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Made available in DSpace on 2014-06-11T19:24:48Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-03-28Bitstream added on 2014-06-13T20:13:08Z : No. of bitstreams: 1 almeida_fc_me_bauru.pdf: 2833020 bytes, checksum: c01e3aadb9839f2cd43b28c57967821f (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho tem como objetivo analisar os Livros Didáticos de Matemática para o Ensino Fundamental, 3º e 4° ciclos, em relação à abordagem dos Temas Transversais/Político-Sociais, como e quanto abordam estes temas, através da análise e estudo dos conteúdos referentes ao bloco de Grandezas e Medidas. Para a realização desta pesquisa utilizou-se da técnica de Documentação Indireta e da Análise Direta, em uma amostra de cinco coleções de livros didáticos de Matemática para o 3º e 4º ciclos, coleções essas avaliadas e recomendadas pelo MEC. A pesquisa foi fundamentada na Pedagogia Histórico-Crítica, em estudos sobre o Livro Didático, especificamente o de Matemática e na teoria sobre Temas Transversais/Político-Sociais. A análise possibilitou perceber que há uma preocupação com a formação para a cidadania descrita nos documentos oficiais e que esses documentos, além de discutirem sobre os temas transversais, ainda que de forma restrita, sugerem maneiras de trabalhar os conteúdos transversais nas diversas disciplinas para o alcance da formação para cidadania. A análise possibilitou perceber também que, embora os Livros Didáticos proponham o trabalho com os temas transversais, esse trabalho não ocorre como é proposto pelos PCN - Temas Transversais, tampouco como sugere a teoria sobre temas político-sociais estudada nesta pesquisa, o que ocorre é uma contextualização simplista do conteúdo matemático através de problemas vinculados a uma abordagem prático-utilitária, não propiciando aos estudantes uma formação cidadã que almeje uma sociedade justa e emancipatória para todos. / The present work aims to analyse the Mathematics Schoolbooks for Elementary Education, concerning third and fourth cicles, in relation to the Transversal Themes/ Social-Political approach - how and how much the schoolbooks approach these themes – through the analysis and study of Quantities and Measurement contents. To accomplish this research the techniques of Indirect Documentation and Direct Analysis were applied to a sample of five collections of Mathematics Schoolbooks for third and fourth cicles, which were evaluated and recommended by MEC. The research was based on the Historical-Critical Pedagogy, studies about schoolbooks, especially the Mathematics ones, and the theory about Transversal Themes/ Social- Political Themes. The analysis demonstrated that there is a concern about the education for citizenship that is described on the official documents; besides they discuss the Transversal Themes in a limited form, they also suggest ways to work the transversal contents in several subjects, to achieve the education for citizenship. The analysis also demonstrated that, although the schoolbooks recommend the work with the transversal themes, it does not occur in the way the document PCN – Transversal Themes proposes, neither how the theory of social-political themes suggests; what occurs is a simplist contextualization of the mathematics contents through problems entailed by a practical utilitarian approach, what does not provide to the students the education for citizenship that aspires an equitable and emancipatoty society for everybody.

