abstract: Quadratic growth curves of 2nd degree polynomial are widely used in longitudinal studies. For a 2nd degree polynomial, the vertex represents the location of the curve in the XY plane. For a quadratic growth curve, we propose an approximate confidence region as well as the confidence interval for x and y-coordinates of the vertex using two methods, the gradient method and the delta method. Under some models, an indirect test on the location of the curve can be based on the intercept and slope parameters, but in other models, a direct test on the vertex is required. We present a quadratic-form statistic for a test of the null hypothesis that there is no shift in the location of the vertex in a linear mixed model. The statistic has an asymptotic chi-squared distribution. For 2nd degree polynomials of two independent samples, we present an approximate confidence region for the difference of vertices of two quadratic growth curves using the modified gradient method and delta method. Another chi-square test statistic is derived for a direct test on the vertex and is compared to an F test statistic for the indirect test. Power functions are derived for both the indirect F test and the direct chi-square test. We calculate the theoretical power and present a simulation study to investigate the power of the tests. We also present a simulation study to assess the influence of sample size, measurement occasions and nature of the random effects. The test statistics will be applied to the Tell Efficacy longitudinal study, in which sound identification scores and language protocol scores for children are modeled as quadratic growth curves for two independent groups, TELL and control curriculum. The interpretation of shift in the location of the vertices is also presented. / Dissertation/Thesis / Doctoral Dissertation Statistics 2015

abstract: The thesis covers the development and modeling of the supervisory hybrid controller using two different methods to achieve real-world optimization and power split of a parallel hybrid vehicle with a fixed shaft connecting the Internal Combustion Engine (ICE) and Electric Motor (EM). The first strategy uses a rule based controller to determine modes the vehicle should operate in. This approach is well suited for real-world applications. The second approach uses Sequential Quadratic Programming (SQP) approach in conjunction with an Equivalent Consumption Minimization Strategy (ECMS) strategy to keep the vehicle in the most efficient operating regions. This latter method is able to operate the vehicle in various drive cycles while maintaining the SOC with-in allowed charge sustaining (CS) limits. Further, the overall efficiency of the vehicle for all drive cycles is increased. The limitation here is the that process is computationally expensive; however, with advent of the low cost high performance hardware this method can be used for the hybrid vehicle control. / Dissertation/Thesis / Masters Thesis Engineering 2017

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-09-05T16:23:50Z No. of bitstreams: 1 arquivototal.pdf: 5447841 bytes, checksum: a0295648faf5705131303671d36247c5 (MD5) / Approved for entry into archive by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-09-05T16:39:10Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 5447841 bytes, checksum: a0295648faf5705131303671d36247c5 (MD5) / Made available in DSpace on 2017-09-05T16:39:10Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 5447841 bytes, checksum: a0295648faf5705131303671d36247c5 (MD5) Previous issue date: 2015-08-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work presents one proposal that allows High School teachers and students a historical study of the construction of Conics, developed by Apollonius of Perga, the Mathematician and Astronomer that contributed immensely with the definitions we study nowadays in Mathematics. In a second moment, with Conics well defined by Pierre Fermat, the goal of the work is to address the content of Analytical Geometry as taught in the initial school years and Calculus courses. In a third moment, the approach is done through the study of Quadratic Functions, using a review of the content taught in Sophomore year of High School. / Este trabalho apresenta uma proposta de abordagem que permite tanto ao professor quanto ao aluno do ensino médio um estudo histórico da construção das Cônicas desenvolvidas pelo Matemático e Astrónomo Apolônio de Perga que contribuiu imensamente com as definições hoje estudadas na Matemática. No segundo momento, já bem mais definidas as Cônicas por Pierre Fermat o estudo tem como objetivo abordar o conteúdo da Geometria Analítica como é ensinado nas séries básicas e nas disciplinas de Cálculo. No terceiro momento, a abordagem é feita através do estudo das Funções Quadráticas, uma revisão da primeira série do Ensino Médio.

