<p>On the category of representations of a given quiver we define a tensor product point-wise and arrow-wise. The corresponding Clebsch-Gordan problem of how the tensor product of indecomposable representations decomposes into a direct sum of indecomposable representations is the topic of this thesis.</p><p>The choice of tensor product is motivated by an investigation of possible ways to modify the classical tensor product from group representation theory to the case of quiver representations. It turns out that all of them yield tensor products which essentially are the same as the point-wise tensor product.</p><p>We solve the Clebsch-Gordan problem for all Dynkin quivers of type A, D and E₆, and provide explicit descriptions of their respective representation rings. Furthermore, we investigate how the tensor product interacts with Galois coverings. The results obtained are used to solve the Clebsch-Gordan problem for all extended Dynkin quivers of type Ã_n and the double loop quiver with relations βα=αβ=αⁿ=βⁿ=0.</p>

V této práci se zabýváme r·znými pokrývacími větami a jejich ap- likacemi. Kromě klasických pokrývacích vět (Vitaliova, Besicovitchova a Whitney- ova věta) zde uvádíme i některá jejich zobecnění a další pokrývací věty. Tyto věty pak používáme v d·kazech dalších vět, některé jsou typickými aplikacemi pokrý- vacích vět jako například Lebesgueova věta o derivování, slabý typ (1,1) maximál- ního operátoru nebo Calderónovo-Zygmundovo lemma, v jejichž d·kazech hrají pokrývací věty klíčovou roli. Dále se zabýváme nerovnostmi mezi operátory, po- mocí pokrývacích vět dokazujeme vztahy mezi Hardyovým-Littlewoodovým max- imálním operátorem, maximálním singulárním integrálním operátorem a ostrým maximálním operátorem. 1

O problema de empacotamento em faixas de peças irregulares consiste em cortar um conjunto de peças bidimensionais a partir de um objeto de largura fixa utilizando o menor comprimento possível. Apesar de sua importância econômica para diversos setores industriais, há poucos trabalhos que abordam o problema de forma exata devido a sua dificuldade de resolução. Recentemente, Toledo et al. (2013) propuseram um modelo inteiro misto para este problema, no qual as peças são posicionadas em uma malha de pontos. Este modelo obteve bons resultados, provando a otimalidade para instâncias com até 21 peças. No entanto, o modelo possui um grande número de restrições de não-sobreposição, que cresce rapidamente de acordo com a discretização utilizada e a quantidade de peças distintas que devem ser alocadas. Neste trabalho, são propostas novas formulações matemáticas baseadas neste modelo, com o objetivo de reduzir o número de restrições. Na primeira abordagem, são propostos dois modelos reduzidos que mostraram ser eficientes para instâncias com poucas repetições de peças. Na segunda abordagem, foi proposto um modelo de cobertura por cliques para o problema. Este modelo obteve desempenho igual ou superior ao modelo da literatura para todas as instâncias avaliadas, obtendo uma solução ótima para instâncias com até 28 peças. / The irregular strip packing problem consists of cutting a set of two-dimensional pieces from an object of fixed width using the smallest possible length. Despite its economic importance for many industrial sectors, few exact studies have been made on this problem due to its difficulty of resolution. Recently, Toledo et al. (2013) proposed a mixed-integer model to this problem in which the pieces are placed on a grid. This model has worked successfully proving the optimality for instances up to 21 pieces. However, the model has a large number of non-overlapping constraints, which grows quickly in accordance with the discretization resolution and number of distinct pieces. In this work, we propose new mathematical formulations based on this model in order to reduce the number of constraints. In the first approach, we present two reduced models that have shown to be effective for instances with few repetitions of pieces. In the second approach, it was proposed a clique covering model for the problem. This model achieved a greater or equal performance than the literature for all instances, getting an optimal solution for instances up to 28 pieces.

