In mathematical physics, Laplace's equation plays an especially significant role. It is fundamental to the solution of problems in electrostatics, thermodynamics, potential theory and other branches of mathematical physics. It is for this reason that this investigation concerns the development of some general properties of continuous solutions of this equation.

In 1909, F. Riesz succeeded in giving an integral represntation for continuous linear functionals on C[0,1]. Although other authors, notably Hadamard and Frechet, had given representations for continuous linear functionals on C[0,1], their results lacked the clarity, elegance, and some of the substance (uniqueness) of Riesz's theorem. Subsequently, the integral representation of continuous linear functionals has been known as the Riesz Representation Theorem. In this paper, three different proofs of the Riesz Representation Theorem are presented. The first approach uses the denseness of the Bernstein polynomials in C[0,1] along with results of Helly to write the continuous linear functionals as Stieltjes integrals. The second approach makes use of the Hahn-Banach Theorem in order to write the functional as an integral. The paper concludes with a detailed presentation of a Daniell integral development of the Riesz Representation Theorem.

The aim of this study was to compare the incidence of root canal dentinal micro-cracks after canal instrumentation using reciprocating files (WaveOne Gold® and Twisted Adaptive®) and continuous rotation files (Edge Evolve® and EndoSequence®) in an ex-vivo benchtop study. This project used a novel methodology of finding dentinal defects using the “K-cube”, which allows evaluators to visualize sectioned root surfaces before instrumentation and after instrumentation. Mesial roots from 40 human mandibular first molars were divided into 4 groups of 10 for each file type. Root section pictures were taken with a Zeiss Discovery V20 stereomicroscope before and after canal instrumentation. Each of the pre-instrumentation and post-instrumentation images were evaluated for dentinal defects by four calibrated endodontists utilizing REDCap survey. Using a chi-square analysis, there was no statistically significant difference between dentinal defects created by continuous and reciprocating rotation (p=0.1924) and no difference between the four file types (p=0.2317).

La mejora de los procesos es fundamental en el crecimiento de cualquier organización que tenga metas cada más ambiciosa. Entre estas organizaciones se encuentra las empresas del rubro joyero que requieres de diversos recursos como la mano de obra calificada, tecnología y proveedores confiables, que cumplan los plazos de entrega establecidos y cuenten con productos de calidad. Es por ello, que las empresas de este rubro buscan a estos proveedores para mantener una relación a largo plazo con sus clientes, ya que de ellos dependerá del ritmo de producción que tendrá la empresa productora de joyas. En la presente investigación se realiza con la finalidad de analizar la situación actual de trabajo en una empresa productora de joyas y presentar propuestas de mejora en los procesos realizados por esta que pueda aumentar su rentabilidad y satisfacer las necesidades que tengan sus clientes actuales y potenciales. En primer lugar, en el proyecto se dará una presentación de los conceptos teóricos que son necesarios para realizar el diagnóstico de la problemática, de esta manera se tendrá diversas herramientas que serán útiles para poder plantear las diversas propuestas de mejora en Arin S.A. Las propuestas de mejoras estarán planteadas para poder optimizar los procesos que realizan y de esta manera establecer una cultura de mejora continua dentro de la organización. Por último, el objetivo de esta investigación es que se pueda ordenar el área de producción y ejecutar las propuestas de mejora que se consideren necesarias. Gracias a ello, se optimizará los procesos internos de tal manera que se consigan procedimientos eficientes y eficaces cambiando procedimientos, modificando métodos de trabajo, eliminando procesos improductivos y elevando el ritmo de producción. / Process improvement is fundamental to the growth of any organization with increasingly ambitious goals. Among these organizations are the jewelry companies that require various resources such as skilled labor, technology and reliable suppliers, that meet delivery deadlines and have quality products. It is for this reason that the companies in this area look for these suppliers to maintain a long-term relationship with their customers, since they will depend on the rate of production that will have the jewelry producing company. This research is carried out with the aim of analysing the current work situation in a jewellery production company and presenting proposals for improving the processes carried out by this one, so as to increase its profitability and satisfy the needs of its current and potential clients. In the first place, the project will give a presentation of the theoretical concepts that are necessary to make the diagnosis of the problem, in this way will have various tools that will be useful to raise the various proposals for improvement in Arin SA. The proposals for improvements will be raised to optimize the processes they perform and thus establish a culture of continuous improvement within the organization. Finally, the objective of this research is to be able to organize the production area and execute the improvement proposals that are considered necessary. As a result, internal processes will be optimized in such a way that efficient and effective procedures are achieved by changing procedures, modifying working methods, eliminating unproductive processes and increasing the production rate. / Tesis

