[pt] As técnicas de agrupamentos aplicadas a um grande número de cenários de incerteza permitem a escolha de um conjunto reduzido, porém, representativo da população de cenários completa. Em outras palavras, selecionar uma amostra que contenha uma quantidade menor de elementos a ponto de reduzir suficientemente o volume total de dados e obter ganhos significativos de eficiência no processamento dos dados. Esta amostra deve, sobretudo, conseguir preservar as características do processo estocástico que o originou. Com este intuito, o presente trabalho propõe uma metodologia de seleção de cenários estocásticos utilizando o modelo clássico de Cobertura de Conjuntos, inspirada no método forward selection proposto por Heitsch e Romisch (2003). Aplicada na etapa de cálculo de demanda estocástica de ferramentas e serviços para construção de poços marítimos de exploração de petróleo, esta abordagem apresenta uma concepção de cenário diferente da usada pelos autores. O conjunto de cenários consiste em cronogramas de atividades gerados a partir da introdução de incertezas no planejamento de cada atividade, sendo eles estáticos, independentes e com múltiplos atributos. Uma análise de sensibilidade compara os resultados das demandas calculadas com os cenários selecionados pelo Problema de Cobertura de Conjuntos (PCC) e a demanda calculada com o conjunto universo de cenários. O PCC foi solucionado, nesta aplicação, em sua versão clássica da literatura a partir de um algoritmo exato e um heurístico. Os resultados apontam diferenças pouco representativas no resultado final das demandas calculadas com cenários reduzidos e com o total de cenários. A heurística, ainda que seja first solution, apresentou um resultado satisfatório em relação ao ganho de desempenho versus confiabilidade, e indica o potencial do método se aplicado em conjunto com algoritmos de metaheurística e busca local. / [en] Clustering techniques applied to a large number of scenarios under uncertainty allows the selection of a reduced, however, representative set of the complete set of scenarios. In other words, it allows to select a sample that contains a smaller amount of elements to the point of sufficiently reducing the total data volume and obtaining efficiency gains in data processing. The challenge is that the sample must, above all, be able to preserve the characteristics of the stochastic process that originated it. To this end, this study proposes a methodology for selecting stochastic scenarios using the classic Set Covering model, inspired by the forward selection method proposed by Heitsch and Romisch (2003). Applied in the calculating of stochastic demand for tools and services for the construction of offshore oil exploration wells, this approach presents a different scenario conception from the one used by the authors. The set of scenarios consists of activity schedules generated from the introduction of uncertainties in the planning of each activity, which are static, independent and with multiple attributes. A sensitivity analysis compares the results of the demands calculated with the scenarios selected by the Set Covering Problem (SCP) and the demand calculated with all the universe of scenarios. The SCP was solved, in this application, in its classic version using an exact algorithm and a heuristic algorithm. The results appoint na unexpressive loss in the final result of the demand calculated with reduced scenarios and with the complete set of scenarios. The simple first solution heuristic presented a satisfactory result in relation to the performance gain versus reliability, and indicates the potential of the method if solved with metaheuristic and local search algorithms.

La conjecture du coureur solitaire est un problème formulé indépendamment par J.M. Wills en (1972) et par Thomas Cusick (1973). Soit ∥·∥ la distance avec les entiers ∥x∥ = mink∈Z(|x − k|) pour pour x ∈ R. La conjecture nous demande si pour un ensemble de n + 1 réels {v1,v2 . . . vn+1} distincts il existe pour tout k ∈ {1,2,3, . . . ,n,n + 1} un temps t ∈ R tel que pour toute autre vitesse vi,i ̸= k on a ∥t(vi − vk)∥ ≥ 1 n+1 . La conjecture a été montrée pour n + 1 ≤ 7, le cas n + 1 = 7 montré en 2007 par Barajas et Serra. Plusieurs auteurs ont écrit à propos de ce sujet. Dans ce mémoire, il sera question d’exposer les différentes techniques qui ont été utilisées pour les cas n + 1 ≤ 7, certains scénarios dans lesquels la conjecture tient ainsi que les efforts pour trouver des meilleures bornes inférieures pour l’écart de solitude. / The lonely runner conjecture was formulated by J.M. Wills en (1972) and Thomas Cusick (1973). If ∥·∥ denotes the distance from integers, for x ∈ R ∥x∥ = mink∈Z(|x − k|), this conjecture is asking whether or not for any set of n + 1 distinct real numbers {v1,v2 . . . vn+1} and for any k ∈ {1,2,3 . . . ,n + 1} there is a time t ∈ R such that for any other speed vi,i ̸= k we have ∥t(vi − vk)∥ ≥ 1 n+1 . It has been proven to be true for n + 1 ≤ 7 , the last case n + 1 = 7 was shown by Barajas and Serra in 2007. Many authors have wrote about this subject each bringing more knowledge. In this thesis, there will be an exposure on different techniques that have been used to prove the cases for n + 1 ≤ 7, differents cases in wich the conjecture holds and the problem of getting better lower bounds for the gap of loneliness.

