String trimmers or weed cutter or strimmer is one of the inevitable tool for a professional gardener. They are helping gardeners for maintaining the lawn and farmland. These machines have been used by human for a quite long time. Professionals normally uses the bike handle type string trimmer and the amateurs who has small gardens normally uses loop handle one. The bike handle models are more powerful and gives more comfort for long time working. While performing the trimming process users are using the handles to steer and control the machine. Handle is the main touch point of the machine and it needs to provide enough comfort and assist the functions.Cramer, a German garden tools brand owned by The Globe Group, is focusing on researching and developing Garden power tools for amateurs as well as professional users. For them it is important to satisfy the customer and improve the user experience of their products.This project is focused only on the handle of the string trimmer to improve the overall user experience. This project mainly deals with the ergonomic aspects of the handle for a larger percentile of population. It is very important to make a handle were the professional users are going to use longer period of time. Along with the comfort this project put stress on increase the user experience by giving modern, friendly and premium expression visually as well as physically. Even though the project is to develop a handle concept, it needs to go along with the overall brand language.

O Quarteto de cordas em sol menor de Claude Debussy é uma obra marcada por importantes dicotomias. Composta em 1893, ela se encontra permeada de elementos harmônicos e formais ligados à tradição tonal e ao final do século XIX, particularmente ao compositor César Franck. Ao mesmo tempo, a peça utiliza procedimentos que são observados apenas em obras maduras do compositor, nas quais o tonalismo se encontra pouco presente, e análises que dependam exclusivamente de elementos tonais mostramse pouco eficientes para o Quarteto. Essa relação entre tradição e inovação é investigada nesta pesquisa, que traz como enfoque duas características diretamente relacionadas: a maneira como Debussy utiliza elementos repetidos nesta peça, assunto pesquisado por Sylveline Bourion, e aspectos relativos à forma cinética, elemento descrito por Richard Parks. Uma comparação entre o primeiro movimento do Quarteto e o primeiro movimento da Sonata para flauta, viola e harpa, peça do final da carreira de Debussy, é oportuna para que sejam observados elementos formais semelhantes aplicados em contextos diferentes. / Claude Debussy\'s String quartet in G minor is a work characterized by important dichotomies. Written in 1893, the piece is permeated by harmonic and formal elements attached to the tonal tradition and to the end of the 19th century, and specially to the composer César Franck. At the same time, the Quartet uses procedures observed only in Debussy\'s mature works, in which the presence of tonalism is weak, and analyses that rely exclusively on tonal elements are proven to have little efficiency regarding this piece. The relation between tradition and innovation is examined in this research, which focuses on two related characteristics: the way in which Debussy uses repeated elements in this piece, a matter also examined by Sylveline Bourion, and aspects related to the kinetic form described by Richard Parks. A comparison between the Quartet\'s first movement and the first movement from the Sonata for flute, viola and harp, composed at the end of Debussy\'s career, is useful for observing similar formal elements applied in different contexts.

In this doctoral thesis, we propose new iterative methods for solving a class of convex optimization problems. In general, we consider problems in which the objective function is composed of a finite sum of convex functions and the set of constraints is, at least, convex and closed. The iterative methods we propose are basically designed through the combination of incremental subgradient methods and string-averaging algorithms. Furthermore, in order to obtain methods able to solve optimization problems with many constraints (and possibly in high dimensions), generally given by convex functions, our analysis includes an operator that calculates approximate projections onto the feasible set, instead of the Euclidean projection. This feature is employed in the two methods we propose; one deterministic and the other stochastic. A convergence analysis is proposed for both methods and numerical experiments are performed in order to verify their applicability, especially in large scale problems. / Nesta tese de doutorado, propomos novos métodos iterativos para a solução de uma classe de problemas de otimização convexa. Em geral, consideramos problemas nos quais a função objetivo é composta por uma soma finita de funções convexas e o conjunto de restrições é, pelo menos, convexo e fechado. Os métodos iterativos que propomos são criados, basicamente, através da junção de métodos de subgradientes incrementais e do algoritmo de média das sequências. Além disso, visando obter métodos flexíveis para soluções de problemas de otimização com muitas restrições (e possivelmente em altas dimensões), dadas em geral por funções convexas, a nossa análise inclui um operador que calcula projeções aproximadas sobre o conjunto viável, no lugar da projeção Euclideana. Essa característica é empregada nos dois métodos que propomos; um determinístico e o outro estocástico. Uma análise de convergência é proposta para ambos os métodos e experimentos numéricos são realizados a fim de verificar a sua aplicabilidade, principalmente em problemas de grande escala.

