Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-15T13:04:40Z No. of bitstreams: 1 arquivototal.pdf: 6077553 bytes, checksum: 3cad3094833d2fdc458897bedccb4917 (MD5) / Made available in DSpace on 2016-03-15T13:04:40Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 6077553 bytes, checksum: 3cad3094833d2fdc458897bedccb4917 (MD5) Previous issue date: 2014-08-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we investigate in parallel physical and mathematical aspects inherent to the problem of confinement of massless Dirac fermions in graphene nanostructures. In a low energy approach, we propose models to describe confining systems in graphene and study how the choice of boundary conditions of the problem - or, equivalently, of domains of the Dirac operator - affects the physical properties of such systems. In this scenario, we concentrate essentially on the study of the physical behavior of graphene nanorings and nanoribbons in response to aspects such as topology, edge and interface geometry and interactions with external fields. At the same time, a rigorous investigation concerning formal aspects of the problem and the way that they manifest themselves physically is also performed. In light of the theory of linear operators on Hilbert spaces, we analyze the role played by the notion of self-adjointness in the problem and establish sets of boundary conditions physically acceptable in graphene, which mathematically corresponds to the definition of self-adjoint extensions of the Dirac Hamiltonian from the continuum description. Sets proposed in the treatment of some studied configurations are approached in this context. In addition, we present a particular study in which we examine the influence of topological defects on the physics of massive fermions in graphene in the presence of Coulomb and uniform magnetic fields. / Neste trabalho, investigamos paralelamente os aspectos físicos e matemáticos inerentes ao problema do confinamento de férmions de Dirac sem massa em nanoestruturas de grafeno. Em uma abordagem no limite de baixas energias, propomos modelos para descrever sistemas confinantes no âmbito da física do grafeno e estudamos de que modo a escolha das condições de contorno do problema - ou, equivalentemente, dos domínios do operador de Dirac - exercem influência sobre as propriedades físicas de tais sistemas. Neste cenário, concentramo-nos essencialmente no estudo do comportamento físico de nanoanéis e nanofitas de grafeno em resposta a aspectos como topologia, geometria de borda e interface e interações com campos externos. Ao mesmo tempo, também é realizada uma rigorosa investigação acerca dos aspectos formais do problema e do modo como eles se refletem fisicamente. À luz da teoria dos operadores lineares em espaços de Hilbert, analisamos o papel desempenhado pela noção de self-adjointness na modelagem do problema e estabelecemos conjuntos de condições de contorno fisicamente aceitáveis relativamente ao grafeno, o que corresponde matematicamente à definição de extensões auto-adjuntas do Hamiltoniano de Dirac da descrição do contínuo. Conjuntos propostos no tratamento de algumas das configurações estudadas são abordados neste contexto. Além disso, apresentamos um estudo à parte em que examinamos a influência de defeitos topológicos na física de férmions com massa no grafeno na presença de interações de Coulomb e de campos magnéticos uniformes.

Made available in DSpace on 2015-05-14T12:14:00Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 687609 bytes, checksum: ea5be67d908f758c02b556a96eb78d28 (MD5) Previous issue date: 2011-03-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this dissertation we will approach the lepton and barion number simmetries as low energy manifestation of more fundamental theories at higher energies. By using effective operators we investigate the possibility of generating reasonable mass terms for leptons as well as suppressed proton lifetime in the Standard Model. We also look at the proton decay processes in a specific grand unified theory (the minimal SU(5)) and comment about the experimental bounds on proton lifetime from Superkamiokande. Finally, we consider a simple gauge extension of Standard Model, the minimal SUC(3) SUL(3) UN(1) model, pointing some drawbaces in this model concerning lepton masses and proton lifetime. We study how it is possible to diminish its scalar content and solve the lepton mass and proton decay issues. / Nesta dissertação abordaremos as simetrias de número bariônico e leptônico do modelo padrão como manifestações em baixas energias de teorias mais fundamentais. Por meio de operadores efetivos, estudaremos termos de massa para léptons e modos de decaimento para o próton. Também estudaremos a predição quanto ao tempo de decaimento do próton num modelo de grande unificação específico (modelo SU(5) mínimo), comparando com o limite experimental do Super-Kamiokande. Por último apontaremos alguns problemas numa extensão de gauge do modelo padrão (modelo SUC(3) SUL(3) UN(1) mínimo), diminuindo seu conteúdo de campos escalares, onde os operadores efetivos para massa dos léptons e decaimento do próton serão manipulados através da introdução de certas simetrias discretas.