Submitted by Douglas Vinicius Rosato Costa null (douglas_vrc@yahoo.com) on 2018-03-13T02:13:44Z No. of bitstreams: 1 Dissertação Douglas Costa Versão Final.pdf: 1946320 bytes, checksum: 336b5ddb2211738253b95133f808aa2e (MD5) / Approved for entry into archive by Elza Mitiko Sato null (elzasato@ibilce.unesp.br) on 2018-03-13T19:05:51Z (GMT) No. of bitstreams: 1 costa_dvr_me_sjrp.pdf: 1946320 bytes, checksum: 336b5ddb2211738253b95133f808aa2e (MD5) / Made available in DSpace on 2018-03-13T19:05:51Z (GMT). No. of bitstreams: 1 costa_dvr_me_sjrp.pdf: 1946320 bytes, checksum: 336b5ddb2211738253b95133f808aa2e (MD5) Previous issue date: 2018-03-02 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho é apresentado um estudo sobre funções afim e quadrática e resolução de situações-problema através do uso de programação, tendo como público alvo os estudantes do último ano do ensino fundamental e primeiro ano do ensino médio. Atualmente, notamos no ensino básico apatia e desmotivação por parte dos estudantes, por não julgarem necessário o que aprendem na escola e, principalmente, ao encarar as dificuldades apresentadas em Matemática. Partindo dessa premissa, objetiva-se apontar uma ligação direta entre resolução de situações-problema e programação, e abordar de forma interativa e atraente uma maneira de adquirir as habilidades necessárias nessas duas áreas. Utilizando o software Scratch para resolver as atividades propostas sobre funções afim e quadrática, conseguimos cativar o interesse dos estudantes e atingimos maior participação em sala de aula, por meio de atividades diferenciadas e criativas. Incluem-se ainda os benefícios de aprender a programar, que é considerada uma habilidade essencial para o futuro. / In this work, it is presented a study on linear and quadratic functions and problem-solving through the use of programming, focusing on the students of the last year of elementary school and the first year of high school. Nowadays we notice apathy and demotivation from the students in the basic education due to their belief that what they learn in the school is unnecessary and, mainly, when facing the usual difficulties concerning Mathematics. Based on this premise, this work aims to point out a direct link between problem-solving and programming, interactively and attractively approaching a way to acquire the necessary skills in these two areas. Using the Scratch software to solve the proposed activities on linear and quadratic functions, we were able to captivate students' interest and achieve greater participation in the classroom through differentiated and creative activities. It also includes the benefits of learning how to program, which is considered an essential skill for the future.

Orientador: Adalberto Spezamiglio / Banca: Heloísa Helena Marino Silva / Banca: Luiz Augusto da Costa Ladeira / Resumo: Neste trabalho estudamos os sistemas dinâmicos caóticos através da definição apresentada por Devaney, composta basicamente de três condições. Investigamos todas as implicações possíveis entre essas condições. Por fim, analisamos o estudo apresentando uma definição mais sucinta e provamos a sua equivalência com a apresentada por Devaney. / Abstract: In this work we study the chaotic dynamic systems through the definition presented by Devaney, basically composed of three conditions. We investigate all the possible implications among these conditions. Finally, we finish the study presenting briefer definition and prove its equivalence to the one presented by Devaney. / Mestre

Nesta dissertação, discute-se o problema de otimização de carteiras de investimento para estratégia passiva de Index Tracking. Os objetivos principais são (i) apresentar um modelo de otimização de Index Tracking e (ii) a solucionar esse modelo com uso do método heurístico de Algoritmos Genéticos (AG) para formação de carteiras com número reduzido de ativos. O índice de referência utilizado é o Ibovespa, para o período de Janeiro/2009 a Julho/2012, com um total de 890 observações diárias de preços. A partir de uma amostra de 67 ativos, são formadas carteiras sem limite de ativos e limitadas a 40, 30, 20, 10 e 05 ativos; os intervalos de rebalanceamento das carteiras são 20, 40 e 60 períodos (dias úteis), ou seja, rebalanceamento mensal, bimestral e trimestral. É verificado que, para essa amostra, não é possível formar carteiras de 20 ou menos ativos via otimização direta com o solver Cplex com menos de 1 hora de processamento e gap abaixo de 5%. Com uso da heurística de Algoritmos Genéticos, são formadas carteiras de 10 e 05 ativos com tempo de processamento em torno de 5 minutos; nesse caso, o gap médio fica abaixo de 10% para ambos os tipos de carteira. E, com tempo de processamento do AG um pouco maior, em torno de 8 minutos, o algoritmo fornece soluções para carteiras de 10 e 05 ativos com gap médio abaixo de 5%. / In this master’s thesis it is discussed the portfolio optimization problem using the passive investment strategy of Index Tracking. The main goals are (i) to present an optimization model for the Index Tracking problem and (ii) to solve this model using the heuristic approach of Genetic Algorithms (GA) to create portfolios with reduced amount of stocks. The benchmark used is the Ibovespa Index (main reference for the Brazilian Stock Market), during the period from January/2009 to July/2012 (using a total of 890 daily stock prices). The sample contains 67 assets, and the model is used to build portfolios without limit in the amount of assets and portfolios limited to 40, 30, 20, 10 and 05 assets; the ranges of time to rebalance the portfolios are 20, 40, and 60 trading days, which means to rebalance monthly, bimonthly and quarterly. The results show that, considering this sample, it is not possible to build portfolios with 20 stocks (or less than 20) through direct optimization using the solver Cplex with computational processing time less than 1 hour and results with gap below 5%. On the other hand, using the Genetic Algorithms heuristic approach, portfolios limited to 10 and 05 stocks are built with computational time close to 5 minutes; for both types of portfolio, the solutions provided by the GA have average gap below 10%. Also, with a computational time slightly bigger, close to 8 minutes, the algorithm provides solutions with average gap below 5% for portfolios limited to 10 and 05 stocks.