Dans cette thèse nous considérons deux problèmes d'optimisation combinatoire.Le premier s'appelle problème du double voyageur de commerce avec contraintes de piles. Dans ce problème, un véhicule doit ramasser un certain nombre d'objets dans une région pour les livrer à des clients situés dans une autre région. Lors du ramassage, les objets sont stockés dans les différentes piles du véhicule et la livraison des objets se fait selon une politique de type last-in-first-out. Le ramassage et la livraison consistent chacune en une tournée Hamiltonienne effectuée par le véhicule dans la région correspondante.Nous donnons une formulation linéaire en nombres entiers pour ce problème. Elle est basée sur des variables de précédence et sur des contraintes de chemins infaisables. Nous donnons par la suite des résultats polyédraux sur l'enveloppe convexe des solutions de notre formulation. En particulier, nous montrons des liens forts avec un polytope associé au problème du voyageur de commerce et des liens avec un polytope de type set covering. Cette étude polyédrale nous permet de renforcer la formulation initiale et de développer un algorithme de coupes et branchements efficace. Le deuxième problème que nous considérons consiste à trouver la description des polytopes lexicographiques. Ces derniers sont les enveloppes convexes des points entiers lexicographiquement compris entre deux points entiers fixés. Nous donnons une description complète de ces polytopes en termes d'inégalités linéaires. Nous démontrons que la famille des polytopes lexicographiques est fermée par intersection. / In this thesis we consider two problems arising in combinatorial optimization.The first one is the double traveling salesman problem with multiple stacks. In this problem a vehicle picks up a given set of items in a region and subsequently delivers them to demanding customers in another region. When an item is picked up, it is put in a stack of the vehicle. The items are delivered observing a last-in-first-out policy. The pickup phase and the delivery phase consist in two Hamiltonian circuits, each performed by the vehicle in the corresponding region. We give a new integer linear programming formulation for this problem. Its main features are the presence of precedence variables and new infeasible path constraints. We provide polyhedral results on the convex hull of the solutions to our formulation. In particular, we show strong links with a specific TSPpolytope and a specific set covering polytope. We deduce strengthening inequalities for the initial formulation, subsequently embedded in an efficient branch-and-cut algorithm. The second problem we consider consists in finding the description of the lexicographical polytopes. These are convex hulls of the integer points lexicographically between two given integer points. We give a complete description of these polytopes by means of linear inequalities. We show that the lexicographical polytope family is closed under intersection.

Este trabalho é focado num problema clássico das Ciências e Engenharia, que consiste em cobrir um objeto por esferas de mesmo raio, a ser minimizado. A abordagem prática usual conta com sérias desvantagens. Logo, faz-se necessário trabalhar com isto de forma diferenciada. A técnica proposta aqui envolve a utilização de resultados célebres da geometria algébrica real, que tem como peça central o positivstellensatz de Stengle e, fazendo a devida relação entre esses resultados e otimização com restrições envolvendo representações naturais por somas de quadrados, é possível reduzir o problema original a um de programação semidefinida não linear. Mas, por contar com particularidades que favorecem a aplicação do paradigma de restauração inexata, esta foi a técnica utilizada para resolvê-lo. A versatilidade da técnica e a possibilidade de generalização direta dos objetos envolvidos destacam-se como grandes vantagens desta abordagem, além da visão algébrica inovadora do problema. / This work is focused on a classic problem from Engineering. Basically, it consists of finding the optimal positioning and radius of a set of equal spheres in order to cover a given object. The common approach to this carries some substantial disadvantages, what makes it necessary to nd a dierent way. Here, we explore some renowned results from real algebraic geometry, which has Stengle\'s positivstellensatz as one of its central pieces, and SOS optimization. Once the proper link is made, the original problem can be reduced to a nonlinear semidenite programming one, which has peculiarities that favours the application of an inexact restoration paradigm. We point out the algebraic view and the no use of discretizations as great advantages of this approach, besides the notable versatility and easy generalization in terms of dimension and involved objects.

