Uma almost disjoint family é uma coleção infinita de subconjuntos infinitos de números naturais tal que a interseção de quaisquer dois de seus elementos distintos é finita. Almost disjoint families podem ser utilizadas para construir um espaço topológico associado chamado de Psi-espaços, também conhecido como espaços de Mrówka. As propriedades topológicas deste espaço topológico dependem das propriedades combinatórias da família que o deu origem, e estes espaços podem ser utilizados para responder perguntas sobre topologia geral, muitas vezes não inicialmente relacionadas com almost disjoint families ou seus respectivos espaços de Mrówka. Neste documento, exploramos diversas construções envolvendo estes objetos utilizando combinatória infinita e princípios combinatórios como diamante, Axioma de Martin e técnicas como Forcing e tratamos de problemas envolvendo compactificações de Stone-Cech, espaços sequenciais, a propriedade de Lindelöf em espaços de funções, hiperespaços de Vietoris, dentre outros. O primeiro capítulo contém diversos pré-requisitos necessários para a leitura desta dissertação a fim de torná-la o mais autocontida possível. O segundo capítulo introduz as almost disjoint families e seus Psi-espaços associados, provando diversas propriedades importantes. Os demais capítulos são independentes entre si e tratam de problemas de Topologia Geral que podem ser solucionados com estes conceitos, ou de problemas que derivam destes conceitos. / An almost disjoint family is an infinite collection of infinite subsets of natural numbers such that the intersection of any two of its elements is finite. Almost disjoint families may be used to construct an associated topological space called psi space, also know as Mrówka space. The topological properties of this topological space depends on the combinatorical properties of the family that originated it, and these spaces may be used to answer questions in general topology, many times initially unrelated to almost disjoint families or to their Mrówka spaces. In this document, we explore several constructions involving these objects by using infinitary combinatorics and combinatorical principles like diamond, Martin\'s Axiom, forcing techniques and we treat abour problems regardins Stone-Cech compactifications, sequencial spaces, the property of Lindelöf on spaces of functions, hyperspaces of Vietoris, among others. The first chapter contains several pre requirements that are neccessary to read this dissertation in order to make it as self contained as possible. The second chapter introduces almost disjoint families and their associated Psi spaces, proving several important properties. The following chapters are independent from each other and treat about problems on General Topology that may be solved by using these concepts, or about problems that arises from these concepts.

Les principaux résultats obtenus dans ce travail concernent l’existence et l’unicité des solutions de différents types de l’équation de Liénard forcée et des résultats de dépendance pour les solutions S-asymptotiquement w-périodiques d’équations d’évolution. Pour réaliser notre objectif, nous utilisons des outils d’analyse fonctionnelle non linéaire et des résultats sur des équations linéaire. / No English summary available.

“Homeomorphic'' is the standard equivalence relation in topology. To a topologist, spaces which are homeomorphic to each other aren't merely similar to each other, they are the same space. We study a class of functions which are homeomorphic at “most'' of the points of their domains and codomains, but which may fail to satisfy some of the properties required to be a homeomorphism at a “small'' portion of the points of these spaces. Such functions we call “almost homeomorphisms.'' One of the nice properties of almost homeomorphisms is the preservation of almost open sets, i.e. sets which are “close'' to being open, except for a “small'' set of points where the set is “defective.'' We also find a surprising result that all non-empty, perfect, Polish spaces are almost homeomorphic to each other.A standard technique in algebraic topology is to pass between a continuous map between topological spaces and the corresponding homomorphism of fundamental groups using the π1 functor. It is a non-trivial question to ask when a specific homomorphism is induced by a continuous map; that is, what is the image of the π1 functor on homomorphisms?We will call homomorphisms in the image of the π1 functor “tangible homomorphisms'' and call homomorphisms that are not induced by continuous functions “intangible homomorphisms.'' For example, Conner and Spencer used ultrafilters to prove there is a map from HEG to Z2 not induced by any continuous function f : HE→ Y , where Y is some topological space with π1(Y ) = Z2. However, in standard situations, such as when the domain is a simplicial complex, only tangible homomorphisms appear..Our job is to describe conditions when intangible homomorphisms exist and how easily these maps can be constructed. We use methods from Shelah and Pawlikowski to prove that Conner and Spencer could not have constructed these homomorphisms with a weak version of the Axiom of Choice. This leads us to define and examine a class of pathological objects that cannot be constructed without a strong version of the Axiom of Choice, which we call the class of inscrutable objects. Objects that do not need a strong version of the Axiom of Choice are scrutable. We show that the scrutable homomorphisms from the fundamental group of a Peano continuum are exactly the homomorphisms induced by a continuous function.

No description available.

