Let G be a finite graph with vertex set V and edge set E. A graph complex on G is an abstract simplicial complex consisting of subsets of E. In particular, we may interpret such a complex as a family of subgraphs of G. The subject of this thesis is the topology of graph complexes, the emphasis being placed on homology, homotopy type, connectivity degree, Cohen-Macaulayness, and Euler characteristic. We are particularly interested in the case that G is the complete graph on V. Monotone graph properties are complexes on such a graph satisfying the additional condition that they are invariant under permutations of V. Some well-studied monotone graph properties that we discuss in this thesis are complexes of matchings, forests, bipartite graphs, disconnected graphs, and not 2-connected graphs. We present new results about several other monotone graph properties, including complexes of not 3-connected graphs and graphs not coverable by p vertices. Imagining the vertices as the corners of a regular polygon, we obtain another important class consisting of those graph complexes that are invariant under the natural action of the dihedral group on this polygon. The most famous example is the associahedron, whose faces are graphs without crossings inside the polygon. Restricting to matchings, forests, or bipartite graphs, we obtain other interesting complexes of noncrossing graphs. We also examine a certain "dihedral" variant of connectivity. The third class to be examined is the class of digraph complexes. Some well-studied examples are complexes of acyclic digraphs and not strongly connected digraphs. We present new results about a few other digraph complexes, including complexes of graded digraphs and non-spanning digraphs. Many of our proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this thesis provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees, which we successfully apply to a large number of graph and digraph complexes. / QC 20100622

The one dimensional position dependent effective mass problem is studied by solving the Schr&ouml / dinger equation for some well known potentials, such as the deformed Hulthen, the Mie, the Kratzer, the pseudoharmonic, and the Morse potentials. Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions exactly. By introducing a free parameter in the transformation of the wave function, the position dependent effective mass problem is reduced to the solution of the Schr&ouml / dinger equation for the constant mass case. At the same time, the deformed Hulthen potential is solved for the position dependent effective mass case by applying the method directly. The Morse potential is also solved for a mass distribution function, such that the solution can be reduced to the constant mass case.

Les travaux de ma thèse s'articulent en trois parties distinctes.Dans la première partie j'étudie les mesures de Malliavin-Shavguldize sur les difféomorphismes du cercle et de l'intervalle. Il s'agit de mesures de type " Haar " pour ces groupes de dimension infinie : elles furent introduites il a une vingtaine d'années pour permettre une étude de leur théorie des représentations. Un premier chapitre est dédié à recueillir les résultats présents dans la littérature et et les représenter dans une forme plus étendue, avec un regard particulier sur les propriétés de quasi-invariance de ces mesures. Ensuite j'étudie de problèmes de nature plus dynamique : quelle est la dynamique qu'on doit s'attendre d'un difféomorphisme choisi uniformément par rapport à une mesure de Malliavin-Shavguldize ? Je démontre en particulier qu'il y a une forte présence des difféomorphismes de type Morse-Smale.La partie suivante vient de mon premier travail publié, obtenu en collaboration avec Andrés Navas. Inspirés d'un théorème récent de Avila et Kocsard sur l'unicité des distributions invariantes par un difféomorphisme lisse minimal du cercle, nous analysons le même problème en régularité faible, avec des argument plus géométriques.La dernière partie est constituée des résultats récemment obtenus avec Mikhail Khristoforov et Victor Kleptsyn. Nous abordons les problèmes reliés à la gravité quantique de Liouville en étudiant des espaces auto-similaires qui sont la limite de graphes finis. Nous démontrons qu'il est possible de trouver des distances aléatoires non-triviales sur ces espaces qui sont compatibles avec la structure auto-similaire.

