O perfil de consumo de energia elétrica dos consumidores necessita ser conhecido em detalhe para muitos estudos, sejam eles técnicos ou comerciais. Esse conhecimento pode ser alcançado através da obtenção das curvas de carga de todos os clientes da empresa, porém, devido ao grande número de medidores necessários, essa prática é inviável. A alternativa utilizada atualmente nas revisões tarifárias do sistema elétrico brasileiro emprega a teoria de amostragem associada a técnicas de análise de dados. Após a obtenção das informações, são calculadas as tipologias de carga que representam cada cliente ou transformador, através de etapas de caracterização da carga. Os resultados obtidos permitem uma análise mais precisa do mercado de energia elétrica e, principalmente, o conhecimento da forma como cada classe de consumidores utiliza a rede. Este trabalho envolve parte do estudo mencionado sobre a análise dos dados coletados nas campanhas de medição, propondo e avaliando metodologias alternativas para duas etapas do processo de caracterização de tipologias de carga, a seleção de curvas típicas e a classificação de dados, adequadas às necessidades das revisões tarifárias e com base em métodos heurísticos e nas práticas do setor. Após o desenvolvimento e implementação das metodologias, foram realizados testes entre os processos propostos, comparando e avaliando suas particularidades para duas situações: a semelhança entre as tipologias encontradas para os transformadores e consumidores de um mesmo nível de tensão e o impacto nos custos marginais de capacidade. A análise das comparações realizadas permitiu a identificação dos impactos e características das metodologias desenvolvidas, para cada etapa estudada. / Knowing the way consumers use the energy is necessary for many studies, either commercial or technical. This knowledge can be reached by obtaining the load curves from all the customers of the company. However, given the great number of measurers necessary, this practice is not viable. The alternative used currently in tariff review in the Brazilian electrical system is based on the sampling theory associated with data analysis techniques. After obtaining the information, the load typologies that represent each transformer or customer are calculated through stages of load characterization. The results obtained allow a more precise analysis of the electric energy market and, specially, the knowledge of how each consumer class uses the electricity network. This research involves part of the previously mentioned study on the analysis of the data collected in the measurement campaigns, considering and evaluating alternative methodologies for two stages of the load typologies characterization process, the election of typical curves and the data classification, adjusted to the necessities of the tariff revisions and on the basis of heuristical methods and electricity sector practices. After the development and implementation of the methodologies, tests have been carried between the considered processes, comparing and evaluating their particularitities for two situations: the similarity between the typologies found for transformers and consumers on the same tension level and the impact in the marginal capacity costs. The analysis of the comparisons carried through allowed the identification of the impacts and characteristics of the developed methodologies, for each studied stage.

The purpose of this thesis is to give a detailed group theoretic proof of the rank formula in a more general setting. By using the proof of Mordell-Weil theorem, a formula for the rank of the elliptical curves in certain cases over algebraic number fields can be obtained and computable.

<p>For the moduli stack $\mathcal{M}_{g,n/\mathbb{F}_p}$ of smooth curves of type $(g,n)$ over Spec $\mathbb{F}_p$ with the function field $K$, we show that if $g\geq3$, then the only $K$-rational points of the generic curve over $K$ are its $n$ tautological points. Furthermore, we show that if $g\geq 3$ and $n=0$, then Grothendieck's Section Conjecture holds for the generic curve over $K$. A primary tool used in this thesis is the theory of weighted completion developed by Richard Hain and Makoto Matsumoto.</p> / Dissertation

