A dissertação aborda a evolução doutrinária e a identificação das Funções do Estado, entendidas estas como o meio para o atingimento dos fins do Estado; bem como a especificidade de cada uma das funções identificadas. Como premissa inicial se apresentam as Funções do Estado e a racionalidade inerente à divisão sugerida, identificando-se seis funções, a saber: administrativa, jurisdicional, governamental, legislativa, moderadora e controladora. A seguir explora especificamente a função de controle de constitucionalidade e as opções institucionais de controle separado, com a instituição do Tribunal Constitucional, ou cumulado, com a fusão das funções jurisdicional e de controle no Poder Judiciário; as respectivas origens, justificativas e fundamentos. Os efeitos de cada uma das opções institucionais (controle de constitucionalidade cumulado ou separado) serão a abordagem principal, especialmente os problemas decorrentes da opção de controle cumulado de constitucionalidade e seus reflexos na segurança jurídica e no Estado Democrático de Direito. Por fim, será abordada a mitigação dos problemas do controle cumulado de constitucionalidade através da adoção da técnica dos precedentes. / The essay discusses the doctrinal evolution and the identification of State Functions, understood as the means to achieve the ends of the State; also the specificity of each of the functions identified. As an initial premise the functions of the State and the inherent rationality of the suggested division are presented, identifying six functions: administrative, jurisdictional, governmental, legislative, moderating and controlling. The following specifically discusses the constitutional control function and the institutional options for separate control, with the establishment of the Constitutional Court, or cumulated, with the merger of the jurisdictional and control functions in the Judiciary Power; the respective origins, justifications and fundamentals. The effects from each of the institutional options (cumulative or separate constitutional control) will be the main approach, especially the problems arising from the option of cumulative control of constitutionality and its effects on legal certainty and the Democratic State of Law. Finally, it will be approached the mitigation of the problems of the cumulated control of constitutionality through the adoption of the precedent technique.

Swarms are groups of agents, which we model as point particles, whose collective behavior emerges from individual interactions. We study a first-order swarming model in a periodic coordinate system with pairwise social forces, investigating its stable configurations for differing numbers of agents relative to the periodic width. Two states emerge from numerical simulations in one dimension: even spacing throughout the period, or clumping within a certain portion of the period. A mathematical analysis of the energy of the system allows us to determine stability of these configurations. We also perform numerical simulations for evolution to equilibrium over time, and find results in agreement with our mathematical analysis. For certain values of the periodic width relative to the number of agents, our numerical simulations show that either clumping or even spacing can be stable equilibria, and which equilibrium is reached depends on on starting conditions, indicating hysteresis.

In this thesis we develop new mathematical models, using dynamical systems, to represent localized gene delivery of bone morphogenetic protein 2 into bone marrow-derived mesenchymal stem cells and rat calvarial defects. We examine two approaches, using pDNA or cmRNA treatments, respectively, towards the production of calcium deposition and bone regeneration in in vitro and in vivo experiments. We first review the relevant scientific literature and survey existing mathematical representations for similar treatment approaches. We then motivate and develop our new models and determine model parameters from literature, heuristic approaches, and estimation using sparse data. We next conduct a qualitative analysis using dynamical systems theory. Due to the nature of the parameter estimation, it was important that we obtain local and global sensitivity analyses of model outputs to changes in model inputs. Finally we compared results from different treatment protocols. Our model suggests that cmRNA treatments may perform better than pDNA treatments towards bone fracture healing. This work is intended to be a foundation for predictive models of non-viral local gene delivery systems.

My dissertation applies narrative theory and ordinary language philosophy to two major works bookending medieval English literature: Beowulf and Le Morte Darthur. Capitalizing on the descriptive power of narrative theory's lexicon, I outline the aesthetics, rhetoric, and other effects on the reader when these medieval writers depict transgressive movements--theoretically termed metalepsis--across borders in the story world, and over boundaries separating that world from our own. I often find that spatial transgressions, as they are visualized in narrative terms, entail or simultaneously occur with a breakdown of the fourth wall separating fiction from its audience. Malory's Sir Lancelot crosses into a spiritual world in pursuit of the Holy Grail only to arrive at an awareness of his existence as narrated fiction. My dissertation argues that moments like this, first analyzed through narrative theory, challenge the reader to recognize the fictional character's force of life, and in so doing expand the imagination to reconsider those metaphysical distinctions that have long rendered the nonhuman inferior. Those distinctions are unnecessary and often senseless, I argue. The ethics of reading fiction that I propose seeks the acknowledgment of limits to knowledge, to what we can claim to know about literature, its characters, and, indeed, our fellow human beings. Given that they are constructed by our ordinary language use, fictional characters are the essence of the other. Fictions, then, and as Stanley Cavell would agree, serve as testing grounds for our capacities of acknowledgment. I argue that both the Beowulf poet and Malory fashioned fictional worlds that preserve a secular heroism from potentially hostile contexts. In the process, these medieval narratives show us that fictional characters move us as a matter of ordinary language--our ordinary interactions with narrative: they play a significant role in our lives that cannot be reduced to any particular theory. There is no need for recourse to ontological, or theological, frameworks to invest them with some unutterable or mysterious meaning. They matter as a matter of course.