Zeolites are porous aluminosilicates that occur both naturally and synthetically, having numerous applications in catalysis, adsorption and separations. Despite over a half century of characterization and synthetic optimization of hundreds of frameworks, the exact mechanism of synthesis remains highly contested, with crystallization typically occurring under transport-limited regimes. In this work, a microcrystallization reactor working under segmented oscillatory flow has been designed to produce a semi-continuous flow of zeolite A. The fast injection of the reactants in a mixing section forms droplets of aqueous precursors in a stream of paraffin, dispersing microdroplets and avoiding any clog from occurring in the system. The crystallization occurred in the system at atmospheric pressure and isothermal conditions (65ºC). This allowed for a rather slow crystallization kinetics which was important to study and highlight the different crystallization mechanisms between flow and batch synthesis. The morphology, size distributions, crystallinity, and porosity were examined by ex-situ characterization of the samples by scanning electron microscopy, X-ray diffraction, Raman spectroscopy, and N2 Physisorption to support the conclusions drawn. The size distribution of the particles achieved in the flow reactor was conclusively narrower than the distribution achieved in the batch reactor. The average size of the crystals for both synthesis methods is reported as 400 nm and the crystallinity achieved was comparable between the two. However, the morphology was quite different between the two systems, the flow products having a much higher mesoporosity due to the presence of crystal aggregates at high crystallinity when compared to the batch crystals. Finally, extended crystallization times leads to a decline of the crystallinity of the product, which might be explained by the metastable state of zeolites in solution.

Zeolites are porous aluminosilicates that occur both naturally and synthetically, having numerous applications in catalysis, adsorption and separations. Despite over a half century of characterization and synthetic optimization of hundreds of frameworks, the exact mechanism of synthesis remains highly contested, with crystallization typically occurring under transport-limited regimes. In this work, a microcrystallization reactor working under segmented oscillatory flow has been designed to produce a semi-continuous flow of zeolite A. The fast injection of the reactants in a mixing section forms droplets of aqueous precursors in a stream of paraffin, dispersing microdroplets and avoiding any clog from occurring in the system. The crystallization occurred in the system at atmospheric pressure and isothermal conditions (65ºC). This allowed for a rather slow crystallization kinetics which was important to study and highlight the different crystallization mechanisms between flow and batch synthesis. The morphology, size distributions, crystallinity, and porosity were examined by ex-situ characterization of the samples by scanning electron microscopy, X-ray diffraction, Raman spectroscopy, and N2 Physisorption to support the conclusions drawn. The size distribution of the particles achieved in the flow reactor was conclusively narrower than the distribution achieved in the batch reactor. The average size of the crystals for both synthesis methods is reported as 400 nm and the crystallinity achieved was comparable between the two. However, the morphology was quite different between the two systems, the flow products having a much higher mesoporosity due to the presence of crystal aggregates at high crystallinity when compared to the batch crystals. Finally, extended crystallization times leads to a decline of the crystallinity of the product, which might be explained by the metastable state of zeolites in solution.

