Nesse trabalho apresentaremos alguns exemplos clássicos que evidenciam as diferenças entre a geometria Riemanniana e a semi-Riemanniana (Lorentziana) quanto à completude de geodésicas. Para isso, revisitaremos conceitos básicos de Geometria, seguido de uma introdução aos espaços vetoriais de Lorentz e um estudo inicial sobre o grupo de Lorentz. Nos capítulos finais discutiremos sobre completude de geodésicas e como se distanciam do caso Riemanniano. / In this work we intend to present some classical examples that display the differences between Riemannian and semi-Riemannian (Lorentzian) geometry in relation to the completeness of geodesics. For this, we will revisit basic Geometry concepts followed by an introduction to the vector spaces of Lorentz and a simple study on the Lorentz group. In the final chapters we will discuss about the completeness of geodesics and how it distances itself from the Riemannian case.

We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncompact, but the boundary is assumed to be compact. We require a symmetry property of the principal symbol of the operator along the boundary. This is satisfied by Dirac type operators, for instance. We provide a selfcontained introduction to (nonlocal) elliptic boundary conditions, boundary regularity of solutions, and index theory. In particular, we simplify and generalize the traditional theory of elliptic boundary value problems for Dirac type operators. We also prove a related decomposition theorem, a general version of Gromov and Lawson's relative index theorem and a generalization of the cobordism theorem.

Mixed regimes are often viewed as inherently less stable and more war prone than fully democratic or autocratic systems due to their low levels of institutionalization. I ask, are certain mixed regimes more or less war prone than other mixed regimes, based on the strength and orientation (more democratic or autocratic) of their political institutions? At ends with previous research, my findings suggest that institutionalization levels play little, if any role in the onset of interstate war.

Neste trabalho, estudamos algumas formas de combinar sistemas de Lógica Modal, analisando quando a combinação preserva propriedades como correção, completude e decidibilidade. Estendemos um estudo já realizado sobre combinações de sistemas de Lógica Modal Normal para sistemas de Lógica Modal Não-normal. O principal resultado deste trabalho é a preservação de completude da aplicação externa de um sistema de Lógica Modal Não-normal M em um sistema lógico L. Outro resultado importante é um exemplo de interação forte na combinação independente, ou fusão, de dois sistemas de Lógica Modal Não-normal. / In this work, we study a few ways of combining Modal Logic systems, analysing when the combination preserves properties like soundness, completeness and decidability. We extend a study of the combination of Normal Modal Logic systems to Non-normal Modal Logic systems. The main result of this work is the completeness preservation in the external application of a Non-normal Modal Logic system M to a logic system L. Another important result is an example of strong interations arising in the fusion of two Non-normal Modal Logic system.

Philosophiae Doctor - PhD / The advantage of a well-developed health information system is the significant role played by records produced by such a system beyond recording medical history of individuals. They are the foundation for birth registrations which when fully complete is an important tool for acquiring data necessary for planning and monitoring child and maternal health in a country. This study aimed to investigate the potential of hospital birth records to estimate the number of births in the country and supplement birth registrations data. Data was abstracted from public facilities where births occur in two municipalities; Germiston in Gauteng and Nkomazi in Mpumalanga for the period 2014 to 2016. Modified version of the BORN Data Quality Framework (BORN-DQF) of the Ontario Agency for Health Protection and Promotion (2016) was used to assess the contents and quality of hospital birth records. / 2022

The completeness of eigenfunctions for linearized equations is critical for many applications, such as the study of stability of solitary waves. In this thesis, we work with the Nonlinear Schr{\"o}dinger (NLS) equation, associated with the Zakharov-Shabat spectral problem. Firstly, we construct a complete set of eigenfunctions for the spectral problem. Our method involves working with an adjoint spectral problem and deriving completeness and orthogonality relations between eigenfunctions and adjoint eigenfunctions. Furthermore, we prove completeness of squared eigenfunctions, which are used to represent solutions of the linearized NLS equation. For this, we find relations between the variation of potential and the variation of scattering data. Moreover, we show the connection between the squared eigenfunctions of the Zakharov-Shabat spectral problem and solutions of the linearized NLS equation. / Thesis / Master of Science (MSc)

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In this thesis, we study problems related to the reconstruction (up to bi-interpretability) of first-order theories from various functorial invariants: automorphism groups, endomorphism monoids, (categories of) countable models, and (ultra)categories of models. / Thesis / Master of Science (MSc)

In this master thesis we investigate completeness theorems in the framework of abstract algebraic logic. Our main interest lies in the completeness with respect to the so called relatively (finitely) subdirectly irreducible models. Notable part of the presented theory concerns the difference between finitary and infinitary logical systems. We focus on the well-known fact that the completeness theorem with respect to relatively (finitely) subdirectly irreducible models can be proven in general for all finitary logics and we discuss the possible of generalizing this theorem even to infinitary logics. We show that there are two interesting inter- mediate properties between this completeness and finitarity, namely (completely) intersection-prime extension properties. Based on these notions we define five classes of logics and propose a new hierarchy of finitary and infinitary logics. As a main contribution of this dissertation we present an example of a logic separat- ing some of these classes. Keywords: Abstract algebraic logic, completeness, relatively (finitely) sub- directly irreducible models, RSI-completeness, RFSI-completeness, (completely) intersection-prime extension property, IPEP, CIPEP.