Die vorliegende Dissertationarbeit ist dem Problem der analytischen Beschreibung des Confinement-Mechanismus in der QCD und in anderen Eichtheorien gewidment. Als Leitprinzip der Arbeit wurde das sogenannte Wilsonsche-Confinement-Kriterium gewählt, gemäss welchem diese Erscheinung durch eine effektive Stringtheorie beschrieben werden kann. Die entstehenden Strings des Eichfeldes verbinden farbige-Objekte (Quarks, Gluonen) miteinander und hindern ihr Auseinandergehen auf makroskopische Abstände. Es werden verschiedene Verfahren der Ableitung dieser Stringstheorien aus unterschiedlichen Eichtheorien, einschliesslich der QCD, vorgestellt. Kapitel 2 enthält die Untersuchung der nichtlokalen effektiven Stringwirkung, die im Rahmen des sogenannten stochastischen Vakuum-Modells der QCD entsteht, wobei die Wechselwirkung zwischen den Elementen der String-Weltfläche durch den phänomenologischen Background-Gluon-Propagator vermittelt wird. Durch Entwicklung dieser Wirkung nach Ableitungen wurden die ersten Terme niedrigster Ordnung bestimmt. Die ersten beiden Terme dieser Entwicklung sind die Nambu-Goto- und Rigidity-Terme mit Kopplungskonstanten, die sich durch das Gluon-Kondensat und die Korrelationlänge des QCD-Vakuums ausdrücken lassen. Die Vorzeichen dieser Konstanten zeigen, dass die durch dieses Verfahren erhaltenen Strings stabil sind. Danach wurde eine mögliche Lösung des ``Crumpling'' Problems auf der Basis eines zusätzlichen topologischen Stringtermes im Instantongas-Modell des QCD-Vakuums vorgestellt. Mittels Störungstheorie im nicht-störungstheoretischen QCD-Background berechneten wir zusätzliche-Korrekturen zur ursprünglichen nicht-störungstheoretischen Stringwirkung. Diese Korrekturen führen zu neuen Formen der nichtlokalen effektiven Stringwirkung, die den störungstheoretischen Gluon-Propagator im Backgroundfeld zwischen den Elementen der Weltfläche enthalten. Durch Ableitungsentwicklung dieser Wirkung bekommen wir eine Korrektur zur Kopplungskonstante des Rigidity-Terms; die Stringsspannung des Nambu-Goto-Terms jedoch bleibt unverändert. Am Ende dieses Kapitels wurde der Hamilton-Operator des QCD-Strings mit spinlosen Quarks hergeleitet, der der effektiven Stringwirkung mit Rigidity-Term entspricht. Dieser Hamilton-Operator liefert einen Korrekturterm zur Wechselwirkung im relativistischen Quarkmodell-Operator. Im Kapitel 3 untersuchten wir das Problem der Stringdarstellung von Abelsch-projezierten Eichtheorien. Als erstes wurde die Herleitung der Stringdarstellung der erzeugenden Funktion für das einfachste Modell dieser Art, d.h. die Abelsch-projezierte SU(2)-QCD gegeben, die einem dualen Abelschen Higgs-Modell mit äusseren elektrisch geladendenen Teilchen äquivalent ist. Der Vorteil dieses Stringszuganges im Vergleich zum Zugang des stochastischen Vakuum-Modells der QCD besteht in der Berücksichtigung der Integration über String-Weltflächen, die auf Grund der Integration über den Singulärteil der Higgsfeld-Phase entsteht. Zusätzlich zur Stringdarstellung der erzeugenden Funktion wurde im London-Limes die Stringdarstellung für die erzeugenden Funktionale der Feldstärke- und Monopolstromkorrelatoren hergeleitet. Dies gab uns die Möglichkeit, die entsprechenden bilokalen Kumulanten zu finden und zu zeigen, dass die bilokalen Kumulanten der Feldstärke für grosse Abstände das gleiche Verhalten wie die entsprechenden eichinvarianten Kumulanten der QCD zeigen. Das Letztere wurde durch das stochastische Vakuum-Modell vorhergesagt und durch Gitterexperimente berechnet. Dieses Ergebnis unterstützt einerseits die Methode der Abelschen Projektion und gibt anderseits dem stochastischen Vakuum-Modell der QCD einen neuen feldtheoretischen Status. Danach erweiterten wir unsere Analyse über den Rahmen des London-Limes hinaus untersuchten den Zusammenhang von quartischen Kumulanten und bilokalen Kumulanten. Anschliessend wurde die Stringdarstellung der SU(3)-Gluodynamik hergeleitet. Dabei wurde die Stringdarstellung für ein entsprechendes duales Modell formuliert, das drei Arten des magnetischen Higgs-Feldes