Este trabalho tem como principal objetivo estudar extensões de aplicações multilineares, de polinômios homogêneos e de funções analíticas entre espaços de Banach. Desta maneira, nos baseamos em importantes trabalhos sobre o assunto. Inicialmente apresentamos o produto de Arens para álgebras de Banach, extensões de Aron-Berner e de Davie-Gamelin para aplicações multilineares e provamos que todas estas extensões coincidem. A partir destes resultados, apresentamos a extensão de polinômios homogêneos e o Teorema de Davie-Gamelin que afirma que, assim como no caso de aplicações multilineares, as extensões de polinômios preservam a norma e, como consequência deste teorema, apresentamos uma generalização do Teorema de Goldstine. Em seguida estudamos espaços de Banach regulares e simetricamente regulares, que são propriedades relacionadas com a unicidade de extensão e são definidas a partir do ideal de operadores lineares fracamente compactos K^w(E, F) . Finalmente apresentamos a extensão de uma função de H_b(E) para H_b(E\'\') e o resultado, de Ignacio Zalduendo, que caracteriza esta extensão em termos da continuidade fraca-estrela do operador diferencial de primeira ordem. / The main purpose of this work is to study extensions of multilinear mappings, homogeneous polynomials and analytic functions between Banach Spaces. In this way, we rely on important works on the subject. Firstly we present the Arens-product for Banach algebras, the Aron-Berner and Davie-Gamelin extensions for multilinear mappings and we prove that all these extensions are the same. From these results, we present an extension for homogeneous polynomials and the Davie-Gamelin theorem which asserts that, as in the case of multilinear mappings, the polynomial extension is norm-preserving and, as a consequence of this theorem, we present a generalization of the Goldstine theorem. After that we study regular and symmetrically regular Banach spaces which are properties related to the uniqueness of the extension and are defined in the setting of weakly compact linear operators K^w(E, F) . Lastly, we present the extension of a function of H_b(E) to one in H_b(E\'\') and the result, according to Ignacio Zalduendo, which characterizes this extension in terms of weak-star continuity of the first order differential operator.

A infiltração é o processo pelo qual a água atravessa a superfície do solo, com grande importância para a hidrologia, irrigação e agricultura. À medida que a água infiltra, as camadas superiores do solo vão se umedecendo, alterando gradativamente o perfil de umidade. Sob condições de campo, a água que infiltra pode fluir tanto na vertical, como na horizontal, dependendo do tipo de solo e declividade do terreno. A taxa de infiltração da água no solo é afetada, principalmente, pelas características do solo que afetam a geometria de seu sistema poroso, como textura e estrutura, e pode ser determinada tanto no campo como em laboratório, por diferentes métodos. Com a intenção de otimizar a previsão da infiltração da água no solo, diversos modelos foram desenvolvidos, podendo ser classificados em três grupos: empíricos, semi-empíricos e com base física. O objetivo deste trabalho foi avaliar a infiltração de água em solos com diferentes texturas e comparar a qualidade do ajuste de diferentes modelos usualmente empregados. As curvas da taxa de infiltração e da infiltração acumulada foram determinadas em laboratório utilizando amostras de solo homogeneamente acondicionadas em colunas e comparadas pelos seguintes modelos: Kostiakov, Horton, Green & Ampt, e Philip. Dentre os solos estudados, o solo 3 (textura franco arenosa) foi o que apresentou a maior taxa de infiltração e a maior VIB, provavelmente devido a menor proporção de argila e maior presença de macroporos, facilitando a infiltração da água no solo. Dos modelos analisados, o de Kostiakov, seguido pelo de Philip, foram os que apresentaram em média os melhores valores estimados da taxa de infiltração quando comparados com os valores medidos em laboratório. O gráfico do avanço da frente de molhamento com a raiz quadrada do tempo de infiltração (horizontal) ajustou-se perfeitamente ao modelo de Philip. No que respeita a infiltração vertical tal gráfico foi semelhante ao da horizontal (linha reta), mas com maior inclinação. / Infiltration is the process in which the water passes through the soil surface, being of great importance for hydrology, irrigation and agriculture. As the water infiltrates, the soil water content profile will changing and the infiltrated water can flow vertically or horizontally, depending on the soil type and land slope. The soil water infiltration rate is mainly affected by soil properties that affect its porous geometry, such as texture and structure, and can be determined in the field and in the laboratory, using different methods. In order to optimize the prediction of the soil water infiltration, many different models have been developed and may be classified into three groups: empirical, semi-empirical and physically based. The objective of this study was to evaluate the water infiltration in soils with different textures and compare the quality of fit of the different used models. The infiltration rate curves and the cumulative infiltration curves were determined in the laboratory using soil samples homogeneously packed in column and compared by the following models: Kostiakov, Horton, Green & Ampt and Philip. Among the studied soils, the soil 3 (sandy loam texture) presented the highest infiltration rate and the highest basic infiltration rate, probably due to lower clay content and larger quantity of macropores, facilitating the water infiltration into the soil. Among the tested models, Kostiakov, followed by Philip, presented, on average, the best estimated values of the infiltration rate compared to the values measured in the laboratory. The front of the advancing wetting graph of the square root of the infiltration time (horizontal) well set to Philip model. With respect to this vertical graph infiltration was similar to the horizontal (straight line) but more inclined.

