The 17;18O(p,α)14;15N nuclear reactions play an important role in several astrophysical scenarios, and in Asymptotic Giant Branch (AGB) stars in particular. These stars are the site of several mixing and recirculating processes that transport matter from their hot cores to their cooler surfaces, and vice versa. Some of these mixing processes are still not well understood. Constraining them would improve our knowledge of stars that are in, or will enter, the AGB phase, including our own Sun. An ideal way to trace these poorly understood mixing processes are provided by the rare, stable 17;18O isotopes. Their abundances are strongly sensitive to the 17;18O(p,α)14;15N reactions. At temperatures of astrophysical interest, the 17O(p,α)14N reaction is dominated by a narrow, isolated resonance at Eproton=70 keV. This resonance has been studied several times in the past, using both direct and indirect methods. However, the picture painted in the literature is still not completely satisfying. The situation is more complex for the 18O(p,α)15N, for which an interference pattern between at least three resonances dominates the reaction rate at the temperatures of interest. This thesis work concerns an experimental campaign aimed at measuring both reactions at energies of astrophysical interest. These challenging measurements were performed by exploiting the low radiation background at the underground LUNA accelerator in Gran Sasso Laboratories, Italy. The two reactions were investigated in direct kinematics. A proton beam was accelerated onto solid Ta2O5 targets and the alpha particles produced were detected at backward angles using an array of silicon detectors mounted in a purpose-built scattering chamber. Our results indicate that the 17O(p,α)14N reaction rate at temperatures of astrophysical interest is approximately a factor of two higher than previously reported, solving a long standing puzzle on the origin of some pre-solar grains. For the 18O(p,α)15N reaction, we find a reaction rate largely in agreement with previous investigations, but with a significantly reduced uncertainty which could help improve the accuracy of stellar models of a number of stellar sites.

We study certain confluences of equations with two Fuchsian singularities which produce an irregular singularity of Poincaré rank one. We demonstrate a method to understand how to pass from solutions with power-like behavior which are analytic in neighbourhoods to solutions with exponential behavior which are analytic in sectors and have divergent asymptotic behavior. We explicitly calculate the Stokes' matrices of the confluent system in terms of the monodromy data, specifically the connection matrices, of the original system around the merging singularities. The confluence of Gauss' hypergeometric equation gives an excellent opportunity to show our approach with a concrete example. We explicitly show how the Stokes' data arise in the confluences of the isomonodromic deformation problems for the Painlevé equations PVI to PV and PV to PIII(D6).

We present a theoretical approach to the statistical analysis of the dependence of the gap time length between consecutive recurrent events, on a set of explanatory random variables and in the presence of right censoring. The dependence is expressed through regression-like and overdispersion parameters, estimated via estimating functions and equations. The mean and variance of the length of each gap time, conditioned on the observed history of prior events and other covariates, are known functions of parameters and covariates, and are part of the estimating functions. Under certain conditions on censoring, we construct normalized estimating functions that are asymptotically unbiased and contain only observed data. We then use modern mathematical techniques to prove the existence, consistency and asymptotic normality of a sequence of estimators of the parameters. Simulations support our theoretical results.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-10T17:19:34Z No. of bitstreams: 1 MISAELLE DO NASCIMENTO OLIVEIRA - DISSERTAÇÃO PPGMAT 2015..pdf: 1209511 bytes, checksum: 5d4b2e49f1d20c974e738f463c1e1165 (MD5) / Made available in DSpace on 2018-08-10T17:19:34Z (GMT). No. of bitstreams: 1 MISAELLE DO NASCIMENTO OLIVEIRA - DISSERTAÇÃO PPGMAT 2015..pdf: 1209511 bytes, checksum: 5d4b2e49f1d20c974e738f463c1e1165 (MD5) Previous issue date: 2015-08 / Capes / O estudo do comportamento assintótico de sistemas dissipativos é um campo de pesquisa em Equações Diferenciais Parciais-EDP. Existem na literatura várias técnicas para abordar o comportamento assintótico. Contudo, o objetivo deste trabalho é aplicar a técnica devido ao resultado obtido por Gearhart (ver Z. Liu e S. Zheng [21]) que consiste em explorar as propriedades dissipativas do semigrupo associado ao sistema. / The study of the asymptotic behavior of dissipative systems is an important part of the research of Partial Di erential Equations-PDE. Consequently, there are various methods to analize this one. The objective of this work is to apply the a result due to Gearhart (see Z. and S. Liu Zheng [21]) which consits in to explore the dissipation properties of the semigroups associated to dissipative systems.

With reference to the existing literature on liquidity, three key questions have emerged during the last several decades: (i) How to measure liquidity in the most efficient way? (ii) What is the empirical pattern in the relation between market liquidity and stock returns? (iii) What are the determinants of the changes in the Return-Liquidity Relationship? This thesis take the above three questions as its principal focus and studies them by undertaking three separate empirical chapters, using a substantial dataset that covers all the listed firms in these four global economies – Germany, the UK, the US and China from 2001 to 2013. The empirical results imply the following: (i) The Transaction-Cost based liquidity measures, particularly the Quoted Proportional Spread, should be regarded as the most representative liquidity measurement. (ii) There is no evidence consistent with a fixed empirical pattern in the Return-Liquidity Relationship across these four countries as market liquidity is preferred in both Germany and UK, while the opposite results have been obtained for the Chinese stock market. That is, higher market leads to higher stock returns in these two European countries as the higher market liquidity facilitates capital movements to more efficient investments. However in China, the huge number of individual investors generates higher market liquidity through speculative trading rather than as a result of value-related investments, which heightens market risk and thus results in a decrease in stock prices. (iii) There is weak evidence that stock market returns have positive determinant effects on both MLIs (the market impact of liquidity on stock returns) and FLIs, (the firm-level impact of liquidity on stock returns) Return-Liquidity relation on market and firm level respectively. While only FLIs are positively correlated with stock market volatility and the inflation rate and negatively affected by the short-term interest rate.