enthält. Infolgedessen liefert das Modell drei Strings, von denen nur zwei wirklich unabhängig sind. Alle diese Strings wechselwirken untereinander durch Austausch zweier massiver dualer Eichbosonen. Ausserdem erhielten wir die bilokalen Kumulanten des effektiven dualen Modells der SU(3)-Gluodynamik. Die entsprechenden bilokalen Kumulanten zeigen für grosse Abstände ein Verhalten wie es durch das stochastische Vakuum-Modell vorhergesagt wurde. Zum Schluss dieses Kapitels geben wir eine nützliche Darstellung für erzeugende Funktionen von Abelsch-projezierten Theorien in Form von Integralen über Monopolströme an. Im Kapitel 4 wurde ein weiteres Modell untersucht, das eine analytische Beschreibung des Confinement-Mechanismus zulässt, nämlich die 3D kompakte QED. Für den Wilson-Loop der entsprechenden Theorie mit Monopoldichten wurde die Äquivalenz zur sogenannten Confining-Stringtheorie demonstriert. Ausserdem wurde das Verhalten der bilokalen Kumulante der Feldstärke im Limes schwacher Felder untersucht. Dieses Verhalten befindet sich ebenfalls in Übereinstimmung mit den Voraussagen des stochastischen Vakuum-Modells. Erwartungsgemäss sind die Stringdarstellungen der erzeugenden Funktionen der 3D kompakten QED im Limes schwacher Felder und der dualen Abelschen Higgs-Modelle sehr ähnlich. Wir zeigten ausserdem, dass diese Entsprechung nicht zufällig ist. Die 3D kompakte QED ergibt sich nämlich im Limes verschwindender Eichbosonmasse aus dem 3D Abelschen Higgs-Modell mit äusseren Monopolen. Zum Schluss wurde ein allgemeines Verfahren der Beschreibung der Anregungen der Stringweltfläche in Abelsch-projezierten Theorien (kompakte QED und QCD) ausgearbeitet. Es ist auf der Methode der nicht-linearen Sigma-Modelle gegründet und gibt eine Möglichkeit, die in diesen Fluktuationen quadratische Effektive Wirkung zu erhalten. In der Dissertation wurden analytische nicht-störungstheoretische Verfahren ausgearbeitet, die neue Informationen über den Confinement-Mechanismus in der QCD und anderen Eichtheorien liefern und zum besseren Verständnis der Vakuumstruktur dieser Theorien beitragen können. Sie sind insbesondere relevant für die Herleitung effektiver Stringtheorien aus Eichtheorien. / The main problem addressed in the present Dissertation was an attempt of an analytical description of confinement in QCD and other gauge theories. As a guiding principle for our investigations served the so-called Wilson's picture of confinement, according to which this phenomenon can be described in terms of some effective theory of strings, joining coloured objects to each other and preventing them from moving apart to macroscopic distances. In this Dissertation, we have proceeded with a derivation of such string theories corresponding to various gauge ones, including QCD, i.e. with the solution of the problem of string representation of gauge theories. We have started our analysis with the nonlocal string effective action, arising within the so-called Stochastic Vacuum Model of QCD, where the interaction between the string world-sheet elements is mediated by the phenomenological background gluon propagator. By performing the derivative expansion of this action, we have derived the first few terms of a string Lagrangian. The first two nontrivial of them turned out to be the Nambu-Goto and rigidity terms with the coupling constants expressed completely via the gluonic condensate and correlation length of the QCD vacuum. The signs of these constants ensure the stability of strings in the so-obtained effective string theory. After that, we have investigated the problem of crumpling for the string world-sheets by derivation of the topological string term in the instanton gas model of the gluodynamics vacuum. Next, by making use of perturbation theory in the nonperturbative QCD vacuum, we have calculated perturbative corrections to the obtained string effective action. Those lead to a new form of the nonlocal string effective action with the propagator between the elements of the world-sheet being the one of a perturbative gluon in the