Les composites à matrice céramique (CMC) sont des matériaux constitués d’une matrice céramique renforcée par des fibres céramiques continues (généralement à base de SiC ou de C). Le travail de thèse présenté, réalisé en collaboration avec Snecma Propulsion solide et l’Agence De l’Environnement et de la Maîtrise de l’Energie, a pour objectif d’introduire des matériaux CMC au sein de pièces de moteurs d’avions civils, concurrençant ainsi les alliages métalliques actuellement utilisés. Pour ce faire, les matériaux CMC devront répondre aux exigences propres à l’aéronautique civil, à savoir qu’ils devront présenter une longue durée de vie en atmosphère oxydante dans une gamme de basse température (400-600°C) et avoir un coût compétitif. Dans ce contexte, des matériaux CMC constitués de fibres SiC de première génération, de coût moins élevé, sont étudiés, mais leur inconvénient majeur est leur plus grande sensibilité à l’oxydation. Des matrices auto-cicatrisantes multicouches à base de Si, B, et C ont été développées ces dernières années afin d’assurer une tenue à l’oxydation des fibres, mais elles ne sont pas opérantes dans la gamme de température imposée. Compte tenu d’études précédemment réalisées et des exigences requises pour l’application visée, l’objectif du travail présenté dans ce mémoire est de proposer des solutions pour améliorer la tenue à l’oxydation de renforts fibreux à base de fibres de SiC de première génération, dans la gamme de température 400-600°C, en évitant un surcoût de production trop important. / Continuous fiber-reinforced ceramic matrix composites (CFCCs) are an important class of materials for structural applications at elevated temperatures because of their improved flaw tolerance, large fracture resistance, improved toughness by crack deflection and crack bridging mechanism, low density and noncatastrophic mode of failure comparing with metallic materials. Fibers play a critical role in both the processing and performance of CFCCs. SiC-based fibers are considered leading candidate materials in the aerospace application, such as engine turbines. However, the major shortcoming of SiC-based fibers is their oxidative embrittlement and degradation, which is caused by the oxygen ingression from the micro cracks and interstitials in the composites, is the dominant life-limiting phenomenon of non-oxide composites. This study carried out with the financial supply of both Snecma Propulsion Solide and Agence De l’Environnement et de la Maîtrise de l’Energie has for objective to integrate SiC-based as reinforcement in CFCCs for civil aircraft engine application. In order to reach this objective, it is imperative to find a novel approach to diminish the oxygen ingression by developing protective fiber coatings.

Thesis (M.Ed.)--University of the Witwatersrand, Faculty of Education, 1999.