Escoamentos multifásicos estão presentes em diversas aplicações industriais, principalmente na indústria do petróleo. Um dos casos de aplicação, objeto de estudo desse trabalho, é a determinação da produção de poços de petróleo através de válvulas choke. É apresentada uma revisão dos efeitos físicos e do equacionamento adotado pelos principais modelos multifásicos existentes para tais válvulas. Um estudo de sensibilidade de tais efeitos físicos é realizado, analisando as possíveis alternativas para a diferença de velocidade entre as fases, o mecanismo adotado para a troca de calor entre as fases, a influência da energia cinética a montante da válvula, a influência da área efetiva da garganta e a metodologia de cálculo da recuperação de pressão a jusante da válvula. Conclui-se que dos diversos fatores que influenciam no cálculo da vazão mássica e da condição crítica, a área efetiva da garganta é um parâmetro importante e que é necessário uma maior investigação de como determinar tal parâmetro. / Multiphase flow are present in many industrial applications, mainly at the petroleum industry. One of these application cases, aim of this work study, is to determine a petroleum well production by the choke valves. It is presented a revision of the physical effects and for the adopted equation by the main existing multiphase models for such valves. A sensibility study of such physical effects is performed, analyzing the possible alternatives for the phases velocities difference, the adopted mechanism for the heat transfer between the phases, the upstream kinetic energy influence, the throat effective area influencie and the calculation methodology adopted for the valve downstream pressure recover. It is concluded that from many factors that influence in the mass flow and critical condition calculation, the throat effective area is a important parameter and it is necessary a deeper investigation in how to determine such parameter.

A infiltração é o processo pelo qual a água atravessa a superfície do solo, com grande importância para a hidrologia, irrigação e agricultura. À medida que a água infiltra, as camadas superiores do solo vão se umedecendo, alterando gradativamente o perfil de umidade. Sob condições de campo, a água que infiltra pode fluir tanto na vertical, como na horizontal, dependendo do tipo de solo e declividade do terreno. A taxa de infiltração da água no solo é afetada, principalmente, pelas características do solo que afetam a geometria de seu sistema poroso, como textura e estrutura, e pode ser determinada tanto no campo como em laboratório, por diferentes métodos. Com a intenção de otimizar a previsão da infiltração da água no solo, diversos modelos foram desenvolvidos, podendo ser classificados em três grupos: empíricos, semi-empíricos e com base física. O objetivo deste trabalho foi avaliar a infiltração de água em solos com diferentes texturas e comparar a qualidade do ajuste de diferentes modelos usualmente empregados. As curvas da taxa de infiltração e da infiltração acumulada foram determinadas em laboratório utilizando amostras de solo homogeneamente acondicionadas em colunas e comparadas pelos seguintes modelos: Kostiakov, Horton, Green & Ampt, e Philip. Dentre os solos estudados, o solo 3 (textura franco arenosa) foi o que apresentou a maior taxa de infiltração e a maior VIB, provavelmente devido a menor proporção de argila e maior presença de macroporos, facilitando a infiltração da água no solo. Dos modelos analisados, o de Kostiakov, seguido pelo de Philip, foram os que apresentaram em média os melhores valores estimados da taxa de infiltração quando comparados com os valores medidos em laboratório. O gráfico do avanço da frente de molhamento com a raiz quadrada do tempo de infiltração (horizontal) ajustou-se perfeitamente ao modelo de Philip. No que respeita a infiltração vertical tal gráfico foi semelhante ao da horizontal (linha reta), mas com maior inclinação. / Infiltration is the process in which the water passes through the soil surface, being of great importance for hydrology, irrigation and agriculture. As the water infiltrates, the soil water content profile will changing and the infiltrated water can flow vertically or horizontally, depending on the soil type and land slope. The soil water infiltration rate is mainly affected by soil properties that affect its porous geometry, such as texture and structure, and can be determined in the field and in the laboratory, using different methods. In order to optimize the prediction of the soil water infiltration, many different models have been developed and may be classified into three groups: empirical, semi-empirical and physically based. The objective of this study was to evaluate the water infiltration in soils with different textures and compare the quality of fit of the different used models. The infiltration rate curves and the cumulative infiltration