confining background. By the derivative expansion of this action, we got a correction to the rigidity term coupling constant, whereas the string tension of the Nambu-Goto term occurs to get no corrections due to perturbative gluonic exchanges. Finally, we have derived the Hamiltonian of QCD string with spinless quarks at the ends, associated with the obtained string effective action including the rigidity term. In the particular case of vanishing orbital momentum of the system, this Hamiltonian reduces to that of the so-called relativistic quark model, albeit with some modifications due to the rigidity term, which might have some influence on the dynamics of the QCD string with quarks. All these topics have been elaborated on in Section 2, and form the essence of the string representation of QCD within the Stochastic Vacuum Model. In Section 3, we have addressed the problem of string representation of Abelian-projected theories. In this way, we have started with the string representation for the partition function of the simplest model of this kind, namely the Abelian-projected SU(2)-QCD, which is argued to be the dual Abelian Higgs Model with external electrically charged particles. The advantage of this approach to the string representation of QCD w.r.t. the one based on the Stochastic Vacuum Model is a possibility to get an integration over the string world-sheets, resulting from the integration over the singular part of the phase of the Higgs field. After the string representation of the partition function in the London limit, we have proceeded with the string representation for the generating functionals of the field strength and monopole current correlators. Those enabled us to find the corresponding bilocal cumulants and demonstrate that the large-distance asymptotic behaviour of the bilocal field strength cumulant matches the one of the corresponding gauge-invariant cumulant in QCD, predicted by the Stochastic Vacuum Model and measured in the lattice experiments. This result supports the method of Abelian projection on the one hand and gives a new field-theoretical status to the Stochastic Vacuum Model on the other hand. After that, we have extended our analysis beyond the London limit, and studied the relation of the quartic cumulant, which appears there, with the bilocal one in the London limit. Next, by making use of the Abelian projection method, we have addressed the problem of string representation of the SU(3)-gluodynamics. Namely, we have casted the related dual model, containing three types of magnetic Higgs fields, into the string form. Consequently, the latter one turned out to contain three types of strings, among which only two ones were actually independent. As a result, we have found, that both the ensemble of strings as a whole and individual strings display confining properties in a sense that all types of strings (self)interact via the exchanges of the massive dual gauge bosons. We have also derived bilocal cumulants in the effective dual model of confinement, corresponding to the SU(3)-gluodynamics, and they turned out to be also in line with the ones predicted by the Stochastic Vacuum Model. In conclusion of this topic, we have obtained another useful representation for the partition functions of the Abelian-projected theories in the form of an integral over the monopole currents. In Section 4, we have studied another model, allowing for an analytical description of confinement, which is 3D compact QED. In this way, by virtue of the integral over the monopole densities, we have derived string representation for the Wilson loop in this theory and demonstrated the correspondence of this representation to another recently found one, the so-called confining string theory. After that, we have calculated the bilocal cumulant of the field strength tensors in the weak-field limit of the model under study. It also turned out to be in line with the general concepts of the Stochastic Vacuum Model and therefore matches the corresponding results known from the lattice measurements in QCD and