Este trabalho aborda principalmente dois tópicos em Análise Funcional. No primeiro tópico, estudamos zeros de polinômios em espaços de Banach reais. Apresentamos resultados devidos a J. Ferrer, estabelecendo que todo polinômio fracamente contínuo sobre os subconjuntos limitados de um espaço de Banach, de dual não separável na topologia fraca estrela, admite um subespaço linear fechado de dual não separável na topologia fraca estrela, no qual o polinômio se anula. No segundo tópico, exibimos a versão multilinear do Lema de Phelps devido a R. Aron, A. Cardwell., D. García e I. Zalzuendo. / We study two topics in Functional Analysis. In the first topic, we study zeros of polynomials on real Banach spaces. We present results due to J. Ferrer, stating that every polynomial weakly continuous on bounded subsets of a Banach space, whose dual is not separable in the weak-star topology, admits a closed linear subspace whose dual is not separable in the weak- star topology either, where the polynomial vanishes. In the second topic, we show a multilinear version for the Phelps\' Lemma by R. Aron, A. Cardwell., D. García and I. Zalzuendo.

The purpose of this study has been to write a biography on the life of the versatile William Wines Phelps in conjunction with his contributions to and influence on the issues and problems of Mormon Pioneer History from Kirtland, Ohio, to the Great Basin.Prior to the year 1831, W.W. Phelps was active in the State of New York as an Anti-Masonic newspaper editor. The Anti-Masonic movement had grown out of the political enviornment that existed throughout the nation and especially in the State of New York during that period of time.During the year of 1831, W.W. Phelps completely abandoned the cause of Anti-Masonry to accept "Mormonism." As a result, when Joseph Smith, W.W. Phelps and others arrived in Missouri, Phelps was called to be the first Mormon editor-publisher, bringing with him the same enthusiasm and skill to the cause of Mormonism.

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On August 4, 2012, white American swimmer Michael Phelps was awarded a Lifetime Achievement Award by the international swimming federation in recognition of his Olympic achievements. The unprecedented award – a specially commissioned sculpture – proclaimed Phelps as “the greatest Olympian of All Time.” This title may, at one level, be perceived as a benign honorific bestowed upon an extra-ordinary athlete. On another level, the title should be viewed as a result of the hidden ideological work done by and through discourses of swimming in America, discourses that are always racialized, classed, nationalized, and gendered. Michael Phelps is the point of entry to unpack how modern sport and the Olympics reproduce these dominant views and processes that lead to contemporary social inequalities. My focus is an examination of the power relations that enabled and produced him as the Greatest Olympian of All-Time. Phelps’s phenomenal performance in the pool is undeniable, but I argue that the ensuing adulation and recognition results as much from his privileged position as a white American man as from his hard work, skill, and determination. This dissertation unpacks and explains how these processes work in the contemporary sporting world. Scholars have long argued that sport is a site for understanding how race, class, gender, and nationalisms are performed and/or constructed. In this dissertation, I take a critical cultural studies approach to demonstrate that, from an ideological and cultural point of view, Michael Phelps is the greatest Olympian of all time because he is the physical and symbolic embodiment of the modern Olympic movement, a movement founded upon 19th century ideals of humanism, liberalism, and modernity that continues to stabilize and reinforce dominant views of race, gender, class, nationalism and sexuality. To make this argument, I first historicize the sport of swimming itself. As one of the sports at the first Modern Olympics in 1896, swimming is an ideal site for understanding the modernization process through sport. Swimming has long been dominated by white athletes, and I deploy the recent concept of the sporting racial project to grasp how modernization is a racialized project fundamental to constructions of institutional racism. Next, I examine media representations of Michael Phelps in the early 21st century. These representations reveal the role of sport in popular imaginations of the nation and, specifically, the importance of the white male sporting hero in constructions of America in the post-9/11 world. Then, I explore and contextualize notions and meanings of “amateur” and “eligibility” within late 20th and early 21st century structures of Olympic swimming, including the complex and contradictory relationships between inter/national governing bodies. Finally, I show how these three seemingly independent processes involving race, class, gender, and nation are interdependent and fundamental to modern sport and the Olympics.

Thesis (Ph. D.)--University of Washington, 1989. / Vita. Includes bibliographical references (leaves [211]-218).