Há várias evidências experimentais da existência de matéria escura no universo. Apesar destas evidências, pouco se sabe sobre sua constituição, sabendo-se apenas que interage gravitacionalmente, mas não eletromagneticamente. Neste projeto, investigamos a possibilidade da matéria escura ser composta por partículas supermassivas e fortemente interagentes (Simpzillas). Para isto determinamos o sinal que deve ser deixado no telescópio IceCube por neutrinos resultantes de aniquilações de matéria escura no Sol. Após determinarmos o espectro de neutrinos no centro do Sol, simulamos sua propagação até a superfície, depois até a Terra e através da Terra até o detector. Comparamos então estes resultados com os fornecidos pelo IceCube. Esta comparação permite testar uma região do espaço de fase massa versus seção de choque previamente não-excluída por outros tipos de experiência que não telescópios de neutrinos. Como resultado, concluímos que partículas supermassivas e fortemente interagentes não podem constituir a matéria escura. / There are many experimental evidences for the existence of dark matter in the universe. Despite these evidences, there is no knowledge about its constitution other than the fact that it interacts gravitationally but not electromagnetically. In this project, we investigate the possibility that dark matter is composed of strongly interacting massive particles (Simpzillas). We determine the expected signal in the IceCube telescope from Simpzilla annihilation in the center of the Sun. We first determine the neutrino spectrum in the core of the Sun. We then simulate its propagation through both the Sun and Earth, and finally the rate of neutrinos at the detector. A comparison of these results to the ones published by the IceCube collaboration covers a large region of the yet not excluded regions of the mass versus cross-section phase space. As a result, the possibility of Simpzillas composing the dark matter is ruled out.

Neste trabalho estudamos algumas características das álgebras de Koszul, como por exemplo, a maneira como elas se relacionam com suas respectivas álgebras de Yoneda. Descrevemos a álgebra de Yoneda de uma álgebra monomial e como aplicação construímos uma família de álgebras: as chamadas homologicamente auto-duais. Uma álgebra de Koszul pode ser definida a partir da existência de resoluções lineares dos módulos simples. Por isso faz-se necessário a dedicação de parte de nossa atenção ao estudo destas resoluções. Além disso, achamos interessante estudar métodos para a construção de resoluções projetivas de módulos sobre quocientes de álgebras de caminhos. Para tal construção usamos essencialmente a teoria de bases de Gröbner não comutativas. Finalmente, para o caso de módulos lineares sobre álgebras de Koszul, veremos que é possível modicar essa construção de modo que a resolução resultante seja linear. / In this work we study some features of Koszul algebras as, for example, the way that they are related with their Yoneda algebras. We describe the Yoneda algebra of a monomial algebra and as an application we construct a family of algebras: the so called homologically self-dual algebras. A Koszul algebra can be dened as an algebra for which there are linear resolutions of their simple modules. Because of this we dedicate part of our attention to the study of projective resolutions. The study of methods for the construction of projectives resolutions of modules over quotients of path algebras, has an of interest its own. For the study of projective resolutions we used the theory of noncommutative, Gröbner bases. Finally, for the case of linear modules over Koszul algebras, we will see that it is possible to modify the general construction described here, so that the resulting resolution is linear.