Trata-se de uma pesquisa teórica e de campo, com o objetivo de analisar as práticas de recuperação que foram implantadas nas escolas estaduais paulistas, como resultado da opção pelo regime de progressão continuada e da organização do ensino fundamental em ciclos a partir de 1998. O objetivo central de nosso trabalho foi o de caracterizar a concepção das práticas de recuperação na Lei de Diretrizes e Bases nº 9394/96 e como as mesmas foram regulamentadas no Estado de São Paulo, por meio do Conselho Estadual de Educação de São Paulo e da Secretaria da Educação do Estado de São Paulo. Não obstante, as práticas de recuperação se vinculam sempre a um posicionamento político e a uma opção por determinados valores e princípios que norteiam a avaliação escolar. Longe de representar um aspecto apenas técnico do cotidiano escolar, a avaliação envolve esferas muito mais amplas e complexas, já que se apóia em orientações legais (legislação federal e estadual) que, por sua vez, espelham fundamentações teóricas que lhes apontam diretrizes. O desenvolvimento deste trabalho de pesquisa acompanhou um período de sucessivas transformações em relação ao sistema de avaliação e às práticas de recuperação nas escolas de 1ª a 4ª série da rede pública estadual de São Paulo. Embora a Lei nº 9394/96 continue a representar a orientação legal mais ampla para as práticas de recuperação em nível federal, o Parecer CEE/SP nº 67/98, a Resolução SE 05/98 e a Resolução SE 06/08 (alterada pela Resolução 26/08) representam indicadores legais estaduais paulistas sobre as práticas de recuperação que revelam aspectos vitais para o entendimento do sistema de recuperação que tem vigorado em nossas escolas. Além da análise da legislação federal e estadual que apóia as atividades de recuperação nas escolas estaduais, aplicamos um questionário a trinta professores da rede pública estadual de São Paulo sobre as práticas de recuperação no regime de progressão continuada. O conjunto de dados obtidos permitiu concluir que a maioria dos professores considera que houve mudanças significativas na organização da escolarização em ciclos, principalmente porque afasta o fantasma da repetência (63%), mas 37% se declararam contra a recuperação no sistema de ciclos por considerar que não há respaldo suficiente aos professores para trabalhar com as práticas de recuperação e que o tempo que antecede a recuperação ao final de ciclo é longo demais (quatro anos). / It is a theorical and field-work research, which has the aim to annalyse the revision classes that were implanted in the public schools of the State of São Paulo as result of the option for the continuous promotion and the new organization of primary school that happened in 1998. The central objective of this work was the characterization of the conception of the revision classes in Leis de Diretrizes e Bases (LDB -Guidelines and Bases Act of Education)-, Law n. 9394/96 and how it was regulated in the State of São Paulo, by the Conselho Estadual de Educação de São Paulo (CNE - Brazilian Council for Education) and by the Secretaria da Educação do Estado de São Paulo (State Secretariat of Education of São Paulo). Nevertheless, the practice of revision classes are always linked to a political position and to an option for some values and principles that structure the educational evaluation. The intention is not only represent the technical aspect; the educational evaluation involves more complexes questions because of the fact that is based in legal orientation (federal and state legislation) that revels theorycal fundaments of the guidelines. The development of this research followed a period of transformations in the relation of education evaluation system and the revision classes in the 1st to 4th grades in the public schools of the state of São Paulo. Although the Law nº 9394/96 continues to represent a broaden legal orientation to the revision in the federal level, the resolutions Parecer CEE/SP nº 67/98, a Resolução SE 05/98 e a Resolução SE 06/08 (modified by Resolução 26/08) represent state legal indicators about the revision classes, which revels vital aspects for the understanding of revision classes system existent in our schools. Besides the analyze of the federal and state legislation that supports the revision activities in the state schools, we collected data of 30 teachers using a questionnaire about the revision classes in the universe of continuous promotion. The data we have obtained permitted conclude that the large majority of teachers consider that it had important changes in the organization in cycles. It hides the ghost of repeater (63%), but 37% declare themselves against the revision classes in the system of cycles owing to the fact that there is no sufficient base for the teachers to work with the repetition practice and that the time that occurs before the recuperation in the end of the cycle is too long (four years).

