In this work we study the existence of nontrivial weak solutions for some Hamiltonian elliptic systems in dimension two, involving a potential function and nonlinearities which possess maximal growth with respect to a critical curve (hyperbola). We consider four different cases. First, we study Hamiltonian systems in bounded domains with potential function identically zero. The second case deals with systems of equations on the whole space, the potential function is bounded from below for some positive constant and satisfies some integrability conditions, while the nonlinearities involve weight functions containing a singulatity at the origin. In the third case, we consider systems with coercivity potential functions and nonlinearities with weight functions which may have singularity at the origin or decay at infinity. In the last case, we study Hamiltonian systems, where the potential can be unbounded or can vanish at infinity. To establish the existence of solutions, we use variational methods combined with Trudinger-Moser type inequalities for Lorentz-Sobolev spaces and a finite-dimensional approximation. / Neste trabalho estudamos a existência de soluções fracas não triviais para sistemas hamiltonianos do tipo elíptico, em dimensão dois, envolvendo uma função potencial e não linearidades tendo crescimento exponencial máximo com respeito a uma curva (hipérbole) crítica. Consideramos quatro casos diferentes. Primeiramente estudamos sistemas de equações em domínios limitados com potencial nulo. No segundo caso, consideramos sistemas de equações em domínio ilimitado, sendo a função potencial limitada inferiormente por alguma constante positiva e satisfazendo algumas de integrabilidade, enquanto as não linearidades contêm funções-peso tendo uma singularidade na origem. A classe seguinte envolve potenciais coercivos e não linearidades com funções peso que podem ter singularidade na origem ou decaimento no infinito. O quarto caso é dedicado ao estudo de sistemas em que o potencial pode ser ilimitado ou decair a zero no infinito. Para estabelecer a existência de soluções, utilizamos métodos variacionais combinados com desigualdades do tipo Trudinger-Moser em espaços de Lorentz-Sobolev e a técnica de aproximação em dimensão finita.

Muitos equipamentos utilizados para quantificar substâncias, como toxinas em alimentos, freqüentemente apresentam deficiências para quantificar quantidades baixas. Em tais casos, geralmente indicam a ausência da substância quando esta existe, mas está abaixo de um valor pequeno \'ksi\' predeterminado, produzindo valores iguais a zero não necessariamente verdadeiros. Em outros casos, detectam a presença da substância, mas são incapazes de quantificá-la quando a quantidade da substância está entre \'ksai\' e um valor limiar \'tau\', conhecidos. Por outro lado, quantidades acima desse valor limiar são quantificadas de forma contínua, dando origem a uma variável aleatória contínua X cujo domínio pode ser escrito como a união dos intervalos, [ómicron, \"ksai\'), [\"ksai\', \'tau\' ] e (\'tau\', ?), sendo comum o excesso de valores iguais a zero. Neste trabalho, são propostos modelos que possibilitam discriminar a probabilidade de zeros verdadeiros, como o modelo de mistura com dois componentes, sendo um degenerado em zero e outro com distribuição contínua, sendo aqui consideradas as distribuições: exponencial, de Weibull e gama. Em seguida, para cada modelo, foram observadas suas características, propostos procedimentos para estimação de seus parâmetros e avaliados seus potenciais de ajuste por meio de métodos de simulação. Finalmente, a metodologia desenvolvida foi ilustrada por meio da modelagem de medidas de contaminação com aflatoxina B1, observadas em grãos de milho, de três subamostras de um lote de milho, analisados no Laboratório de Micotoxinas do Departamento de Agroindústria, Alimentos e Nutrição da ESALQ/USP. Como conclusões, na maioria dos casos, as simulações indicaram eficiência dos métodos propostos para as estimações dos parâmetros dos modelos, principalmente para a estimativa do parâmetro \'delta\' e do valor esperado, \'Epsilon\' (Y). A modelagem das medidas de aflatoxina, por sua vez, mostrou que os modelos propostos são adequados aos dados reais, sendo que o modelo de mistura com distribuição de Weibull, entretanto, ajustou-se melhor aos dados. / Much equipment used to quantify substances, such as toxins in foods, is unable to measure low amounts. In cases where the substance exists, but in an amount below a small fixed value \'ksi\' , the equipment usually indicates that the substance is not present, producing values equal to zero. In cases where the quantity is between \'\'ksi\' and a known threshold value \'tau\', it detects the presence of the substance but is unable to measure the amount. When the substance exists in amounts above the threshold value ?, it is measure continuously, giving rise to a continuous random variable X whose domain can be written as the union of intervals, [ómicron, \"ksai\'), [\"ksai\', \'tau\' ] and (\'tau\', ?), This random variable commonly has an excess of zero values. In this work we propose models that can detect the probability of true zero, such as the mixture model with two components, one being degenerate at zero and the other with continuous distribution, where we considered the distributions: exponential, Weibull and gamma. Then, for each model, its characteristics were observed, procedures for estimating its parameters were proposed and its potential for adjustment by simulation methods was evaluated. Finally, the methodology was illustrated by modeling measures of contamination with aflatoxin B1, detected in grains of corn from three sub-samples of a batch of corn analyzed at the laboratory of of Mycotoxins, Department of Agribusiness, Food and Nutrition ESALQ/USP. In conclusion, in the majority of cases the simulations indicated that the proposed methods are efficient in estimating the parameters of the models, in particular for estimating the parameter ? and the expected value, E(Y). The modeling of measures of aflatoxin, in turn, showed that the proposed models are appropriate for the actual data, however the mixture model with a Weibull distribution fits the data best.