Submitted by Marilene Donadel (marilene.donadel@unioeste.br) on 2017-09-19T18:43:57Z No. of bitstreams: 1 Renato_F_Merli_2016.pdf: 2940827 bytes, checksum: 2fdcd7a1048f212c5d632e6f0849a570 (MD5) / Made available in DSpace on 2017-09-19T18:43:57Z (GMT). No. of bitstreams: 1 Renato_F_Merli_2016.pdf: 2940827 bytes, checksum: 2fdcd7a1048f212c5d632e6f0849a570 (MD5) Previous issue date: 2016-10-27 / Mathematics, according to most people, is an exact science - but what it means to be exact? Or, if it is accurate, as are their objects? Exactly? Or rather, what is a mathematical object? How to differentiate a mathematical object to another? What characteristics / properties are necessary for an object to be mathematical? Be accurate means to be intelligible? These questions, which are not the subject of discussions in this work were the triggering of this study. The proposal is to discuss the Cartesian refusal of the Greek criterion of demarcation between the two types of curves and try to understand the establishment of new criteria adopted by Descartes. Thus, looking along the dissertation seek to understand the reasons that led the philosopher to discuss and reclassify the curves. To understand the Cartesian distinction between geometric curves and mechanical curves we must first present the context in which these curves appear. In this aspect, it is initially held a historical retrospect of the main curves studied and investigated by the Greeks, as well as its main geometers representatives. In this context, it is reviewed and discussed the key role of the classic problems, which influenced the appearance and desevolvimento of such curves. Are they triggered new investigations and the appearance of new curves. Following a discussion of the Geometry test is carried out, containing an overview of the work, a characterization and demarcation of curves in this area. Next is discussed the understanding of Descartes to distinguish between geometrical and mechanical curves. Finally, conclusions are drawn about the view expressed here. According to Bos (2001), the argument adopted by Descartes to classify the curves was the "philosophical analysis of gemétrica intuition", namely the construction and representation of curves served to create objects known. Behind any choice of procedures for the construction was the intuition of "known-unknown", or, in general, the certainty of intuition in geometry. The overview that fincava her stakes was that the geometry has been shaped by a philosophical concern based on the certainty of geometrical operations, particularly buildings, ie the Cartesian mathematics was (and still is) the mathematics of a philosopher, in this context, that mathematics can not posit no arguments. In this respect, it is understood that Descartes had an idea of rationality based on continuity. Continuing this presupposes that a continuous movement of insights that can be reduced in a whole or in several movements, since continuous and intelligible. For example, in a spider's web, there is a main wire which is touched, it moves all other wires. So is the intuitive continuous movement presupposed by Descartes to the understanding of a geometric curve. The continuity of the generation of a geometric object corresponds to the continuity of mathematical thinking and therefore of understanding of the object continuously. / Matemática, segundo a maioria das pessoas, é uma ciência exata - mas o que significa ser exata? Ou ainda, se é exata, como são seus objetos? Exatos? Ou melhor, o que é um objeto matemático? Como diferencio um objeto matemático de outro? Que características/propriedades são necessárias para que um objeto seja matemático? Ser exato significa ser inteligível? Essas perguntas, que não serão alvo de discussões neste trabalho, foram as desencadeadoras do presente estudo. A proposta é discutir a recusa cartesiana do critério grego de demarcação entre os dois tipos de curvas e procurar entender o estabelecimento de novos critérios adotados por Descartes. Sendo assim, procura-se ao longo da dissertação buscar entender as razões que levaram o filósofo a discutir e reclassificar as curvas. Para compreender a distinção cartesiana entre as curvas geométricas e as curvas mecânicas é preciso inicialmente apresentar o contexto em que tais curvas aparecem. Nesse aspecto, inicialmente é realizado um retrospecto histórico das principais curvas estudadas e investigadas pelos gregos, bem como os seus principais geômetras representantes. Nesse contexto, é comentado e discutido o papel fundamental dos problemas clássicos, os quais influenciaram no aparecimento e desevolvimento de tais curvas. São eles que desencadearam novas investigações e o aparecimento de novas curvas. Na sequência, é realizada uma discussão sobre o ensaio A Geometria, contendo um panorama geral sobre a obra, uma caracterização e uma demarcação das curvas nesse âmbito. Em seguida é discutido o entendimento de Descartes para a distinção entre as curvas geométricas e mecânicas. Por fim, são apresentadas as conclusões a respeito da tese aqui defendida. Segundo Bos (2001), o argumento adotado por Descartes para classificar as curvas foi a “análise filosófica da intuição gemétrica”, ou seja, a construção e a representação das curvas serviram para criar objetos conhecidos. Por trás de qualquer escolha dos procedimentos para a construção estava a intuição do “conhecido-desconhecido”, ou, em geral, a intuição da certeza na geometria. A visão geral que fincava suas estacas era a de que a geometria foi moldada por uma preocupação filosófica baseada na certeza das operações geométricas, em particular das construções, ou seja, a matemática cartesiana era (e ainda é) a matemática de um filósofo e, nesse contexto, essa matemática não se pode postular sem argumentos. Nesse aspecto, fica compreendido que Descartes teve uma ideia de racionalidade baseada na continuidade. Continuidade essa que pressupõe um movimento contínuo de intuições que podem se reduzir em um todo ou em vários movimentos, desde que contínuos e intelegíveis. Por exemplo, em uma teia de aranha, há um fio principal que se tocado, movimenta todos os outros fios. Assim também o é o movimento contínuo intuitivo pressuposto por Descartes para o entendimento de uma curva geométrica. A continuidade da geração de um objeto geométrico corresponde à continuidade do pensamento matemático e, portanto, de compreensão desse objeto de forma contínua.

