La simulation numérique modélise des phénomènes toujours plus complexes. De tels problèmes, souvent de grande dimension, exigent des codes sophistiqués et coûteux en temps de calcul. Le recours systématique au simulateur devient alors illusoire. L'approche privilégiée consiste à définir un nombre réduit de simulations organisées selon un plan d'expériences numériques à partir duquel une surface de réponse est ajustée pour approcher le simulateur. Nous considérons ici les plans générés par des simulateurs déterministes en phase exploratoire i.e. lorsqu'il n'y a aucune connaissance a priori. Les plans requièrent donc certaines propriétés comme le remplissage de l'espace et la bonne répartition des points en projection. Deux indicateurs quantifiant la qualité intrinsèque des plans ont été développés. Le point essentiel de ce travail concerne un procédé de planification basée sur la simulation d'échantillons selon une loi de probabilité par une méthode de Monte Carlo par chaînes de Markov.

University of Macau / Faculty of Science and Technology / Department of Mathematics

En esta memoria se incluyen diversas alternativas a una teoría de krein-milman no arquimediana las cuales vienen sugeridas bien por intentos anteriores de otros autores bien por conseguir una teoría unificada en los casos arquimediano o no o bien por lograr una teoría independiente del cuerpo valuado y que en condiciones de comparación dan lugar a resultados muy similares / This monography provides several alternatives to a non-Archimedan Krein-Milman Theory. They are suggested by some previous attempts to this subject carried out by other authors, as well as by the aim of getting an unified theory that works in the Archimede and in the non-Archimedean cases, in the sense that in the Archimedean context, this theory coincides with the well-known one existing in the classical literature

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In image processing, partial differential equation (PDE) based approaches have been extensively used in segmentation and smoothing applications. The Perona-Malik nonlinear diffusion model is the first PDE based method used in the image smoothing tasks. Afterwards the classical Mumford-Shah model was developed to solve both image segmentation and smoothing problems and it is based on the minimization of an energy functional. It has numerous application areas such as edge detection, motion analysis, medical imagery, object tracking etc. The model is a way of finding a partition of an image by using a piecewise smooth representation of the image. Unfortunately numerical procedures for minimizing the Mumford-Shah functional have some difficulties because the problem is non convex and it has numerous local minima, so approximate approaches have been proposed. Two such methods are the Ambrosio-Tortorelli approximation and the Chan-Vese active contour method. Ambrosio and Tortorelli have developed a practical numerical implementation of the Mumford-Shah model which based on an elliptic approximation of the original functional. The Chan-Vese model is a piecewise constant generalization of the Mumford-Shah functional and it is based on level set formulation. Another widely used image segmentation technique is the &ldquo / Active Contours (Snakes)&rdquo / model and it is correlated with the Chan-Vese model. In this study, all these approaches have been examined in detail. Mathematical and numerical analysis of these models are studied and some experiments are performed to compare their performance.

In this study, the effect of surface crystallography on hydrogen molecule adsorption properties on FeTi surfaces is presented. Furthermore, the substitutional adsorption of 3d-transition metals on (001), (110) and (111) surfaces of FeTi is studied. Using ab initio pseudopotential methods, the adsorption energies of hydrogen and 3d-transition metals are calculated. In substitutional adsorption of 3d-transition metals, Fe-terminated (111) and Ti-terminated (001) surfaces, are found to express the lowest adsorption energies. The adsorption energy versus adsorbed elements&rsquo / curves are very alike for all the surfaces. According to this, going from the left to right of periodic table, the adsorption energies increase first. The maximum energy belongs to Cr, Mn and Fe for all the surfaces. Then a minimum is observed in Co for all the surfaces and after that the energy increases again. Adsorption energies of atomic and molecular hydrogen are calculated on high symmetry sites of surfaces. As a result, top and bridge sites came out to be the most stable positions for molecular and atomic hydrogen adsorption, respectively, for (001) and (111) surfaces in all terminations. In (110) surface / however, 3-fold (Ti-Ti)L-Fe and 3-fold (Ti-Ti)S-Fe hollow sites express the lowest adsorption energies for molecular and atomic hydrogen, respectively. Considering the minimum adsorption energy sites for hydrogen molecule and atom, a path of dissociation of hydrogen molecule on surfaces is represented. After that by fully relaxing the hydrogen molecule on the surface and using CI-NEB method the activation energy for hydrogen dissociation is calculated. So it has been found that on Fe-terminated (111) and FeTi (110) surfaces the dissociation of hydrogen molecule happens without activation energy. Meanwhile, the activation energy for Fe-terminated (001) surface and Ti-terminated (001) surface, is calculated to be 0.178 and 0.190 eV, respectively.

