In this thesis we study elliptic PDEs and PDE systems with e-pcriodic coeffi- cients, for small E, using the theory of two-scale homogenisation. We study a class of PDEs of partially degenerating type: PDEs with coefficients that are not uniformly elliptic with respect to E, and become degenerate in the limit E -t O. We review a recently developed theory of homogenisation for a general class of partially degenerating PDEs via the theory of two-scale convergence, and study two such problems from physics. The first problem arises from the study of a linear elastic composite with periodically dispersed inclusions that are isotropic and (soft' in shear: the shear modulus is of order E2. By passing to the two- scale limit as E -t 0 we find the homogenised limit equations to be a genuinely two-scale system in terms of both the macroscopic variable x and the micro- scopic variable y. We discover that the corresponding two-scale limit solutions must satisfy the incompressibility condition in y and therefore the composite only undergoes microscopic deformations when a (microscopically rotational' force is applied. We analyse the corresponding limit spectral problem and find that, due to the y-incompressibility, the spectral problem is an uncoupled two-scale prob- lem in terms of x and y. This gives a simple representation of the two-scale limit spectrum. We prove the spectral compactness result that states: the spectrum of the original operator converges to the spectrum of the limit operator in the sense of Hausdorff. The second problem we study is the propagation of electro- magnetic waves down a photonic fibre with a periodic cross section. We seek solutions to Maxwell's equations, propagating down the waveguide with wave number k E2-close to some (critical' value. In this setting, Maxwell's equations are reformulated as a partially degenerating PDE system with z-periodic coeffi- cients. Using the theory of homogenisation we pass to the limit as E -t 0 to find a non-standard two-scale homogenised limit and prove that the spectral compact- ness result holds. We finally prove that there exist gaps in the limit spectrum for two particular examples: a one-dimensionally periodic 'multilayer ' photonic crystal and a two-dimensionally periodic two-phase photonic crystal with the in- clusion phase consisting of arbitrarily small circles. Therefore, we prove that these photonic fibres have photonic band gaps for certain k.

Comparative analysis is an essential part of understanding how and why things work the way they do. Why postgraduate degree holders really earn more money than those with an undergraduate degree? What factors contribute to pre-term births? Why are some students more successful than others? The above questions require comparison between various classes. Contrast-set mining was first proposed as a way to identify attributes that significantly differentiate between various classes (groups). While contrast-set mining has been widely applied for differentiating between different groups however, no clear picture seems to have emerged regarding how to extract the contrast-sets that discriminate most between the classes. In this thesis we try to address the problem of finding meaningful contrast sets by applying Association Rule Mining. We report a new family of contrast-sets, and we present and compare the results of our experiments with the well known algorithm for contrast-set mining - STUCCO.

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For several common inkjet, laser and thermal dye printers, a method of evaluating prints that is not associated with the level of dental expertise of the observer is introduced. In addition, an automated analysis that mimics the observations made by observers is tested. Metrics that are evaluated in this study include spatial resolution, contrast uniformity, the type of paper, and overall observer preference. The results demonstrate that observer preference is associated with a high print contrast uniformity and with the use of glossy paper, but not with increased spatial resolution. The automated analysis produced results that were in general agreement with the observer data for spatial resolution, which concluded that the Lexmark C543DN printer produced prints with the highest spatial resolution. A thermal dye printer (Kodak CMI1000) produced prints with the highest contrast uniformity, and the print most favored by observers overall was produced by the Kodak ESP-9 inkjet printer on Kodak Everyday Glossy Photo paper.

For several common inkjet, laser and thermal dye printers, a method of evaluating prints that is not associated with the level of dental expertise of the observer is introduced. In addition, an automated analysis that mimics the observations made by observers is tested. Metrics that are evaluated in this study include spatial resolution, contrast uniformity, the type of paper, and overall observer preference. The results demonstrate that observer preference is associated with a high print contrast uniformity and with the use of glossy paper, but not with increased spatial resolution. The automated analysis produced results that were in general agreement with the observer data for spatial resolution, which concluded that the Lexmark C543DN printer produced prints with the highest spatial resolution. A thermal dye printer (Kodak CMI1000) produced prints with the highest contrast uniformity, and the print most favored by observers overall was produced by the Kodak ESP-9 inkjet printer on Kodak Everyday Glossy Photo paper.

Thesis (Ph.D.)--Drexel University, 2007. / Includes abstract and vita. Includes bibliographical references (leaves 70-74).

L'imagerie par résonance magnétique est une des méthodes de diagnostic les plus utilisées, aussi bien dans le domaine médical que dans les études précliniques. Cependant, la relaxivité des agents de contraste commerciaux ne représente qu'une fraction de la relaxivité prédite par la théorie et il est nécessaire d'optimiser les différents paramètres dont elle dépend pour atteindre des valeurs de relaxivité plus élevées : nombre de molécules d'eau en première sphère de coordination, vitesse d'échange de l'eau, dynamique de rotation du complexe, relaxation électronique, distance Gd(III)-proton. Dans ce travail, nous présentons la synthèse, la stabilité et la relaxivité des complexes de Gd(III) de deux séries de ligands tripodes dérivés de la 8-hydroxyquinoléine, basés l'une sur une plateforme 1,4,7 triazacyclononane, l'autre sur un pivot azote central. Ces complexes ont montré des stabilités comparables à celles des agents commerciaux, des valeurs de relaxivités élevées dans l'eau ainsi qu'en milieu biologique. L'utilisation de la 8-hydroxyquinoléine comme base des ligands a permis de sensibiliser le Nd(III) et l'Yb(III) pour la luminescence proche infrarouge, ouvrant la possibilité pour le développement de nouveaux systèmes bimodaux. / Magnetic resonance imaging is a commonly used diagnostic method in medicinal practice as well as in biological and preclinical research. However, the relaxivity of commercial contrast agents is only a few percent of the theoretically predicted relaxivity. An optimisation of the different parameters who have an impact on the relaxivity (number of gadolinium bound water molecules, water exchange rate, rotation dynamic of the complex, electronic relaxation, Gd(III)-proton distance) is needed to obtain higher relaxivities. In this work, we present the synthesis, the stability and the relaxivity of the Gd(III) complexes of two series of 8-hydroxyquinolinate-based ligands, one using a 1,4,7 triazacyclononane platform, the other one using a central nitrogen architecture. Theses complexes show stabilities comparable to commercial agents, and high relaxivities in both water and serum. The 8-hydroxyquinolinate moiety allows these ligands to sensitize Nd(III) and Yb(III) for Near Infra Red (NIR) luminescence, leading to a new class of potential bimodal systems.

published_or_final_version / abstract / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

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