This thesis analyses the semialgebraic sets, that is, a finite union of solu- tions to a finite sequence of polynomial inequalities. We introduce a notion of cylindrical algebraic decomposition as a tool for the construction of a semialge- braic stratification and a triangulation of a semialgebraic set. On this basis, we prove several important and well-known results of real algebraic geometry, such as Hardt's semialgebraic triviality or Sard's theorem. Drawing on Morse theory, we finally give a proof of a Thom-Milnor bound for a sum of Betti numbers of a real algebraic set. 1

Cette thèse porte sur deux aspects de la théorie de Morse: théorie de Morse discrète de Forman (cas de la dimension finie) et homologie de Heegaard-Floer (cas de la dimension infinie).<br />Dans une première partie, on s'intéresse au problème de relèvement de signe pour l'homologie de Heegaard-Floer combinatoire. On montre que la construction originale faite par Manolescu, Ozsváth, Szabó et D. Thurston peut être refaite de manière plus conceptuelle. On donne ensuite le lien entre ces deux constructions puis finalement on décrit un algorithme qui permet de calculer les signes.<br />La seconde partie porte sur la théorie de Morse discrète définie par Forman. Après avoir fait le lien entre l'algèbre sur les complexes de chaînes et la théorie de Morse discrète, on montre que le complexe de Thom-Smale donné par une fonction de Morse lisse sur variété lisse close peut être réalisé par une triangulation et une fonction de Morse discrète sur celle-ci. On utilise cela pour obtenir une représentation particulière sous forme de couplage complet de toute structure d'Euler sur une variété de dimension 3 close orientée.

This thesis reassesses American AIDS literature of the 1980s and 1990s by focusing on four major writers: the poets Thom Gunn (1929-2004), James Merrill (1926-1995) and Mark Doty (1953-), and the novelist Michael Cunningham (1952-). It questions the dominant critical discourse on literature of the epidemic, contending that while competing versions of the postmodern provided useful models for reading AIDS in the 1980s and 1990s, it is now necessary to adjust the critical position in line with the intellectual turn away from the cultural theories of that time. The introduction provides an overview of the most prevalent constructions of AIDS’ postmodernity through the period, arguing that critics were anxious to fit the epidemic to the theoretical models of the day, and going on to suggest that the writers under scrutiny actively question or even resist these models. Chapter One reads the later collections of Thom Gunn against his earlier work, arguing that he writes a "poetry of prophylaxis" which draws on his literary past in order to construct a defence against the uncertainties of the epidemic age. Chapter Two develops this question of self-reconstruction, examining the last two collections of James Merrill and his 1993 memoir in light of his own diagnosis with HIV. It proposes that in the renegotiation of his body, he might help the reader both remember and "re-member" him. Chapter Three turns to the work of Mark Doty, in particular the memoir Heaven’s Coast and the two collections, My Alexandria (1995) and Atlantis (1996), suggesting that Doty reclaims metaphor for palliative good at a time when AIDS theorists such as Paula Treichler registered scepticism during the "epidemic of signification". Chapter Four discusses the 1990s novels of Michael Cunningham, arguing that in order to “know” AIDS, outside of contemporaneous postmodern readings, it is necessary to "re-know" or "recognise" older literary models. The thesis ends with a brief account of post-1990s AIDS literature and theory, before concluding that each writer argues for models of literary continuity as a means of neutralising the possible creative rupture wrought by immunodeficiency.

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A bound for Betti numbers of sets definable in o-minimal structures is presented. An axiomatic complexity measure is defined, allowing various concrete complexity measures for definable functions to be covered. This includes common concrete measures such as the degree of polynomials, and complexity of Pfaffian functions. A generalisation of the Thom-Milnor Bound [17, 19] for sets defined by the conjunction of equations and non-strict inequalities is presented, in the new context of sets definable in o-minimal structures using the axiomatic complexity measure. Next bounds are produced for sets defined by Boolean combinations of equations and inequalities, through firstly considering sets defined by sign conditions, then using this to produce results for closed sets, and then making use of a construction to approximate any set defined by a Boolean combination of equations and inequalities by a closed set. Lastly, existing results [12] for sets defined using quantifiers on an open or closed set are generalised, using a construction from Gabrielov and Vorobjov [11] to approximate any set by a compact set. This results in a method to find a general bound for any set definable in an o-minimal structure in terms of the axiomatic complexity measure. As a consequence for the first time an upper bound for sub-Pfaffian sets defined by arbitrary formulae with quantifiers is given. This bound is singly exponential if the number of quantifier alternations is fixed.