No description available.

No description available.

Durant cette thèse, nous avons introduit les problèmes de Bin Covering avec Contrainte de Distance (BCCD) et de Bin Packing avec Contrainte de Distance (BPCD), qui trouvent leur application dans les réseaux de grande échelle, tel Internet. L'étude de ces problèmes que nous effectuons dans des espaces métriques quelconques montre qu'il est impossible de travailler dans un tel cadre sans avoir recours à de l'augmentation de ressources, un procédé qui permet d'élaborer des algorithmes construisant des solutions moins contraintes que la solution optimale à laquelle elles sont comparées. En plus de résultats d'approximation intéressants, nous prouvons la difficulté de ces problèmes si ce procédé n'est pas utilisé. Par ailleurs, de nombreux outils ont pour objectif de plonger les grands réseaux qui nous intéressent dans des espaces métriques bien décrits. Nous avons alors étudié nos problèmes dans les espaces métriques générés par certains de ces outils, comme Vivaldi et Sequoia.

Dans ce mémoire, on étudie les extensions galoisiennes finies de C(x). On y démontre le théorème d'existence de Riemann. Les notions de rigidité faible, rigidité et rationalité y sont développées. On y obtient le critère de rigidité qui permet de réaliser certains groupes comme groupes de Galois sur Q. Plusieurs exemples de types de ramification sont construis. / In this master thesis we study finite Galois extensions of C(x). We prove Riemann existence theorem. The notions of rigidity, weak rigidity, and rationality are developed. We obtain the rigidity criterion which enable us to realise some groups as Galois groups over Q. Many examples of ramification types are constructed.