curves were determined in the laboratory using soil samples homogeneously packed in column and compared by the following models: Kostiakov, Horton, Green & Ampt and Philip. Among the studied soils, the soil 3 (sandy loam texture) presented the highest infiltration rate and the highest basic infiltration rate, probably due to lower clay content and larger quantity of macropores, facilitating the water infiltration into the soil. Among the tested models, Kostiakov, followed by Philip, presented, on average, the best estimated values of the infiltration rate compared to the values measured in the laboratory. The front of the advancing wetting graph of the square root of the infiltration time (horizontal) well set to Philip model. With respect to this vertical graph infiltration was similar to the horizontal (straight line) but more inclined.

Embora a ablação a laser venha sendo bastante utilizada em materiais em geral, pouco é entendido sobre o comportamento deste processo perto de uma interface separando dois materiais distintos. Neste contexto, o principal objetivo deste trabalho foi realizar um estudo macroscópico e microscópico dos processos que envolvem a ablação a laser em regime de femtossegundos em materiais homogêneos e estruturados. No caso de materiais estruturados, o estudo focou-se em uma situação de interface, na qual ocorrem mudanças nas propriedades de ablação. Baseado nos resultados, nós pretendemos obter subsídios científicos para entender as aplicações da ablação em regime de pulsos ultracurtos para estruturas estratificadas, tais como de dentes, ossos, interface resina-dente, dente-metal, e outras. Diferentes técnicas experimentais foram idealizadas para determinar a progressão da ablação dentro do material e obter dados extraídos da superfície. Utilizando luz espalhada de uma fonte externa, o processo de ablação foi temporalmente monitorado, permitindo determinar a velocidade de ablação em materiais transparentes, assim como perfis típicos de ablação nestes materiais. Em um segundo experimento, nosso estudo permitiu quantificar a variação da geometria de ablação perto de uma interface separando dois materiais distintos. Nossos dados foram suficientes para prever a ocorrência de uma descontinuidade no perfil da ablação entre dois meios: resina A e resina B, mostrando uma repentina descontinuidade do diâmetro da cavidade ablacionada. Adicionalmente, foi realizada uma análise dos aspectos morfológicos de diferentes tecidos biológicos irradiados e nosso estudo mostrou a eficiência da ablação utilizando laser de femtossegundos no processamento de tecidos duros e a possibilidade de utilizar esses sistemas sem causar danos térmicos e mecânicos nos tecidos remanescentes. Finalmente nós aplicamos a microperfuração a laser para produzir micro-poros na superfície de tecidos biológicos (fígados), melhorando a penetração do medicamento ALA e a aumentando a profundidade de tratamento. / Although laser ablation has been long used in general materials, little is known regarding the behavior of theses process near an interface separating two distinct materials. In this context, the main aim of this work was to perform a microscopic and macroscopic study of the processes that include femtosecond laser ablation in homogeneous and/or structured materials. In the case of structured materials, the study focused on an interface situation, in which sudden changes occurred in the properties. Based on the results, we aimed to obtain scientific subsidies to understand the application of ultrashort pulses to stratified structures, such as teeth, bones, resin-teeth or metal-teeth interface, and others. Distinct experimental techniques were used to determinate the ablation progression into the materials and to obtain data extracted from their surface. By using the scattered light from an external source, the ablation process was monitored temporally, allowing to determine the velocity of ablation in transparent materials, besides determining the typical profiles of ablated cavities in these materials. In a second experiment, our study allowed quantifying the overall variation in the ablation geometry that takes place on the interface of two different materials. Our data were sufficient to predict the occurrence of a discontinuity in the ablation profile on the interface between two media: resin A and resin B, showing a sudden discontinuity of the ablated cavity diameter. In addition, an analysis of the morphological aspects of different biological tissues irradiated by femtosecond laser pulses was performed and a comparative study showed the ablation efficiency of the femtosecond lasers in hard tissues processing and the possibility of using these systems with no thermal and mechanic damage. Finally, we applied a laser micromachining producing micro-pores on the tissue surface, improving the ALA penetration and increasing the treatment depth.