Dans la première partiede cette thèse, nous étudions la monodromie du problème de Cauchy ramifié pour un opérateur à caractéristiques multiples de multiplicité constante. Plus précisément, nous donnons une estimation du spectre de la monodromie. Notre méthode est basée sur le calcul de la monodromie de certains opérateurs intégro-différentiels. Dans la seconde partie, on étudie le problème de Cauchy pour certains opérateurs. Nous écrivons la solution sous forme intégrale puis nous étudions le prolongement analytique decette intégrale.

Made available in DSpace on 2014-06-11T19:24:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-09-03Bitstream added on 2014-06-13T19:52:48Z : No. of bitstreams: 1 oliveira_arc_me_rcla.pdf: 769124 bytes, checksum: 51f07e82a0a21b5c9270a52d5d3e2500 (MD5) / Universidade Estadual Paulista (UNESP) / Este trabalho trata da classificação geométrica das formas binárias quádricas e cúbicas. Além disto, aplicamos esta classificação ao estudo de máquinas de catástrofes / This work make reference of the geometry classification of the two variables quadratic, cubic and quartic forma. Before that, the aplication that classification in study of the catastrophe machines

Aristotle proclaimed in his Poetics that there were six elements to drama: spectacle, music, diction, thought, character, and plot. This paper will analyze the play Thom Pain (based on nothing) against these six elements. I will discuss the aspects of each element that are present in the show as well as the ideas and concepts my director, Tad Ingram, and I brought to the show. Through the rehearsal and performance process I discovered a seventh element; the element of fearlessness. In his Poetics, Aristotle does not fully address what the actor brings to the performance and this aspect is just as important as what the script and staging bring to the performance.

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Dans cette thèse, nous nous intéressons à plusieurs aspects des systèmes de racines des algèbres de Lie simples. Dans un premier temps, nous étudions les coordonnées des vecteurs propres des matrices de Cartan. Nous commençons par généraliser les travaux de physiciens qui ont montré que les masses des particules dans la théorie des champs de Toda affine sont égales aux coordonnées du vecteur propre de Perron -- Frobenius de la matrice de Cartan. Puis nous adoptons une approche différente, puisque nous utilisons des résultats de la théorie des singularités pour calculer les coordonnées des vecteurs propres de certains systèmes de racines. Dans un deuxième temps, en s'inspirant des idées de Givental, nous introduisons les matrices de Cartan q-déformées et étudions leur spectre et leurs vecteurs propres. Puis, nous proposons une q-déformation des équations de Toda et construisons des 1-solitons solutions en adaptant la méthode de Hirota, d'après les travaux de Hollowood. Enfin, notre intérêt se porte sur un ensemble de transformations agissant sur l'ensemble des bases ordonnées de racines comme le groupe de tresses. En particulier, nous étudions les bases distinguées, qui forment l'une des orbites de cette action, et des matrices que nous leur associons. / In this thesis, our goal is to study various aspects of root systems of simple Lie algebras. In the first part, we study the coordinates of the eigenvectors of the Cartan matrices. We start by generalizing the work of physicists who showed that the particle masses of the affine Toda field theory are equal to the coordinates of the Perron -- Frobenius eigenvector of the Cartan matrix. Then, we adopt another approach. Namely, using the ideas coming from the singularity theory, we compute the coordinates of the eigenvectors of some root systems. In the second part, inspired by Givental's ideas, we introduce q-deformations of Cartan matrices and we study their spectrum and their eigenvectors. Then, we propose a q-deformation of Toda's equations et compute 1-solitons solutions, using the Hirota's method and Hollowood's work. Finally, our interest is focused on a set of transformations which induce an action of the braid group on the set of ordered root basis. In particular, we study an orbit for this action, the set of distinguished basis and some associated matrices.