Este trabalho é dedicado ao estudo do comportamento a longo prazo de uma equação de placas extensíveis acoplada a uma equação de calor do tipo hiperbólico. O problema corresponde a um modelo de termo-elasticidade baseado em teorias de calor do tipo não-Fourier. Considerando que efeitos de inércia de rotação estão presentes no modelo, mostramos que o efeito dissipativo do calor e suficiente para estabilizar exponencialmente o sistema, sem dissipações adicionais. Além disso, provamos que o sistema possui um atrator global de dimensão fractal finita e também atratores exponenciais. Nossos resultados generalizam e complementam diversos trabalhos existentes / This work is concerned with long-time dynamics of solutions of extensible plate equations with thermal memory. It corresponds to a model of thermoelasticity based on a theory of non-Fourier heat flux. By considering the case where rotational inertia is present we show that the thermal dissipation is sufficient to stabilize the system exponentially and guarantee the existence of a finite-dimensional global attractor. In addition the existence of an exponential attractor and some further properties are also considered. Our results complements several existing results

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-03-07T14:25:21Z No. of bitstreams: 1 victorteixeirademelomayrink.pdf: 2587774 bytes, checksum: 1319cc37a15480796050b618b4d7e5f7 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-03-07T15:06:57Z (GMT) No. of bitstreams: 1 victorteixeirademelomayrink.pdf: 2587774 bytes, checksum: 1319cc37a15480796050b618b4d7e5f7 (MD5) / Made available in DSpace on 2017-03-07T15:06:57Z (GMT). No. of bitstreams: 1 victorteixeirademelomayrink.pdf: 2587774 bytes, checksum: 1319cc37a15480796050b618b4d7e5f7 (MD5) Previous issue date: 2016-08-31 / FAPEMIG - Fundação de Amparo à Pesquisa do Estado de Minas Gerais / O armazenamento de energia elétrica em larga escala ainda não é viável devido a restrições técnicas e econômicas. Portanto, toda energia consumida deve ser produzida instantaneamente; não é possível armazenar o excesso de produção, ou tampouco cobrir eventuais faltas de oferta com estoques de segurança, mesmo que por um curto período de tempo. Consequentemente, um dos principais desafios do planejamento energético consiste em realizar previsões acuradas para as demandas futuras. Neste trabalho, apresentamos um modelo de previsão para o consumo de energia elétrica a curto prazo. A metodologia utilizada compreende a construção de um comitê de previsão, por meio da aplicação do algoritmo Gradient Boosting em combinação com modelos de árvores de decisão e a técnica de amortecimento exponencial. Esta estratégia compreende um método de aprendizado supervisionado que ajusta o modelo de previsão com base em dados históricos do consumo de energia, das temperaturas registradas e de variáveis de calendário. Os modelos propostos foram testados em duas bases de dados distintas e demonstraram um ótimo desempenho quando comparados com resultados publicados em outros trabalhos recentes. / The storage of electrical energy is still not feasible on a large scale due to technical and economic issues. Therefore, all energy to be consumed must be produced instantly; it is not possible to store the production leftover, or either to cover any supply shortages with safety stocks, even for a short period of time. Thus, one of the main challenges of energy planning consists in computing accurate forecasts for the future demand. In this paper, we present a model for short-term load forecasting. The methodology consists in composing a prediction comitee by applying the Gradient Boosting algorithm in combination with decision tree models and the exponential smoothing technique. This strategy comprises a supervised learning method that adjusts the forecasting model based on historical energy consumption data, the recorded temperatures and calendar variables. The proposed models were tested in two di erent datasets and showed a good performance when compared with results published in recent papers.