The East African Rift System diverges in the Lake Natron Basin of Northern Tanzania and is a major zone of continental extension and crustal thinning with resulting in active tectonics and volcanism. The discovery of Acheulean technology in Olduvai Gorge and Peninj as well as the presence of significant volcanic centers, has made in the region subject to studies in various disciplines. However, lack of precise radiometric age constraints due to the complex geology of the region is a major drawback. The basin is bordered on the western side by an escarpment that contains thick sequences of volcanic (nephelinites, basanites, hawaiites, alkali basalts), volcaniclastic and lacustrine strata that predates 1.2 Ma. This thesis is based on 41 rock samples that were collected from two geological sections, the Endukai Kete (EK) and Waterfall (WF) sections and aims to establish a preliminary geomagnetic polarity time scale (GPTS) for the Natron Escarpment, together with establishing possible flow directions of the volcanic lavas within these sections. Nephelinites of EK section have an inferred NW-SE direction of flow, based on study of anisotropy of magnetic susceptibility. They record a normal polarity that most likely correspond to the Cobb Mountain Event (CMT; 1.187-1.208 Ma), although there is an 80-ka discrepancy between the CMT event and the dated lavas. The most probable source is the Mosonik that erupted nephelinitic lavas 1.28 Ma ago. The palagonitic tuff layer below the nephelinites displays reverse polarity and a NE-SW direction of flow. Due to the absence of approximately 200 m strata within the basanite series of the section, regional lithological correlation is used to constrain the GPTS pattern. Hajaro Beds of the Peninj Group to the north of the escarpment, postdates the Olduvai Event (1.71 to 1.86 Ma) and lacustrine strata of the escarpment for EK and WF sections are deposited over the same unconformity and share depositional similarities. Therefore, the lacustrine strata are correlative to Hajaro beds and the normal event observed within the basanite series of both sections is attributed to the Réunion Event (2.116 – 2.137 Ma). The establishment of a preliminary magnetostratigraphic sequence presented in this thesis demonstrate that the rift escarpment in northern Tanzania is suitable for paleomagnetic dating. Future studies should be conducted to establish a more detailed and constrained magnetostratigraphic section, which will be of great use in this part of the African Rift where radiometric dating has been challenging.

[pt] Neste trabalho nós procuramos uma solução para o problema: como construir uma escala de tempo atômico baseada em um pequeno grupo de relógios atômicos? Nós geramos uma escala de tempo atômico independente a partir de um conjunto de relógios atômicos, chamada ETAB1(onrj). Nós propomos que a ETAB1(ONRJ) seja usada como referência para a geração de um o novo Tempo Universal Coordenado Brasileiro, chamado de TUC(ONRJ) proposto. Nós mostramos que o TUC(ONRJ) proposto será mantido coordenado com o TUC(BIPM) dentro dos limites recomendados pelo Comité Consultatif pour la Définition de la Seconde, isto é, a diferença entre TUC e TUC(ONRJ) proposto, menor que mais ou menos 100ns. Para menter a Hora Legal Brasileira (TUC(ONRJ)) coordenada com a Hora Mundial (TUC(BIPM) é necessário realizar a rastreabilidade internacional da grandeza tempo. Um método é proposto para obtenção de uma estimativa diária da posição do TUC(ONRJ) utilizando o filtro de Kalman e um receptor GPS, com uma incerteza de mais ou menos 35ns. Uma comparação do desempenho entre as escalas de tempo TUC (ONRJ) proposto, TUC(NIST) e TUC(USNO) é apresentada / [en] In the present work we look we look for a solution of the problem: how to construction na atomic time scale based in a smallgroup of atomic clocks. We generate an independent atomic time scale from an ensemble of atomic clocks, named ETAB 1 (ONRJ). We propose that ETAB 1(ONRJ) be used as a reference for the generation of a new Brazilian Coordinated Universal Time, named UTC (ONRJ)proposed. We show that the UTC (ONRJ)proposed will be maintained coordinated with UTC (BIPM) within the limitis recommended by the Comité consultatif pour la Définition de la Seconde, that is, the difference between UTC (BIMP) and UTC (ONRJ)proposed less than +/-100ns. To maintain the UTC (onrj) coordinated with UTC(BIPM) it is necessary to realize the international traceability of time quantity. A method is proposed for obtain ddaily estimates of UTC (ONRJ) - UTC(BIPM) using Kalman filter and GPS receiver with uncertainty of +/-35ns. A comparison of performance between the time scales UTC(ONRJ)proposed, UTC(NIST) and UTC(USNO) is presented.