<p>Mogućnost primene polivinilhloridnih (PVC) podnih obloga je određena krajnjim svojstvima koja zavise od sastava obloge i načina proizvodnje. Zbog složenog sastava i različitih načina pripreme PVC podnih obloga, veoma je te&scaron;ko tačno proceniti uticaj pojedinačnog procesnog parametara na svojstva dobijenog proizvoda. U ovom radu, da bi se ispitao uticaj sastava polivinilhloridnih sme&scaron;a na svojstva PVC podnih obloga pripremljeno je 27 receptura u kojima su varirane: koncentracije kalcijumkarbonata (40, 70 i 100 phr), koncentracije sredstva za ekspanziju, azodikarbonamida ADC (0,8, 1,0 i 1,2 mas. % u odnosu na ukupnu masu) kao i odnos &bdquo;kikeraˮ i sredstva za ekspanziju, ZnO/ADC (0,33; 0,50 i 0,67). Da bi se proučio uticaj procesnih parametara na svojstva PVC podnih obloga menjani su tehnolo&scaron;ki uslovi proizvodnje: temperatura (180, 184, 188, 192 i 196 &deg;C) i vreme (90, 120 i 150 sekundi) ekspanzije poleđinskog sloja PVC podne obloge. Na taj način je od svake PVC paste dobijeno 15 uzoraka. Za svaki uzorak određena su sledeća svojstva: stepen ekspanzije, zatezna sila pri kidanju, prekidna sila kidanja, zatezno i prekidno izduženje, početni otpor cepanju, otpor cepanju, ukupna deformacija, zaostala deformacija, povratna elastičnost, gustina pene i indeks žućenja. S obzirom na ovako veliki broj podataka urađena je statistička obrada dobijenih eksperimentalnih podataka metodom vi&scaron;estruke linearne regresione analize, kako bi procenili uticaji pojedinačnih procesnih parametara na ispitivana svojstva. Napisan je originalni programski kod primenom Garson-ovog i Yoon-ovog modela u programu Matlab koji omogućava formiranje neuronske mreže i njenu upotrebu u cilju fitovanja eksperimentalnih podataka. Rezultati dobijeni primenom modela po Garson-u nisu pogodni za određivanje uticaja sastava PVC sme&scaron;e i uslova prerade na konačna svojstva proizvoda, jer ne pokazuju pravac uticaja. Dok je ve&scaron;tačka neuronska mreža koja se zasniva na Yoon-ovom modelu uspe&scaron;no primenjena u razvoju novih i pobolj&scaron;anju postojećih svojstava heterogenih PVC proizvoda. Ispitan je i uticaj veličine čestice ZnO koji je upotrebljen kao &bdquo;kikerˮ (sredstvo koje utiče na smanjenje temperature raspada ADC) na svojstva penastih podnih obloga. Napravljene su dve PVC paste, jedna sa komercijalnim ZnO, a druga sa nano ZnO, pri čemu je sastav ostalih komponenti bio identičan. Na osnovu dobijenih eksperimentalnih podatka može se zaključiti da kod uzoraka u kojima je upotrebljen nano ZnO dolazi do intenzivnijeg &bdquo;curenjaˮ gasa nastalog raspadom ADC i međusobnog povezivanja pora. Kao posledica ovakve strukture pora uzorci sa nano ZnO imaju lo&scaron;ija mehanička svojstva. Na osnovu dobijenih karakterističnih temperatura na TG krivama nije uočen uticaj veličine čestica ZnO na termičku stabilnost ispitivanih uzoraka.</p> / <p>The application of PVC floor coverings is strongly connected with their end-use properties which depend on the composition and processing conditions. It is very difficult to estimate the proper influence of production parameters on the characteristics of PVC floor coverings due to their complex composition and various preparation procedures. In this paper, in order to investigate the effect of the PVC mixture composition on the properties of PVC floor coverings, 27 formulations are prepared varying concentration of calcium carbonate (40, 70 and 100 phr), concentration of blowing agent, azodicarbonamide ADC (0.8, 1.0 and 1.2 wt. % relative to the total weight) and the ratio of &quot;kicker&quot; and blowing agent, ZnO/ADC (0.33; 0.50 and 0.67). To study the influence of process parameters on the properties of PVC floor coverings technological production conditions are varied: expansion temperature (180, 184, 188, 192 and 196 &deg;C) and expansion time (90, 120 and 150 seconds) of the PVC floor covering back layer. In this way, 15 samples are made of each PVC paste. The following properties are determined for each sample: expansion ratio, tensile strength, braking strength, tensile extension, breaking extension, initial resistance to tearing, tearing resistance, identation, residual identation, elasticity, density foam and yellowing index. Having such a large amount of data, statistical analysis of experimental data are made with multiple linear regression analysis in order to assess the effects of process parameters on investigated properties. The original program code is written using the Garson&#39;s and Yoon&#39;s models in the Matlab programme that allows the formation of neural networks and its use for the purpose of fitting the experimental data. Results obtained by using the Garson model are not suitable for determining the influence of composition of the PVC mixture and processing conditions on the properties of the final product because it does not show the direction of impact. While the artificial neural network based on Yoon&#39;s model is successfully applied to the development of new as well as to the improvement of the existing properties of the heterogeneous PVC products. The influence of ZnO particle size, used as a&ldquo;kicker&ldquo; (this material reduces the decomposition temperature of ADC) is examined on the properties of the foam flooring. Two PVC pastes are made, one with commercial ZnO and the other with nano ZnO, with the other components of the compositions identical. Based on the obtained experimental data, it can be concluded that there is more intensive gas &bdquo;leak&ldquo; resulting from disintegration of the ADC and also more intensive interconnection of pores in the samples where nano ZnO is used. As a result of this structure of pores, samples with nano ZnO have inferior mechanical properties. Based on the characteristic temperature obtained on TG curves, the influence of ZnO particle size on the thermal stability of the investigated samples is not observed.</p>

We define a general notion of closure scheme to systematically study the classes of Fréchet, sequetial, (pseudo)radial, (weakly) (discretely) Whyburn, and (weakly) discretely generated spaces. First, several general propositions on closure schemes and preservation of induced properties under topological constructions are proved and later applied when we systematically summarize the properties of the classes mentioned above. Next, we focus on a detailed overview of inclusions between the classes in the general case, in the case of Hausdorff spaces, and under additional conditions like compactness and countable compactness. Valid inclusions between the classes are summarized in well arranged diagrams, invalid inclusions are demonstrated by several counterexamples.

