Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-21T14:11:17Z No. of bitstreams: 1 arquivo total.pdf: 931330 bytes, checksum: 351b504f68153fb01d23f3fd1d96d2a0 (MD5) / Made available in DSpace on 2016-03-21T14:11:17Z (GMT). No. of bitstreams: 1 arquivo total.pdf: 931330 bytes, checksum: 351b504f68153fb01d23f3fd1d96d2a0 (MD5) Previous issue date: 2013-04-29 / In this work, after the introduction of some concepts of Commutative Algebra, for instance dimension, minimal number of generators, and multiplicity, we prove the existence of a very special class of modules over Cohen-Macaulay rings, the so-called Ulrich modules. It is known that, if M is a maximal Cohen-Macaulay module over such ring, then (M) e(M). Our goal in this study is to prove the main cases where the equality (M) e(M) holds. / Neste trabalho, após introduzirmos alguns conceitos de Álgebra Comutativa, como dimensão, número mínimo de geradores, e multiplicidade, provamos a existência de uma classe de módulos bastante especial sobre anéis Cohen-Macaulay, os chamados módulos de Ulrich. É sabido que, se M é um A-módulo Cohen-Macaulay maximal sobre um tal anel, então (M) e(M). O objetivo do nosso estudo é demonstrar os principais casos em que vale (M) = e(M).

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The purpose of this dissertation is to introduce the notion of local cohomology as well as some of its applications. Initially, we performed a brief review on the main homological tools used in this work, such as: homology of a complex, isomorphism of complexes, injective resolutions, derived functors, etc. Next, we detail properties of the injective modules in the context of Noetherian rings. Finally, we present di erent ways of de ning local cohomology and we show how this notion is used to investigate the arithmetical rank of an ideal. / O objetivo dessa dissertação é introduzir a noção de cohomologia local bem como algumas de suas aplicações. Inicialmente, realizamos um breve apanhado sobre as principais noções homológicas utilizadas no trabalho, tais como: homologia de um complexo, isomorfismo de complexos, resoluções injetivas, funtores derivados, etc. Em seguida, detalhamos propriedades dos módulos injetivos no contexto dos anéis Noetherianos. Finalmente, apresentamos formas variadas de definir cohomologia local e mostramos como essa noção é utilizada para investigar o posto aritmético de um ideal.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / David Mumford introduced the concept of regularity of a coherent beam into the projective space in terms of local cohomology, generalizing a classic argument of Castelnuovo. In this dissertation under view of commutative algebra, we will introduce the concept of regularity of finitely generated graduated modules on the ring of polynomials. First, we perform a preliminary study on dimension theory and especially on Hilbert’s function. We also studied the basics of Cohen- Macaulay modules, properties of Betti’s graduated numbers, and the local cohomology functors. In the main chapter, we define the regularity of Castelnuovo-Mumford using the free resolution shifts. Soon after, we show that the definition of regularity can be given in terms of local cohomology, with emphasis on the cases of Artinian and Cohen-Macaulay modules. / David Mumford introduziu o conceito de regularidade de um feixe coerente no espac¸o projetivo em termos de cohomologia local, generalizando um argumento cl´assico de Castelnuovo. Nessa dissertac¸ ˜ao sob a vis˜ao da ´algebra comutativa, introduziremos o conceito de regularidade de m´odulos graduados finitamente gerados sobre o anel de polinˆomios. Primeiramente realizamos um estudo preliminar sobre teoria da dimens˜ao e em especial sobre a func¸ ˜ao de Hilbert. Tamb´em estudamos noc¸ ˜oes b´asicas em m´odulos Cohen-Macaulay, propriedades dos n´umeros graduados de Betti e dos funtores de cohomologia local. No cap´ıtulo principal, definimos a regularidade de Castelnuovo-Mumford utilizando os shifts de resoluc¸ ˜oes livres. Logo ap´os, mostramos que a definic¸ ˜ao de regularidade pode ser dada em termos de cohomologia local, dando ˆenfase aos casos de m´odulos Artinianos e Cohen-Macaulay. / São Cristóvão, SE

Ce travail est consacré a l'étude des déformations covariantes des orbites co-adjointes du groupe de Lie SL(2,R).Nous établissons un lien entre des méthodes de quantification basées sur les crochets de Rankin-Cohen et les matrices de fusion pour les modules de Verma. Par ailleurs nous formalisons et étudions la notion associée d'algèbre de Rankin-Cohen qui contrôle l'associativité de ces déformations. / This work is devoted to the study of covariant star-product on coadjointorbits of the Lie group SL(2,R). We establish a correspondence between two quantization methods. The first is based on the Rankin-Cohen brackets and the second is based in the canonical element associate to the Shapovalov form and fusion matrices for Verma modules.Furthermore we formalize and study the associated notion of non-commutative algebra that controls the associativity of these deformations.