As regiões do Cerrado brasileiro são caracterizadas por temperaturas altas e ocorrência de chuvas em grande intensidade no verão, porém com inverno seco. Essas condições resultam em maiores limitações para a sustentabilidade do plantio direto, devido à baixa produção de palha no período de outono-primavera, aliada a rápida decomposição durante a estação das chuvas. Uma das formas para tentar solucionar estes problemas é pelo cultivo consorciado de culturas produtoras de grãos com espécies forrageiras, o qual tem apresentado resultados promissores, dando sustentabilidade ao plantio direto, podendo fornecer forragem para os animais no período de maior escassez nas regiões caracterizadas com inverno seco. Entretanto, esta tecnologia é recente havendo necessidade de estudos nas várias áreas abrangidas por esse sistema de produção. Nesse sentido, o objetivo do capítulo I foi avaliar a produção de palha e o desempenho agronômico de soja consorciada com diferentes espécies forrageiras sobressemeadas, em plantio direto. O delineamento utilizado foi em blocos completos casualizados com quatro repetições em esquema fatorial 5 x 2 + 2 , sendo cinco espécies forrageiras consorciadas com soja (Urochloa brizantha cv. Marandu; Urochloa ruziziensis; Panicum maximum cv. Mombaça; Panicum infestans cv. Massai e; Pennisetum americanum), em duas safras agrícolas (2013/2014 e 2014/2015), mais dois tratamentos testemunhas (Pennisetum americanum em sucessão ao cultivo da soja e pelo cultivo tradicional de soja, seguido de pousio no inverno). Foram avaliados os componentes de rendimento da soja e a produtividade de palha das forrageiras. O consórcio da soja com as espécies forrageiras Urochloa ruziziensis, U. brizantha cv. Marandu, Panicum maximum cv. Mombaça e P. infestans cv. Massai em sobressemeadura não diminui a produtividade de grãos da soja. O consórcio soja x mombaça aumenta a estatura das plantas e produtividade de grãos da soja quando comparada a soja solteira. O P. maximum cv. Mombaça é mais eficiente no acúmulo de matéria seca quando cultivado em sobressemeadura na soja no período de outono/primavera em relação às demais forrageiras. O capítulo II teve como objetivo avaliar a produção de forragem e a composição bromatológica de diferentes espécies forrageiras consorciadas com a soja e em cultivo solteiro. O delineamento utilizado foi em blocos completos casualizados com quatro repetições em esquema fatorial 5 x 2 + 1, sendo cinco espécies forrageiras (Urochloa brizantha cv. Marandu; Urochloa ruziziensis; Panicum maximum cv. Mombaça; Panicum infestans cv. Massai e Pennisetum americanum), em dois sistemas de cultivo (consorciado com a soja e solteiro), mais um tratamento padrão (Pennisetum americanum em sucessão ao cultivo da soja). Foram avaliados componentes de produtividade de forragem e a composição bromatológica das espécies forrageiras. As espécies Urochloa ruziziensis, U. brizantha, Panicum maximum e P. infestans apresentam maior capacidade produtiva de forragem, tanto cultivadas em consórcio com a soja quanto solteiras em relação ao Pennisetum americanum. O cultivo das forrageiras Urochloa ruziziensis, U. brizantha, Panicum maximum e Pennisetum americanum de forma solteira, proporciona maiores produtividades de forragens em relação ao cultivo consorciado com a soja. As forrageiras Urochloa ruziziensis e U. brizantha quando semeadas em cultivo consorciado, revela melhor valor nutritivo com o decorrer do período de outono-inverno. / The regions Brazilian Cerrado are characterized by high temperatures and rainfall in great intensity in the summer, but with dry winter. These conditions result in major constraints for the sustainability of tillage due to low straw production in the autumn-spring period, combined with rapid decomposition during the rainy season. One way to try to solve these problems is for the intercropping of grain crops with forage species, which has shown promising results, giving sustainability to tillage and can provide fodder for livestock in most lean period in areas characterized with winter dry. However, this technology is new and there is need for studies in the various areas covered by the production system. As such, the objective of chapter I was to evaluate the straw production and the agronomic performance of soybean intercropped with different forage species oversowing, in direct planting. The experiment was in a complete randomized block, with four replications in a factorial arrangement 5 x 2 + 2, being five species forage intercropped with soybean (Urochloa brizantha cv. Marandu; Urochloa ruziziensis; Panicum