The goal of this thesis is to study the dynamics behind the evolution of virulence. We examine first the underlying mechanics of linear systems of ordinary differential equations by investigating the classification of fixed points in these systems, then applying these techniques to nonlinear systems. We then seek to establish the validity of a system that models the population dynamics of uninfected and infected hosts---first with one parasite strain, then n strains. We define the basic reproductive ratio of a parasite, and study its relationship to the evolution of virulence. Lastly, we investigate the mathematics behind superinfection.

Inflammation in the lungs can occur for many reasons, from bacterial infections to stretch by mechanical ventilation. In this work we compare and contrast various mathematical models for lung injuries in the categories of acute infection, latent versus active infection, and particulate inhalation. We focus on systems of ordinary differential equations (ODEs), agent-based models (ABMs), and Boolean networks. Each type of model provides different insight into the immune response to damage in the lungs. This knowledge includes a better understanding of the complex dynamics of immune cells, proteins, and cytokines, recommendations for treatment with antibiotics, and a foundation for more well-informed experiments and clinical trials. In each chapter, we provide an in-depth analysis of one model and summaries of several others. In this way we gain a better understanding of the important aspects of modeling the immune response to lung injury and identify possible points for future research.

Delay differential equations have a wide range of applications in engineering. This work is devoted to the analysis of delay Duffing equation, which plays a crucial role in modeling performance on demand Micro Electro Mechanical Systems (MEMS). We start with the stability analysis of a linear delay model. We also show that in certain cases the delay model can be efficiently approximated with a much simpler model without delay. We proceed with the analysis of a non-linear Duffing equation. This model is a significantly more complex mathematical model. For instance, the existence of a periodic solution for this equation is a highly nontrivial question, which was established by Struwe. The main result of this work is to establish the existence of a periodic solution to delay Duffing equation. The paper claimed to establish the existence of such solutions, however their argument is wrong. In this work we establish the existence of a periodic solution under the assumption that the delay is sufficiently small.

Proper heart function results from the periodic execution of a series of coordinated interdependent mechanical, chemical, and electrical processes within the cardiac tissue. Central to these processes is the action potential - the electrochemical event that initiates contraction of the individual cardiac myocytes. Many models of the cardiac action potential exist with varying levels of complexity, but none account for the electrophysiological role played by caveolae - small invaginations of the cardiac cell plasma membrane. Recent electrophysiological studies regarding these microdomains reveal that cardiac caveolae function as reservoirs of 'recruitable' sodium ion channels. As such, caveolar channels constitute a substantial and previously unrecognized source of sodium current that can significantly influence action potential morphology. In this thesis, I formulate and analyze new models of cardiac action potential which account for these caveolar sodium currents and provide a computational venue in which to develop and test new hypotheses. My results provide insight into the role played by caveolar ionic currents in regulating the electrodynamics of cardiac myocytes and suggest that in certain pathological cases, caveolae may play an arrhythmogenic role.

Concrete is the most common building material in the world and its use has been increasing during the last century as the need for construction projects has escalated. Traditionally, concrete uses Ordinary Portland Cement (OPC) as binder, water as the activator of cement and aggregate. Finding an appropriate replacement for traditional concrete is a desirable solution to obviate the environmental problems caused by cement production. The use of fly ash as a partial replacement for Portland cement is a method to maintain the properties of concrete and reduce the need for cement. Fly ash is a by-product from coal-fired power plants and is abundantly available. The percentage of cement replacement can be varied according to application and mix design. One of the potential materials to substitute for conventional concrete is geopolymer concrete (introduced by Davidovits in 1979). Geopolymer concrete is an inorganic alumino-silicate polymer synthesized from predominantly silicon, aluminum and byproduct materials such as fly ash. Geopolymer properties have been investigated for several years and it is still a major area of interest among researchers and industry partners as it does not contain cement and uses fly ash and alkali liquids as binders to produce a paste to consolidate aggregates. Furthermore, the aggregate comprises a substantial portion of concrete. Including coarse and fine aggregates it is normally obtained from natural sources. Fine aggregate in Australia is usually mined from sand quarries. As the demand for concrete production increases, more natural sand is needed. The need for fine aggregate should be addressed in an environmentally friendly manner, considering the diminishing sources of natural sand. Red sand is a by-product generated from the manufacture of alumina from bauxite by the Bayer process. / Previous studies on properties of red sand have shown that it has the potential to be used in concrete as a fine aggregate. While the use of red sand in traditional concrete has been investigated by some researchers, no research has been reported regarding the use of this by-product in manufacturing geopolymer concrete. This research looks into the replacement of natural sand fine aggregates with red sand in geopolymer concrete. Initially, an extensive series of mixtures was prepared and tested. The objective of the research was to identify the salient parameters affecting the properties of geopolymer concrete when natural sand is replaced by red sand. At the next stage, attempts were made to enhance the mechanical and durability features of red sand geopolymer concrete. The final stage consisted of testing red sand geopolymer concrete to find out the various properties of this novel construction material.

<p>This report consider a system describing three competing species with populations <em>x</em>, <em>y</em> and <em>z</em>. Sufficient conditions for every positive equilibrium to be asymptotically stable have been found. First it is shown that conditions on the pairwise competitive interaction between the populations are needed. Actually, these conditions are equivalent to asymptotic stability for any two-dimensional competing system of the three species. It is also shown that these alone are not enough, and that a condition on the competitive interaction between all three populations is also needed. If all conditions are fulfilled, each population will survive on a long-term basis and there will be a stable coexistence.</p>