Thesis (Ph.D.)--Baylor University, 2007. / Includes bibliographical references (p. 64-66).

Thesis (Ph. D.)--University of Chicago, Dept. of Physics, March 2003. / Includes bibliographical references. Also available on the Internet.

Thesis (doctoral)--Bonn, 1997. / On t.p. x̲ and y̲ are superscript. Includes bibliographical references (p. 117-119).

Thesis (Ph.D.)--Baylor University, 2009. / Includes bibliographical references (p. 141-147).

ARAUJO, H. R. M. Sobre invariantes topológicos de folheações holomorfas com singularidade isolada. 2017. 62 f. Dissertação (Mestrado Acadêmico em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017. / Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-05-25T20:23:00Z No. of bitstreams: 1 2017_dis_hrmaraujo.pdf: 556971 bytes, checksum: 9f274c4a5c917004f3b67a3fc72c5547 (MD5) / Rejected by Rocilda Sales (rocilda@ufc.br), reason: Boa tarde, Conferi a Dissertação de HAMILTON REGIS MENEZES DE ARAUJO, e constatei apenas dois erros na formatação no trabalho que dever ser alterados pelo autor: 1- Epígrafe ( a estrutura desse elemento deve ser a que se segue, com alinhamento à direita: "O sucesso é ir de fracasso em fracasso sem perder o entusiasmo." (Winston Churchill) 2- Títulos das seções (os títulos das seções que se encontram no sumário e ao longo do texto estão incorretos. As normas da ABNT recomendam que apenas a primeira letra do título das seções esteja em maiúscula, com exceção de nomes próprios. Ex.: 2.2 Índice de um Campo em uma Singularidade Isolada deve ser alterado para: 2.2 Índice de um campo em uma singularidade isolada Atenciosamente, on 2017-05-26T16:04:16Z (GMT) / Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-05-29T13:43:41Z No. of bitstreams: 1 2017_dis_hrmaraujo.pdf: 556572 bytes, checksum: cae2a014846c47e96be936dd25bbd9da (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2017-05-29T14:07:05Z (GMT) No. of bitstreams: 1 2017_dis_hrmaraujo.pdf: 556572 bytes, checksum: cae2a014846c47e96be936dd25bbd9da (MD5) / Made available in DSpace on 2017-05-29T14:07:05Z (GMT). No. of bitstreams: 1 2017_dis_hrmaraujo.pdf: 556572 bytes, checksum: cae2a014846c47e96be936dd25bbd9da (MD5) Previous issue date: 2017-05-19 / Considering the foliation induced by a complex holomorph vector field, we will look for topological invariants in the neighborhood of a singular point. At first, the Milnor Number of a vector field becomes important, in the sense that this number is topological invariant. In another discussion, we will emphasize vector fields in dimension two, in which case the leaves, whose foliation is induced by the field, will be integral curves of a 1-form. In this sense, we will deal with Desingularization, that is, after a finite number of processes, which we will call Blow-ups or explosions, we will turn the initial foliation into a foliation whose singularities are all simple. Finally, the Desingularization process of a field will give us tools that make it possible to relate the data obtained in this process to the objects treated throughout the work, with this we will present other topological invariants of foliations. / Considerando a folheação induzida por um campo vetorial complexo holomorfo, buscaremos exibir invariantes topológicos na vizinhança de um ponto singular. Num primeiro momento, ganha importância o Número de Milnor de um campo vetorial, no sentido desse número ser invariante topológico. Em outra discussão, daremos ênfase a campos vetoriais em dimensão dois, nesse caso, as folhas, cuja folheação é induzida pelo campo, serão curvas integrais de uma 1-forma. Nesse sentido, trataremos de Desingularização, ou seja, após um número finito de processos, que chamaremos de Blow-ups, ou explosões, transformaremos a folheação inicial em uma folheação cujas singularidades são todas simples. Por fim, o processo de Desingularização de um campo nos dará ferramentas que possibilitam relacionar os dados obtidos nesse processo com os objetos tratados ao longo de todo o trabalho, diante disto apresentaremos outros invariantes topológicos de folheações.