maximum cv. Mombaça; Panicum infestans cv. Massai and; Pennisetum americanum), in two growing seasons (2013/2014 e 2014/2015), more two treatments witnesses (Pennisetum americanum in succession to soybean cultivation and the traditional soybean cultivation, followed by fallow in winter). Were assessed the soybean yield components and straw productivity of forage. The soybean intercropped with forage species Urochloa ruziziensis, U. brizantha cv. Marandu, Panicum maximum cv. Mombaça and P. infestans cv. Massai in oversowing does not reduce the soybean grain yield. The soybean x Mombasa intercropped increases plant height and soybean grain yield when compared to single soybeans. The Mombasa is more efficient in dry matter accumulation when grown in oversowing in soybeans in autumn/spring compared to other forages. The chapter II to aimed was to evaluate forage production and bromatologic composition of different forage species intercropping with soybean in oversowing system and single crop. The experiment was in a complete randomized block, with four replications in a factorial arrangement 5 x 2 + 1, being five species forage (Urochloa brizantha cv. Marandu; Urochloa ruziziensis; Panicum maximum cv. Mombaça; Panicum infestans cv. Massai e; Pennisetum americanum), in two crop systems (intercropped with soybean and single), more a standard treatment (Pennisetum americanum in succession to soybean cultivation). Were evaluated forage yield components and the chemical composition of the forage species. The species Urochloa ruziziensis, U. brizantha, Panicum maximum and P. infestans have higher production capacity de forage both grown intercropped with soybeans as compared to single Pennisetum americanum. The cultivation of the forages Urochloa ruziziensis, U. brizantha, Panicum maximum and Pennisetum americanum way single, provides higher productivity of forages compared to intercropping with soybean. The forages Urochloa ruziziensis and U. brizantha when sown in intercropping, reveals better nutritional value over the course of the autumn-winter period.

O revestimento de argamassa de fachada é utilizado em praticamente todos os edifícios residenciais;assim, sua importância é caracterizada tanto pelo uso intenso, quanto por desempenhar importantes funções estéticas e de proteção do edifício, além de representar importante parcela do custo direto de construção e de manutenção das fachadas. O presente trabalho busca caracterizar, analisar e propor melhorias ao processo de produção dos revestimentos de argamassa de fachada de edifícios, particularmente quanto às etapas de projeto, execução e controle, através de levantamentos realizados em quatro obras de importantes empresas de construção na cidade de Santos. A metodologia utilizada consistiu em revisão bibliográfica, e posterior aplicação dos conceitos levantados nos estudos de caso. Com base neste estudo, foi possível identificar as condições locais de produção e os principais problemas enfrentados ao longo do processo, tendo sido possível à elaboração de sugestões de melhoria ao processo analisado. Além disso, espera-se que se possa contribuir também para a disseminação de ações de racionalização do processo de produção dos revestimentos de argamassa de fachada de edifícios; e, por conseqüência, contribuir para diminuir os problemas patológicos e os custos de produção das empresas construtoras. / The façade mortar covering is used in practically all residential buildings; thus, its importance is characterized by its intense use and also for playing important esthetic functions in building protection. Besides the fact, that it represents an important parcel of the direct cost of construction and façade\'s maintenance. The present work searches to characterize, analyze and consider improvements in the process of production of mortar covering, particularly related to each stage of the project, execution and control by surveys carried through four construction sites of important construction companies in the city of Santos. The methodology used consisted of bibliographical revision, and posterior application of the concepts researched in the case studies. Based on this study, it was possible to identify local conditions of production and the main problems faced throughout the process, having been possible to elaborate suggestions of improvement to the analyzed process. Moreover, it is expected that it can also contribute to the dissemination of façade\'s production management. Consequently, contributing to diminish the pathological problems and lowering the cost of production for contractors.