Almost contact metric submersions constitute a class of Riemannian submersions whose total space is an almost contact metric manifold. Regarding the base space, two types are studied. Submersions of type I are those whose base space is an almost contact metric manifold while, when the base space is an almost Hermitian manifold, then the submersion is said to be of type II. After recalling the known notions and fundamental properties to be used in the sequel, relationships between the structure of the fibres with that of the total space are established. When the fibres are almost Hermitian manifolds, which occur in the case of a type I submersions, we determine the classes of submersions whose fibres are Kählerian, almost Kählerian, nearly Kählerian, quasi Kählerian, locally conformal (almost) Kählerian, Gi-manifolds and so on. This can be viewed as a classification of submersions of type I based upon the structure of the fibres. Concerning the fibres of a type II submersions, which are almost contact metric manifolds, we discuss how they inherit the structure of the total space. Considering the curvature property on the total space, we determine its corresponding on the fibres in the case of a type I submersions. For instance, the cosymplectic curvature property on the total space corresponds to the Kähler identity on the fibres. Similar results are obtained for Sasakian and Kenmotsu curvature properties. After producing the classes of submersions with minimal, superminimal or umbilical fibres, their impacts on the total or the base space are established. The minimality of the fibres facilitates the transference of the structure from the total to the base space. Similarly, the superminimality of the fibres facilitates the transference of the structure from the base to the total space. Also, it is shown to be a way to study the integrability of the horizontal distribution. Totally contact umbilicity of the fibres leads to the asymptotic directions on the total space. Submersions of contact CR-submanifolds of quasi-K-cosymplectic and quasi-Kenmotsu manifolds are studied. Certain distributions of the under consideration submersions induce the CR-product on the total space. / Mathematical Sciences / D. Phil. (Mathematics)

Almost contact metric submersions constitute a class of Riemannian submersions whose total space is an almost contact metric manifold. Regarding the base space, two types are studied. Submersions of type I are those whose base space is an almost contact metric manifold while, when the base space is an almost Hermitian manifold, then the submersion is said to be of type II. After recalling the known notions and fundamental properties to be used in the sequel, relationships between the structure of the fibres with that of the total space are established. When the fibres are almost Hermitian manifolds, which occur in the case of a type I submersions, we determine the classes of submersions whose fibres are Kählerian, almost Kählerian, nearly Kählerian, quasi Kählerian, locally conformal (almost) Kählerian, Gi-manifolds and so on. This can be viewed as a classification of submersions of type I based upon the structure of the fibres. Concerning the fibres of a type II submersions, which are almost contact metric manifolds, we discuss how they inherit the structure of the total space. Considering the curvature property on the total space, we determine its corresponding on the fibres in the case of a type I submersions. For instance, the cosymplectic curvature property on the total space corresponds to the Kähler identity on the fibres. Similar results are obtained for Sasakian and Kenmotsu curvature properties. After producing the classes of submersions with minimal, superminimal or umbilical fibres, their impacts on the total or the base space are established. The minimality of the fibres facilitates the transference of the structure from the total to the base space. Similarly, the superminimality of the fibres facilitates the transference of the structure from the base to the total space. Also, it is shown to be a way to study the integrability of the horizontal distribution. Totally contact umbilicity of the fibres leads to the asymptotic directions on the total space. Submersions of contact CR-submanifolds of quasi-K-cosymplectic and quasi-Kenmotsu manifolds are studied. Certain distributions of the under consideration submersions induce the CR-product on the total space. / Mathematical Sciences / D. Phil. (Mathematics)

Eine almost Einstein-Struktur (M,g,sigma) ist eine n-dimensionale zusammenhängende Mannigfaltigkeit M mit einer pseudo-riemannschen Metrik g und einer glatten Skalenfunktion sigma deren almost Einstein-Tensor A[g,sigma] (der spurfreie Anteil von Hess[g] sigma + sigma P[g], wobei P[g] den Schouten-Tensor bezeichnet) verschwindet. Sie verallgemeinert die Idee einer Einsteinmannigfaltigkeit in dem Sinne, dass die konform geänderte Metrik 1/sigma^2 g außerhalb der Nullstellenmenge Sigma = sigma^(-1)(0) eine Einstein-Metrik ist. Ziel dieser Doktorarbeit ist es, ein detailiertes Bild von Sigma in Lorentzsignatur (-+...+) zu erhalten. Teil dieser Arbeit ist zudem eine indexfreie Darstellung ausgewählter Resultate für konform kompaktifizierbare Einsteinmannigfaltigkeiten in Lorentzsignatur im Rahmen von almost Einstein-Strukturen. Diese Umformulierung wird dann benutzt, um eine Verallgemeinerung der konformen Wellengleichungen für beliebige gerade Dimensionen n = 2m > 4 vorzuschlagen. / An almost Einstein structure (M,g,sigma) is an n-dimensional connected manifold M equipped with a pseudo-Riemannian metric g and a scale factor sigma in C^infty(M) such that the almost Einstein tensor A[g,sigma] (the trace-free part of Hess[g] sigma + sigma P[g], with Schouten tensor P[g]) vanishes. It generalises the idea of an Einstein manifold in the way that 1/sigma^2 g is an Einstein metric away from the singularity set Sigma = sigma^(-1)(0). The purpose of this thesis is to get a detailed picture of Sigma in Lorentzian signature (-+...+). Part of this thesis is also an index-free survey of selected results on conformally compact Einstein manifolds in Lorentzian signature in the framework of almost Einstein structures. This reformulation is used to suggest a generalisation of the conformal wave equations to arbitrary even dimensions n = 2m > 4.