Nous étudions différentes propriétés d'hyperbolicité pour les variétés intersection complète. Étant donnée une variété intersection complète lisse X ⊂ M dans une variété projective complexe lisse, nous démontrons que si k est plus grand que dim X/ codimM X et si le multidegré de X est suffisamment grand alors il existe sur X des équations différentielles de jets d'ordre k et de degré m pour m suffisamment grand. Ensuite nous étudions une conjecture de O. Debarre : si X ⊂ P^N est l'intersection d'au moins N/2 hypersurfaces génériques de degré suffisamment grand, alors le fibré cotangent de X est ample. Nous donnons différents résultats partiels en direction de cette conjecture. Nous démontrons que si X vérifie les hypothèses de la conjecture alors X est hyperbolique et le fibré cotangent de X est numériquement positif, gros, et ample en dehors d'un lieu de codimension au moins 2. Nous donnons ensuite une stratégie pour calculer explicitement des formes différentielles symétriques sur des variétés intersection complète particulières. Enfin, nous démontrons un théorème d'annulation pour la cohomologie des fibrés de différentielles de jets de Green-Griffiths, généralisant ainsi un théorème de Schneider et un théorème de Diverio. Pour finir, nous étudions la cohomologie des fibrés en droites sur l'hypersurface universelle des diviseurs dans P^1.

Made available in DSpace on 2014-06-11T19:22:54Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-04-29Bitstream added on 2014-06-13T18:08:49Z : No. of bitstreams: 1 slade_gg_me_sjrp.pdf: 1409630 bytes, checksum: 016bbc3e589fef407db769347efaba7e (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / A dinâmica do DNA apresenta movimentos de grande amplitude e localizados ao longo da cadeia que, mesmo na sua temperatura biológica, são capazes de abrir um único par de bases. Com o objetivo de compreender essa dinâmica, discutimos a formação e a estabilidade de soluções espacialmente localizadas e periódicas no tempo, breathers, no modelo de Peyrard-Bishop. O limite anticontínuo é utilizado para gerar o breather, então no início o acoplamento entre os osciladores é nulo. Depois de construir o breather, nós utilizamos a teoria de Floquet para estudar sua estabilidade. Os resultados foram analisados pelos multiplicadores de Floquet e a dinâmica energética do sistema. Teste com diferentes frequências do breather e intervalos de acoplamento foram feitos; esses parâmetros estão intimamente relacionados com a energia do sistema. / A dinâmica do DNA apresenta movimentos de grande amplitude e localizados ao longo da cadeia que, mesmo na sua temperatura biológica, são capazes de abrir um único par de bases. Com o objetivo de compreender essa dinâmica, discutimos a formação e a estabilidade de soluções espacialmente localizadas e periódicas no tempo, breathers, no modelo de Peyrard-Bishop. O limite anticontínuo é utilizado para gerar o breather, então no início o acoplamento entre os osciladores é nulo. Depois de construir o breather, nós utilizamos a teoria de Floquet para estudar sua estabilidade. Os resultados foram analisados pelos multiplicadores de Floquet e a dinâmica energética do sistema. Teste com diferentes frequências do breather e intervalos de acoplamento foram feitos; esses parâmetros estão intimamente relacionados com a energia do sistema.

Computational chemistry has gained interest as a characterization tool to predict photoluminescence, reactivity and structural properties of organic and transition metal complexes. With the rise of methods including relativity, these studies have been expanded to the accurate modeling of luminescence spectra of complexes with considerable spin-orbit splitting due to heavy metal centers as well as the reaction pathways for these complexes to produce natural products such as hydrogen gas. These advances have led to the synthesis and utility of more effective catalysis as well as the development of more effective organic light emitting diodes (OLEDs) through the incorporation of organometallic complexes as emitters instead of typical organic emitters. In terms of significant scientific advancement presented in this work is in relation to the discovery of significant spin-orbit splitting in a gold(I) alkylphosphine complex, where the splitting results in the states that emit in different colors of the visible region of the electromagnetic spectrum. This work also reveals the discovery both computationally and experimentally, of a genuine polar-covalent bond between two-closed shell metals. This work highlights a complex with an incredibly short gold(I) – copper(I) intermetallic distance leading to a vibrational frequency and dissociation energy that is on par with those of other systems with single-bonded metal centers. Lastly, this work outlines a strategy for the production of hydrogen gas through the use of trinuclear cyclic coinage metal complexes as catalysis to split hydrohalic acids.