Amplitudes in theories with a massless gauge boson suffer from so-called infrared divergences where off-shell states become asymptotically close to the mass-shell in loop or phase-space momentum integrals. These singularities have been shown to cancel intricately order-by-order in the perturbative expansion. However, in order to obtain meaningful and precise predictions for physical observables, we must understand and compute such divergences to high orders. This can be accomplished by calculating webs: weighted sets of Feynman diagrams which, when exponentiated give the complete infrared singular component of the amplitude, known as the soft function. This quantity is formally equivalent to a vacuum expectation value of a product of Wilson lines. In this thesis we shall study webs correlating multiple Wilson lines, which differs from the two line case due to the possibility of non-trivial colour flows. This renders the soft function matrix valued in the space of colour flows, thus making its calculation and renormalisation non-trivial. At present, the infrared singularities of non-abelian, multiparton scattering amplitudes are known only to two loops in general kinematics, and to three loops in a simplifying kinematic limit. This thesis will thus form part of a program of work aimed at calculating and understanding the three-loop singularities in general kinematics and in doing so we aim to gain all-order insights into the pertubative structure of non-abelian gauge theories. We first specialise to a subset of webs which we have called Multiple Gluon Exchange Webs (MGEWs), which contain only those diagrams with direct exchanges of soft gauge bosons directly between Wilson lines with no intervening three- or four- boson vertices. Studing their properties allows us to construct a basis of functions which describes all examples of such webs, and we conjecture will continue to do so at any order. Furthermore, we find that the basis functions can be described by a simple, one-dimensional integral over only logarithms. We go on to compute several examples providing evidence for the validity of our basis and demonstrate the utility of the framework we have built by computing a four-loop web and providing some all-order results for particular classes of MGEW. We then consider a step beyond MGEWs, that is, webs which contain a single three-gluon vertex sub-diagram. In particular we study the simplest web in this class correlating four lines at three loops and attempt to calculate it through the numerical fitting of a physically motivated ansatz. We show that this web cannot carry kinematic dependence through conformal invariant cross ratios, which arise when connected subdiagrams correlate at least four lines. Hence, it is subject to the same constraints as MGEWs with regards to their symbol alphabet, from the physical considerations in their lightlike limit and spacelike/timelike analytic continuation. Like all other known webs satisfying such constraints, we therefore argue that it can be written in terms of sums of products of MGEW basis functions. Symmetries inherent to our parameterisation of the cusp angles, Bose symmetry and transcendental weight further constrain this ansatz, resulting in forty parameters for which we present preliminary results of a numerical fit.