Thesis (M.A.)--University of Wisconsin--Madison, 1968. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Issued also in microfilm form, as thesis, Columbia University, under title: The life of William E. Dodge.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Na tentativa de facilitar o diagnÃstico dos diversos fatores que afetam a qualidade da Ãgua e antever possÃveis impactos futuros sobre o meio ambiente , sÃo adotadas aÃÃes que racionalize m o uso da Ãgua a partir da otimizaÃÃo de processos naturais ou tecnolÃgicos. A modelagem matemÃtica à um exemplo disso e, em conjunto com a Teoria Fuzzy , que permite fazer a anÃlise dos resultados sem necessidade de significativos bancos de dados, pode - se estabelecer o risco como indicador de contaminaÃÃo das Ãguas de rios, sendo de valor prÃtico na tomada de decisÃo e concessÃo de outorga de lanÃamentos. Neste estudo, foi desenvolvido um modelo matemÃtico aplicado Ãs equaÃÃes completas de Streeter - Phelps utilizando a Teoria dos nÃmeros Fuzzy , a fim de analisar o risco de contaminaÃÃo de um curso d'Ãgua que recebe agentes poluentes de mÃltiplas fontes de lanÃamento. Pelas simulaÃÃes do modelo, foram analisados diferentes cenÃrios, verificando a influÃncia d os seus parÃmetros, bem como o lanÃamento de fontes poluidoras pontuais e difusas, nos percentuais de risco. De acordo com os resultados, observou - se que a quantidade de carga lanÃada tem influÃncia no tempo de diluiÃÃo desta massa no sistema, de forma que , para maiores valores de lanÃamento, o tempo de diluiÃÃo à menor, favorecendo os processos de decaimento e formaÃÃo da camada bentÃnica; em relaÃÃo Ãs reaÃÃes fÃsicas, quÃmicas e biolÃgicas, verifica - se que os processos de sedimentaÃÃo, fotossÃntese e res piraÃÃo, para os dados mÃdios encontrados em literatura, tem pequena influÃncia no comportamento das curvas de concentraÃÃo de OD e curvas de risco, enquanto que o processo de nitrificaÃÃo tem forte influÃncia; jà a temperatura desempenha um significativo papel no comportamento do OD, onde, para valores maiores, maior serà o dÃficit OD e, em consequÃncia, aumento dos percentuais de risco. Por fim, o modelo desenvolvido como proposta de facilitar a tomada de decisÃo no controle de lanÃamento de efluentes em rios mostrou - se uma alternativa viÃvel e de valor prÃtico de anÃlise, jà que os objetivos foram alcanÃados / In an attempt to facilitate the diagnosis of the various factors that affect water quality and predict possible future impacts on the environment, actions to rationalize the use of water from the optimization of natural and technological processes are adopted. Mathematical modeling is one example and, together with Fuzzy Theory, which allows the analysis of the results without the need for significant databases, one can establish the risk as an indicator of contamination of rivers, and of practical value in decision making and allocation of grant releases. In this study, the full Streeter-Phelps equations, using the Fuzzy set Theory, was applied, in order to analyze the risk of contamination of a watercourse that receives multiple sources release pollutants. Through the model simulations, different scenarios were analyzed, and the influence of its parameters as well as the launch point and nonpoint pollution sources, in the calculation of the risk. According to the results, it was observed that the amount of discharge released influences the time of the mass dilution in the system, so that for higher values of launch, the dilution time is less favoring the formation and decay processes of benthic layer; regarding the physical, chemical and biological reactions, it appears that sedimentation processes, photosynthesis and respiration, concerning with the average data found in literature, have little influence on the behavior of the curves of DO concentration curves and risk, while the nitrification process has a strong influence; with respect to the temperature, the results showed that it plays a significant role in the behavior of DO, where, for larger values of it, the higher the DO deficit and, consequently, increase in the risk. Finally, the model developed as a proposal to facilitate the decision making in the control of discharge of effluents into rivers proved to be a viable and practical analytical alternative way, since the goals were achieved.

