ABSTRACT Taitung area was commonly seen as a particularly clean environment. But the air quality has diminished lately similar to that seen in some parts of the populated western area in Taiwan, with ozone (O3) concentration levels rising every year. Because ozone is a byproduct of photochemistry, its accumulation is not only related to the discharge of local pollutants such as nitrogen oxide compounds (NOx), volatile organic compounds (VOC) and the introduction of external pollutants, but also related to the meteorological conditions. This research began with comparing the long-term trends of ozone concentration level and related pollutants in the Taitung area with those found in other survey stations spread in Taiwan. Through factor analysis, the relationship between air pollutants and meteorological parameters are analyzed. Finally, a screening of the events of abnormal ozone concentrations, followed with detailed analysis of the hourly data during these events and the discussion of the possible reasons for the comparatively poor air quality during these events and their correlations with seasons and meteorological conditions. Analysis of the trends in monthly averaged concentration of ozone shows that the annual rate of change (AR) is increasing at all stations under this study, except the Guanyin station being -0.18%. Taitung station has relatively higher levels every spring (March - May) and fall (October ¡V November); the annual rate of change is higher than other east area in Taiwan and the Hengchun station. These seasonal variation (SV) shows a progressively increasing north to south trend, Hengchun station being the highest and Taitung station being the second highest, indicates that concentrations of ozone are influenced by seasonal changes. By using the method of factor analysis to analyze the relation among ozone concentrations, meteorological parameters and pollution parameters, resulted in a direct relationship to the wind speeds over the four seasons. The results show a negative relationship to the atmospheric pressure during summer. The ozone concentrations of the Taitung station show a direct relationship to the Hualian station, which indicates the north to south dispersion relationship. The Analysis of the abnormal event also shows that typhoons may be an important carrier for transporting external pollutants into the area.

Made available in DSpace on 2016-04-27T16:57:20Z (GMT). No. of bitstreams: 1 Edson Rodrigues da Silva.pdf: 2574600 bytes, checksum: fe11256e07c5f09808b243d5f8f0ce49 (MD5) Previous issue date: 2012-10-09 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work aims to lead students in the 3rd year of high school to construct meaning to the idea of instantaneous rate of change. With this intention, and based on the premises of Didactic Engineering, we elaborated, applied and analyzed a didactic sequence for eight students of a public school in the state of São Paulo. As theoric support, we used the Theory of Didactical Situation (TDS) and the Representation Theory of Semiotics Register. The TDS assisted us in development, tests and analysis of results of didactic sequence, while the Representation Theory of Semiotics Registers emphasized the diversity and articulation of different registers of representation in mathematical activities. The analysis of didactic sequence indicated that teaching students in the 3rd year of high school, through the simultaneous mobilization of records graphing, algebraic and tabular can construct meaning to the idea of rate of change / O presente trabalho tem por objetivo conduzir estudantes do 3º ano do Ensino Médio a construir significado para a ideia de taxa de variação instantânea. Com esse intuito, e fundamentados nos pressupostos da Engenharia Didática, elaboramos, aplicamos e analisamos uma sequência didática para oito alunos de uma escola pública do Estado de São Paulo. Como aporte teórico utilizamos a Teoria das Situações Didáticas (TSD) e a Teoria de Registros de Representação Semiótica. A TSD nos auxiliou na elaboração, experimentação e análise dos resultados da sequência didática, enquanto a Teoria de Registros de Representação Semiótica, enfatizou a diversidade e a articulação de diferentes registros de representação nas atividades matemáticas. A análise da sequência didática apontou que estudantes do 3º ano do Ensino Médio, por meio da mobilização simultânea dos registros de representação gráfica, algébrica e tabular, podem construir significado para a ideia de taxa de variação