The topic of ability level grouping of students for instructional purposes is one of the most studied areas of research in educational literature. However, because of the inconclusive findings in the literature, no clear answer to the question of whether homogeneous or heterogeneous grouping is in the best educational interest of students has been established. Middle level administrators play a particularly important role in the debate concerning the use of ability grouping in individual schools because the pattern for future educational tracks of students is established at the middle level. An exploration of the factors that affect the decision making processes of middle school principals concerning whether to implement homogeneous versus heterogeneous grouping was deemed to be important in lending understanding to practitioners in the field faced with the responsibility of implementation of middle school programming. The purpose of this qualitative study was to explore the factors that influence middle level principals in the east Tennessee region when deciding to implement homogeneous or heterogeneous grouping of students in their schools. Data were collected through a series of audio taped interviews and transcribed for inductive analysis. Themes that emerged from the data analysis of the open-ended interviews were deducted into findings presented within the context of reviewed literature. The impact of student achievement, standardized test accountability, social factors that affect students, the perceptions of teachers and parents, programming for special education and gifted students, the impact of educational research, and the personal philosophies of the research participants concerning homogeneous versus heterogeneous instruction emerged as influential themes that affected principals' decisions to implement ability level grouping. Specific recommendations for educational practice included the implementation of ability grouping at the middle level exclusively in the areas of mathematics, language, and reading, flexible scheduling that allows for movement of students between groups, and changing the yearly assignment of teachers to a specific ability group for instruction. The need for additional quantitative and qualitative research was also suggested.

A one-dimensional, steady-state numerical model of the combustion of homogeneous solid propellant has been developed. The combustion processes is modeled in three regions: solid, two-phase (liquid and gas) and gas. Conservation of energy and mass equations are solved in the two-phase and gas regions and the eigenvalue of the system (the mass burning rate) is converged by matching the heat flux at the interface of these two regions. The chemical reactions of the system are modeled using a global kinetic mechanism in the two-phase region and an elementary kinetic mechanism in the gas region. The model has been applied to RDX, HMX and GAP. There is very reasonable agreement between experimental data and model predictions for burning rate, temperature sensitivity, surface temperature, adiabatic flame temperature, species concentration profiles and melt-layer thickness. Many of the similarities and differences in the combustion of RDX and HMX are explained from sensitivity analysis results. The combustion characteristics of RDX and HMX are similar because of their similar chemistry. Differences in combustion characteristics arise due to differences in melting temperature, vapor pressure and initial decomposition steps. A reduced mechanism consisting of 18 species and 39 reactions was developed from the Melius-Yetter RDX mechanism (45 species, 232 reactions). This reduced mechanism reproduces most of the predictions of the full mechanism but is 7.5 times faster. Because of lack of concrete thermophysical property data for GAP, the modeling results are preliminary but indicate what type of experimental data is necessary before GAP can be modeled with more certainty.