La théorie des champs de vecteurs logarithmiques et des formes différentielles logarithmiques d’une hypersurface singulière réduite est développée par K.Saito. Ces notions apparaissent dans l’étude de la connexion de Gauss-Manin de certaines familles de singularités et de leur déploiement semi-universel.Lorsque le module des champs de vecteurs logarithmiques est libre, l’hypersurface est appelée diviseur libre. A.G. Aleksandrov et A. Tsikh généralisent les notions de formes différentielles logarithmiques et de résidus logarithmiques aux intersections complètes et aux espaces de Cohen-Macaulay réduits.Nous étudions dans ce travail les formes différentielles logarithmiques d’un espace singulier réduit de codimension quelconque plongé dans une variété lisse, et nous développons une notion de singularités libres qui étend la notion de diviseurs libres. Les résidus des formes différentielles logarithmiques d’une hypersurface ainsi que leur généralisation aux espaces de codimension supérieure interviennent de façon cruciale dans ce travail de thèse. Notre premier objectif est de donner des caractérisations de la liberté pour les intersections complètes et les espaces de Cohen-Macaulay qui généralisent le cas des hypersurfaces. Nous accordons ensuite une attention particulière à une famille de singularités libres, à savoir les courbes, pour lesquelles nous décrivons le module des résidus logarithmiques en termes de multi-valuations. / The theory of logarithmic vector fields and logarithmic differential forms along a reduced singular hypersurface is developed by K. Saito. These notions appear in the study of the Gauss-Manin connection of some families of singularities and their semi-universal unfolding. If the module of logarithmic vector fields is free, the hypersurface is called a free divisor. A.G. Aleksandrov and A. Tsikh generalize the notions of logarithmic differential forms and logarithmic residues to reduced complete intersections and Cohen-Macaulay spaces. In this work, we study the logarithmic differential forms of a reduced singular space of any codimension embedded in a smooth manifold, and we develop a notion of free singularity which extend the notion of free divisor. The residues of logarithmic differential forms as well as theirgeneralization to higher codimension spaces are crucial in this thesis. Our first purpose is to give characterizations of freeness for complete intersections and Cohen-Macaulay spaces which generalize the case of hypersurfaces. We then give a particular attention to a family of free singularities, namely the curves, for which we describe the module of logarithmic residues thanks to their set of values.

Práce se zaměřuje na efektivní výpočet dvourozměrné diskrétní vlnkové transformace. Současné metody jsou v práci rozšířeny v několika směrech a to tak, aby spočetly tuto transformaci v jediném průchodu, a to případně víceúrovňově, použitím kompaktního jádra. Tohle jádro dále může být vhodně přeorganizováno za účelem minimalizace užití některých prostředků. Představený přístup krásně zapadá do běžně používaných rozšíření SIMD, využívá hierarchii cache pamětí moderních procesorů a je vhodný k paralelnímu výpočtu. Prezentovaný přístup je nakonec začleněn do kompresního řetězce formátu JPEG 2000, ve kterém se ukázal být zásadně rychlejší než široce používané implementace.

This thesis assesses the relation between equality and justice by exploring and identifying the relation between equality and justice in Rawls's theory of justice, Sandel's communitarian account of Justice and Sen's capability approach. And these accounts of justice are evaluated from an egalitarian point of view. The main argument defended in the thesis is that justice requires equality. Accordingly, these three accounts of justice are evaluated by taking their understanding of equality into consideration. Egalitarian evaluation of these accounts of justice reveals that all three of them fall short in accordance with the relation between equality and justice in their understanding of justice. Keywords: Capabilities, distributive justice, egalitarianism, equality, fairness, inequality, justice, social justice, virtues