found analytically for the effective Abelian-projected theories in the previous Section. Besides that, string representations of the partition functions of the weak-field limit of 3D compact QED and of the dual Abelian Higgs Model turned out to be also quite similar. We have illustrated later on that this correspondence is not accidental. Namely, we have shown that 3D compact QED is nothing else, but the limiting case of 3D Abelian Higgs Model with external monopoles, corresponding to the vanishing gauge boson mass. Finally, we have elaborated on a unified method of description of the string world-sheet excitations in the Abelian-projected theories, compact QED, and QCD, based on the techniques of nonlinear sigma-models, and obtained the effective action, quadratic in the world-sheet fluctuations. In conclusion, the proposed nonperturbative techniques provide us with some new information on the mechanisms of confinement in QCD and other gauge theories and shed some light on the vacuum structure of these theories. They also show the relevance of string theory to the description of this phenomenon and yield several prescriptions for the construction of the adequate string theories from the corresponding gauge ones.

Der Gegenstand dieser Arbeit ist Bestandteil der Stringtheorie und betrifft insbesondere die geometrischen Aspekte der Realisierung von Eichtheorien innerhalb der Stringtheorie. Wir studieren die Eichtheorie von D3-Branes an verallgemeinerten Singularitaeten wie der Orbifold- oder Conifold-Singularitaet. Die Einfuehrung der sogenannten Branediamanten fuehrt auf ein konsistentes Bild. Fuer diese Klasse von Modellen wird die Wirkung der Mirrorsymmetrie diskutiert. Im zweiten Teil untersuchen wir die Feldtheorie der M5-Brane auf der Grundlage des Supereinbettungsformalismus. Das Hauptresultat dieses Kapitels ist eine explizite Identifikation der selbstdualen 3-Form mit den Parametern der komplexen Struktur des Einbettungsraumes. Das heuristische Material, das in den vorangegangenen Kapiteln angesammelt wurde, weist darauf hin, dass die Informationen, die ein supersymmetrischer 3-Zykel enthaelt, zumindest teilweise auf supersymmetrische 2-Zykel zurueckgefuehrt werden koennen. Daher studieren wir den Fall von Brane-Boxen, die durch Ueberlagerung von gewoehnlichen N=2 Systemen aus D4 und NS5-Branes gewonnen werden koennen. Diese Konfigurationen erfuellen die Bedingung des `uniform bending' und der Lift auf einen supersymmetrischen 3-Zykel kann explizit ausgefuehrt werden. Im letzten Teil konstruieren wir eine neue superkonforme N=1 Eichtheorie, die aus einer Massendeformation der N=4 SYM entsteht und eine duale Supergravitationsbeschreibung durch die AdS/CFT-Korrespondenz besitzt. / The subject of this work is part of the theory of strings and in particular concerned with geometrical aspects of the realization of gauge theory within string theory. In particular we study the gauge theory of D3-branes at generalised singularities like orbifolds and the orbifolded conifold singularities. The introduction of the so called diamonds leads to a consistent picture. The action of mirror symmetry for this class of models is discussed. In a second part the field theory of the M5-brane will be investigated on the basis of the superembedding approach. The main result here will be a rather explicit identification of the self dual three form field with the parameters of the complex structure of the embedding space. The heuristic material collected from the previous chapters states that the information contained in supersymmetric 3-cycles can be partially extracted from supersymmetric 2-cycles. Thus we study the case of brane boxes, which can be obtained by sewing together usual N=2 setups of D4 and NS5-branes. These systems satisfy the condition of uniform bending and the lift to a supersymmetric 3-cycle can be performed explicitly. In the last part a new superconformal N=1 gauge theories will be constructed which arise as certain deformations of N=4 SYM and have a dual description due to the AdS/CFT correspondence.

