Absolutely pure modules act in ways similar to injective modules. Therefore, through-out this document we investigate many of these properties of absolutely pure modules which are modelled after those similar properties of injective modules. The results we develop can be broken into three categories: localizations, covers and derived functors. We form S1M, an S1R module, for any Rmodule M. We state and prove some known results about localizations. Using these known techniques and properties of localizations, we arrive at conditions on the ring R which make an absolutely pure S1Rmodule into an absolutely pure Rmodule. We then show that under certain conditions, if A is an absolutely pure Rmodule, then S1A will be an absolutely pure S1Rmodule. Also, we dene conditions on the ring R which guarantee that the class of absolutely pure modules will be covering. These include R being left coherent, which we show implies a number of other necessary properties. We also develop derived functors similar to Extn R (whose development uses injective modules). We call these functors Axtn R, prove they are well dened, and develop many of their properties. Then we dene natural maps between Axtn(M;N) and Extn(M;N) and discuss what conditions on M and N guarantee that these maps are isomorphisms.

摘要 本文主要在探討絕對正則隨機變數序列的隨機修剪L統計量的漸近性，當修剪係系數收斂至a和b時(O<a<b<l)，對它們的分配函數限制並不多；然而當a=0及b=1 時，則限制的條件須更加嚴格，這也就是為什麼我們要做隨機修剪的主要原因。同時，由於大部分的時間序列模式都是絕對正則的隨機變數序列，這也是研究本文的主要動機之一。 本文是想嘗試著把G. R. Shorack (1989)的論文隨機修剪L統計量，推廣，把該文中立相獨立的隨機變數序列換成絕對正則的隨機變數序列。在這同時，我們必需將一些經驗累積分配函數的不等式推廣，推廣過程中將重覆使用Yoshihara (1978) 的機率不等式。 / ABSTRACT We will prove central limit theorem for randomly trimmed L-statistics with absolutely regular random variables. When the fractions trimmed converge to a and l-b, (with 0<a<b<l) there are little restrictions on the df's of the r.v.'s, - but the limiting r.v. has several contributing terms, making the studentization complicated unless the trimming fractions converge fast enough. For a=0 and b=l, the restriction on the rate of convergence of the trimming fractions is more severe, however this is a most reasonable way to trim.

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-22T16:24:35Z No. of bitstreams: 1 arquivototal.pdf: 1096557 bytes, checksum: 096bafe0cd5d1cf118a6fa1546070e5d (MD5) / Made available in DSpace on 2017-08-22T16:24:35Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1096557 bytes, checksum: 096bafe0cd5d1cf118a6fa1546070e5d (MD5) Previous issue date: 2016-03-03 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we study a recent general version of the Extrapolation Theorem, due to Botelho, Pellegrino, Santos and Seoane-Sep ulveda [6] that improves and uni es a number of known Extrapolation-type theorems for classes of mappings that generalize the ideal of absolutely p-summing linear operators. / Neste trabalho, dissertamos sobre uma recente vers~ao geral do Teorema de Extrapola c~ao, devida a Botelho, Pellegrino, Santos e Seoane-Sep ulveda [6], que melhora e uni ca v arios teoremas do tipo Extrapola c~ao para certas classes de fun c~oes que generalizam o ideal dos operadores lineares absolutamente p-somantes.

Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-29T12:08:37Z No. of bitstreams: 1 arquivototal.pdf: 967006 bytes, checksum: bd1b76a7b376f5fda6d282d14e851d1a (MD5) / Made available in DSpace on 2016-03-29T12:08:37Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 967006 bytes, checksum: bd1b76a7b376f5fda6d282d14e851d1a (MD5) Previous issue date: 2014-03-12 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we study two generalizations of the well-known concept of absolutely summing operators. The rst one consists of the multiple summing multilinear operators and it is focused on a result of coincidence that is equivalent to the Bohnenblust- Hille inequality. This inequality asserts that, for K = R or C and every positive integer m there exists positive scalars BK;m 1 such that N X i1;:::;im=1 U(ei1 ; : : : ; eim) 2m m+1!m+1 2m BK;m sup z1;:::;zm2DN jU(z1; :::; zm)j for every m-linear mapping U : KN KN ! K and every positive integer N, where (ei)N i=1 denotes the canonical basis of KN: In this line our main goal is the investigation of the best constants BK;m satisfying the above inequality. The second generalization involves the concept of absolutely summing multilinear operators at a given point; we present an abstract version of these operators involving many of their properties. We prove that, considering appropriate sequence spaces, we have other kind of operators as particular cases of our version. / No presente trabalho vamos trabalhar com duas generalizações dos bem conhecidos operadores absolutamente somantes. A primeira envolve os operadores multilineares múltiplo somantes e nos focaremos num resultado de coincidência que é equivalente à desigualdade multilinear de Bohnenblust-Hille. Esta a rma que, para = R ou C, e todo inteiro positivo m 1, existem escalares BK;m 1 tais que N X i1;:::;im=1 U(ei1 ; : : : ; eim) 2m m+1!m+1 2m BK;m sup z1;:::;zm2DN jU(z1; :::; zm)j para toda forma m-linear U : KN KN ! K e todo inteiro positivo N, onde )N i=1 é a base canônica de KN: Nessa linha, nosso objetivo será a investigação das melhores constantes BK;m que satisfazem essa desigualdade. A segunda generalização envolve o estudo dos operadores multilineares absolutamente somantes num ponto; apresentaremos uma versão abstrata destes operadores que engloba várias de suas propriedades. Veremos que, considerando os espaços de sequências adequados, teremos outros tipos de operadores como casos