Nous étudions les triangulations dans des espaces de courbure négative constante, en théorie et en pratique. Ce travail est motivé par des applications dans des domaines variés. Nous considérons les complexes de Delaunay et les diagrammes de Voronoï dans la boule de Poincaré, modèle conforme de l'espace hyperbolique, en dimension quelconque. Nous utilisons l'espace des sphères pour la description des algorithmes. Nous étudions aussi les questions algébriques et arithmétiques et observons que les calculs effectués sont rationnels. Les démonstrations sont basées sur des raisonnements géométriques et n'utilisent aucune formulation analytique de la distance hyperbolique. Nous présentons une implantation complète, exacte et efficace en dimension deux. Le code est développé en vue d'une intégration dans la bibliothèque CGAL, qui permettra une diffusion à un large public. Nous étudions ensuite les triangulations de Delaunay des surfaces hyperboliques fermées. Nous définissons une triangulation comme un complexe simplicial afin de permettre l'adaptation de l'algorithme incrémentiel connu pour le cas euclidien. Le cœur de l'approche consiste à montrer l'existence d'un revêtement fini dans lequel les fibres définissent toujours une triangulation de Delaunay. Nous montrons une condition suffisante sur la longueur des boucles non contractiles du revêtement. Dans le cas particulier de la surface de Bolza, nous proposons une méthode pour construire un tel revêtement, en étudiant les sous groupes distingués du groupe fuchsien définissant la surface. Nous considérons des aspects liés à l'implantation. / We study triangulations of spaces of constant negative curvature -1 from both theoretical and practical points of view. This is originally motivated by applications in various fields such as geometry processing and neuro mathematics. We first consider Delaunay complexes and Voronoi diagrams in the Poincaré ball, a conformal model of the hyperbolic space, in any dimension. We use the framework of the space of spheres to give a detailed description of algorithms. We also study algebraic and arithmetic issues, observing that only rational computations are needed. All proofs are based on geometric reasoning, they do not resort to any use of the analytic formula of the hyperbolic distance. We present a complete, exact, and efficient implementation of the Delaunay complex and Voronoi diagram in the 2D hyperbolic space. The implementation is developed for future integration into the CGAL library to make it available to a broad public. Then we study the problem of computing Delaunay triangulations of closed hyperbolic surfaces. We define a triangulation as a simplicial complex, so that the general incremental algorithm for Euclidean Delaunay triangulations can be adapted. The key idea of the approach is to show the existence of a finite-sheeted covering space for which the fibers always define a Delaunay triangulation. We prove a sufficient condition on the length of the shortest non-contractible loops of the covering space. For the specific case of the Bolza surface, we propose a method to actually construct such a covering space, by studying normal subgroups of the Fuchsian group defining the surface. Implementation aspects are considered.

[pt] A presente tese trata de técnicas de baixo custo econômico, acessíveis à população e adequadas ao emprego de materiais que possam ser utilizados em seu estado natural, com pouco beneficiamento. O bambu, a terra crua e as fibras e resinas vegetais, são basicamente os materiais utilizados. Primeiramente foram realizados e testados objetos experimentais para funcionar como elementos de vedações, de cobertura, de sobrecobertura, de proteção externa – brise-soleil e arcos estruturais. Em seguida descreve o aperfeiçoamento de processos de encapsulamento do bambu em desenvolvimento no Laboratório de Investigação Livre Desenho da PUC-Rio. Dando continuidade ao trabalho sobre essas técnicas construtivas, a partir da manipulação de uma determinada bolha de sabão, foi elaborada uma série de modelos experimentais mecânicos e virtuais para uma sala multiuso de 7,70m x 6,00m de base, com altura de 3,20m, feita de fitas de bambu, mantas de barro cru, fibras e resinas vegetais. Na geometria destes modelos, paredes e cobertura se fundem em uma superfície contínua, com duas camadas superpostas, espaçadas e interligadas, formando uma casca que se apoia em toda a extensão do seu perímetro. A seguir, foi feita uma construção em escala real em que fitas de bambu descreviam a geometria base da bolha para testarmos de maneira não instrumentalizada possibilidades de montagem e desmontagem e os índices de resistência devidos ao particular formato da bolha. Finalmente, baseado neste último experimento, são apresentadas soluções gerais inovadoras para o conforto higrotérmico em climas tropicais úmidos que substituem a estratégia da inércia térmica dos materiais espessos e pesados pela leveza de uma dupla casca estrutural que abriga câmaras de ar ventiladas em seu interior. / [en] This thesis studies low cost building techniques that are accessible to a wide range of population groups and are suitable for the use of materials in their natural state with little or no processing. The materials used are basically bamboo, raw earth and vegetable fibers and resins. First a series of tests were carried out with experimental objects to assess suitability for use as sealants, covering, outer covering and external protection – brise –soleil panels and structural arches. Following this, we describe the perfecting of the bamboo coating process in progress the Free Design Laboratory of Rio’s Catholic University. Building on these construction techniques, inspired by the manipulation of a soap bubble a series of experimental mechanical and virtual models were elaborated for a multi-use space measuring 7.7m by 6m at the base with a height of 3.2m, made of bamboo tapes, with a raw earth, fiber and resin covering. In the geometry of these models the walls and covering are a continuous surface with two layers one on another, separated but interconnected. In this way the outer wall is formed which extends over and is supported by the entire perimeter of the structure. The following step was to make a full scale construction in which bamboo tapes were used to form the geometric shape of the base of the bubble in order to do practical tests of the possibilities of assembly and disassembly of such a structure. Tests were also done on the resistance factors afforded by the singular bubble format. Finally, based on the previous experiment we present innovative solutions to the problem of hygrothermic comfort in humid tropical climates which substitute the thermal inertia strategy of thick, heavy building materials with the lightness of a double outer layer that holds ventilated air chambers between these layers.