This work is divided into two major topics: many-worlds (or multiverse) theories in cosmology and Richard Dawids string theory-based epistemology, or non-empirical confirmation theory, as he calls it. The former is discussed in part I and the latter in part II of this dissertation. These topics are not intertwined in this work, as are not the essays that compose each chapter: in part I, first chapter, probability arguments that are presented in the literature as indications a multiverse must exist are accessed, whereas the second chapter is concerned with analyzing the metaphysical view that motivates many-world theory building, namely, the need to find unconditioned explanations in physics. Non-empirical confirmation theory is built upon three arguments, the No Alternatives Argument, the Meta-Inductive Argument from the Success of Other Theories in the Research Program and the Unexpected Explanatory Coherence Argument. Each compose a chapter in part II of this work, as they encode different philosophical issues that require for their assessment different tools from the philosophers arsenal. Skeptical conclusions are drawn at the end of each chapter. The wide spectrum of questions this work touches are designed to give at least slight indication that critical exploration of foundational theories made upon grounds familiar to philosophers can be found as internal to scientific practice itself, if that practice is concerned with the discovery, refinement and revision of fundamental theories. / Este trabalho divide-se em dois grandes tópicos: teorias de muitos mundos (ou multiverso) em cosmologia e a epistemologia não-empírica, embasada na teoria das cordas, de Richard Dawid. O primeiro é discutido na parte I e o segundo compõe a parte II deste trabalho. Tais tópicos não estão ligados, e a problemática desenvolvida em cada capítulo deste trabalho é, em larga medida, independente das demais: no primeiro capítulo da parte I argumentos probabilísticos indicados a literatura em prol da existência de muitos mundos são analisados, enquanto no segundo capítulo os pressupostos metafísicos que motivam a construção de teorias de muitos mundos em cosmologia, a saber, o fundamentalismo que busca explicações não-condicionadas para os fenômenos com os quais lida a física, são discutidos. A teoria da confirmação não-empírica de Dawid, tema da segunda parte deste trabalho, tem por base três argumentos, a saber, o argumento das alternativas inexistentes, o argumento meta-indutivo do sucesso de outras teorias no programa de pesquisa e o argumento da coerência explanatória inesperada. Cada um destes argumentos é tema de um capítulo neste trabalho, posto que desvelam problemáticas filosóficas distintas que requerem, por sua natureza, ferramentas de análise diferentes. Conclusões céticas são indicadas ao final de cada capítulo. O amplo espectro de questões que aborda este trabalho é desenhado com o propósito de fornecer ao menos vaga indicação de que a exploração crítica de teorias fundamentais, levadas a cabo a partir de vieses familiares ao filósofo, pode ser vista como interna à própria prática científica, se esta prática é preocupada com a descoberta, refinamento e revisão de teorias fundamentais.