ABSTRACT In jet problems the conserved quantity plays a central role in the solution process. The conserved quantities for laminar jets have been established either from physical arguments or by integrating Prandtl's momentum boundary layer equation across the jet and using the boundary conditions and the continuity equation. This method of deriving conserved quantities is not entirely systematic and in problems such as the wall jet requires considerable mathematical and physical insight. A systematic way to derive the conserved quantities for jet °ows using conservation laws is presented in this dissertation. Two-dimensional, ra- dial and axisymmetric °ows are considered and conserved quantities for liquid, free and wall jets for each type of °ow are derived. The jet °ows are described by Prandtl's momentum boundary layer equation and the continuity equation. The stream function transforms Prandtl's momentum boundary layer equation and the continuity equation into a single third- order partial di®erential equation for the stream function. The multiplier approach is used to derive conserved vectors for the system as well as for the third-order partial di®erential equation for the stream function for each jet °ow. The liquid jet, the free jet and the wall jet satisfy the same partial di®erential equations but the boundary conditions for each jet are di®erent. The conserved vectors depend only on the partial di®erential equations. The derivation of the conserved quantity depends on the boundary conditions as well as on the di®erential equations. The boundary condi- tions therefore determine which conserved vector is associated with which jet. By integrating the corresponding conservation laws across the jet and imposing the boundary conditions, conserved quantities are derived. This approach gives a uni¯ed treatment to the derivation of conserved quantities for jet °ows and may lead to a new classi¯cation of jets through conserved vectors. The conservation laws for second order scalar partial di®erential equations and systems of partial di®erential equations which occur in °uid mechanics are constructed using di®erent approaches. The direct method, Noether's theorem, the characteristic method, the variational derivative method (mul- tiplier approach) for arbitrary functions as well as on the solution space, symmetry conditions on the conserved quantities, the direct construction formula approach, the partial Noether approach and the Noether approach for the equation and its adjoint are discussed and explained with the help of an illustrative example. The conservation laws for the non-linear di®usion equa- tion for the spreading of an axisymmetric thin liquid drop, the system of two partial di®erential equations governing °ow in the laminar two-dimensional jet and the system of two partial di®erential equations governing °ow in the laminar radial jet are discussed via these approaches. The group invariant solutions for the system of equations governing °ow in two-dimensional and radial free jets are derived. It is shown that the group invariant solution and similarity solution are the same. The similarity solution to Prandtl's boundary layer equations for two- dimensional and radial °ows with vanishing or constant mainstream velocity gives rise to a third-order ordinary di®erential equation which depends on a parameter. For speci¯c values of the parameter the symmetry solutions for the third-order ordinary di®erential equation are constructed. The invariant solutions of the third-order ordinary di®erential equation are also derived.

This thesis has been performed in Gaborone, Botswana, where all interviews and relevant research data collection took place. The main method of data collection was a semi-structured interviews with relevant parties involved in waste management and generation in Gaborone.This work is part of a larger feasibility study called “Gaborone Transfer and Recycling Station (GTARS)”. The main objective is to make waste management in Gaborone more sustainable, taking environmental, social and economic aspects into account. The aim of this master thesis is to investigate the waste flow rates and composition in the capital city of Botswana, Gaborone. Taking this into account, other factors which directly influence waste generation and composition are identified. The findings show that currently in the year 2014, the city of Gaborone is generating about 348 tons of solid waste per day.Further investigation showed that illegal dumping is a prominent practice in Gaborone, mostly due to the long distance to the landfill and generally low environmental awareness amongst the citizens of the city. The waste generation rates are increasing every year, because the city of Gaborone is expanding rapidly and economic conditions facilitate the increasing urbanization rate. The analysis done till the year 2024 indicate that waste amounts might reach up to 433 tons of solid waste generated per day. Waste composition analysis is constrained, because of the limited data sources available on this subject, but the analysis shows that paper, biodegradable waste and plastics are the main fractions found in the municipal waste stream. / Gaborone Transfer and Recycling Station (GTARS)