Submitted by Marina Rosa Severian null (mari.severian@gmail.com) on 2016-07-18T14:41:23Z No. of bitstreams: 1 Relações de poder em uma escola pautada nas singularidades.pdf: 6510661 bytes, checksum: d18ccbd9ac8e0ea7c85bf1ad91413c28 (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-07-18T20:47:52Z (GMT) No. of bitstreams: 1 severian_mr_me_arafcl.pdf: 6510661 bytes, checksum: d18ccbd9ac8e0ea7c85bf1ad91413c28 (MD5) / Made available in DSpace on 2016-07-18T20:47:52Z (GMT). No. of bitstreams: 1 severian_mr_me_arafcl.pdf: 6510661 bytes, checksum: d18ccbd9ac8e0ea7c85bf1ad91413c28 (MD5) Previous issue date: 2016-05-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O discurso doutrinário produzido e veiculado nas sociedades disciplinares do século XVIII permitiu a instauração tanto das dicotomias quanto dos paradigmas que norteiam, até o presente século, a maneira como as instituições escolares devem atuar e refletir sobre o âmbito educacional, condicionando, consequentemente, não apenas as metodologias e as práticas adotadas nessas instituições, como também a crença que envolve o pensar e o fazer educacional na nossa sociedade contemporânea. Com isso, as escolas passaram a adotar algumas tendências mercadológicas e fabris as quais visam legitimar diretrizes autoritárias e ratificar uma hierarquia pré-estabelecida de poder nas instituições de ensino. De maneira contrária, Dewey (1959), Freire (1967 e 1979) e Morin (2000 e 2007) propõem outras maneiras de compreender a educação, enfatizando o papel primordial dessa para o desenvolvimento tanto do caráter quanto da personalidade “autênticos” do indivíduo, permitindo o despertar da singularidade e da ética nos alunos e nos professores. De acordo com essa perspectiva que visa construir uma educação singular, a nossa intenção neste trabalho é analisar e compreender de que forma se estabelecem as relações de poder (FOUCAULT, 1987 e 1989) nas práticas de língua estrangeira em uma escola, situada no interior de São Paulo, que segue os princípios da singularidade como fio condutor de sua prática. Dentro dessa abordagem, pretendemos depreender os discursos e as práticas referentes às singularidades e à democracia, a fim de refletir sobre a maneira como as relações verticais e horizontais se constroem nesse processo peculiar de ensino-aprendizagem de língua estrangeira. Para isso, realizamos uma pesquisa qualitativa de base etnográfica, com o intuito de observar como se estabelecem essas relações nas práticas de idioma e coletar os dados. / The doctrinal speech produced and conveyed in the disciplinary societies from 18th century consented the instauration both of the dichotomies and of the paradigms which guide, until the present century, the way how educational institutions must act and reflect on the educational field, hence conditioning not only the methodologies and practices in these institutions, as well as the belief that involves thinking and doing education in our contemporary society. The schools have adopted some trends similar to marketing and manufacturing procedures which legitimate authoritarian directives and ratify a pre-established hierarchy of power within and also outside the educational institution. Conversely, Dewey (1959), Freire (1967 and 1979) and Morin (2000 and 2007) present alternative ways to comprehend the education emphasizing its essential role to the development of both the authentic character and personality of the individual, enabling the arousal of singularity and ethic in students and educators. In accordance with this perspective that aims to erect an education based on humanity and singularity, this paper intents to analyze and comprehend how the power relantionships (FOUCAULT, 1987 and 1989) are established during the classes of foreign language at a specific school, situated in a city in the state of São Paulo, which follows the principles of singularity as a guideline to its practice. Within this approach, we intend to understand the discourse and practice with regard to singularities and democracy in education to reflect on how the vertical and horizontal relationships are built in this peculiar process of foreign language teaching and learning. To achieve this, we conducted a qualitative ethnographic research in order to observe how these relationships are established in foreign language classes and collect data.

La signature est un vecteur de choix pour définir l’épistémè dans laquelle s’inscrivent les artistes depuis les années 1960 car, signe de validation de l’œuvre mais aussi signe d’identité, elle est l’épicentre de plusieurs problématiques. Comprise communément comme inscription du nom de l’artiste sur l’œuvre, les nombreuses métamorphoses esthétiques dont elle fait l’objet, depuis que les frontières de l’art s’élargissent à tous les domaines de la vie, nous permettent d’interroger l’ontologie de l’art tout en soulignant les enjeux profonds dont elle relève. En effet, la signature dans l’art nous parle de notre monde contemporain. Pour en rendre compte nous avons problématisé notre recherche à partir des diagnostics désenchantés de la « postmodernité » et de trois formes de la signature, le signe autographique, l’autoportrait et le nom. À la croisée de diverses disciplines, sémiotique, esthétique, philosophie et littérature, économie, Droit juridique et politique, la signature dans l’art contemporain atteste une expérience commune et partageable. / The signature is a chosen vector for defining the épistémè to which the artists evolve since the 1960’s because, as a sign of the work’s validation but also as a sign of identity, it is the epicentre of several problems. The signature is commonly understood to be the inscription of the name of the artist on the work. However, since the boundaries of art have extended into all fields in life, many aesthetic metamorphoses to the signature enable us to question the ontology of art while underlining the major challenges it incurs. Indeed, signature in art tells us of our contemporary world and to account for this we have problematized our research on the basis of the disillusioned diagnoses of “postmodernity” and of three forms of signature : autographic sign, self-portrait and name. At the crossroad of various disciplines such as semiotics, aesthetics, philosophy and literature, economy, legal Right and politics, the signature in contemporary art attests a common and shareable experience.