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因有數學式子，所以無法編輯。 / 因有數學式子，所以無法編輯。

Neste trabalho, estudamos alguns colóides magnéticos dos tipos iônico e surfactado com partículas de estrutura tipo espinélio. Usamos a técnica de varredura-Z para investigar as amostras nas escalas de tempo de femtossegundos e milissegundos. Medimos o índice de refração não-linear nas duas escalas de tempo. Na escala de milissegundos todas as amostras apresentaram comportamento tipo lente divergente, e os valores obtidos são da ordem de 10^(-7) cm^2/W. Na escala de femtossegundos, as amostras iônicas apresentaram comportamento tipo lente convergente, com valores típicos do índice de refração não-linear da ordem de 10^(11) cm^2/W. Também medimos a absorção não-linear na escala de tempo de femtossegundos. Os valores obtidos são da ordem de 10^2 cm/GW. Com os dados obtidos na escala de femtossegundos calculamos a susceptibilidade elétrica de terceira ordem (chi(3)). O módulo de chi(3) encontrado é da ordem de 10^(-17) m^2/V^2 (ou 10^(-9) esu). Obtivemos evidências experimentais da contribuição da susceptibilidade elétrica de quinta-ordem nas medidas de absorção não-linear. Verificamos a presença do efeito de tamanho das partículas no valor de chi(3) ao estudar partículas de mesma composição e de diâmetros diferentes. / In this work, we studied some magnetic colloids of kind ionic and surfacted with particles of spinel struture. We used the Z-Scan technique to investigate the samples in the time scales of femto- and milliseconds. We measured the nonlinear refractive index in both time scales. In the scale of milliseconds all samples showed divergent-lens-type behavior, and the obtained values are of order of 10^(-7) cm^2/W. In the femtoseconds scale, the ionic-type samples have convergent-lens-type behavior, with the typical values of order of 10^(11) cm^2/W. Also we measured the nonlinear absorption in the femtoseconds time scale. The obtained values are of order of 10^2 cm/GW. With the data obtained in the femtoseconds time scale we calculated the third-order electric susceptibilities (chi(3)). The found modulus of chi(3) is of order of 10^(-17) m^2/V^2 (or 10^(-9) esu). We obtained experimental evidences that fifth-order electric susceptibilities can contribute to the measurements of nonlinear absorption. We observed the dependence of particles\' size effect in the values of chi(3) in the studies of particles of the same composition and different diameters.

The present work introduces a methodology to obtain a discrete time state space representation of an electrical network using the nodal [G] matrix of the Electromagnetic Transients Program (EMTP) solution. This is the first time the connection between the EMTP nodal analysis solution and a corresponding state-space formulation is presented. Compared to conventional state space solutions, the nodal EMTP solution is computationally much more efficient. Compared to the phasor solutions used in transient stability analysis, the proposed approach captures a much wider range of eigenvalues and system operating states. A fundamental advantage of extracting the system eigenvalues directly from the EMTP solution is the ability of the EMTP to follow the characteristics of nonlinearities. The system's trajectory can be accurately traced and the calculated eigenvalues and eigenvectors correctly represent the system's instantaneous dynamics. In addition, the algorithm can be used as a tool to identify network partitioning subsystems suitable for real-time hybrid power system simulator environments, including the implementation of multi-time scale solutions. The proposed technique can be implemented as an extension to any EMTP-based simulator. Within our UBC research group, it is aimed at extending the capabilities of our real-time PC-cluster Object Virtual Network Integrator (OVNI) simulator.