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2017-12-12T11:31:22Z No. of bitstreams: 1 Rogério dos Santos Lobo.pdf: 18965412 bytes, checksum: 14b5b24686e27326f72185c306819116 (MD5) / Made available in DSpace on 2017-12-12T11:31:22Z (GMT). No. of bitstreams: 1 Rogério dos Santos Lobo.pdf: 18965412 bytes, checksum: 14b5b24686e27326f72185c306819116 (MD5) Previous issue date: 2017-10-18 / Reflected on how a subject that uses the fundamental idea of Change is the source of various problems in regard to the initial concept of the Derivative. We elaborated the following research questions: What explanations of the concepts of Change and Rate of Change are given in Secondary School and Higher Education Textbooks? How are these explanations organised in Secondary School and Higher Education Textbooks? What meaning of Derivative can be constructed from Higher Education Textbooks? Moreover, in order to answer these questions, we seek the following general objective "to investigate the meanings of Change, Rate of Change and Derivative that can be constructed from the Secondary School and Higher Education Textbooks." The advancement of this objective is based on the achievement of the following specific objectives: To study the approaches given to the concepts of Change and Rate of Change in Secondary School Textbooks, more specifically in the Analytical Geometry - Study of the Tangent Line chapter; To Analyse the links between entries Semiotic Representation entries and the criteria for Epistemic Suitability for understanding the Rate of Change as applications of the Angular Coefficient, Calculation of Speeds, Average Economic Functions (Average Revenue, Average Profit, Average Cost), Direct Reasoning and the Rate of Relative Change (Percentage); To Analyse the links between Semiotic Representation entries and the criteria for Epistemic Suitability for understanding the Derivative and emphasising it as Rate of Change, alongside the applications of the Angular Coefficient, Calculation of Speeds, Marginal Economic Functions (Marginal Revenue, Marginal Profit and Marginal Cost), Direct Reasoning and Relative Change Rate (Percentage). For these analyses, we construct tables that use our theoretical-methodological references: Bardin's Content Analysis, Duval's Registers of Semiotic Representation Theory, the Holistic Meaning of the Derivative, and the criteria for Epistemic Impartiality. In the final considerations, we answer our research questions. The analyses of the Secondary School textbooks enabled us to draw a conclusion, among others, that the authors of these books explore the fundamental ideas of Change and Rate of Change mainly as an application of the Angular Coefficient and that meaning is constructed in alignment with only one of our various indicators. In the introduction to the Derivative, this concept is dealt with, among other approaches, as an application of the Angular Coefficient and the construction of meanings does not use any of our indicators / Refletimos, constantemente, como um assunto que utiliza a ideia fundamental de Variação é fonte de vários problemas no que diz respeito ao conceito inicial de Derivada. Elaboramos as seguintes questões de pesquisa: Quais significados dos conceitos de Variação e de Taxa de Variação são dados em Livros Didáticos do Ensino Médio e Ensino Superior? Como tais significados são organizados em Livros Didáticos do Ensino Médio e Ensino Superior? Qual significado de Derivada pode ser construído a partir de Livros Didáticos de Ensino Superior? E para respondermos a essas indagações, traçamos o seguinte objetivo geral “investigar os significados da Variação, da Taxa de Variação e da Derivada que podem ser construídos a partir da abordagem de Livros Didáticos do Ensino Médio e Ensino Superior” e o desdobramento deste objetivo apoia-se no alcance dos seguintes objetivos específicos: Estudar as abordagens dadas aos conceitos de Variação e da Taxa de Variação em Livros Didáticos de Ensino Médio, mais especificadamente no capítulo de Geometria Analítica – Estudo da Reta; Analisar as articulações entre registros os registros de Representação Semiótica e os critérios de Idoneidade Epistêmica para a compreensão da Taxa de Variação como aplicações de Coeficiente Angular, Cálculo de Velocidades, Funções Médias da Economia (Receita Média, Lucro Médio, Custo Médio), as Razões Diretas e a Taxa de Variação Relativa (Porcentagem); Analisar as articulações entre os registros de Representação Semiótica e os critérios de Idoneidade Epistêmica para a compreensão da Derivada e a enfatizando como Taxa de Variação, enquanto aplicações do Coeficiente Angular, Cálculo de Velocidades, Funções Marginais da Economia (Receita Marginal, Lucro Marginal e Custo Marginal), as Razões Diretas e a Taxa de Variação Relativa (Porcentagem). Para estas análises, construímos quadros que empregam nossos referenciais teórico-metodológicos: a Análise de conteúdo de Bardin, a Teoria dos Registros de Representação Semiótica de Duval, o Sentido Holístico da Derivada e os critérios de Idoneidade Epistêmica. Nas considerações finais, respondemos nossas questões de pesquisa. As análises dos livros didáticos do Ensino Médio permitiram concluir, entre outras, que os autores desses livros exploram as ideias fundamentais da Variação e Taxa de Variação como aplicação, principalmente, do Coeficiente Angular e a organização dos significados é feito no sentido de apenas, entre tantos, um de nossos indicadores. Na introdução da Derivada a abordagem deste conceito é feita, entre tantas, como aplicação do Coeficiente Angular e na organização dos significados não é utilizando um dos nossos indicadores