This thesis is concerned with the mathematical modelling of elastic-plastic deformation in regimes of stress far exceeding the yield stress. Such scenarios are typically encountered in violent impact testing, where millimetre-thick samples of metal are subjected to pressures on the order of the bulk modulus of the material. We begin with an overview of violent impact testing, with particular attention paid to a specific class of experiments known as isentropic compression experiments (ICEs), which will provide motivation for the mathematical modelling and analysis in subsequent chapters. In chapter 2, by appealing to sound notions from rational mechanics and thermodynamics, we construct a mathematical model which aims to encapsulate the essential phenomena involved in violent elastic-plastic deformation. This is followed in chapter 3 with a numerical analysis of the mathematical model in uniaxial strain, which is the geometry relevant ICEs. In chapters 4 and 5, we corroborate the observations made in chapter 3 via a systematic mathematical analysis. In particular, our focus will be on the elastic and plastic waves that can propagate through finite metal samples during isentropic compression. Finally, in chapter 6, we explore the applicability of our model to other geometries, specifically the radially axisymmetric expansion of a circular cavity embedded in an infinite elastic-plastic medium. We conclude with a summary of our findings and suggest some avenues for future investigation.

In screen-printed silicon-crystalline solar cells, the contact resistance of a thin interfacial glass layer between the silicon and the silver electrode plays a limiting role for electron transport. The motivation of this project is to gain increased understanding of the transport mechanisms of the electrons across this layer, which can be exploited to provide higher performance crystalline silicon solar cells. Our methodology throughout is to formulate and analyse mathematical models for the electron transport, based on the drift diffusion equations. In the first chapter we outline the problem and provide a summary of relevant theory. In Chapter 2 we formulate a one-dimensional model for electron transport across the glass layer, that we solve both numerically and by employing asymptotic techniques. Chapter 3 extends the model presented in Chapter 2 to two dimensions. To solve the two-dimensional model numerically we devise and validate a new spectral method. The short circuiting of current through thinner regions of the glass layer enables us to find limiting asymptotic expressions for the average current density for two different canonical glass layer profiles. In Chapter 4 we include quantum mechanical effects into the one-dimensional model outlined in Chapter 2 and find that they have a negligible effect on the contact resistance of the glass layer. We model the boundary effects present at the silicon emitter-glass interface in Chapter 5. Finally, in Chapter 6 we summarise our key results, suggest possible future work, and outline the implications of our work to crystalline silicon solar cell manufacturers.

We introduce random fluctuations on contact and recovery rates in three basic deterministic models in mathematical epidemiology and obtain stochastic counterparts. This paper addresses qualitative and quantitative analysis of stochastic SIS model with disease deaths and demographic effects, and stochastic SIR models with/without disease deaths and demographic effects. We prove the global existence of a unique strong solution and discuss stochastic asymptotic stability of disease free and endemic equilibria. We also investigate numerical properties of these models and prove the convergence of the Balanced Implicit Method approximation to the analytic solution. We simulate the models with fairly realistic parameters to visualize our conclusions.

We propose a new method for analyzing longitudinal data which contain responses that are missing at random. This method consists in solving the generalized estimating equation (GEE) of [7] in which the incomplete responses are replaced by values adjusted using the inverse probability weights proposed in [14]. We show that the root estimator is consistent and asymptotically normal, essentially under some conditions on the marginal distribution and the surrogate correlation matrix as those presented in [12] in the case of complete data, and under minimal assumptions on the missingness probabilities. This method is applied to a real-life dataset taken from [10], which examines the incidence of respiratory disease in a sample of 250 pre-school age Indonesian children which were examined every 3 months for 18 months, using as covariates the age, gender, and vitamin A deficiency.

Orientador: Claudio Aguinaldo Buzzi / Banca: Maurício Firmino Silva Lima / Banca: Marcelo Messias / Resumo: Neste trabalho estudamos o Método Averaging. Este método é uma ferramenta extremamente útil para quantificar o número de ciclos limites que podem bifurcar de uma singularidade do tipo centro de um sistema de equações diferenciais. A parte inicial do trabalho apresenta a Teoria de Aproximação Assintótica e um primeiro contato com o Averaging. Posteriormente apresentamos uma versão do Averaging via a Teoria do Grau de Brouwer. Finalmente fizemos algumas aplicações do método apresentando uma cota superior para o número de ciclos limites que podem bifurcar a partir das órbitas periódicas de centros de um sistema de equações diferenciais. Além disso, mostramos através de exemplos concretos que esta cota superior pode ser realizada. / Abstract: In this work we study the Averaging Method. This method is a useful tool in order to give the maximum number of limit cycles that can bifurcate from a center type singularity of a di®erential equation system. In the first part of the work we present the Asymptotic Approximation Theory and a first view of the averaging. After that, we present a version of the averaging via Brouwer Degree Theory. Finally we give some applications of this method presenting an upper bound for the number of limit cycles that can bifurcate from a center type singularity of a di®erential equation system. Moreover, we show by presenting concrete examples that this upper bound can be realized. / Mestre