Almost p-ary perfect and nearly perfect sequences are equivalent to certain relative difference sets and direct product difference sets, respectively. This feature enables Chee, Tan and Zhou to determine the existence status of those sequences by using the tools of Design Theory. In particular, they determined the existence status of almost p-ary perfect and nearly perfect sequences of period n+1 for n 100, except some open cases in [6]. In this thesis, we obtained a set of Diophantine equations in integers while observing relative difference sets, and proved nonexistence of almost p-ary perfect sequences of period n + 1 for n (50,76,94,99,100).Also, we observed that it was possible to extend Diophantine equations that we used for relative difference sets to the direct product difference sets, thereby proved the nonexistence of almost p-ary nearly perfect sequences of type II of period n + 1 for p = 2, p = 3 and p = 5 at certain values of n. As a result, we answered two questions posed by Chee, Tan and Zhou in [6].

Doctor of Philosophy / Department of Agricultural Economics / Vincent R. Amanor-Boadu / This dissertation is composed of two essays in applied microeconomics. Using farm level data, the first essay applied nonparametric methods to test the adherence of individual farm’s production choices to profit maximization objective. Results indicate that none of the farms consistently satisfy the joint hypothesis of profit maximization. The study took into account the uncertainty prevalent in agricultural production by systematically modeling the optimization behavior of farms. Departures of observed data of individual farms from profit maximization objectives were attributed more due to stochastic influences caused by output production decisions than input use decisions. Results also support the existence of technological progress during the study period for Kansas farms. At an alpha level of 5%, assuming both input and output quantities as stochastic, only 5.3% of the farms violated the joint hypothesis of profit maximization with standard error exceeding 10%. Whereas when only input quantities are considered stochastic, a total of 71.73% and 2.09% of the farms had minimum standard errors of greater than 10% and 20% respectively required for the joint profit maximization hypothesis to hold. When only output quantity measurements were assumed as stochastic, a total of 80.10 % and 18.84 % of the farms had minimum standard errors of greater than 10% and 20% respectively required for the profit maximization hypothesis to hold. The second essay examines the demand for alcoholic beverages (beer, wine and distilled spirits) for the U.S. using time series data from 1979-2006. The estimation is done using an error correction form of the Almost Ideal Demand System . Results indicate that there is a significant difference between short run and long run elasticity estimates. The paper addresses the exogeneity of log of prices and log of real expenditures. For the beer and wine equations, the hypothesis of joint exogeneity of price index and real expenditure cannot be rejected at all the conventional levels of significance. For the spirits equation, the tests strongly reject the simultaneous exogeneity of price index and real expenditure. When independently tested, price index appears to be endogenous variable where as real expenditure seems exogenous variable. Based on these results, the real expenditure was considered as an exogenous variable, where as the price index for spirits as an endogenous variable.

