Les hexaphyrines sont des macrocycles constitués de six unités pyrroliques, elles possèdent des propriétés physico-chimiques intéressantes, dont notamment leur capacité à exister sous deux états oxydés stables, à 26 et 28 électrons π délocalisés. Elles peuvent coordonner jusqu’à deux cations métalliques au sein du macrocycle, cependant elles souffrent d’un manque de réactivité et de prédictibilité quant à la nature des complexes formés. Pour pallier à ces problèmes, nous avons décidé de suivre une stratégie de post-modification du macrocycle, mettant en jeu l’incorporation sans précédent d’un habillage périphérique ou apical fonctionnel. Nous avons cherché à diversifier la nature de l’habillage, en travaillant dans un premier temps sur des fonctions acides carboxyliques portées par un bras, puis par une anse dans le but d’augmenter la préorganisation du système. Cette stratégie s’est montrée fructueuse et durant les études de coordination, quatre cations métalliques, le ZnII, le CdII, le PbII ainsi que le HgII ont montré des réactions de métallations instantanées et inédites à température ambiante. Dans un second temps, nous avons étudié l’influence d’un habillage tripodal sur les propriétés de coordination du macrocycle hexaphyrinique. La métallation dans des conditions spécifiques de ces nouvelles hexaphyrines, a mis en évidence la première synthèse hautement diastéréosélective d’un complexe aromatique avec une topologie en anneau de Möbius. Cette synthèse nous à servi de preuve de concept sur le développement de potentiels détecteurs chiroptiques, basés sur un changement de topologie et d’aromaticité du ligand après métallation induit par l’analyte. / Hexaphyrins are six-pyrrole member macrocycles, which possess several interesting physico-chemical properties, and specially their abilities to exist as two stable oxidation states. They also can coordinate two metallic cations, unfortunately they suffer from a lack of reactivity and from unpredictable behaviors regarding the nuclearity of the complexes. To overcome these problems, we decided to follow a macrocycle post-modification strategy, using the unprecedented peripheral dressing of the hexaphyrin. We tried to explore few functions and started working with carboxylic acid groups on a piquet and then on a strap to extend the preorganization of the coordinated function. This strategy showed good results and instantaneous metalation with four metalics cations, ZnII, CdII, PbII and HgII at room temperature. Meanwhile we studied the behavior in coordination chemistry of novel tren-capped hexaphyrin. Thus we highlight the first diastereoselective synthesis, involving the formation of complexes showing Möbius strip topology. This system was used as proof of concept for the development of potential chiroptical sensors, based on a topology switch after metalation triggered by the analyte.

The purpose of this thesis is to study the effects of hyperbolic transformations on the cubic that is determined by locus of centroids of the equilateral triangles in H² whose base coincides with the line y=0, and whose common vertex is at the origin. The derivation of the formulas within this work are based on the Poincaré disk model of H², where H² is understood to mean the hyperbolic plane. The thesis explores the properties of both the untransformed cubic (the original locus of centroids) and the transformed cubic (the original cubic taken under a linear fractional transformation).

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20927号 / 理博第4379号 / 新制||理||1629(附属図書館) / 京都大学大学院理学研究科化学専攻 / (主査)教授 大須賀 篤弘, 教授 丸岡 啓二, 教授 依光 英樹 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

yes / The properties of quantum probabilities are linked to the geometry of quantum mechanics, described by the Birkhoff-von Neumann lattice. Quantum probabilities violate the additivity property of Kolmogorov probabilities, and they are interpreted as Dempster-Shafer probabilities. Deviations from the additivity property are quantified with the Möbius (or non-additivity) operators which are defined through Möbius transforms, and which are shown to be intimately related to commutators. The lack of distributivity in the Birkhoff-von Neumann lattice Λd, causes deviations from the law of the total probability (which is central in Kolmogorov’s probability theory). Projectors which quantify the lack of distributivity in Λd, and also deviations from the law of the total probability, are introduced. All these operators, are observables and they can be measured experimentally. Constraints for the Möbius operators, which are based on the properties of the Birkhoff-von Neumann lattice (which in the case of finite quantum systems is a modular lattice), are derived. Application of this formalism in the context of coherent states, generalizes coherence to multi-dimensional structures.