Dans le contexte du réchauffement climatique et de l’usage abusif de combustibles fossiles, la recherche de sources d’énergie propres et durables est l’un des défis les plus importants de notre époque. Récemment, le stockage d’énergie solaire par la réduction de CO2 a fait l’objet d’un nouvel intérêt. Bien que la réduction de CO2 en carburants liquides ou gazeux soit une question à la fois fascinante et fondamentale, sa mise en œuvre dans les dispositifs technologiques reste très difficile à cause de la grande stabilité de CO2 et du caractère endergonique de sa transformation. On outre, les réactions impliquent multiples électrons et protons et ainsi demandent des catalyseurs efficaces et stables pour diminuer les barrières cinétiques importantes.Cette comprend deux parties. Après une introduction, la première partie décrit des études sur des catalyseurs homogènes en combinaison avec un photosensibilisateur, soit séparément soit connecté par liaison covalente. Grâce à la possibilité de les modifier par synthèse et à leur facile caractérisation, les photosystèmes moléculaires homogènes sont plus modulables et peuvent permettre un meilleur contrôle de la sélectivité des réactions et l’étude des mécanismes réactionnels.Cependant, les catalyseurs moléculaires ne peuvent être facilement transposés pour des applications à plus large échelle dans un contexte industriel. En effet, les catalyseurs homogènes sont moins stables et plus difficilement recyclables que les catalyseurs hétérogènes. Dans ce contexte, l’intégration de catalyseurs moléculaires au sein d’un support solide a l’avantage de maintenir leur activité catalytique tout en permettant une séparation et un recyclage plus faciles. La deuxième partie de cette thèse porte donc sur l’immobilisation de catalyseurs moléculaires dans les matériaux. Le but ultime de cette thèse est d’incorporer à la fois le catalyseur et le photosensibilisateur dans le support solide. / In the context of global warming and the necessary substitution of renewable energies (solar and wind energy) for fossil fuels, efficient energy-storage technologies need to be urgently developed. Recently, energy storage via the reduction of CO2 has seen renewed interest. Although reduction of CO2 into energy-dense liquid or gaseous fuels is a fascinating fundamental issue, its practical implementation in technological devices is highly challenging due to the high stability of CO2 and thus the endergonic nature of its transformation. Furthermore, the reactions involve multiple electrons and protons and thus require efficient catalysts to mediate these transformations.The objective of this thesis is to investigate different strategies for the storage of solar energy in chemical compounds, through visible-light-driven CO2 reduction. This thesis comprises of two main parts. After an introduction, the first part describes the investigation of homogeneous catalysts in combination with a photosensitizer, either separately or connected covalently. Due to the easily-tunable synthesis and facile characterization of molecular catalysts, homogeneous photosystems are more controllable and can give deep insight into product selectivity and mechanistic issues.With regards to future applicability, however, homogeneous catalysis often suffers from additional costs associated with solvents, product isolation and catalyst recovery, amongst other factors. The integration of molecular catalysts into solid platforms offers the possibility to maintain the advantageous properties of homogeneous catalysts while moving towards practical system designs afforded by heterogeneous catalysis. The second part of this thesis is therefore the immobilization of molecular catalysts within solid materials, namely MOFs and PMO. The ultimate goal of this thesis is to incorporate both catalyst and photosensitizer into the solid support.

Let $\overline{R}$ be a finitely bordered Riemann surface, and let $\mathfrak{E}_\rho(\overline{R})$ be a flat matrix $PU_n(\mathbb{C})$-bundle over $\overline{R}$. Let $\Gamma_c(\overline{R}, \mathfrak{E}(\overline{R}))$ denote the $C^*$-algebra of continuous cross-sections of $\mathfrak{E}(\overline{R})$, and let $\Gamma_h(\overline{R},\mathfrak{E}(\overline{R}))$ denote the subalgebra consisting of the continuous holomorphic sections, i.e.~the continuous cross-sections that are holomorphic on the interior of $\overline{R}$. The algebra $\Gamma_c(\overline{R}, \mathfrak{E}(\overline{R}))$ is an example of an $n$-homogeneous $C^*$-algebra, and the subalgebra $\Gamma_h(\overline{R},\mathfrak{E}(\overline{R}))$ is the principal object of study of this thesis. The algebras $\Gamma_h(\overline{R},\mathfrak{E}(\overline{R}))$ appeared in the earlier works \cite{Abrahamse1976} and \cite{Blecher2000}. Operators that can be viewed as elements in $\Gamma_h(\overline{R},\mathfrak{E}(\overline{R}))$ are the subject of \cite{Abrahamse1976}. The Morita theory of $\Gamma_h(\overline{R},\mathfrak{E}(\overline{R}))$, under the guise of a fixed-point algebra and in the special case of an annulus $R$, is studied in \cite[Ex.