O presente trabalho aborda o problema de estabilização local de sistemas não lineares quadráticos contínuos no tempo (possivelmente instáveis em malha aberta) e sujeitos a saturação de atuadores. Além disso o trabalho apresenta um estudo de técnicas de síntese de compensadores de anti-windup para sistemas quadráticos sujeitos à saturação de atuadores. A abordagem do estudo é comparativa em relação a duas formas de representação dos sistemas quadráticos. A primeira forma de abordagem é a Representação Algébrico-Diferencial — DAR (do inglês, Differential Algebraic Representation), aplicável a toda a classe de sistemas racionais. A segunda forma, por sua vez, consiste em uma decomposição quadrática, particular para sistemas quadráticos. Em ambos os casos, utiliza-se a não linearidade de zona morta e uma condição generalizada de setor para tratar da saturação. Para ambas representações, condições baseadas em Desigualdades Matriciais Lineares — LMIs (do inglês, Linear Matrix Inequalities) dependentes dos estados são obtidas para fornecer uma lei de controle linear, com o objetivo de estabilizar o sistema em malha fechada enquanto fornece uma região maximizada de estabilidade garantida associada a uma função de Lyapunov. A partir da mesma metodologia, são propostas técnicas de síntese de compensadores de anti-windup estáticos e dinâmicos. Exemplos numéricos são apresentados para verificar a eficácia dos métodos propostos. / This work addresses the problem of local stabilization of continuous-time quadratic systems (possibly open-loop unstable) and subject to actuator saturation. Furthermore, the work addresses a study of techniques for synthesis of anti-windup compensators for quadratic systems subject to actuator saturation. The study approach is comparative in the sense of considering two representations of quadratic systems. The first one is the Differential Algebraic Representation — DAR, suitable for the entire class of rational systems. The second representation consists in a quadratic decomposition, particular for quadratic systems. In both cases, it is used the deadzone nonlinearity and the generalized sector condition in order to deal with the saturation. For both representations, state-dependent Linear Matrix Inequalities — LMIs conditions are obtained to provide a control law with the aim of stabilize the closed-loop system while providing a region of guaranteed stability, associated to a Lyapunov function. Based on the same methodology, techniques are proposed for the synthesis of static and dynamic anti-windup compensators. Numerical examples are presented to verify the effectiveness of proposed methods.

abstract: This thesis addresses the issue of making an economic case for energy storage in power systems. Bulk energy storage has often been suggested for large scale electric power systems in order to levelize load; store energy when it is inexpensive and discharge energy when it is expensive; potentially defer transmission and generation expansion; and provide for generation reserve margins. As renewable energy resource penetration increases, the uncertainty and variability of wind and solar may be alleviated by bulk energy storage technologies. The quadratic programming function in MATLAB is used to simulate an economic dispatch that includes energy storage. A program is created that utilizes quadratic programming to analyze various cases using a 2010 summer peak load from the Arizona transmission system, part of the Western Electricity Coordinating Council (WECC). The MATLAB program is used first to test the Arizona test bed with a low level of energy storage to study how the storage power limit effects several optimization out-puts such as the system wide operating costs. Very high levels of energy storage are then added to see how high level energy storage affects peak shaving, load factor, and other system applications. Finally, various constraint relaxations are made to analyze why the applications tested eventually approach a constant value. This research illustrates the use of energy storage which helps minimize the system wide generator operating cost by "shaving" energy off of the peak demand. / Dissertation/Thesis / M.S. Electrical Engineering 2013