No description available.

This thesis covers pretty much everything about the 4’th movement of “I Ching” by Per Nørgård (“IV. Towards Completion. Fire over Water”). I have delved deep into an analysis, that helped me develop my own interpretation and understanding of the piece.  While I was doing my research, I discovered fascinating links between music and mathematics, that showed me how much we don’t know and that there are interesting subjects left for us to find. My exploration did not stop there just yet, I also found out about the “I Ching”, an ancient Chinese book, that covers a broad topic, which can be summed up in two words: Yin & Yang. This, combined with a bit of mathematics contributed to the creation of a unique vocabulary that Per Nørgård pioneered, called: “infinity series”. My thesis aim is to promote Per Nørgård’s music, that has not yet been discovered by enough percussionists.

O grande desafio da Implantodontia é alcançar resultados a longo prazo com maior preservação dos tecidos ósseos, resposta adequada dos tecidos conjuntivos e manutenção da estabilidade secundária adequada para a retenção de próteses. Estes fatores evitam a perda indesejável tanto do tratamento reabilitador quanto dos tecidos ósseos de suporte. A região extraoral apresenta menores espessuras ósseas em comparação às regiões de maxila e mandíbula, especialmente no osso temporal. Portanto, os seguintes aspectos foram investigados: (i) Análise pelo Método dos Elementos Finitos (FEA) de 16 modelos virtuais, com aplicação de forças estáticas de tensão e compressão nos pontos médios entre os implantes. Três implantes maxilofaciais extraorais foram posicionados no osso temporal, onde um deles foi posicionado sobre o processo mastóide. Este estudo foi totalmente realizado em ambiente computacional. Foram empregados dois tipos de conexões protéticas e intermediários retos de conicidades 20º e 45º, posicionados virtualmente no modelo de osso temporal, com paralelismo entre eles. Foi desenhada uma barra virtual para retenção protética do tipo barra-clipe da prótese auricular. Foram consideradas as melhores configurações aquelas apresentando distribuição uniforme e branda das tensões de von Mises sobre o tecido ósseo adjacente aos implantes. (ii) Confecção de corpos de prova com graus variáveis de pigmentação para (a) melhorar a reprodutibilidade da coloração (b) entender e reduzir o processo de descoloração para melhorar a longevidade das próteses. Um elastômero maxilofacial tipo A foi pigmentado intrinsecamente de acordo com os seis tons da Escala de Fitzpatrick. Uma técnica de pigmentação foi desenvolvida a partir dos resultados obtidos a partir de uma Escala de Fitzpatrick impressa em papel e dos pigmentos intrínsecos de cores primárias. Este dimetil-metilvinil-siloxano reforçado por platina A 223-30 (Factor II, Inc., Lakeside, AZ, USA) apresenta dureza \"Shore-A\" 30. As amostras foram expostas a fotoenvelhecimento acelerado, e sua degradação mapeada com Espectroscopia UV/Vis/NIR. Concluiu-se que: (i) Os implantes com conexão cone Morse plataforma 3.7 tem melhor comportamento biomecânico com intermediários de 45o e altura de 2mm. Sugere-se planejamento cirúrgico visando a instalação a 3 horas para o temporal esquerdo e 9 horas para o temporal direito, mais 6 horas (mastóide). Implantes com conexão cone Morse plataforma 4.0 apresentaram comportamento biomecânico desejável com intermediários de 20o e alturas de 2mm or 4mm. Para implantes com conexão cone Morse plataforma 4.0, sugere-se a instalação a 6-9-12 horas para o temporal direito, e 12-6-3 para o esquerdo, visando comportamento biomecânico adequado. Sugere-se que os implantes extraorais Brånemark hexágono externo com plataforma 4.1 regular ou expandida sejam preferencialmente empregados com intermediários de 20o. (ii) O SiO2 5% pode ser adicionado à preparação do silicone para retardar o desbotamento da prótese maxilofacial. O TiO2 traz mudanças visuais significativas e pode ser considerado como opacificador. / Major challenges in Implantology include: achieving longevity of implants, bone tissue preservation, connective tissue suitable answer and maintenance of secondary stability in order to retain prosthesis. These factors avoid the undesirable loss of both rehabilitation treatment and supporting bone tissues. The extraoral region has less bone depth compared to the maxilla and mandible regions, especially for the temporal bone. Therefore, the following aspects were investigated: (i) Finite Elements Analysis (FEA) of 16 virtual models, with static application of tension and compression forces in medium points between implants. Three extraoral maxillofacial implants were placed on the temporal bone, which one of them was placed on the mastoid process. This study was made entirely in a computational environment. Two prosthetic connection types and straight Intermediários were employed, with conicities of 20º and 45º, placed virtually on the temporal bone model, mutually parallel. A virtual bar for bar-clip prosthetic retention of auricular prosthesis was designed. The best configurations were considered to be the ones presenting uniform and mild von Mises tension distribution over the bone tissue around the implants. (ii) Generation of samples with varying degree of pigmentation to (a) improve the reproducibility of the colouration (b) understand and minimise the discolouration process to improve prosthetics longevity. A maxillofacial elastomer type A was intrinsically pigmented according to the six tones of the Fitzpatrick Scale. A pigmentation technique was developed from spectroscopy outcomes of paper printed Fitzpatrick Scale and the primary colors pigments. This platinum reinforced dimethyl methylvinyl siloxane A 223-30 (Factor II, Inc., Lakeside, AZ, USA) presents \"Shore-A\" hardness 30. The samples were exposed to accelerated photo aging, and their degradation mapped with UV/Vis/NIR Spectroscopy. The effects of exclusion of oxygen and inclusion of nanoparticle fillers during prosthetic formulation were investigated. It was concluded that: (i) Morse taper prosthetic connection 3.7 platform implants, should be employed with 45o abutments with 2mm height. The surgical planning shall be for placement 3 hours for the left temporal bone and 9 hours for the right, and in 6 hours (mastoid). Morse taper prosthetic connection 4.0 platform implants behaved biomechanically desirably with 20o abutments in 2mm or 4mm heights. For the Morse taper connection 4.0 platform implants, their placement shall be in 6-9-12 hours, for the right temporal, and 12-3-6, for the left temporal, in order to achieve proper biomechanical behaviour. The Brånemark extraoral external hexagon implant, with 4.1 platform (normal or expanded) should preferrably be used with 20o abutments. (ii) The SiO2 5% may be added to the silicone preparation in order to slow maxillofacial prosthesis colour fading. The TiO2 brings visually significant changes and may be considered as an opacifier.

