sndmit, Et₂Sndmit and Bu₂Sndmit. Since Et₂Sndmitshowed different tin environments by solid phase state N.M.R. and clearly different powder patterns after recrystallisation, the compound was recrystallised from various solvents in an attempt to determine how many crystalline forms exist. To date, two forms have been identified: orthorhombic and monoclinic. The single crystal X-ray structure analyses of these are described. It has also been shown that upon heating a transition from the orthorhombic to the monoclinic form occurs at 140°C. The crystal strict of Me₂Sndmit has also been determined and is reported, along with Mossbauer parameters for Me₂Sndmit and Me₂Sndmio (dmio = 1,3-dithiole-2-one-4,5-dithiolate). Anionic organotin bis-dmit complexes of the form [RSn(dmit)₂][Q]⁺ have also been prepared, with a view to investigating their electrochemical properties. The syntheses of complexes with R chain length ranging from 4 to 18 carbons are described. The problem of formation of [Sn(dmit)₃][Q]₂ is also discussed. D.S.C. curves and cyclic voltammograms for [C₁₄H₂₉Sn(dmit)₂][C₁₄H₂₉NMe₃] and [NEt₄][(dmit)₂SnC₁₀H₂₀Sn(dmit)₂][NEt₄] are also described. Chiral macrocycles have potential uses as catalysts for asymmetric bond-forming reactions and as selective to metal ions. A chiral macrocyclic derivative of dmit was synthesised from methyl-4,6-<I>O</I>-benzylidene-2,3-bis-<I>O</I>-[(2-iodoethoxyethyl)-ethyl]-α-D-glucopyranoside. Since reaction of this with dmit proved to be unexpectedly problematic, attempted reactions of the sugar derivative with Na₂dmit<I> in situ</I>, isolated Na₂dmit, [Zn(dmit)₂][NEt₄]₂, [Ph₂Sn(dmit)I][NEt₄] and Cs₂dmit are described.

Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-02-22Bitstream added on 2014-06-13T20:27:28Z : No. of bitstreams: 1 ferrari_aj_me_sjrp.pdf: 927602 bytes, checksum: 80285856c8ad55e7993124cb6f12c22f (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Dado um ideal A do anel dos inteiros algébricos de um corpo de números, tem-se que a imagem deste ideal via o homomorfissmo de Minkowski é um reticulado no Rn, chamado de reticulado algébrico. Deste modo, o principal objetivo do presente trabalho é a construção de reticulados algébricos no Rn que sejam versões rotacionadas de reticulados conhecidos na literatura, e trabalhamos de modo particular até a dimensão 8. Além disso, vimos também reticulados obtidos via perturbações do homomorfismo de Minkowski. / We stablished that the image of an ideal A of the algebraic integer ring of a number field by the Minkowski homomorphism is a lattice in Rn, named algebraic lattice. In this way, the main goal of this work is the construction of algebraic lattices in Rn that be rotated versions of known lattices in the literature, and particularly we worked in dimensions up to 8. We also studied lattices obtained by perturbations of Minkowski homomorphism.

Made available in DSpace on 2014-10-09T12:29:37Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T13:59:41Z (GMT). No. of bitstreams: 1 01257.pdf: 1883679 bytes, checksum: 16dcaa8a2de2f071f89d7e49a9912605 (MD5) / Dissertacao (Mestrado) / IEA/D / Instituto de Fisica, Universidade de Sao Paulo - IF/USP