Orientador: Michelle Ferreira Zanchetta Morgado / Banca: Aldicio José Miranda / Banca: João Carlos Ferreira Costa / Resumo: Neste trabalho estudamos germes de funções sob a ação do grupo R_I dos germes de difeomorfismos em C^n que preservam um ideal I, descrevendo os conceitos de codimensão e determinação finita associados. Isso nos fornece ferramentas para caracterizar um tipo especial de germes com singularidades não isoladas, as chamadas singularidades do tipo D(q,p). Conseguimos ainda relacionar o conceito de R_I-estabilidade com estes germes, para o caso em que I é um ideal radical que define uma intersecção completa quase homogênea com singularidade isolada. Além disso, apresentamos um sistema de coordenadas através do qual obtemos uma fórmula explícita para alguns dos números de Lê destes germes / Abstract: In this work we study germs of functions under the action of the R_I group of diffeomorphisms of germs in C^n which preserving an ideal I, describing the concepts of codimension and finite determination associated. This provides the tools to characterize a particular type of germ with non isolated singularities, the so called D(q,p) singularities. We can still relate the concept of R_I-stability with these germs, in the case where I is a radical ideal that defines complete intersection with isolated singularity. Moreover, we present a coordinate system by which we obtain an explicit formula for some Lê numbers of these germs / Mestre

Les réseaux de Chebyshev sont des systèmes de coordonnées sur les surfaces que l'on obtient par cisaillement d'un domaine du plan. Ceux-ci sont utilisés en particulier pour modéliser les gridshells qui constituent une construction architecturale notamment reconnue pour son faible coût environnemental. La difficulté principale dans la conception des gridshells est le manque de diversité des formes accessibles. En effet, bien que toute surface admette localement en tout point un réseau de Chebyshev, l'existence globale de ce type de coordonnées n'est possible que sur un ensemble restreint de surfaces. La recherche de conditions suffisantes pour l'existence globale de réseaux de Chebyshev est toujours d'actualité. Un des résultats de cette thèse est l'amélioration de ces conditions. Les possibilités d'améliorations en ce sens étant néanmoins limitées, nous élargissons la perspective en considérant des réseaux de Chebyshev avec singularités. Notre résultat principal est l'existence de réseaux de Chebyshev avec singularités coniques, lisses par morceaux, sur toute surface dont la courbure totale positive est inférieure à $2pi$ et dont la courbure totale négative est finie. Notre preuve est constructive, ce qui permet de déterminer ces réseaux dans des cas pratiques. Nous avons implémenté un cas particulier de notre algorithme dans le logiciel Rhinoceros et nous présentons des exemples de réseaux construits par cette méthode / Chebyshev nets are coordinate systems on surfaces obtained by pure shearing of a planar domain.These nets are used in particular to model gridshells, an architectural construction which is well-known for its low environmental impact. The main issue when designing a gridshell is the lack of diversityof the accessible shapes. Indeed, although any surface admits locally a Chebyshev net at any point, the global existence for these coordinate systems is only possible for a restricted set of surfaces. The research for sufficient conditions ensuring the global existence of Chebyshev nets is still ongoing. A result achieved in this thesis is an improvement on these conditions. Since the improvement in this direction seems to be rather limited, we broaden the perspective by introducing Chebyshev nets with singularities. Our main result is the existence of a global Chebyshev net with conical singularities on any surface with total positive curvature less than $2pi$ and with finite total negative curvature. Our proof is constructive, so that this method can be applied to practical cases. We have implemented a special instance of this algorithm in the software Rhinoceros and some discrete Chebyshev nets constructed using this method are presented