<div>In the first part of this thesis, we study Rees algebras of modules. We investigate their Cohen-Macaulay property and their defining ideal, using <i>generic Bourbaki ideals</i>. These were introduced by Simis, Ulrich and Vasconcelos in [65], in order to characterize the Cohen-Macaulayness of Rees algebras of modules. Thanks to this technique, the problem is reduced to the case of Rees algebras of ideals. Our main results are the following.</div><div><br></div><div><div>In Chapters 3 and 4 we consider a finite module <i>E</i> over a Gorenstein local ring <i>R</i>. In Theorem 3.2.4 and Theorem 4.3.2, we give sufficient conditions for <i>E</i> to be of linear type, while Theorem 4.2.4 provides a sufficient condition for the Rees algebra <i>R(E)</i> of <i>E</i> to be Cohen-Macaulay. These results rely on properties of the residual intersections of a generic Bourbaki ideal <i>I</i> of<i> E</i>, and generalize previous work of Lin (see [46, 3.1 and 3.4]). In the case when <i>E</i> is an ideal, Theorem 4.2.4 had been previously proved independently by Johnson and Ulrich (see [39, 3.1]) and Goto, Nakamura and Nishida (see [20, 1.1 and 6.3]).</div></div><div><br></div><div><div>In Chapter 5, we consider a finite module <i>E</i> of projective dimension one over <i>k</i>[X₁, . . . , X_n]. Our main result, Theorem 5.2.6, describes the defining ideal of <i>R(E)</i>, under the assumption that the presentation matrix φ of <i>E</i> is <i>almost linear</i>, i.e. the entries of all but one column of φ are linear. This theorem extends to modules a known result of Boswell and Mukundan on the Rees algebra of almost linearly presented perfect ideals of height 2 (see [5, 5.3 and 5.7]).</div></div><div><br></div><div><div>The second part of this thesis studies the Cohen-Macaulay property of the special fiber ring<i> F(E)</i> of a module <i>E</i>. In Theorem 6.2.14, we prove that the generic Bourbaki ideals of Simis, Ulrich and Vasconcelos allow to reduce the problem to the case of fiber cones of ideals, similarly as for Rees algebras. We then provide sufficient conditions for <i>F(E)</i> to be Cohen-Macaulay. Our Theorems 6.2.15, 6.1.3 and 6.2.18 are module versions of results proved for the fiber cone of an ideal by Corso, Ghezzi, Polini and Ulrich (see [10, 3.1] and [10, 3.4]) and by Monta˜no (see [47, 4.8]), respectively.</div></div><div><br></div>

This essay is concerned with two explanations of why oppressive social orders persist. According to the first, the so-called gunman theory of oppression (GT), these social orders persist because the oppressed are afraid being punished if they participated in a revolt. According to the second, the so-called ideology theory of oppression (IT), oppression persists because the oppressed are subject to ideology. Traditionally, the former has been associated with rational choice theory, and the latter with Marxism and critical theory. Analytical philosophers have been suspicious of IT since it involves functional claims. This essay shows that it is possible to make sense of both IT and its associated functional claim within the framework of rational choice theory. Chapter one provides an overview of the discussion and a presentation of the general argument against IT. Chapter two specifies the explanandum for the two theories in more detail. The chapter concludes with a description of three real-life persistent oppressive social orders. In chapter three, the basics of rational choice theory are introduced and GT spelled out. Some problems for the theory are identified and then dealt with. It is concluded that GT does a good job at explaining the persistence of tyrannies. Chapter four argues that ideology is necessary to provide satisfactory explanations of the other two cases of oppression described in chapter two. The chapter concludes with a specification of IT where the functional claim is made explicit. Chapter five defends Gerald Cohen's account of functional explanations against a dilemma formulated by Ann Cudd. In chapter six, three mechanisms are provided that indicate how the functional claim of IT can be demystified. Chapter seven concludes by indicating a statistical method for testing IT and describing some policy implications. / EXPLANATIONS OF REPRESSION BY A MINORITY OF THE MAJORITY — A RESEARCH PROGRAM

In this thesis, I defend John Rawls’s assertion that political liberalism does not use the concept of truth. I respond to objections from Joshua Cohen and David Estlund. I argue that Cohen fails to show that public reason needs a minimalist conception of truth, since individuals with a range of conceptions of moral truth can meet the requirements of public reason. I dispute Estlund’s argument that the liberal principle of legitimacy is merely insular. Estlund assumes that the claim that the liberal principle of legitimacy is reasonable is no different than the claim that the principle is acceptable to reasonable persons. I argue that this assumption is incorrect, and that therefore the liberal principle of legitimacy is justifiable on the grounds that it is reasonable. I argue that political liberals need not worry that doing without the concept of truth will undermine the semantic coherence or objectivity of political liberalism.