Submitted by Sandra Pereira (srpereira@ufrrj.br) on 2018-05-09T12:45:23Z No. of bitstreams: 1 2010 - Ananias de Oliveira Lima.pdf: 5673141 bytes, checksum: c85c1dd5947492ba2e6f14cf595a0a03 (MD5) / Made available in DSpace on 2018-05-09T12:45:24Z (GMT). No. of bitstreams: 1 2010 - Ananias de Oliveira Lima.pdf: 5673141 bytes, checksum: c85c1dd5947492ba2e6f14cf595a0a03 (MD5) Previous issue date: 2010-02-28 / The objective of this research was to evaluate the effectiveness of methodology of projects in the context of the concepts of physics in the teaching of Soil Science, arousing interest in the scientific research while working as a team, contributing for the education of the student and promoting a meaningful learning. Such research is warranted because the contemporary pedagogical proposals must have a focus on new meaning of education, centered on the idea that education means preparing the individual to meet personal needs and desires of a society in constant transformation. Unfortunately, most schools have established a methodology represented by the traditional lecture, in whose model the teacher conveys to the student the content through the verbal exposition of the subject, exercises of memorization and retention. However, for learning to be meaningful it becomes necessary for one school with previous experience of students, allowing the formulation and solution of problems that encourage the construction of knowledge. The traditional methodology of physics has not met the goal of educating the young for the exercise of technical and scientific activities, being disconnected from the vocational subjects, therefore, does not attract the interest of the student, being unable to stimulate development skills of teamwork. In this sense, it is believed that the teaching-learning process could be enhanced with the implementation of interdisciplinary activities in order to understand concepts in physics laboratory activities in their professional practice. The research was conducted at IFES Campus Santa Teresa with a group of students from the Technical Course on Integrated Agricultural High School, enrolled in physics, consisting of 24 students. Initially, the students participated in educational activities of conceptual physics, and the theme generator design methodology was selected as the objective of developing an interdisciplinary and contextualized, referring to the concepts of soil. Following these concepts were used to carry out laboratory activities using the equipment available for the determination of texture, density, humidity and porosity of the soil samples, which resulted in completing reports. Students planned activities, preparing reports on their group, to determine the density, humidity and porosity of the fields according to the standard reports. Throughout this study, it was observed that the methodology allowed a greater interest by students, demonstrated by enthusiasm during the development of activities. It also promoted a better understanding of the concept of soil and a contextualized view of the behavior of soil water in the face of the texture features and their correlations with the physical quantities such as mass, density, velocity and humidity studied in high school. Project activities also allowed students to experience teamwork, allowing them to interact with equipment and materials, acquiring skills and acquire skills that only work on a project using the methodology. / The objective of this research was to evaluate the effectiveness of methodology of projects in the context of the concepts of physics in the teaching of Soil Science, arousing interest in the scientific research while working as a team, contributing for the education of the student and promoting a meaningful learning. Such research is warranted because the contemporary pedagogical proposals must have a focus on new meaning of education, centered on the idea that education means preparing the individual to meet personal needs and desires of a society in constant transformation. Unfortunately, most schools have established a methodology represented by the traditional lecture, in whose model the teacher conveys to the student the content through the verbal exposition of the subject, exercises of memorization and retention. However, for learning to be meaningful it becomes necessary for one school with previous experience of students, allowing the formulation and solution of problems that encourage the construction of knowledge. The traditional methodology of physics has not met the goal of educating the young for the exercise of technical and scientific activities, being disconnected from the vocational subjects, therefore, does not attract the interest of the student, being unable to stimulate development skills of teamwork. In this sense, it is believed that the teaching-learning process could be enhanced with the