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-05-26T14:51:38Z No. of bitstreams: 1 luiseduardoreyesperez.pdf: 2784061 bytes, checksum: f741a9cf532f95435bbd639a2f2df42f (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-05-26T15:01:37Z (GMT) No. of bitstreams: 1 luiseduardoreyesperez.pdf: 2784061 bytes, checksum: f741a9cf532f95435bbd639a2f2df42f (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-05-26T15:01:55Z (GMT) No. of bitstreams: 1 luiseduardoreyesperez.pdf: 2784061 bytes, checksum: f741a9cf532f95435bbd639a2f2df42f (MD5) / Made available in DSpace on 2017-05-26T15:01:55Z (GMT). No. of bitstreams: 1 luiseduardoreyesperez.pdf: 2784061 bytes, checksum: f741a9cf532f95435bbd639a2f2df42f (MD5) Previous issue date: 2015-11-26 / Este trabajo es el resultado de una investigación sobre las praxeologias matemáticas realizadas por alumnos de enseñanza media, sobre el concepto matemático de función exponencial, en la Institución Educativa Técnica de Tunia en el Departamento del Cauca, Colombia. En este documento las reflexiones fueron enfocadas hacia adolescentes colombianos de enseñanza media en Colombia y la propuesta fue investigar qué tipos de praxeologías puntuales surgen en el momento de realizar actividades acerca de función exponencial. Buscando responder esta pregunta, orientamos esta disertación mediante la metodología de Ingeniería Didáctica, con la intención de direccionar el trabajo del investigador. En ese sentido se cuenta también con los procedimientos metodológicos los cuales permitieron verificar si a partir de la intención de conocer e identificar las potencialidades de las praxeologías puntuales estas sean idóneas a fin de trasformarlas en praxeologías contextualizadas para una cierta institución de enseñanza I desarrollada por el profesor titular y en consecuencia ésta sea apropiada e interiorizada convirtiéndose en una herramienta potencialmente valida para el profesor. Por tanto, surgen preguntas en el contexto educativo, sobre la forma y construcción de lo que se enseña, en particular el concepto de función exponencial. La construcción de las praxeologías puntuales, así como su formulación, serán enfocadas a través de la teoría antropológica de lo didáctico que además de identificar, ayudará a orientar la construcción de secuencias didácticas relacionadas con la función exponencial que formarán parte del producto educacional de esta disertación y en especial a la contribución de nuevas investigaciones. / This work is the result of the research about the mathematic praxeologies made by students the middle education about the mathematic concept of exponential function, in the Technical Educational Institution from Tunia located in the department of Cauca. On this document the considerations were directed to colombians youngers on the middle education in Colombia and the proposal is to research which types of punctual praxeologies arise in the moment of effect questions about of exponential fuction. In order to answer this question, we focused this dissertation through the methodology of didactic engineering, with the intention of focussed of work de researcher. also included the methodological procedures, which allowed to assess whether, based on the intention to know and identify the potential of specific praxeologies in order to turn them into praxeologies contextualized in an educational institution I and developed by the main professor and as a consequence, that praxeology turn into an educational concept, about the form and construction itself of what we teach, in particular,the concept of exponential fuction. The construction of the puctual praxeologies as their formulation, will be focused by through the anthropological theory of didactic. That in addition to identifying, will help to guide the construction of teaching sequences relating with the exponential fuction that will take part on the educational product of this dissertation and in special the contribution of new researches.