論文名稱：非典型原住民活力：傑偌•維森諾《熱線療者》中的 後印地安、喜劇與移動力 指導教授：梁一萍 教授 研究生：尤吟文 論文提要內容： 傑偌•維森諾（Gerald Vizenor）認為所謂的「印地安」（indian）是一個沒有指涉目標的空集合（absence without reference），而「原住民」（native）才是指這個文化所代表的真正的意涵。相較於其他原住民作家的作品，維森諾的寫作方式可說是獨樹一幟。在原住民文學中，許多的主題不外乎是尋找身分認同（identity）的過程、強調人與自然之間的和諧關係、表現白人社會與原住民文化之間的隔閡等等。這種思鄉式（nostalgia）的描寫方式對於維森諾來說不只是種老掉牙的（stereotypical）表現方式，更是主流文學（literature of dominance）加諸在原住民文化上的表現方式（manifest manners）。為了與主流文學抗衡，維森諾以搗蛋鬼論述（trickster discourse）的寫作技巧來顛覆原住民文學的傳統，以天馬行空的想像力及奇異怪誕的內容來表現另類的原住民作品。 《熱線療者》是維森諾在1997年的作品，書中的主人翁－－差不多部朗（Almost Browne）是本書中的搗蛋鬼，他穿越時空的限制，帶給讀者一個又一個的故事，這些故事不具有教導意義，而是表現出想像力的無限。差不多部朗曾經在許多維森諾的小說故事中呈現，在《熱線療者》一書中，他與他的姪子，也就是小說的敘述者，以插訶打諢、嘻笑怒罵的方式與政治界和學術界有了第一線接觸，他們也回到過去，目睹了原住民傳說的起源。每個小故事，不管時間地點為何，差不多部朗和他的姪子總是在場。這些故事也搭著原住民第一列火車－－納那波佐快車（Naanabozho Express），隨著列車的移動傳出去。 本文的第一章為總論，簡述維森諾生平、《熱線療者》的故事情節與維森諾自成一格的批評理論。為了表現出原住民文化以及生活的生命力、多樣性和複雜性，維森諾提出所謂的「後印地安」的觀念，指出「印地安」是一種虛擬的再現（simulated representation），只有具有想像力和生命力的「後印地安」才是真正的存在（presence），這也是第二章所討論的部分。第三章則是從喜劇出發，檢討原住民文學的悲劇犧牲性（tragic victimry）實為主流文學的表現方式，只有透過全喜劇論述（comic holotrope）才能真正了解原住民文學。第四章則聚焦於移動力（motion），直指原住民文學的不可限制性，唯有透過對於移動力的了解，原住民文學才能表現出其生命力及想像力，就像差不多部朗或是納那波佐列車一樣，永遠在宇宙間移動（always in motion）。第五章為結論，《熱線療者》是維森諾寫的最後一本有關差不多部朗的小說，在這本小說中，維森諾以另類的筆調及呈現方式將原住民文學帶到一個充滿創造力的世界，經由他的喜劇效果，《熱線療者》提供了另一個檢視原住民文學的角度（alternative, alter-native）。 / Indian, as Gerald Vizenor points out, is the absence of natives without reference to real native cultures while native is the presence of the native survivance. In the field of Native American Literature, the most common themes are the quest for identity, the harmony between nature and people and the conflict between native and white cultures. The nostalgic representation of natives depicted in these common themes, for Vizenor, is not only a stereotypical clich□ but also the manifest manners imposed on Native American Literature by the literature of dominance. In order to resist the burden imposed on Native American Literature, Vizenor, with his unique writing style, applies trickster discourse to subvert the stereotypes brought forth by the literature of dominance. With creativity and imagination, Vizenor presents alternative aspects for Native American Literature. Fascinated by the extraordinary writing style and narrative strategy, I find that the novel, Hotline Healers, illustrates Vizenor’s comprehensive viewpoints on Native American literature. Hotline Healers is Vizenor’s most recent novel which was published in 1997. In the novel, Almost Browne is a protagonist trickster who travels beyond the spatial and temporal limitations. The stories he tells with his travels are not intended to provide lessons; on the contrary, they are the true representation of native imagination. Almost Browne and his cousin, the narrator in the novel, take the first Native train, the Naanabozho Express, to give lectures in several occasions and result in several funny and hilarious encounters with politicians as well as academia. They also return to the past and witness the origins of the native folklores. Almost Browne and his cousin are omnipresent in the stories. With the moving of the Naanabozho Express, more and more stories disseminate native imagination and creativity. There are five chapters in my thesis. The first chapter, “Introduction,” summarizes the life and works of Gerald Vizenor, gives a plot summary of Hotline Healers, and introduces Vizenor’s critical conceptions on Native American Literature. In Chapter Two, I illustrate Vizenor’s view on postindian. Postindian, as Vizenor indicates, absolves the burden of stereotypical indian representations. With the idea of postindian, Vizenor focuses on the presence of natives as well as native vitality and imagination and thus subverts the culturalist stereotypical portraita of indian which is the simulated representation without reference. In Chapter Three, I concentrate on the comic effect employed by Vizenor in Hotline Healers. Comic holotrope is one of Vizenor’s writing techniques which is different from the themes of tragic victimry found in most Native American literary works. Comic holotrope presents the vitality of native culture while tragic victimry burdens Native American Literature with “manifest manners.” In Chapter Four, I explore the concept of motion in the novel. The idea of motion is not only the demonstration of the bounderlessness of Native American literary imaginatinos but also the representation of the transformative native wisdom. In the fifth chapter, I conclude that the novel, being Vizenor’s latest novel on Almost Browne, incorporates his alternative vision of tribal survivance and critical concepts of postindian, comic holotrope, and motion to elevate Native American Literature to a creative and imaginative world. The novel provides readers with an alternative point of view toward Native American Literature.