Scytalidium thermophilum produces a novel phenol oxidase, which has turned out to be a bifunctional catalase-phenol oxidase (CATPO) during the course of this work, by other researchers of our group. Therefore, in the beginning of the studies, substrate specificity and inhibitor assays were conducted on the crude enzyme, followed by production, purification, cloning, expression, and mutagenesis and crystallography studies for further functional and structural analysis of CATPO. Accordingly, substrate specificity and inhibitory tests applied for crude enzyme characterisation presented the similarity of the phenol oxidase nature of CATPO essentially to catechol oxidase. Production studies were performed to investigate the effects of different factors including induction time, growth temperature, exogenous iron and hydrogen peroxide addition. In view of that, CATPO is constitutively produced in a growth associated manner. However, some phenolic compounds enhance its production. In this study, 15 phenolic compounds were tested for their ability to affect CATPO production. Of the phenolic compounds tested, catechol, resorcinol and vanillic acid caused repression of CATPO production. On the other hand, caffeic acid, myricetin and resveratrol enhanced CATPO production. As a biocatalyst, the efficiency of CATPO was examined and found to be a good candidate for getting pharmaceutically important drug intermediates. Its dual mechanism was analysed through side-directed mutagenesis. Two conserved residues (His101 and Val142) were mutated to discriminate catalase and phenol oxidase activities. Spectroscopic and mutagenesis studies exhibited the presence of heme d centre. Lastly, its structure was analysed by X-ray crystallography and found to have a tetrameric structure.

In this thesis, a market is assumed with n competing buyers where price is an inverse linear function of the quantity supplied to the market. The buyers get engaged in Cournot competition, but may also collaborate on purchasing decisions from a supplier. The supplier offers a quantity discount, as the quantity purchased increases unit price decreases. Furthermore, the demand base in the market is uncertain, but the buyers may get a signal of the demand. In this setting, the value of collaboration, information sharing and non-linear pricing is analyzed.

This thesis will present new results involving Hardy and Hardy-Sobolev-Maz'ya inequalities for fractional integrals. There are two key ingredients to many of these results. The first is the conformal transformation between the upper halfspace and the unit ball. The second is the pseudosymmetric halfspace rearrangement, which is a type of rearrangment on the upper halfspace based on Carlen and Loss' concept of competing symmetries along with certain geometric considerations from the conformal transformation. After reducing to one dimension, we can use the conformal transformation to prove a sharp Hardy inequality for general domains, as well as an improved fractional Hardy inequality over convex domains. Most importantly, the sharp constant is the same as that for the halfspace. Two new Hardy-Sobolev-Maz'ya inequalities will also be established. The first will be a weighted inequality that has a strong relationship with the pseudosymmetric halfspace rearrangement. Then, the psuedosymmetric halfspace rearrangement will play a key part in proving the existence of the standard Hardy-Sobolev-Maz'ya inequality on the halfspace, as well as some results involving the existence of minimizers for that inequality.

The interface of a zinc-terminated polar zinc oxide surface (0002) with a series of chemisorbed fluorinated benzylphosphonic acids has been studied using density functional theory. The calculations indicate that there is a substantial change in the binding energies and work function modification depending on the binding motif. The results also indicate that there is a pronounced difference in the magnitude and trends of the factors determining the total change in work function. The oxygen core-level binding shifts have been calculated and compared to available experimental data.