Cláudio Santoro (1919-1989) compôs, ao todo, quatorze sinfonias ao longo de toda a sua vida. A Primeira Sinfonia para duas orquestras de cordas (1940), além de possuir uma formação instrumental curiosa, também representa uma das obras inaugurais de sua primeira etapa como compositor, procurando ao lado de Koellreutter, novos paradigmas para a composição musical de seu tempo, tendo influenciado uma geração de compositores brasileiros. Este trabalho pretendeu desenvolver uma atenta e inédita análise da Primeira Sinfonia de Cláudio Santoro, procurando demonstrar sobre qual estética atonal, sendo ela dodecafônica ou livre, a obra foi escrita. Além da identificação sugerida, propõe-se também a averiguação de possíveis hibridismos estéticos que podem ter ocorrido na Primeira Sinfonia de Santoro. A análise atenta dos movimentos que constituem essa obra, utilizando métodos como a Teoria dos Conjuntos desenvolvido por Allen Forte, a Teoria dos Contornos Musicais de Robert Morris e a relação parcimoniosa entre diferentes coleções tal como proposto por Dmitri Tymoczko, nos permitiu identificar alguns processos pós-tonais, que indicam influencias de autores como Claude Debussy, Paul Hindemith e Heitor Villa-Lobos no primeiro movimento Allegro Majestoso da Primeira Sinfonia de Santoro. A manutenção de algumas sonoridades como a coleção pentatônica, a escala de tons inteiros e a coleção acústica, são alguns dos indícios que nos permite identificar tais influencias na obra de Santoro. No segundo movimento Andante quasi adagio, podemos observar um processo serial tradicional, que se desenvolveu a partir de duas séries que se relacionam. Tal apontamento foi possível a partir do método da identificação e contagem serial, tal como proposto por autores como Kostka e Francolí. No terceiro movimento, observamos uma estrutura que é engendrada a partir de coleções simétricas como a coleção eneatônica e a escala octatônica paradigmática, além de outras formatações simétricas que ocorrem a partir de sobreposições entre camadas, procedimento que também é encontrado na obra de Villa-Lobos. Nesse sentido, a Primeira Sinfonia para duas orquestras de cordas de Cláudio Santoro, foi engendrada através de procedimentos pós tonais considerados livres e sistêmicos, sendo possível observar hibridismos estilísticos nesta obra. / Cláudio Santoro (1919-1989) composed, in all, fourteen symphonies throughout his life. The First Symphony for two stringed orchestras (1940), in addition to possessing a curious instrumental formation, also represents one of the inaugural works of his first stage as composer, looking alongside Koellreutter, new paradigms for the musical composition of his time, having influenced a generation of Brazilian composers. This work developed a complete, attentive and unpublished analysis of the First Symphony of Claudio Santoro, trying to demonstrate on which atonal aesthetic, being it dodecaphonic or free, had written the work in question. Besides the suggested identification, it is also proposed the investigation of possible aesthetic hybridity that may have occurred in the First Symphony of Santoro. The careful analysis of the movements that constitute this work, using methods such as the Theory of Sets developed by Allen Forte, Robert Morris\'s Theory of Musical Constraints and the parsimonious relation between different collections as proposed by Dmitri Tymoczko allowed us to identify some post Which indicate influences by authors like Claude Debussy, Paul Hindemith and Heitor Villa-Lobos in the first Allegro Majestic movement of the First Symphony of Santoro. The maintenance of some sonorities such as the pentatonic collection, the whole-tone scale and the acoustic collection are some of the indications that allowed us to identify such influences in Santoro\'s work. In the second Andante quasi adagio movement, we can observe a traditional serial process, which developed from two series that relate, such an approach was possible from the method of serial identification and counting, as proposed by authors such as Kostka and Francolí. In the third movement, we observe a structure that is generated from symmetrical collections such as the eneatonic collection and the paradigmatic octatonic scale, as well as other symmetrical formations that occur from overlaps between layers, a procedure that is also found in the work of Villa-Lobos. In this sense, the First Symphony for two chord orchestras by Claudio Santoro was conceived through postural procedures considered free and systemic, being possible to observe stylistic hybrids in this work.