implementation of interdisciplinary activities in order to understand concepts in physics laboratory activities in their professional practice. The research was conducted at IFES Campus Santa Teresa with a group of students from the Technical Course on Integrated Agricultural High School, enrolled in physics, consisting of 24 students. Initially, the students participated in educational activities of conceptual physics, and the theme generator design methodology was selected as the objective of developing an interdisciplinary and contextualized, referring to the concepts of soil. Following these concepts were used to carry out laboratory activities using the equipment available for the determination of texture, density, humidity and porosity of the soil samples, which resulted in completing reports. Students planned activities, preparing reports on their group, to determine the density, humidity and porosity of the fields according to the standard reports. Throughout this study, it was observed that the methodology allowed a greater interest by students, demonstrated by enthusiasm during the development of activities. It also promoted a better understanding of the concept of soil and a contextualized view of the behavior of soil water in the face of the texture features and their correlations with the physical quantities such as mass, density, velocity and humidity studied in high school. Project activities also allowed students to experience teamwork, allowing them to interact with equipment and materials, acquiring skills and acquire skills that only work on a project using the methodology. / O objetivo da pesquisa foi avaliar a efic?cia da metodologia de projetos na contextualiza??o dos conceitos de F?sica no ensino da Ci?ncia do Solo, despertando o interesse pela pesquisa cient?fica ao trabalhar em equipe, contribuindo na forma??o integral do aluno e promovendo uma aprendizagem significativa. Tal pesquisa se justifica porque as propostas pedag?gicas contempor?neas precisam ter em foco um novo sentido da educa??o, centrado na id?ia de que educar significa preparar o indiv?duo para responder ?s necessidades pessoais e aos anseios de uma sociedade em constante transforma??o. Infelizmente, na maioria das escolas, vigora a metodologia tradicional representada pela aula expositiva, em cujo modelo o professor passa para o aluno o conte?do, atrav?s da exposi??o verbal da mat?ria, de exerc?cios de memoriza??o e fixa??o. Entretanto, para que a aprendizagem seja significativa torna-se necess?ria uma rela??o escolar com as experi?ncias anteriores dos alunos, permitindo a formula??o e resolu??o de problemas que incentivam a constru??o do saber. No ?mbito da F?sica a metodologia tradicional n?o tem atendido ao objetivo de formar o jovem para o exerc?cio de atividades t?cnicas e cient?ficas, mostrando-se desconectada das disciplinas de forma??o profissional, consequentemente n?o atrai o interesse do estudante, sendo incapaz de estimular o desenvolvimento de habilidades de trabalho em equipe. Neste sentido, acredita-se que o processo ensino-aprendizagem poderia ser aprimorado com a realiza??o de atividades interdisciplinares visando a compreens?o de conceitos de F?sica nas atividades laboratoriais em sua pr?tica profissional. O ensaio experimental foi realizado no IFES Campus Santa Teresa com uma turma de alunos do Curso T?cnico em Agropecu?ria Integrado ao Ensino M?dio, matriculados na disciplina de F?sica, constitu?da por 24 alunos. Inicialmente os alunos participaram de atividades pedag?gicas conceituais de f?sica, sendo que o tema gerador da metodologia de projetos foi selecionado como o intuito de desenvolver um trabalho interdisciplinar e contextualizado, referente aos conceitos de solo. A seguir tais conceitos foram empregados na realiza??o de atividades de laborat?rio empregando os equipamentos dispon?veis para a determina??o da textura, densidade, umidade e porosidade total das amostras de solo, que resultaram no preenchimento de relat?rios. Os alunos planejaram as atividades, elaborando seus relat?rios em grupo para determinar a densidade, a umidade e a porosidade das ?reas experimentais de acordo com o padr?o de relat?rios. Ao longo da pesquisa foi poss?vel perceber que a metodologia utilizada possibilitou maior interesse dos alunos, demonstrado pelo entusiasmo pelas atividades desenvolvidas. Tamb?m promoveu um melhor entendimento do conceito de solo e uma vis?o contextualizada do comportamento da ?gua no solo em face das caracter?sticas da textura e de suas correla??es com as grandezas f?sicas como massa, densidade, velocidade e umidade estudadas no Ensino M?dio. As atividades do projeto ainda possibilitaram aos alunos a viv?ncia do trabalho em equipe, permitindo que eles interagissem com equipamentos e materiais, adquirindo habilidades e compet?ncias que somente adquiririam em um trabalho utilizando a metodologia de projetos. / O objetivo da pesquisa foi avaliar a efic?cia da metodologia de projetos na contextualiza??o dos conceitos de F?sica no ensino da Ci?ncia do Solo, despertando o interesse