Estudamos a propriedade de Bishop-Phelps-Bollobás para operadores, (BP BP ), defi- nidos entre espaços de Banach. Nosso objetivo foi o de procurar pares de espaços de Ba- nach que possuem a BP BP . Assim, provamos que, se o par de espaços de Banach reais L i (c 0 ( i=1 ` 2 ) , Y ) satisfaz a BP BP , onde Y é um espaço de Banach estritamente convexo, então Y é uniformemente convexo. No estudo da BP BP aparecem diversas outras propri- edades, dentre elas destacamos a Approximate hyperplane series property (AHSP ). Nesta direção, considerando (K, (X t ) tK , Z) um espaço de função módulo, provamos que Z satisfaz a AHSP desde que X t satisfaça a AHSP para todo t K. Além disso, sob determinadas condições provamos a recíproca desse resultado. Como consequência, provamos que um es- paço de Banach X tem a AHSP se, e somente se, C 0 (L, X) tem a AHSP , para todo espaço localmente compacto Hausdorff L não-vazio. Concomitantemente ao estudo da BP BP , estudamos técnicas de caracterização dos con- juntos compactos de c 0 . Com essas técnicas, caracterizamos os conjuntos compactos de L i c 0 i=1 ` p , 1 p e do prédual do espaço de Lorentz, d (w, 1). / We study the Bishop-Phelps-Bollobás property for operators, (BP BP ), defined between Banach spaces. Our goal was to look for pairs of Banach spaces satisfying the BP BP . We L i prove that if the pair of real Banach spaces (c 0 ( i=1 ` 2 ) , Y ) satisfy BP BP , where Y is a strictly convex Banach space, then Y is an uniformly convex space. In the study of BP BP , it appears other properties, such the Approximate hyperplane series property for Banach spaces. In this sense, we proved that if (K, (X t ) tK , Z) is function module space, then Z satisfies AHSP if X t has the AHSP for all t K. Moreover, under certain conditions we proved the reciprocal of this result. As a consequence, a Banach space X has the AHSP if, and only if, C 0 (L, X) has the AHSP , for every non-empty locally compact Hausdorff space L. Concomitantly to the study of BP BP , we study techniques of characterization of com- pact sets of c 0 . With these techniques, we characterize the compact sets of the spaces L i c 0 i=1 ` p , 1 p and the predual of Lorentz sequence space d (w, 1).

Este trabalho tem como objetivo principal estudar determinadas propriedades de pares de espaços de Banach de forma que satisfaçam a Propriedade de Bishop-Phelps-Bollobás para operadores (BPBp), acompanhando a evolução histórica do assunto. Inicialmente apresentamos demonstrações dos Teoremas de Bishop-Phelps e Bishop-Phelps-Bollobás, e em seguida passamos a estudar as versões destes resultados para operadores, entre as quais enfatizamos a segunda. Com esse objetivo, definimos a Propriedade de Bishop-Phelps-Bollobás para operadores, introduzida por Acosta et al. em [AAGM08], e apresentamos dois resultados deste artigo, que afirmam que se os espaços de Banach X e Y têm dimensão finita, então (X,Y) satisfaz a BPBp, e que se o espaço de Banach Y tem a propriedade beta de Lindenstrauss, então (X,Y) satisfaz a BPBp para todo espaço de Banach X. Em seguida estudamos o artigo [AGKM17], que apresenta uma classe de espaços de Banach Y tais que (c0,Y) satisfaz a BPBp, e mostra que embora nesta classe estejam contidos os espaços de Banach uniformemente convexos e aqueles que satisfazem a propriedade beta, ela ainda contêm outros exemplos de espaços. / The main purpose of this work is to study certain properties of pairs of Banach spaces in a way that satisfies the Bishop-Phelps-Bollobás property for operators (BPBp), following the historical evolution of the subject. Firstly we present proofs of the Bishop-Phelps and Bishop-Phelps-Bollobás theorems, and then proceed to study versions of these results for operators, of which we emphasize the second one. To this purpose, we define the Bishop-Phelps-Bollobás property for operators, introduced by Acosta et al. in [AAGM08], and present two results of this paper, which state that if X and Y are finite-dimensional Banach spaces, then (X,Y) satisfies BPBp, and that if the Banach space Y has the property beta of Lindenstrauss, then (X,Y) satisfies BPBp for every Banach space X. Next we study paper [AGKM17], which presents a class of Banach spaces Y such that (c0,Y) satisfies BPBp, and shows that although this class contains the uniformly rotund spaces and those satisfying property beta, there are other examples of spaces in it.