The concept of dynamic programming was originally used in late 1949, mostly during the 1950s, by Richard Bellman to describe decision making problems. By 1952, he refined this to the modern meaning, referring specifically to nesting smaller decision problems inside larger decisions. Also, the Bellman equation, one of the basic concepts in dynamic programming, is named after him. Dynamic programming has become an important argument which was used in various fields; such as, economics, finance, bioinformatics, aerospace, information theory, etc. Since Richard Bellman's invention of dynamic programming, economists and mathematicians have formulated and solved a huge variety of sequential decision making problems both in deterministic and stochastic cases; either finite or infinite time horizon. This thesis is comprised of five chapters where the major objective is to study both deterministic and stochastic dynamic programming models in finance. In the first chapter, we give a brief history of dynamic programming and we introduce the essentials of theory. Unlike economists, who have analyzed the dynamic programming on discrete, that is, periodic and continuous time domains, we claim that trading is not a reasonably periodic or continuous act. Therefore, it is more accurate to demonstrate the dynamic programming on non-periodic time domains. In the second chapter we introduce time scales calculus. Moreover, since it is more realistic to analyze a decision maker’s behavior without risk aversion, we give basics of Stochastic Calculus in this chapter. After we introduce the necessary background, in the third chapter we construct the deterministic dynamic sequence problem on isolated time scales. Then we derive the corresponding Bellman equation for the sequence problem. We analyze the relation between solutions of the sequence problem and the Bellman equation through the principle of optimality. We give an example of the deterministic model in finance with all details of calculations by using guessing method, and we prove uniqueness and existence of the solution by using the Contraction Mapping Theorem. In the fourth chapter, we define the stochastic dynamic sequence problem on isolated time scales. Then we derive the corresponding stochastic Bellman equation. As in the deterministic case, we give an example in finance with the distributions of solutions.

Rational expectations provide people or economic agents making future decision with available information and past experiences. The first approach to the idea of rational expectations was given approximately fifty years ago by John F. Muth. Many models in economics have been studied using the rational expectations idea. The most familiar one among them is the rational expectations version of the Cagans hyperination model where the expectation for tomorrow is formed using all the information available today. This model was reinterpreted by Thomas J. Sargent and Neil Wallace in 1973. After that time, many solution techniques were suggested to solve the Cagan type rational expectations (CTRE) model. Some economists such as Muth [13], Taylor [26] and Shiller [27] consider the solutions admitting an infinite moving-average representation. Blanchard and Kahn [28] find solutions by using a recursive procedure. A general characterization of the solution was obtained using the martingale approach by Broze, Gourieroux and Szafarz in [22], [23]. We choose to study martingale solution of CTRE model. This thesis is comprised of five chapters where the main aim is to study the CTRE model on isolated time scales. Most of the models studied in economics are continuous or discrete. Discrete models are more preferable by economists since they give more meaningful and accurate results. Discrete models only contain uniform time domains. Time scale calculus enables us to study on m-periodic time domains as well as non periodic time domains. In the first chapter, we give basics of time scales calculus and stochastic calculus. The second chapter is the brief introduction to rational expectations and the CTRE model. Moreover, many other solution techniques are examined in this chapter. After we introduce the necessary background, in the third chapter we construct the CTRE Model on isolated time scales. Then we give the general solution of this model in terms of martingales. We continue our work with defining the linear system and higher order CTRE on isolated time scales. We use Putzer Algorithm to solve the system of the CTRE Model. Then, we examine the existence and uniqueness of the solution of the CTRE model. In the fourth chapter, we apply our solution algorithm developed in the previous chapter to models in Finance and stochastic growth models in Economics.