The present-day interest in gravitational waves, justified by the recent direct detections made by LIGO, is opening the exciting possibility to answer many questions regarding General Relativity in extreme situations. One of these questions is whether black hole are – indeed – described totally by their mass, charge and angular momentum or whether they can have additional long-range hair. This project is concerned with this question. We aim at studying the influence of additional structure on the black hole horizon in the form of long-range hair by studying linearized Einstein equation the solutions when perturbed. More precisely, we will study the Schwarzschild solution, pierced by an infinitely long and thin cosmic string such that the space-time possesses a global deficit angle. Quasi-normal modes are believed to dominate the gravitational wave emission during the ring down phase of an excited black hole that would e.g. be the result of a merger of two ultra-compact objects, therefore linearized perturbations can be considered. With the advent of gravitational wave astronomy the proposed study will be very important when reconstructing the source of the detected gravitational wave signals. / O atual interesse em ondas gravitacionais, justificado pelas detecções diretas feitas pela colaboração LIGO recentemente, está abrindo a excitante possibilidade de responder várias questões a respeito da Relatividade Geral em condições estremas. Uma dessas questões é se buracos negros são – realmente – totalmente discritos apenas por sua massa, carga e momento angular ou se eles podem ter os chamados cabelos de longo alcance adicionais. Nosso projeto se preocupa em responder esta pergunta. Nosso objetivo está em estudar a influência de uma estrutura adicional no horizonte de eventos de um buraco negro através do comportamento da equação linearizada de Einstein quando a solução é perturbada. Mais precisamente, nós estudaremos a solução de Schwarzschild atravessada por uma corda cósmica infinitamente fina, tal corda faz com que o espaço-tempo tenha um hiato angular em seu plano equatorial. Acredita-se que modos quasi-normais dominem a emissão de ondas gravitacionais durante a fase de ringing down de buracos negros excitados que podem, por exemplo, se originar da colisão de objetos ultra compactos, portanto perturbações lineares podem ser consideradas. Com o advento da astronomia através de ondas gravitacionais o estudo proposto será importante para que se possa reconstruir a origem de sinais detectados.

The central theme of this thesis is the application of mirror symmetry to the study of the arithmetic geometry of Calabi-Yau threefolds. It formulates a conjecture about the properties of the limit mixed Hodge structure at the large complex structure limit of an arbitrary mirror threefold, which is supported by a two-parameter example of a self-mirror Calabi-Yau threefold. It further studies the connections between this conjecture with Voevodsky's mixed motives. This thesis also studies the connections between the conifold transition and Beilinson's conjecture on the values of the L-functions at integral points. It carefully studies the arithmetic geometry of the conifold in the mirror family of the quintic Calabi-Yau threefold and its L-function, which is shown to provide a very interesting example to Beilinson's conjecture.

String diagrams turn algebraic equations into topological moves that have recurring shapes, involving the sliding of one diagram past another. We individuate, at the root of this fact, the dual nature of polygraphs as presentations of higher algebraic theories, and as combinatorial descriptions of "directed spaces". Operations of polygraphs modelled on operations of topological spaces are used as the foundation of a compositional universal algebra, where sliding moves arise from tensor products of polygraphs. We reconstruct several higher algebraic theories in this framework. In this regard, the standard formalism of polygraphs has some technical problems. We propose a notion of regular polygraph, barring cell boundaries that are not homeomorphic to a disk of the appropriate dimension. We define a category of non-degenerate shapes, and show how to calculate their tensor products. Then, we introduce a notion of weak unit to recover weakly degenerate boundaries in low dimensions, and prove that the existence of weak units is equivalent to a representability property. We then turn to applications of diagrammatic algebra to quantum theory. We re-evaluate the category of Hilbert spaces from the perspective of categorical universal algebra, which leads to a bicategorical refinement. Then, we focus on the axiomatics of fragments of quantum theory, and present the ZW calculus, the first complete diagrammatic axiomatisation of the theory of qubits. The ZW calculus has several advantages over ZX calculi, including a computationally meaningful normal form, and a fragment whose diagrams can be read as setups of fermionic oscillators. Moreover, its generators reflect an operational classification of entangled states of 3 qubits. We conclude with generalisations of the ZW calculus to higher-dimensional systems, including the definition of a universal set of generators in each dimension.