Neste projeto, propomos estudar a chamada \"Teoria de Corpos de Classe,\" que oferece uma descrição simples das extensões abelianas de corpos locais e globais, bem como algumas de suas aplicações, como os teoremas de Kronecker-Weber e Scholz-Reichardt / In this work, we study the so called \"Class Field Theory\", which give us a simple description of the abelian extension of local and global elds. We also study some applications, like the Kronecker-Weber and Scholz-Reichardt theorems

Background: During the last decade or so the century old bespoke tailors on Savile Row have become the epitome of luxury brands as far as menswear is concerned. At the same time, the different establishments on Savile Row have started to modernise themselves through various means to better fit into today’s fast paced retail-market. Aims of the research: The purpose of this research is to discover what factors have played part in keeping the founders of Savile Row, Henry Poole & Co., modern and relevant throughout the years. Methods: This research was conducted as a qualitative single case, case study. The data was gathered through semi-structured interviews with upper management and other available published sources and then analysed with the help of former research in relevant areas. Results: It was found that the brand of Henry Poole & Co. stayed true to their origins as a bespoke tailor and that modernising is something that has not been forced upon the company and brand but should more be seen as a continuous process where each new generation bring something new to the company. The company had adapted modern ways of communication such as social media and a responsive website and also incorporated step down line extensions, where they sell ready-to-wear and made-to-measure garments in China and Japan. This is a way to develop their brand into other segments but they still kept their original brand vision intact as being a pure bespoke tailor located on Savile Row and kept their different business operations on a distance. Contributions: This thesis has opened up doors to an area that has not had much interest from the academic world. It hopefully gives way for new research ideas, but it has also highlighted management tools and best practices that has contributed to the success of a more than two century old company.

本論文主要的目的為找出六個身體部位詞-臉、面、眼、目、嘴、口在台灣華語的真實使用情形。本篇所分析的語料皆來自於目前收錄最多筆語料、體裁種類平衡、被廣泛使用的中央研究院現代漢語平衡語料庫４.０版。我們有系統地分析了包含這六個身體部位詞詞彙的內部構造、語意分佈、與詞彙化類型。研究結果發現，在包含這六個身體部位詞詞彙中，[NN]N為最顯著的詞彙內部構造。而在語意分布的部份，相較於臉、眼、嘴，面、目、口較常被用來表達轉喻及隱喻等非字面上的意義。此外，人與情緒為最為普遍的轉喻意，這兩個轉喻用法在六個身體部位詞詞彙中皆可發現。此外，當身體部位詞詞彙表達人這個轉喻意時，其詞彙內部構造多為[NN]N ; 當身體部位詞詞彙表達情緒這個轉喻意時，其詞彙內部構造多為[NN]N與[VN]V。另外，大體上來說，無論身體部位詞詞彙是表達轉喻意或隱喻意，[NN]N為最普遍的內部構造。並且，當身體部位詞詞彙表達轉喻意或隱喻意時，最常出現的詞彙化類型為隱喻詞彙化（metaphorical lexicalization）。本研究結果期望能提供語料庫辨別轉喻及隱喻的方法，並期望轉喻及隱喻的研究可以從長久以來偏向質性的討論分析，擴展到量化的比較與討論。 / This study aims at finding the actual usage patterns of the six body-part terms liǎn, miàn, yǎn, mù, zuǐ, and kǒu extracted from the largest, balanced and widely-used Sinica Corpus 4.0. The word component structures, meaning distribution and lexicalization types in the six body-part terms are systematically analyzed and compared. The results show that, in terms of word component structures, the [NN]N structure is the most dominant word component structure across the six body-part terms. As for meaning distribution, it is found that miàn, mù, and kǒu are more frequently used to denote non-literal meanings (either metonymic or metaphorical meanings) than their counterparts – liǎn, yǎn, and zuǐ. In addition, PERSON and EMOTION are the most prevalent metonymic meanings across the six body part terms. It is also found that when the body-part terms denote PERSON, the most dominant word component structure is [NN]N, while when they denote EMOTION, [NN]N and [VN]V are the most dominant structures. In general, the [NN]N structure shows the highest frequency of occurrences in all the six body part terms when they are used either metonymically or metaphorically. As for the lexicalization types, most of the disyllabic words containing the six body-part terms are in metaphorical lexicalization when they denote metonymic or metaphorical meanings. The results may provide some insights for refining procedures of identifing metaphors and metonymies in corpora so as to accelarate quantification and statistical evaluation.