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Thesis advisor: Dawei Chen / We investigate the count of meromorphic differentials on the Riemann sphere pos-sessing a single zero, multiple poles with prescribed orders, and fixed residues at each pole. Gendron and Tahar previously examined this problem with respect to general residues using flat geometry, while Sugiyama approached it from the perspective of fixed-point multipliers of polynomial maps in the case of simple poles. In our study, we employ intersection theory on compactified moduli spaces of differentials, enabling us to handle arbitrary residues and pole orders, which provides a complete solution to this problem. We also determine interesting combinatorial properties of the solution formula. This thesis is organized as follows: In Chapter 1 we give an introduction to the problem and summarize the main results obtained. In Chapter 2 we review the compactification of moduli spaces of differentials and introduce various divisor classes. In Section 2.3 we explain how to identify the universal line bundle class with the divisor class of the locus of differentials satisfying a general given residue tuple and prove Theorem 1.0.1 (i). In Section 2.4 we impose exactly one independent partial sum vanishing condition to the residues and prove Theorem 1.0.1 (ii). In Section 2.5 we give a polynomial expression in terms of the zero order for the degree of mixed products between powers of the dual tautological class and the psi-class of the zero. Finally in Chapter 3 we prove Theorem 1.0.2 for arbitrary residues and investigate combinatorial properties of the solution formula. We have also verified our formula numerically for a number of cases by using the software package [CMZ2]. / Thesis (PhD) — Boston College, 2024. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

The thesis deals with arithmetics of elliptic curves over finite fields and methods to improve those calculations. In the first part, algebraic geometry helps to define elliptic curves and derive their basic properties including the group law. The second chapter seeks ways to speed up these calculations by means of time-memory tradeoff, i.e. adding redundancy. At last, the third part introduces a wholly new curve form, which is particularly effective for such purposes.

The thesis deals with arithmetics of elliptic curves over finite fields and methods to improve those calculations. In the first part, algebraic geometry helps to define elliptic curves and derive their basic properties including the group law. The second chapter seeks ways to speed up these calculations by means of time-memory tradeoff, i.e. adding redundancy. At last, the third part introduces a wholly new curve form, which is particularly effective for such purposes.

This work deals with the creation of several interactive web applets for education of vector graphics. Described is the image signal, his discretization, vector and bitmap types of image record. Further they describe selected vector curves, their properties, algorithms for their construction and usage. The principles of rasterization of basic vector objects are explained. Using the Figma tool, graphical user interfaces for each applet are designed. These applets are implemented using HTML and Javascript. The implemented applets are placed on web pages that are used in computer graphics education.