O conceito de taxa de variação é muito útil no estudo das funções reais de uma variável real e, por ser elementar, pode ser apresentado e discutido no Ensino Médio. A proposta deste trabalho é fazer um estudo detalhado e criterioso do uso da taxa de variação no estudo das funções afins, quadráticas e cúbicas. Com isso, pretende-se desenvolver resultados e apresentar diversas aplicações deste conceito a estas classes de funções que incluem, por exemplo, novas formas de obtenção dos seus gráficos, a interpretação geométrica de seus coeficientes, bem como resolver problemas simples e interessantes de otimização. Quanto às funções quadráticas, como aplicação do estudo feito sobre estas funções, apresentamos uma maneira matematicamente rigorosa de conceituar o Movimento Retilíneo Uniformemente Variado (MRUV), bem como, obtemos as equações horárias deste movimento. A definição que apresentamos é equivalente a usual, mas não faz uso dos Cálculos Infinitesimal e Integral. Como nosso objetivo é eminentemente matemático, não apresentamos qualquer interpretação Física deste conceito na forma que o introduzimos. Já o estudo das funções cúbicas pode ser visto como uma interessante aplicação das funções quadráticas, uma vez que, através do uso das taxas de variação, a descrição (traçado do gráfico) de uma função cúbica é reduzida ao estudo do sinal de uma função quadrática associada. / The concept of rate of change is very useful in the study of real functions of one real variable. Since this is a simple concept it can be presented and discussed in high school. The purpose of this work is to make a comprehensive study use of the rate of change in the study of the affine, quadratic and cubic functions. We prove results and present several applications of this concept to these classes of functions that include, for example, new ways of obtaining their graphs, geometric interpretation of their coefficients, and the solution of simple and interesting optimization problems. As for the quadratic functions, as an application of our study about these functions, we obtain in a mathematically rigorous definition of Uniformly Varied Rectilinear Motion and obtain the equations of the motion without using the Infinitesimal or Integral Calculus. Since we were essentially concerned with the mathematical aspect of this phenomenon, we did not present a discussion about the physical interpretation of our definition. The study of cubic functions can be seen as an interesting application of the quadratic functions, since through the use of rate changing, the description of the graph of a cubic function is reduced to the study of the sign of a quadratic function associated to the given cubic.

O conceito de taxa de variação é muito útil no estudo das funções reais de uma variável real e, por ser elementar, pode ser apresentado e discutido no Ensino Médio. A proposta deste trabalho é fazer um estudo detalhado e criterioso do uso da taxa de variação no estudo das funções afins, quadráticas e cúbicas. Com isso, pretende-se desenvolver resultados e apresentar diversas aplicações deste conceito a estas classes de funções que incluem, por exemplo, novas formas de obtenção dos seus gráficos, a interpretação geométrica de seus coeficientes, bem como resolver problemas simples e interessantes de otimização. Quanto às funções quadráticas, como aplicação do estudo feito sobre estas funções, apresentamos uma maneira matematicamente rigorosa de conceituar o Movimento Retilíneo Uniformemente Variado (MRUV), bem como, obtemos as equações horárias deste movimento. A definição que apresentamos é equivalente a usual, mas não faz uso dos Cálculos Infinitesimal e Integral. Como nosso objetivo é eminentemente matemático, não apresentamos qualquer interpretação Física deste conceito na forma que o introduzimos. Já o estudo das funções cúbicas pode ser visto como uma interessante aplicação das funções quadráticas, uma vez que, através do uso das taxas de variação, a descrição (traçado do gráfico) de uma função cúbica é reduzida ao estudo do sinal de uma função quadrática associada. / The concept of rate of change is very useful in the study of real functions of one real variable. Since this is a simple concept it can be presented and discussed in high school. The purpose of this work is to make a comprehensive study use of the rate of change in the study of the affine, quadratic and cubic functions. We prove results and present several applications of this concept to these classes of functions that include, for example, new ways of obtaining their graphs, geometric interpretation of their coefficients, and the solution of simple and interesting optimization problems. As for the quadratic functions, as an application of our study about these functions, we obtain in a mathematically rigorous definition of Uniformly Varied Rectilinear Motion and obtain the equations of the motion without using the Infinitesimal or Integral Calculus. Since we were essentially concerned with the mathematical aspect of this phenomenon, we did not present a discussion about the physical interpretation of our definition. The study of cubic functions can be seen as an interesting application of the quadratic functions, since through the use of rate changing, the description of the graph of a cubic function is reduced to the study of the sign of a quadratic function associated to the given cubic.