pela pesquisa cient?fica ao trabalhar em equipe, contribuindo na forma??o integral do aluno e promovendo uma aprendizagem significativa. Tal pesquisa se justifica porque as propostas pedag?gicas contempor?neas precisam ter em foco um novo sentido da educa??o, centrado na id?ia de que educar significa preparar o indiv?duo para responder ?s necessidades pessoais e aos anseios de uma sociedade em constante transforma??o. Infelizmente, na maioria das escolas, vigora a metodologia tradicional representada pela aula expositiva, em cujo modelo o professor passa para o aluno o conte?do, atrav?s da exposi??o verbal da mat?ria, de exerc?cios de memoriza??o e fixa??o. Entretanto, para que a aprendizagem seja significativa torna-se necess?ria uma rela??o escolar com as experi?ncias anteriores dos alunos, permitindo a formula??o e resolu??o de problemas que incentivam a constru??o do saber. No ?mbito da F?sica a metodologia tradicional n?o tem atendido ao objetivo de formar o jovem para o exerc?cio de atividades t?cnicas e cient?ficas, mostrando-se desconectada das disciplinas de forma??o profissional, consequentemente n?o atrai o interesse do estudante, sendo incapaz de estimular o desenvolvimento de habilidades de trabalho em equipe. Neste sentido, acredita-se que o processo ensino-aprendizagem poderia ser aprimorado com a realiza??o de atividades interdisciplinares visando a compreens?o de conceitos de F?sica nas atividades laboratoriais em sua pr?tica profissional. O ensaio experimental foi realizado no IFES Campus Santa Teresa com uma turma de alunos do Curso T?cnico em Agropecu?ria Integrado ao Ensino M?dio, matriculados na disciplina de F?sica, constitu?da por 24 alunos. Inicialmente os alunos participaram de atividades pedag?gicas conceituais de f?sica, sendo que o tema gerador da metodologia de projetos foi selecionado como o intuito de desenvolver um trabalho interdisciplinar e contextualizado, referente aos conceitos de solo. A seguir tais conceitos foram empregados na realiza??o de atividades de laborat?rio empregando os equipamentos dispon?veis para a determina??o da textura, densidade, umidade e porosidade total das amostras de solo, que resultaram no preenchimento de relat?rios. Os alunos planejaram as atividades, elaborando seus relat?rios em grupo para determinar a densidade, a umidade e a porosidade das ?reas experimentais de acordo com o padr?o de relat?rios. Ao longo da pesquisa foi poss?vel perceber que a metodologia utilizada possibilitou maior interesse dos alunos, demonstrado pelo entusiasmo pelas atividades desenvolvidas. Tamb?m promoveu um melhor entendimento do conceito de solo e uma vis?o contextualizada do comportamento da ?gua no solo em face das caracter?sticas da textura e de suas correla??es com as grandezas f?sicas como massa, densidade, velocidade e umidade estudadas no Ensino M?dio. As atividades do projeto ainda possibilitaram aos alunos a viv?ncia do trabalho em equipe, permitindo que eles interagissem com equipamentos e materiais, adquirindo habilidades e compet?ncias que somente adquiririam em um trabalho utilizando a metodologia de projetos.

The purpose of this study is to determine whether oil and gas producing companies smooth their ending reserve quantities. Smoothing is defined as a reduction in variance in the trend of ending reserve quantities over time compared to the trend of ending reserve quantities less the hypothesized smoothing variable over time. This study focuses on two variables that are most susceptible to manipulation—revisions of previous estimates and additions. This study also examines whether revisions are positively or negatively biased and the variability of the revisions. The sample consists of 70 companies chosen from oil & Gas Reserve Disclosures: 1980-1984 Survey of 400 Public Companies by Arthur Andersen and Company. For each company, ending reserve quantities for the years 1978-1984 were regressed over time, and the standard deviation of the estimate (SDE) was calculated. Then the ending reserve quantities less the hypothesized smoothing variable were regressed over time, and the SDE was calculated. A linear model and a semi-logarithmic model were used. A smoothing ratio (SR) was determined by dividing the SDE of reserves less the hypothesized smoothing variable by the SDE of ending reserve quantities. An SR greater than one indicates smoothing, and an SR less than one indicates that smoothing did not occur. The mean percentage revision and a t-test were used to test for positive or negative bias in the revisions. The mean absolute percentage revision was used to assess the relative variability of revisions. The number of companies classified as smoothers of oil reserves was statistically significant for the semi-logarithmic model but not for the linear model. Under both models the number of companies classified as smoothers of gas reserves was statistically significant. Few companies had mean percentage revisions that were significantly different from zero. The majority of companies had mean absolute revisions of under ten percent.