Feature extraction from a tensor based local image representation introduced by Knutsson in [37] is discussed. The tensor representation keeps statements of structure, certainty of statement and energy separate. Further processing for obtaining new features also having these three entities separate is achieved by the use of a new concept, tensor field filtering. Tensor filters for smoothing and for extraction of circular symmetries are presented and discussed in particular. These methods are used for corner detection and extraction of more global features such as lines in images. A novel method for grouping local orientation estimates into global line parameters is introduced. The method is based on a new parameter space, the Möbius Strip parameter space, which has similarities to the Hough transform. A local centroid clustering algorithm is used for classification in this space. The procedure automatically divides curves into line segments with appropriate lengths depending on the curvature. A linked list structure is built up for storing data in an efficient way. / <p>Ogiltigt nummer / annan version: I publ. nr 290:s ISBN: 91-7870-815-X.</p>

For an affine Weyl group W, we explicitly determine the elements for which the Möbius function of the subposet of affine Grassmannians under the Bruhat order is non-zero by utilizing the quantum Bruhat graph of the classical Weyl group associated to W . Then we examine embedding stable and consistent statistics on the affine Weyl group of type A which permit the definition of an affine infinite symmetric group. / Doctor of Philosophy / Similar to the integers, there are groups that have both an infinite number of elements and also a way to partially order those elements. With a partial ordering, we can consider the interval between two elements. When we make a function that sums over an interval of elements, then we can invert the function by using something called the Mӧbius function. For many groups, the Mӧbius function is extremely unpredictable and calculating the inverse may require us to consider an infinite number of elements. In this paper, we focus on groups called affine Weyl groups, which are very useful in algebraic geometry. It turns out that most elements in these groups have a very predictable pattern in their Mӧbius functions which only considers a finite number of elements. The first part of this paper gives very simple rules for calculating it. The second part of this paper focuses on a special type of affine Weyl group: the affine symmetric groups. We provide an attempt at defining a large parent group, which we call the affine infinite symmetric group, that contains all the other affine symmetric groups.

Thèse diffusée initialement dans le cadre d'un projet pilote des Presses de l'Université de Montréal/Centre d'édition numérique UdeM (1997-2008) avec l'autorisation de l'auteur.

No description available.

Thèse diffusée initialement dans le cadre d'un projet pilote des Presses de l'Université de Montréal/Centre d'édition numérique UdeM (1997-2008) avec l'autorisation de l'auteur.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-07-09T17:32:41Z No. of bitstreams: 1 MARTA ÉLID CONCEIÇÃO AMORIM - DISSERTAÇÃO PPGMAT 2006..pdf: 311493 bytes, checksum: 839fa55790d058f7e88a3735ab098065 (MD5) / Made available in DSpace on 2018-07-09T17:32:41Z (GMT). No. of bitstreams: 1 MARTA ÉLID CONCEIÇÃO AMORIM - DISSERTAÇÃO PPGMAT 2006..pdf: 311493 bytes, checksum: 839fa55790d058f7e88a3735ab098065 (MD5) Previous issue date: 2006-02 / Capes / Neste trabalho apresentamos o Polinômio de Tutte com duas e quatro variáveis e o associamos a Função de Möbius, o Polinômio Característico e o Beta Invariante. Veremos, também, que por recursão sobre certas equações, algumas funções relacionadas a matróides podem ser obtidas pela avaliação do Polinômio de Tutte para certos valores. / Inthiswork,weshowTuttePolynomialwithtwoorfourvariablesandweassociateitwith Möbius Function the charateristic Polynomial and the Beta Invariant. We also see, to turn to undersomeequations,somefunctionsrelatedtomatroidscanbeobtainedforTuttePolynomial assessmentforsomevalues.