O conceito de taxa de variação é muito útil no estudo das funções reais de uma variável real e, por ser elementar, pode ser apresentado e discutido no Ensino Médio. A proposta deste trabalho é fazer um estudo detalhado e criterioso do uso da taxa de variação no estudo das funções afins, quadráticas e cúbicas. Com isso, pretende-se desenvolver resultados e apresentar diversas aplicações deste conceito a estas classes de funções que incluem, por exemplo, novas formas de obtenção dos seus gráficos, a interpretação geométrica de seus coeficientes, bem como resolver problemas simples e interessantes de otimização. Quanto às funções quadráticas, como aplicação do estudo feito sobre estas funções, apresentamos uma maneira matematicamente rigorosa de conceituar o Movimento Retilíneo Uniformemente Variado (MRUV), bem como, obtemos as equações horárias deste movimento. A definição que apresentamos é equivalente a usual, mas não faz uso dos Cálculos Infinitesimal e Integral. Como nosso objetivo é eminentemente matemático, não apresentamos qualquer interpretação Física deste conceito na forma que o introduzimos. Já o estudo das funções cúbicas pode ser visto como uma interessante aplicação das funções quadráticas, uma vez que, através do uso das taxas de variação, a descrição (traçado do gráfico) de uma função cúbica é reduzida ao estudo do sinal de uma função quadrática associada. / The concept of rate of change is very useful in the study of real functions of one real variable. Since this is a simple concept it can be presented and discussed in high school. The purpose of this work is to make a comprehensive study use of the rate of change in the study of the affine, quadratic and cubic functions. We prove results and present several applications of this concept to these classes of functions that include, for example, new ways of obtaining their graphs, geometric interpretation of their coefficients, and the solution of simple and interesting optimization problems. As for the quadratic functions, as an application of our study about these functions, we obtain in a mathematically rigorous definition of Uniformly Varied Rectilinear Motion and obtain the equations of the motion without using the Infinitesimal or Integral Calculus. Since we were essentially concerned with the mathematical aspect of this phenomenon, we did not present a discussion about the physical interpretation of our definition. The study of cubic functions can be seen as an interesting application of the quadratic functions, since through the use of rate changing, the description of the graph of a cubic function is reduced to the study of the sign of a quadratic function associated to the given cubic.

This is a case study using qualitative methods to analyze how a first semester calculus student named Mark makes sense of the derivative and the role of the classroom practice in his understanding. Mark is a bright yet fairly average student who successfully makes sense of the derivative and retains his knowledge and understanding. The study takes place within a collaborative, student-centered, task-based classroom where the students are given opportunity to explore mathematical ideas such as rate of change and accumulation. Mark's sense making of the derivative is analyzed in light of his use of physics, Mark as a visual learner, the representations he used to make sense of the derivative using Zandieh's (2000) framework for representations of derivatives, and his conceptions of the limit over time. Classroom practice allowed Mark to exercise his agency and explore tasks in ways that were personally meaningful. The findings in this study contribute new details about how calculus students might solve tasks, develop strategies, and communicate with each other.