Cette thèse examine la dispersion multivariée des modelés normales stables Tweedie. Trois estimateurs de fonction variance généralisée sont discutés. Ensuite dans le cadre de la famille exponentielle naturelle deux caractérisations du modèle normal-Poisson, qui est un cas particulier de modèles normales stables Tweedie avec composante discrète, sont indiquées : d'abord par fonction variance et ensuite par fonction variance généralisée. Le dernier fournit la solution à un problème particulier d'équation de Monge-Ampère. Enfin, pour illustrer l'application de la variance généralisée des modèles Tweedie stables normales, des exemples à partir des données réelles sont fournis. / This thesis examines the multivariate dispersion of normal stable Tweedie (NST) models. Three generalize variance estimators of some NST models are discussed. Then within the framework of natural exponential family, two characterizations of normal Poisson model, which is a special case of NST models with discrete component, are shown : first by variance function and then by generalized variance function. The latter provides a solution to a particular Monge-Ampere equation problem. Finally, to illustrate the application of generalized variance of normal stable Tweedie models, examples from real data are provided.

This thesis examines how to find the best fit to a series of data points when curve fitting using power-exponential models. We describe the different numerical methods such as the Gauss-Newton and Levenberg-Marquardt methods to compare them for solving non-linear least squares of curve fitting using different power-exponential functions. In addition, we show the results of numerical experiments that illustrate the effectiveness of this approach.Furthermore, we show its application to the practical problems by using different sets of data such as death rates and rocket-triggered lightning return strokes based on the transmission line model.

L'objectif principal de cette recherche est d'analyser les effets de l'agrégation sur la prévision de la demande. Cet effet est examiné par l'analyse mathématique et l’étude de simulation. L'analyse est complétée en examinant les résultats sur un ensemble de données réelles. Dans la première partie de cette étude, l'impact de l'agrégation temporelle sur la prévision de la demande a été évalué. En suite, Dans la deuxième partie de cette recherche, l'efficacité des approches BU(Bottom-Up) et TD (Top-Down) est analytiquement évaluée pour prévoir la demande au niveau agrégé et désagrégé. Nous supposons que la série désagrégée suit soit un processus moyenne mobile intégrée d’ordre un, ARIMA (0,1,1), soit un processus autoregressif moyenne mobile d’ordre un, ARIMA (1,0,1) avec leur cas spéciales. / Demand forecasting performance is subject to the uncertainty underlying the time series an organisation is dealing with. There are many approaches that may be used to reduce demand uncertainty and consequently improve the forecasting (and inventory control) performance. An intuitively appealing such approach that is known to be effective is demand aggregation. One approach is to aggregate demand in lower-frequency ‘time buckets’. Such an approach is often referred to, in the academic literature, as temporal aggregation. Another approach discussed in the literature is that associated with cross-sectional aggregation, which involves aggregating different time series to obtain higher level forecasts.This research discusses whether it is appropriate to use the original (not aggregated) data to generate a forecast or one should rather aggregate data first and then generate a forecast. This Ph.D. thesis reveals the conditions under which each approach leads to a superior performance as judged based on forecast accuracy. Throughout this work, it is assumed that the underlying structure of the demand time series follows an AutoRegressive Integrated Moving Average (ARIMA) process.In the first part of our1 research, the effect of temporal aggregation on demand forecasting is analysed. It is assumed that the non-aggregate demand follows an autoregressive moving average process of order one, ARMA(1,1). Additionally, the associated special cases of a first-order autoregressive process, AR(1) and a moving average process of order one, MA(1) are also considered, and a Single Exponential Smoothing (SES) procedure is used to forecast demand. These demand processes are often encountered in practice and SES is one of the standard estimators used in industry. Theoretical Mean Squared Error expressions are derived for the aggregate and the non-aggregate demand in order to contrast the relevant forecasting performances. The theoretical analysis is validated by an extensive numerical investigation and experimentation with an empirical dataset. The results indicate that performance improvements achieved through the aggregation approach are a function of the aggregation level, the smoothing constant value used for SES and the process parameters.In the second part of our research, the effect of cross-sectional aggregation on demand forecasting is evaluated. More specifically, the relative effectiveness of top-down (TD) and bottom-up (BU) approaches are compared for forecasting the aggregate and sub-aggregate demands. It is assumed that that the sub-aggregate demand follows either a ARMA(1,1) or a non-stationary Integrated Moving Average process of order one, IMA(1,1) and a SES procedure is used to extrapolate future requirements. Such demand processes are often encountered in practice and, as discussed above, SES is one of the standard estimators used in industry (in addition to being the optimal estimator for an IMA(1) process). Theoretical Mean Squared Errors are derived for the BU and TD approach in order to contrast the relevant forecasting performances. The theoretical analysis is supported by an extensive numerical investigation at both the aggregate and sub-aggregate levels in addition to empirically validating our findings on a real dataset from a European superstore. The results show that the superiority of each approach is a function of the series autocorrelation, the cross-correlation between series and the comparison level.Finally, for both parts of the research, valuable insights are offered to practitioners and an agenda for further research in this area is provided.