Este trabalho, um estudo do tipo qualitativo, teve como objetivo compreender de que modo os educadores matemáticos podem fazer emergir o conhecimento primeiro dos educandos no que se refere a grandezas e medidas , legitimando-os e procurando formas de dialogar com os educandos. Os dados/fatos foram coletados a partir de entrevistas com oito educandos de uma 6ª série (sete encontros) da Escola Estadual Antonio Candido Correa Guimarães Filho. Em cada encontro era esperado que uma questão associada a grandezas e medidas desencadeasse um processo gerador/problematizador em busca dos conhecimentos (primeiro) dos alunos. Os princípios da etnomatemática e as idéias de Paulo Freire, assim como teorizações sócio-construtivistas, constituíram os fundamentos da pesquisa. No que se refere às evidências de pesquisa, podemos, de início, dizer que as manifestações dos alunos estão envolvidas mais por uma arte ao formular, resolver e buscar aplicações em termos de grandezas e medidas do que por uma compreensão mais ou menos técnica da maneira como se mede; tomam-se padrões para esta ou aquela grandeza; como se os organizam e opera-se com eles. Em termos de conclusão, vale ressaltar que o exercício feito pela pesquisadora de operacionalização de atitudes, de busca e valorização do conhecimento primeiro que aqui já se mostrou voltada para os estudos etnomatemáticos, especialmente no que se refere a o que o outro pensa, como o outro vê ativou mais e mais o olhar da pesquisadora para processos de cunho etnomatemático tanto no âmbito pedagógico como em termos de pesquisa. / This paper, a research of the type qualitative, has as an aim the understanding of how mathematics educators can bring forth the first knowledge (previous knowledge) of the learners regarding quantities and measures , legitimizing them and looking for ways to dialogue with the students. The data/facts were collected from the interviews with eight 6th grade students (seven meetings) of the State School Antonio Candido Correa Guimarães Filho. In each meeting it was expected that a question related to quantities and measures would trigger a generating/problematizing process in search of the knowledge (the first one) of the students. The principles of ethnomathematics and Paulo Freire\'s ideas as well as socioconstructivist theories constituted the basis of the research. Regarding the research evidences we can say, initially, that the students\' answers are involved more by an art when posing, solving and looking for applications in terms of quantities and measures, than by a more or less technical understanding of the way one measures, defines standards for this or that quantity, organizes them and works with them. In general, the research development allowed us to conclude that it is worth to emphasize that the exercise of the operationalization of attitudes, by the researcher, the quest for and the appreciation of first knowledge - that here has already shown itself focusing on ethnomathematics studies, especially with regard to what the \"other\" thinks, how the \"other\" sees - more and more enabled the researcher to look at the processes of an ethnomathematics nature both within the pedagogical scope as in terms of research.

Neste trabalho implementamos as grandezas operacionais no sistema de monitoração de área e individual. Determinamos a combinação ideal dos detectores termoluminescentes para constituírem os monitores de radiação como sendo: dois de fluoreto de cálcio (CaF2), um envolto em filtro de chumbo de (0,50 ± 0,05) mm e outro sem filtro e um de fluoreto de lítio TLD-100, também sem filtro. Aproveitamos a propriedade termoluminescente desses detectores, qual seja a de emissão de luz em intensidade proporcional à dose de radiação recebida, quando eles são aquecidos. A grandeza final avaliada é o equivalente de dose ambiental H*(10) e direcional H(10,) para fins de monitoração de área e o equivalente de dose pessoal Hp(10) para monitoração individual. Para tanto, estudos foram realizados irradiando os monitores no ar no primeiro caso e na frente de um fantoma de PMMA preenchido com água no segundo caso. Para avaliar o desempenho dos monitores de radiação eles foram submetidos a testes de linearidade da resposta com a dose, dependência angular e dependência energética. Uma análise detalhada dos resultados obtidos mostrou que todos os valores dos equivalentes de dose obtidos em testes de desempenho estão dentro dos limites estabelecidos por normas internacionais, com 95% de nível de confiança. Para o monitor escolhido obtivemos para a razão [H(10)determinado/H(10)nominal ± desvio] no caso de equivalente de dose ambiental e pessoal respectivamente os valores: (1,02 ± 0,11) e (0,97 ± 0,25). Os desvios foram calculados com o método t de student, considerando o intervalo que contém o valor nominal com 95% de