Este trabalho é focado num problema clássico das Ciências e Engenharia, que consiste em cobrir um objeto por esferas de mesmo raio, a ser minimizado. A abordagem prática usual conta com sérias desvantagens. Logo, faz-se necessário trabalhar com isto de forma diferenciada. A técnica proposta aqui envolve a utilização de resultados célebres da geometria algébrica real, que tem como peça central o positivstellensatz de Stengle e, fazendo a devida relação entre esses resultados e otimização com restrições envolvendo representações naturais por somas de quadrados, é possível reduzir o problema original a um de programação semidefinida não linear. Mas, por contar com particularidades que favorecem a aplicação do paradigma de restauração inexata, esta foi a técnica utilizada para resolvê-lo. A versatilidade da técnica e a possibilidade de generalização direta dos objetos envolvidos destacam-se como grandes vantagens desta abordagem, além da visão algébrica inovadora do problema. / This work is focused on a classic problem from Engineering. Basically, it consists of finding the optimal positioning and radius of a set of equal spheres in order to cover a given object. The common approach to this carries some substantial disadvantages, what makes it necessary to nd a dierent way. Here, we explore some renowned results from real algebraic geometry, which has Stengle\'s positivstellensatz as one of its central pieces, and SOS optimization. Once the proper link is made, the original problem can be reduced to a nonlinear semidenite programming one, which has peculiarities that favours the application of an inexact restoration paradigm. We point out the algebraic view and the no use of discretizations as great advantages of this approach, besides the notable versatility and easy generalization in terms of dimension and involved objects.

Significant advances have been made in the research and development of electric vehicles (EV’s). Along with the major challenge of energy storage, being also addressed is the efficient design of system energy transfer and consumption. This has had the effect of fundamentally changing perspectives across the mobility and transportation sector. Applied predominantly to road-going vehicles, the industrial context of non-road Electric Vehicles (nrEV’s) and specifically the use of manned electric forklift trucks integrated within the production related materials handling system has, to-date, received far less attention. The overarching aim of this research is to examine the impact and potential for the use of contactless occasional recharging of nrEV’s integrated within a manufacturing line, recognising the need to balance the (sometimes competing) demands of delivering sustainable production while exercising environmental responsibility. Meeting the objectives of this research resulted in the development of a location allocation model for electric charging station determination based on a fundamental understanding of the nature and quality of process inherent key performance indicators (KPI’s) as well as comprehensive process and energy monitoring while considering both Lean and Green Management perspectives. The integration of the generated knowledge and information into a generally valid simulation tool for occasional charging system implementation allows to more thoroughly investigate the impact from occasional charging to overall efficiency and sustainability to be realised. An investigation into relevant literature identified the need for specifically generated energy consumption data and confirmed the need for an energy optimisation model specific to the area of production related materials handling. Empirical data collected from repeated standardised materials handling operations within a selected production related materials handling environment resulted in the development of the Standard Energy Consumption Activity tool (SECA). Further work within this pilot study confirmed the tool as capable of generating reliable and valid data and confirmed the SECA tool as a generally applicable benchmark for energy consumption determination in material handling based on fractional process functions. Integrating this approach into a comprehensive process analysis and charging infrastructure optimisation resulted in the development of an Excel-based simulation model. The (Occasional Charging Station Location Model) OCSLM is based upon Maximal Covering Location Modelling and an endogenous covering distance definition in order to simulate process related potentials and optimal charging system implementation allocations, the target being to increase vehicles usable battery energy. A comprehensive case study based upon six individual and one combined data set confirmed the general and wider applicability of the OCSLM model while the application of the model provides a set of novel results. The application demonstrated a theoretical increase in usable battery energy of between 40% and 60% and within the same case study the impact of technology implementation identified that a reduction in battery and system cost of between 5% and 45% can be realised. However, the use of contactless power transfer resulted in an increase in CO2 emissions of up to 6.89% revealing a negative impact to overall ecology from the use of this energy transfer system. Depending on the availability of fast connecting, contact based energy transmission systems, the approach and results of OCSLM have shown to be directly applicable to contact based systems with resulting CO2 emissions decreasing by 0.94% at an energy transfer efficiency of 96%. Further novelty, of benefit to both academic and industry practice, was realised through the framework and information of the research with the provision of SECA as a process function-based and generally applicable energy consumption standard, OCSLM as a Maximal Covering Location Modell with a focus on occasional charging based on an endogenous covering distance and integrating detailed energy and process monitoring into electric charging station allocation, and the methodology for the application of this approach for fast connecting contactless and contact charging models and cases.