Orientador: Antonio Aparecido de Andrade / Banca: André Luiz Flores / Banca: Tatiana Bertoldi Carlos / Resumo: Dado um ideal A do anel dos inteiros algébricos de um corpo de números, tem-se que a imagem deste ideal via o homomorfissmo de Minkowski é um reticulado no Rn, chamado de reticulado algébrico. Deste modo, o principal objetivo do presente trabalho é a construção de reticulados algébricos no Rn que sejam versões rotacionadas de reticulados conhecidos na literatura, e trabalhamos de modo particular até a dimensão 8. Além disso, vimos também reticulados obtidos via perturbações do homomorfismo de Minkowski. / Abstract: We stablished that the image of an ideal A of the algebraic integer ring of a number field by the Minkowski homomorphism is a lattice in Rn, named algebraic lattice. In this way, the main goal of this work is the construction of algebraic lattices in Rn that be rotated versions of known lattices in the literature, and particularly we worked in dimensions up to 8. We also studied lattices obtained by perturbations of Minkowski homomorphism. / Mestre

Made available in DSpace on 2014-10-09T12:29:37Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T13:59:41Z (GMT). No. of bitstreams: 1 01257.pdf: 1883679 bytes, checksum: 16dcaa8a2de2f071f89d7e49a9912605 (MD5) / Dissertacao (Mestrado) / IEA/D / Instituto de Fisica, Universidade de Sao Paulo - IF/USP

The focus of this dissertation is the existence, stability, and resulting dynamical evolution of localized stationary solutions to Nonlinear Schr¨odinger (NLS) equations with periodic confining potentials in 2(+1) dimensions. I will make predictions about these properties based on a discrete lattice model of coupled ordinary differential equations with the appropriate symmetry. The latter has been justified by Wannier function expansions in a so-called tight-binding approximation in the appropriate parametric regime. Numerical results for the full 2(+1)-D continuum model will be qualitatively compared with discrete model predictions as well as with nonlinear optics experiments in optically induced photonic lattices in photorefractive crystals. The predictions are also relevant for BECs (Bose-Einstein Condensates) in optical lattices.

This thesis contains four papers, where the first two are in the area of geometry of numbers, the third is about class group statistics and the fourth is about free path lengths. A general theme throughout the thesis is lattice points and convex bodies. In Paper A we give an asymptotic expression for the number of integer matrices with primitive row vectors and a given nonzero determinant, such that the Euclidean matrix norm is less than a given large number. We also investigate the density of matrices with primitive rows in the space of matrices with a given determinant, and determine its asymptotics for large determinants. In Paper B we prove a sharp bound for the remainder term of the number of lattice points inside a ball, when averaging over a compact set of (not necessarily unimodular) lattices, in dimensions two and three. We also prove that such a bound cannot hold if one averages over the space of all lattices. In Paper C, we give a conjectural asymptotic formula for the number of imaginary quadratic fields with class number h, for any odd h, and a conjectural asymptotic formula for the number of imaginary quadratic fields with class group isomorphic to G, for any finite abelian p-group G where p is an odd prime. In support of our conjectures we have computed these quantities, assuming the generalized Riemann hypothesis and with the aid of a supercomputer, for all odd h up to a million and all abelian p-groups of order up to a million, thus producing a large list of “missing class groups.” The numerical evidence matches quite well with our conjectures. In Paper D, we consider the distribution of free path lengths, or the distance between consecutive bounces of random particles in a rectangular box. If each particle travels a distance R, then, as R → ∞ the free path lengths coincides with the distribution of the length of the intersection of a random line with the box (for a natural ensemble of random lines) and we determine the mean value of the path lengths. Moreover, we give an explicit formula for the probability density function in dimension two and three. In dimension two we also consider a closely related model where each particle is allowed to bounce N times, as N → ∞, and give an explicit formula for its probability density function. / <p>QC 20151204</p>

The preparation of bicrystal specimens of high interfacial purity and accurately controlled mismatch of orientation between grains with a specific boundary orientation are critical for fundamental studies of the structure and properties of grain boundaries. A method was developed for routinely producing high-purity aluminum bicrystals of desired mismatch and boundary orientation. A strain annealing technique was used for making large single crystals. The orientation, structural perfection, and chemical purity of the seeds were characterized, then the seeds were joined by using an electron beam welder. The welder was designed and built as a major portion of this work.

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