probabilidade. / Operational quantities have been implemented to be applied in individual and area routine monitoring against external radiation exposure. This procedure is based on the use of an ideal combination of thermoluminescent detectors inside a monitor: two pellets of CaF2, one covered by a lead filter of (0,50 ± 0,05) mm and another one without filter and one TLD-100 without filter too. The operational quantities studied for area monitoring are the ambient and directional dose equivalent, H*(10) and H(10,), respectively and for individual monitoring, the personal dose equivalent, Hp(10). To evaluate the personal dose equivalent, all the experiments were performed irradiating the monitor on a slab water phantom made of PMMA walls with outer dimensions 30x30x15 cm, (a substitute of ICRU sphere four-element tissue phantom) completely full of water. Area monitors were irradiated in free air without any phantom. In general, an operational quantity H is determined from the basic physical quantity kerma free-in-air by means of conversion coefficients. The blind performance testing of monitors was performed after type testing, including analysis of the linearity of the response with the dose, the angular and energy dependence. The results of these investigations agree with the values recommended by international organisations within 95 % of confidence level. The ratios (H(10)evaluated/H(10)nominal ± deviation) obtained for ambient and personal dose equivalente are respectively (1,02 ± 0,11) and (0,97 ± 0,25), with the monitor above quoted. The error was estimated with the method of t-student, considering 95 % confidence level.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este é um trabalho de pesquisa sobre um conjunto de números (irracionais) que é pouco trabalhado no ensino básico de matemática. Foi uma procura muito interessante e enriquecedora, pois encontrei matemáticos e historiadores com visões bem diferentes. Muitos deles não aceitavam este novo conjunto. Para Leopold Kronecker, só existia o conjunto dos números inteiros. Já para Cantor e Dedekind, o aparecimento dos irracionais foi extremamente importante para o desenvolvimento da matemática, abrindo novos horizontes. Menciono aqui um pouco da vida e da obra de alguns matemáticos que se envolveram com os números irracionais. Tratamos ainda da descoberta dos incomensuráveis, ou seja, como iniciou-se o problema da incomensurabilidade, e do retângulo áureo e sua importância em outras áreas. O trabalho mostra também dois grupos de números que não são mencionados quando ensinamos equações algébricas, que são os números algébricos e os números transcendentes, assim como teoremas essenciais para a prova da transcendência dos irracionais especiais e . Por fim, proponho uma aula para uma turma do 3 ano do Ensino Médio com o objetivo de mostrar a irracionalidade de alguns números, usando os teoremas pertinentes / This is a research about a set of numbers (irrationals) that is little explored in secondary school mathematics teaching. It was a very interesting and enriching search, because quite contrary facts were found. Several 19th century mathematicians did not accept this new set of numbers. To Leopold kronecker, only the set of the integers existed. To Cantor and Dedekind, the irrational numbers were extremely important for the development of mathematics, opening new horizons. I also mention the life and work of some mathematicians who were involved with the irrational numbers the discovery of the incommensurability was iniciated. The golden rectangle and its importance in other areas. The work also presents two groups of numbers that are not mentioned when algebraic equations are taught, the algebraic numbers and transcendental numbers. Essential theorems for the proof of the special irrational numbers e . Finnaly, I propose a lesson to a 3rd year high school class in order to show the irrationality of some numbers, using the relevant theorems

We develop an extension to the tactical planning model (TPM) for a job shop by the third author. The TPM is a discrete-time model in which all transitions occur at the start of each time period. The time period must be defined appropriately in order for the model to be meaningful. Each period must be short enough so that a job is unlikely to travel through more than one station in one period. At the same time, the time period needs to be long enough to justify the assumptions of continuous workflow and Markovian job movements. We build an extension to the TPM that overcomes this restriction of period sizing by permitting production control over shorter time intervals. We achieve this by deriving a continuous-time linear control rule for a single station. We then determine the first two moments of the production level and queue length for the workstation. / Singapore-MIT Alliance (SMA)