Dans cette thèse, on étudie l'existence, l'unicité et la régularité des solutionsd'équation de type Cahn-Hilliard ainsi que son comportement asymptotiqueen termes d'existence de l'attracteur global et d'un attracteur exponentiel. Cetteéquation est considérée dans un domaine borné et régulier pour différents types denonlinéarités et de conditions au bord.D'abord, on étudie l'équation avec des conditions de type Dirichlet sur le bord etune nonlinéarité régulière. Après, on considère une perturbation du problème et ondémontre l'existence d'une famille robuste d'attracteurs exponentiels lorsque ε tendvers 0.Ensuite, on étudie l'équation avec des conditions dynamiques sur le bord. On considèretout d'abord une nonlinéarité régulière et on donne une étude théorique etnumérique. Après, on illustre ces résultats par des simulations numériques en dimensiondeux d'espace qui permettent d'étudier l'influence des différents paramètres.On termine par une étude du modèle considéré avec une nonlinéarité singulière quel'on approche par des fonctions régulières et on introduit une notion de solutionappropriée. / This thesis is devoted to the study of the existence, uniqueness andregularity of solutions for a Cahn-Hilliard type equation, as well as the asymptoticbehavior in terms of existence of the global attractor and of an exponential attractor.This equation is considered in a bounded and smooth domain under variousassumptions on the nonlinear terms and with different boundary conditions.We start by studying the equation with Dirichlet boundary conditions and a regularnonlinearity. Then, we consider a perturbation of the problem and we prove theexistence of a robust family of exponential attractors as ε tends to 0.For the equation endowed with dynamic boundary conditions, we first consider aregular nonlinearity and we treat the theoretical and numerical analysis. Then, weillustrate the results by numerical simulations in two space dimension which allow usto study the influence of different parameters. Finally, we treat the problem consideredwith a singular nonlinearity which is approximated by regular functions andwe give a suitable notion of solutions.

Abstract This dissertation consists of four articles on irrationality measures. In the first paper we derive explicit irrationality measures by using the simple continued fraction expansions in a completely new way. In the second and third articles we use Padé approximations to construct irrationality measures. In the second paper we obtain an explicit irrationality measure for the values of q-exponential series, for which the earlier corresponding results are not as explicit. Furthermore, we construct a restricted irrationality measure for the values of q-exponential series, which is an improvement on the earlier results in the restricted case. In the third article we derive the best possible asymptotic restricted irrationality exponent for the values of Jacobi's triple product. In the last paper we consider Cantor series. We generalize the earlier results by deriving Sondow's irrationality measure for some Cantor series. / Tiivistelmä Tämä väitöskirja koostuu neljästä artikkelista, jotka kaikki käsittelevät irrationaalisuusmittoja. Ensimmäisessä artikkelissa irrationaalisuusmittoja johdetaan uudella tavalla irrationaalilukujen yksinkertaisista ketjumurtolukuesityksistä. Toisessa ja kolmannessa artikkelissa irrationaalisuusmitat konstruoidaan Padé-approksimaatioiden avulla. Toisessa artikkelissa saadaan eksplisiittinen irrationaalisuusmitta q-eksponenttisarjan arvoille, joiden vastaavat aikaisemmat irrationaalisuusmitat eivät ole näin eksplisiittisiä. Lisäksi samassa artikkelissa konstruoidaan q-eksponenttisarjan arvoille rajoitettu eksplisiittinen irrationaalisuusmitta, mikä parantaa aikaisempia tuloksia rajoitetussa tapauksessa. Kolmannessa artikkelissa johdetaan paras mahdollinen asymptoottinen irrationaalisuuseksponentti Jacobin kolmitulon arvoille. Viimeisessä artikkelissa käsitellään Cantorin sarjoja. Siinä yleistetään aikaisempia tuloksia johtamalla Sondowin irrationaalisuusmitta tietylle joukolle Cantorin sarjoja.