Ce travail propose une nouvelle approche de la description des phénomènes physiques qui interviennent dans le cadre de la modélisation de l'interaction plasma-isolant. Pour cela un code de calcul de dynamique moléculaire à été réalisé pour décrire les mécanismes fondamentaux qui régissent cette interaction à l'échelle microscopique.<br />Une étude fondamentale de la dynamique moléculaire, basée sur l'utilisation des méthodes numériques particulières comme les intégrateurs symplétiques et l'exploitation des différents potentiels d'interactions existants (Morse, Lennard-Jones...), a abouti à deux modèles de polymère : le polyéthylène ou PE (CH2)n. Le premier modèle dit simplifié consiste à considérer un groupement CH2 comme un atome fictif de masse molaire 14g, tandis que le second plus complet traite la dynamique de l'atome d'hydrogène au sein de la macromolécule. Ces deux modèles sont utilsés, dans le cadre de ce travail, pour diverses interactions.<br />Par ailleurs, des mesures expérimentales de perte de masse des matériaux polymères qui interagissent avec un plasma, créé par l'explosion d'un fil de cuivre, sont exposées. Ces résultats sont corrélés par des calculs théoriques de thermodynamique qui montrent une différence de comportement des deux polymères testés : le polyéthylène et le polyoxyméthylène, POM ou Delrin (CH2O)n.