On s'intéresse dans cette thèse à la couverture des produits dérivés dans des marchés incomplets. L'approche choisie peut se voir comme une extension des travaux de M. Schweizer sur la minimisation locale du risque quadratique. En effet, tout en restant dans le cadre de la modélisation des actifs par des semimartingales, notre méthode consiste à remplacer le critère de risque quadratique par un critère de risque plus général, sous la forme d'une fonctionnelle convexe du coût local. Nous obtenons d'abord des résultats d'existence, d'unicité et de caractérisation des stratégies optimales dans un marché sans friction, en temps discret et en temps continu. Puis nous explicitons ces stratégies dans le cadre de modèles de diffusion avec et sans sauts. Nous étendons également notre méthode au cas où la liquidité n'est plus infinie. Enfin nous montrons par le biais de simulations numériques les effets du choix de la fonctionnelle de risque sur la constitution du portefeuille optimal. / This thesis deals with the issue of hedging contingent claims in incomplete markets. The way we tackle this issue may be seen as an extension of M. Schweizer's work on quadratic local risk-minimization. Indeed, while still modelling assets as semimartingales, our method relies on the introduction of a convex function of the local costs to assess risk, thus relaxing the quadratic assumption. The results we obtain are existence and uniqueness results first and characterizations of optimal strategies in a frictionless market, both in discrete and continuous time settings. We then make those strategies explicit by using diffusion models with and without jumps. We further extend our approach in the case when liquidity is given through a stochastic supply curve. Finally we show the effect of the choice of different risk functions on the optimal portfolio by numerically solving the optimality equations.

nÃo hà / Com a presente pesquisa buscou-se verificar se a utilizaÃÃo do software GeoGebra como ferramenta auxiliar da prÃtica pedagÃgica provocava uma melhoria da aprendizagem em funÃÃes quadrÃticas de alunos do 9 ano do Ensino Fundamental do ColÃgio Militar de Fortaleza (CMF). Para isso, fundamentado principalmente em Miorim (1998), Borba (1999), Fiorentini e Lorenzato (2007), Preiner (2008) e NÃbriga e AraÃjo (2010), foi realizado um estudo sobre o surgimento da EducaÃÃo MatemÃtica enquanto campo profissional e Ãrea de conhecimento, e sobre a sua relaÃÃo com o uso de software educativo nos processos de ensino e de aprendizagem, chegando ao caso mais especÃfico da aplicaÃÃo do software GeoGebra no estudo de funÃÃes quadrÃticas. Para o desenvolvimento desta pesquisa, utilizaram-se duas turmas de 9 ano, as quais foram denominadas de grupo de investigaÃÃo e grupo de comparaÃÃo. No primeiro grupo, o GeoGebra foi explorado no estudo de funÃÃes quadrÃticas, e alguns encontros foram realizados no laboratÃrio de informÃtica do CMF, com os alunos manuseando o software. No outro grupo, o GeoGebra nÃo foi utilizado. ApÃs os encontros foi aplicado o mesmo teste em ambos os grupos e um questionÃrio no grupo de investigaÃÃo. Com os dados coletados atravÃs desses instrumentos, com as observaÃÃes feitas e com o registro em diÃrio de bordo das atividades desenvolvidas nos encontros, foram realizadas abordagens quantitativas e qualitativas. Assim, se pÃde verificar que o GeoGebra à de fÃcil manuseio, facilita e dinamiza o processo de aprendizagem, e o seu uso teve boa aceitaÃÃo pela maioria dos alunos. AlÃm disso, o software proporciona que eles, ao interagirem com o computador, cheguem a conclusÃes prÃprias. Quanto à aprendizagem em funÃÃes quadrÃticas, ao se comparar os resultados dos alunos dos dois grupos, foi notÃrio o melhor desempenho dos alunos do grupo de investigaÃÃo. Dessa forma, concluiu-se que a utilizaÃÃo do Geogebra como ferramenta auxiliar da prÃtica pedagÃgica possibilita aos alunos uma melhor aprendizagem dos conceitos matemÃticos estudados. / This research aimed to analyze if the use of GeoGebra software as educational tool improved the pupil learning of quadratic functions in the 9th grade of the Elementary School in The Military School of Fortaleza (CMF). For this purpose, a study on the foundations of Mathematics Education as occupation and area of knowledge was undertaken as well as its relation to educational software use in the process of teaching and learning up to and including the use of GeoGebra software. This study was based mainly on Miorim (1998), Borba (1999), Fiorentini and Lorenzato (2007), Preiner (2008) and NÃbriga and AraÃjo (2010). Two groups of 9th grade were experienced, called Investigation and Comparison groups. In the first group GeoGebra software was explored for quadratic functions studies, part of the studies took place in the computer lab. The second group did not use the software. After the experience both groups were submitted to the same test and the first group answered a questionnaire. With data collected and observations carried out during the experience, qualitative and quantitative approaches were made. It is concluded that the software is easy managing, facilitates and promotes the process of learning with good acceptance by the most of students. Furthermore, the software helps students to get their own conclusion concerning the learning of quadratic functions, comparing the result of the groups experienced, it was notorious a better performance of students from Investigation group than students of Comparison group.