It is well known that there exist domains Ω in Cn,n ≥ 2, such that all holomorphic functions in Ω continue analytically beyond the boundary. We wish to study this remarkable phenomenon. The first chapter seeks to motivate this theme by offering some well-known extension results on domains in Cn having many symmetries. One important result, in this regard, is Hartogs’ theorem on the extension of functions holomorphic in a certain neighbourhood of (D x {0} U (∂D x D), D being the open unit disc in C. To understand the nature of analytic continuation in greater detail, in Chapter 2, we make rigorous the notions of ‘extensions’ and ‘envelopes of holomorphy’ of a domain. For this, we use methods similar to those used in univariate complex analysis to construct the natural domains of definitions of functions like the logarithm. Further, to comprehend the geometry of these abstractly-defined extensions, we again try to deal with some explicit domains in Cn; but this time we allow our domains to have fewer symmetries. The subject of Chapter 3 is a folk result generalizing Hartogs’ theorem to the extension of functions holomorphic in a neighbourhood of S U (∂D x D), where S is the graph of a D-valued function Φ, continuous in D and holomorphic in D. This problem can be posed in higher dimensions and we give its proof in this generality. In Chapter 4, we study Chirka and Rosay’s proof of Chirka’s generalization (in C2) of the above-mentioned result. Here, Φ is merely a continuous function from D to itself. Chapter 5 — a departure from our theme of Hartogs-Chirka type of configurations — is a summary of the key ideas behind a ‘non-standard’ proof of the so-called Hartogs phenomenon (i.e., holomorphic functions in any connected neighbourhood of the boundary of a domain Ω Cn , n ≥ 2, extend to the whole of Ω). This proof, given by Merker and Porten, uses tools from Morse theory to tame the boundary geometry of Ω, hence making it possible to use analytic discs to achieve analytic continuation locally. We return to Chirka’s extension theorem, but this time in higher dimensions, in Chapter 6. We see one possible generalization (by Bharali) of this result involving Φ where is a subclass of C (D; Dn), n ≥ 2. Finally, in Chapter 7, we consider Hartogs-Chirka type configurations involving graphs of multifunctions given by “Weierstrass pseudopolynomials”. We will consider pseudopolynomials with coefficients belonging to two different subclasses of C(D; C), and show that functions holomorphic around these new configurations extend holomorphically to D2 .

In this thesis we study some questions related to vector bundles over hypersurfaces. More precisely, for hypersurfaces of dimension ≥ 2, we study the extension problem of vector bundles. We find some cohomological conditions under which a vector bundle over an ample divisor of non-singular projective variety, extends as a vector bundle to an open set containing that ample divisor. Our method is to follow the general Groethendieck-Lefschetz theory by showing that a vector bundle extension exists over various thickenings of the ample divisor. For vector bundles of rank > 1, we find two separate cohomological conditions on vector bundles which shows the extension to an open set containing the ample divisor. For the case of line bundles, our method unifies and recovers the generalized Noether-Lefschetz theorems by Joshi and Ravindra-Srinivas. In the last part of the thesis, we make a specific study of vector bundles over elliptic curve.

We will extend the conjugacy problem of maximal toral subalgebras for Lie algebras of the form $\g{g} \otimes_k R$ by considering $R=k[t,t^{-1}]$ and $R=k[t,t^{-1},(t-1)^{-1}]$, where $k$ is an algebraically closed field of characteristic zero and $\g{g}$ is a direct limit Lie algebra. In the process, we study properties of infinite matrices with entries in a B\'zout domain and we also look at how our conjugacy results extend to universal central extensions of the suitable direct limit Lie algebras.