Submitted by Leonardo Cavalcante (leo.ocavalcante@gmail.com) on 2018-04-23T21:42:23Z No. of bitstreams: 1 Arquivototal.pdf: 889863 bytes, checksum: feeec177f9d947c98727574b765d8acb (MD5) / Made available in DSpace on 2018-04-23T21:42:23Z (GMT). No. of bitstreams: 1 Arquivototal.pdf: 889863 bytes, checksum: feeec177f9d947c98727574b765d8acb (MD5) Previous issue date: 2017-07-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we study the notion of index of summability for pairs of Banach spaces. This index plays the role of a kind of “measure” of how the space of m-homogeneous polynomials from E to F (or the space of multilinear operators of E1×···×Em to F) are far from being the space of absolutely summing m-homogeneous polynomials (or with the space of multiple summing multilinear operators). In some cases the optimal index of summability is presented. / Neste trabalho, estudamos a noção de índice de somabilidade para pares de espaços de Banach. Esse índice desempenha o papel de um tipo de \medida" de como o espaço dos polinômios m-homogêneos de E em F (ou o espaço dos operadores multilineares de E Em em F) está longe de coincidir com o espaço dos polinômios m- homogêneos absolutamente somantes (ou com o espaço dos operadores multilineares multiplo somantes). Em alguns casos o índice ótimo de somabilidade e apresentado. Palavras-chave: Polinômios absolutamente somantes, operadores multilineares absolutamente somantes, espaços de Banach, índice de somabilidade.

The first chapter gives basic definitions and theorems concerning set functions and set function integrals. The lemmas and theorems are presented without proof in this chapter. The second chapter deals with absolute continuity and Lipschitz condition. Particular emphasis is placed on the properties of max and min integrals. The third chapter deals with approximating absolutely continuous functions with bounded functions. It also deals with the existence of the integrals composed of various combinations of bounded functions and finitely additive functions. The concluding theorem states if the integral of the product of a bounded function and a non-negative finitely additive function exists, then the integral of the product of the bounded function with an absolutely continuous function exists over any element in a field of subsets of a set U.

No description available.

Made available in DSpace on 2015-05-15T11:46:24Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 519154 bytes, checksum: e1f2c33c19a740684327d51d9d1278f5 (MD5) Previous issue date: 2010-01-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we investigate recent results involving lineability and spaceability and the nonlinear theory of absolutely summing mappings. / Neste trabalho estudamos resultados recentes envolvendo o conceito de lineabilidade e espaçabilidade e a teoria não-linear de aplicações absolutamente somantes.

Made available in DSpace on 2015-05-15T11:46:25Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 489943 bytes, checksum: 8456425550cf8ae40851ce99110c0cb5 (MD5) Previous issue date: 2010-12-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we present some results involving lineability and the linear theory of absolutely summing operators. We note that the technique presented is closely related to the theory of hereditarily indecomposable Banach spaces and that the presence of an unconditional basis in one of the spaces involved is crucial to guarantee some results. / Neste trabalho apresentamos alguns resultados envolvendo lineabilidade e a teoria linear dos operadores absolutamente somantes. Observamos que a técnica utilizada está intimamente relacionada com a teoria dos espaços de Banach hereditariamente indecomponíveis e que a presença de uma base incondicional em um dos espaços envolvidos é crucial para garantirmos alguns resultados.

Neste trabalho nós estudamos os expoentes de Lyapunov de aplicações f : Td &rarr; Td homotópicas a uma aplicação Anosov linear e a continuidade absoluta de folheações. Nós mostramos para algumas classes de homotopia de aplicações que a soma dos expoentes de Lyapunov está limitado pela soma dos expoentes de Lyapunov da aplicação Anosov linear. Além disso, admitindo uma propriedade conhecida como densidade uniformemente limitada (UBD) nas folheações, mostramos uma igualdade entre a soma dos expoentes de Lyapunov de f e do Anosov linear. Também construímos um conjunto C1 aberto de difeomorfismos parcialmente hiperbólicos do toro T4, preservando volume, com folheação central bidimensional não compacta e não absolutamente contínua. Ainda construímos um exemplo parcialmente hiperbólico com folhas centrais bidimensionais, não compactas onde a desintegração do volume ao longo da folheação central não é nem Lebesgue nem atômica. / In this work we study the Lyapunov exponents of maps f : Td &rarr; Td homotopic to a linear Anosov map. We proof for some homotopic classes of maps which the sum of Lyapunov exponents is bounded by the sum of the Lyapunov exponents of the linear Anosov map. Moreover, by assuming a property known as uniformly bounded density (UBD) in the foliations, we show an equality between the sum of the Lyapunov exponents of f and the linear Anosov. We also construct an C1 open set of volume preserving partially hyperbolic diffeomorphisms with non compact two dimensional center foliation and non absolutely continuous. We still build an example of partially hyperbolic diffeomorphism with non compact bidimensional center leaves where the disintegration of volume along the center foliation is neither Lebesgue nor atomic.