~8.3]{Blecher2000}. This thesis studies these algebras and their topological data $\mathfrak{E}_\rho(\overline{R})$ motivated by several problems in the theory of nonselfadjoint operator algebras. Boundary representations are an invariant of operator algebras that were introduced by Arveson in 1969. However, it took nearly 50 years to show that boundary representations existed in sufficient abundance in all cases. I show that every boundary representation of $\Gamma_c(\overline{R}, \mathfrak{E}(\overline{R}))$ for $\Gamma_h(\overline{R}, \mathfrak{E}(\overline{R}))$ is given by evaluation at some point $r \in \partial R$. As a corollary, the $C^*$-envelope of $\Gamma_h(\overline{R},\mathfrak{E}(\overline{R}))$ is $\Gamma_c(\partial R, \mathfrak{E}(\partial R))$. Using the $C^*$-envelope, I show that for certain choices of fibre and base space, $\Gamma_h(\overline{R}, \mathfrak{E}_\rho(\overline{R}))$ is not completely isometrically isomorphic to $A(\overline{R})\otimes M_n(\mathbb{C})$ unless the representation $\rho$ is the trivial representation. I also show that $\Gamma_h(\overline{R},\mathfrak{E}(\overline{R}))$ is an Azumaya over its center. Azumaya algebras are the ``pure-algebra'' analogues to $n$-homogeneous $C^*$-algebras \cite{Artin1969}. Thus the structure of the nonselfadjoint subalgebra $\Gamma_h(\overline{R},\mathfrak{E}(\overline{R}))$ reflects some of the structure of its $C^*$-envelope (which is $n$-homogeneous). Finally, I answer a question raised in \cite[Ex.~8.3]{Blecher2000} on the $cb$ and strong Morita theory of $\Gamma_h(\overline{R},\mathfrak{E}_\rho(\overline{R}))$, showing in particular that $\Gamma_h(\overline{R},\mathfrak{E}_\rho(\overline{R}))$ is $cb$ Morita equivalent to its center $A(\overline{R})$. As suggested in \cite[Ex.~8.3]{Blecher2000}, I provide additional evidence that $\Gamma_h(\overline{R},\mathfrak{E}_\rho(\overline{R}))$ may not be strongly Morita equivalent to its center. This evidence, in turn, suggests that there may be a Brauer group -like analysis for these algebras.

This dissertation study describes the development of novel heteroepitaxial growth of 3C-SiC layers by chemical vapor deposition (CVD). It was hypothesized that chloride addition to the "traditional" propane-silane-hydrogen precursors system will enhance the deposition growth rate and improve the material quality via reduced defect density. Thermodynamic equilibrium calculations were performed to obtain a criterion for which chloride specie to select for experimentation. This included the chlorocarbons, chlorosilanes, and hydrogen chloride (HCl) chloride containing groups. This study revealed no difference in the most dominant species present in the equilibrium composition mixture between the groups considered. Therefore, HCl was the chloride specie selected to test the hypothesis. CVD computerized fluid dynamic simulations were developed to predict the velocity, temperature and concentration profiles along the reactor. These simulations were performed using COMSOL Multiphysics and results are presented. The development of a high-temperature (1300 °C -1390°C) 3C-SiC growth process resulted in deposition rates up to ~38 µm/h. This is the highest value reported in the literature to date for 3C-SiC heteroepitaxy. XRD FWHM values obtained varied from 220 to 1160 arcsec depending of the process growth rate or film thickness. These values are superior or comparable to those reported in the literature. It was concluded from this study that at high deposition temperatures HCl addition to the precursor chemistry had the most significant impact on the epitaxial layer growth rate. Low-temperature (1000-1250°C) 3C-SiC growth experiments evidenced that the highest deposition rate that could be attained was ~2.5 µm/h. The best quality layer achieved in this study had a FWHM of 278 arcsec; which is comparable to values reported in the literature and to films grown at higher deposition temperatures in this study. It was concluded from this work that at lower deposition temperatures the HCl addition was more beneficial for the film quality by enhancing the surface. Surface roughness values for films grown with HCl additive were 10 times lower than for films grown without HCl. Characterization of the epitaxial layers was carried out via Nomarski optical microscopy, FTIR, SEM, AFM, XRD and XPS.