Processos industriais de polimerização em emulsão são usualmente realizados em reatores tipo tanque agitado em batelada (ou semi-batelada) ou em contínuo (CSTR). Reatores contínuos tem a vantagem de serem comparativamente de menor porte, e propiciarem melhor controle da qualidade do produto pela redução de variações de batelada a batelada. Reatores tipo CSTR podem exibir oscilações periódicas e autosustentadas de conversão, de tamanho e concentração de partículas. Estas oscilações podem ser minimizadas nos reatores tubulares pulsados devido à diminuição da dispersão axial em relação aos reatores do tipo CSTR. Na presente tese, desenvolveu-se um novo tipo de reator tubular, a Coluna Pulsada de Pratos Perfurados, CPPP, para uso no processo de polimerização contínua do acetato de vinila em emulsão. O reator é operado com escoamento pulsado e contém pratos perfurados como dispositivos internos. Inicialmente foram realizados ensaios de distribuição de tempos de residência, em um reator montado em vidro, com o objetivo de caracterizar o escoamento no reator CPPP quanto ao grau de mistura axial. Os dados foram interpretados usando o modelo de escoamento pistonado com dispersão axial. Valores do coeficiente de dispersão axial foram medidos e correlacionados para diferentes condições de freqüência e amplitude de pulsação, vazão, espaçamento entre pratos, e viscosidade do fluido. Verificou-se que o grau de mistura axial pode ser variado em faixas relativamente amplas pela manipulação da freqüência e amplitude de pulsação. Foi também montado um reator em aço inox e encamisado, com as mesmas dimensões, onde foram realizados ensaios de polimerização em emulsão de acetato de vinila, medindo-se a conversão e a distribuição de tamanhos de partículas (DTP), na saída do reator em regime transiente e permanente, e também ao longo do reator em regime permanente. Verificou-se que as condições operacionais (tempo médio de residência e grau de dispersão axial) influenciam várias características do produto, como, a conversão, tamanho médio e concentração de partículas, porém, não influencia, significativamente, a viscosidade da emulsão produzida, para a receita da reação de polimerização e as condições operacionais estudadas. Os resultados experimentais foram interpretados usando um modelo matemático do reator, o qual foi estabelecido com base em um modelo cinético publicado na literatura para o processo de polimerização em emulsão de acetato de vinila em batelada. Tal modelo foi adaptado incluindo-se os termos convectivos e dispersivos nas equações de balanço de massa, e resolvido numericamente. Foram ajustados apenas dois parâmetros neste modelo, para todas as condições operacionais estudadas e os resultados simulados reproduziram adequadamente o comportamento das principais variáveis de processo para a condição de regime permanente. O novo tipo de reator contínuo apresentado neste trabalho mostrou-se ser possível obter altas conversões em tempos médios de residência da ordem ou mesmo inferiores aos do processo em batelada e atingir regime permanente de operação em um a dois tempos médios de residência. O reator é eficiente, robusto, construtivamente simples, de fácil limpeza e manutenção, e mostrou-se promissor para utilização industrial em processo de polimerização em emulsão de acetato de vinila. / Industrial emulsion polymerization processes are usually carried out in stirred tanks operated in batch/semibatch or in continuous mode (CSTR). In comparison to batch processes, continuous reactors present several advantages such as lower volumes and better quality control by reducing batch-to-batch variations. Continuous emulsion polymerization in CSTR may exhibit sustained oscillations in conversion, particle size and particle concentration. Such oscillations may be reduced in pulsed tubular reactors due to less axial mixing. In this thesis a new type of tubular reactor, called Pulsed Sieve Plate Column, PSPC, was developed for the continuous process of vinyl acetate emulsion polymerization. This reactor is operated using oscillatory pulsed flow and uses perforated plates as internals. Residence time distribution runs were carried out in a glass reactor in order to characterize the axial mixing and flow patterns in the PSPC. The data were treated using the axially dispersed plug flow model. Axial dispersion coefficient was measured for different conditions of pulse frequency and amplitude, flow rate, plate spacing and viscosity. It was found that the degree of axial mixing can be varied in wide ranges by manipulating pulsation frequency and/or amplitude. Vinyl acetate continuous emulsion polymerization runs were carried out in a jacketed stainless steel reactor (with the same size of the glass reactor). Monomer conversion and particle size distribution was measured both at the reactor exit in transient state and along the reactor length at steady-state. It was found that average residence time and degree of axial mixing affect process and product quality variables, such as monomer conversion, mean particle size and concentration, but did not affect the viscosity of the emulsion produced, for the recipe and conditions used. A mathematical model for the reactor was developed. The model used, based on a well-known kinetic model previously developed in the literature for batch emulsion polymerization, was adapted to the continuous tubular reactor by adding the dispersion and convective terms to the balance equations. The model was numerically solved. Only two parameters were adjusted in this model and the simulated results showed excellent agreement with the experimental results, for steady state conditions. The proposed tubular reactor allows to reach high monomer conversion with similar or even lower residence time than those in batch processes and reaches steady state operation in just one to two mean residence times. The reactor is efficient, easy-to-built, easy-to-clean, robust and promising for use in industrial continuous emulsion polymerization of vinyl acetate.