Made available in DSpace on 2017-07-10T17:31:12Z (GMT). No. of bitstreams: 1 Wellington_Barbosa_da_Silva.pdf: 4552878 bytes, checksum: cced6a1f2d0a0c2426792ba3f3f8ce33 (MD5) Previous issue date: 2011-07-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / On the Guarapuava Plateau/Palmas, in a low slope hillside of superficial covering from basaltic origins, on the right bank of the Rio das Pombas, Paraná state, processes of tunnel erosion (pipes) were identified. These are subsuperficial erosion processes with typical features, such as subsidence of the tunnel roof and rebate structures, which tend to evolve to superficial features. The emerging of this erosive process depends on a set of factors, being the main one, the properties of the superficial covering, such as: texture, macroporosity, granulometric composition (chemical matter make-up), density, porosity e chemical elements that make up the matter, those concerning the hydrological conditions and the topography of the hillside. In order to recognize and characterize the superficial covering in the sector of low hillside, sieve analysis was used, as well as real and apparent density, total porosity verified; toposequences were made and X-ray scattering techniques performed. The results showed that the matter which covers the low hillside sector, where the tunnels are, have a sandy texture due to the properties of microagregation generated by clay mineral, gibbsite; leaving the matter with a high porosity level, thus favoring the flowing of water through subsurfaces. The generated flows tend to be exfiltrated to a ditch wall-like surface, which causes the removal of small particles of matter (seepage). With the opening of small gullies through subsurface, the flow tend to become concentrated (tunnel scour) and consequently enlarge the subsuperficial channels by the mechanical action of the water. In a sequence of factors that can be used for the analysis of the process generation, which causes: alteration in basalt rocks, microaggregation of the matter, macroporosity and increase of water flow through subsurface. Therefore, the hydrology conditions in the hillside contributed for erosion mechanisms to emerge in subsurface, development of erosion process, formation of subsuperficial erosion and, ultimately, superficial erosion process development. These both chemical and physical features found in such field of study, show that the superficial covering is a determining factor for the subsuperficial tunnel erosion to originate in the hillside. / No Planalto de Guarapuava/Palmas, em encosta de baixa declividade e cobertura superficial de origem basáltica, à margem direita do Rio das Pombas em Guarapuava (Paraná), foram identificados processos de erosão em túneis (pipes). Trata-se de processos subsuperficiais de erosão que apresentam feições típicas, tais como, subsidência do teto do túnel e estruturas de abatimento, que tendem a evoluir para feições superficiais. A instalação desse processo erosivo depende de um conjunto de fatores, destacando-se como condicionantes, as propriedades da cobertura superficial como: textura, macroporosidade, composição granulométrica, densidade, porosidade e constituintes químicos dos materiais, e aqueles relativos às condições hidrológicas e à topografia da encosta. Buscando-se reconhecer e caracterizar a cobertura superficial do setor de baixa encosta, foram realizadas análises granulométricas, de densidade aparente, real e porosidade total, construção de topossequências e análises químicas de difração de raios-X. Os resultados indicaram que o material que recobre o setor de baixa encosta, onde aparecem os túneis, apresenta textura arenosa devido às propriedades de microagregação gerada pelo argilomineral gibbsita, deixando o material com porosidade alta, favorecendo assim a circulação de água em subsuperficie. Os fluxos gerados tendem a ser exfiltrados para uma superfície de exposição, o que provoca a remoção de pequenas partículas de material (seepage). Com a abertura de pequenos canais em subsuperfície, os fluxos tendem a se concentrar (tunnel scour) e consequentemente ampliar os canais subsuperficiais pela ação mecânica da água. Numa sequência de fatores que possam ser postos para análise da geração do processo, têm-se: alteração da rocha basáltica, microagregação do material, macroporosidade e aumento da circulação de água em subsuperfície. Assume-se que as condições hidrológicas da encosta propiciaram a instalação de mecanismos de erosão em subsuperfície, evolução do processo erosivo, formação de feições erosivas subsuperficiais e, por fim, instalação de feições erosivas superficiais. Essas características físicas e químicas encontradas na área de estudo, demonstram que a cobertura superficial é determinante para a instalação da erosão subsuperficial em túneis na encosta.