The purpose of this study is to describe how university honors calculus students negotiate meaning and language for conceptually important ideas through mathematical discourse. Mathematical discourse has been recognized as an important topic by mathematics education researchers of various theoretical perspectives. This study is written from a perspective that merges symbolic interactionism (Blumer, 1969) with personal agency (Walter & Gerson, 2007) to assert that human choice reflects, but is not determined by, meanings that are primarily developed through social interaction. The process of negotiation of meaning is identified, described, and analyzed in the discourse of four students and their professor as they draw conclusions about the volume of water in a reservoir based on graphs of inflow and outflow. Video data, participant work, and transcript were analyzed using grounded theory and other qualitative techniques to develop three narrative accounts. The first narrative highlights the participants' use of personal pronouns and personal experience to negotiate meaning for the conventional mathematical terms "inflection" and "concavity." The second narrative describes how the participants' choices in discourse reflect an effort to represent both their mathematical and experiential understandings correctly as they negotiate language to describe critical "zero points." The third narrative describes the participants' process of mapping analogical language and meaning from the context of motion to the context of water in a reservoir. Analysis of these three narratives from the perspective of conventional and ordinary mathematical language suggests that the contextualized study of mathematics may provide students access to mathematical discourse if the relevant mappings between mathematical language and language from other appropriate contexts are made explicit. Analysis from the perspective of social speech (Piaget 1997/1896) suggests that specific uses of personal pronouns, personal experience, and revoicing (O'Connor & Michaels, 1996) may serve to invite students to become participants in mathematical discourse. An agency-based definition of mathematical discourse is suggested for application in research and practice.

The electrical distribution system in the United States is considered one of the most complicated machines in existence. Electrical phenomena in such a complex system can inflict serious self-harm. This requires damage prevention from protection schemes. Until recently, there was a safe gap between capacity to deliver power and the demand. Therefore, these protection schemes focused on dependability allowing the disconnection of lines, transformers, or other devices with the purpose of isolating the faulted element. On some occasions, the disconnections made were not necessary. The other extreme of reliability calls for security. This aspect of reliability calls for the operation of the protective devices only for faults within the intended area of protection. There is a tradeoff here; where a dependable protection scheme will assuredly prevent damage, it is prone to unnecessary operation which can lead to cascading outages. Where a secure scheme will not operate unnecessarily, it is prone to pieces of the system becoming damaged when relays fail to operate properly. With microprocessor based relaying schemes, a hybrid reliability focus is attainable through adaptive relaying. Adaptive relaying describes protection schemes that adjust settings and/or logic of operations based on the prevailing conditions of the system. These adjustments can help to avoid relay miss-operation. Adjustments could include, but are not limited to, the logging of data for post-mortem analysis, communication throughout the system, as well changing relay parameters. Several concepts will be discussed, one of which will be implemented to prove the value of the new tools available. / Master of Science

Essay 1 (with Juha Alho and Edward Palmer):  All around the world, public pension schemes are moving in the direction of non-financial (NDC) and financial defined contribution (DC) schemes.  Both rely on accurate projections of life expectancy in the creation of annuities. Accurate projections are critical for system stability, individual utility and inter-generational welfare. This paper suggests a path-breaking innovation that changes the perspective from the Lee-carter (LC) family of trend models which assume a constant rate of change in mortality over time. Our approach is to project the cohort life expectancy on basis of the specific cohort rate of change in mortality. This relaxes the strong trend assumption underlying the LC model, which is the reason why LC model does not work well in the phase of accelerating or decelerating mortality. We use unisex mortality data for $8$ countries to test the performance of our approach both ex-post and ex-ante. The ex-post experiment shows that our approach generally performs better when the rate of change in mortality is accelerating and performs as well as LC model when the rate of change is time-invariant. The ex-ante experiment, on the other hand, shows that our model almost always delivers higher projection of remaining life expectancy than the LC model for the more recent cohorts, which is consistent with the ex-post experimental results. / Essay 2:  Due to the systematic underestimation of cohort life expectancy, NDC pension schemes face a financial risk that can leads to inter-generational unfairness, given the current practice. This paper proposes an alternative method of computing annuity to address this problem. The proposal is to adjust the annuity based on re-estimations of the remaining life expectancy at intervals after retirement, but only up to a ceiling age. The scheme is assessed using 208 cohort annuity pools from eight sample countries. This experiment shows that the proposed scheme succeeds in reducing the inter-generational unfairness for 60-80% of the cohort annuity pools, compared to current practice of fixing the annuity at age 65. Because the adjustment is borne by the relatively large group of younger persons, the per capita change in utility is rather small assuming risk neutrality. / Essay 3:  This paper studies how the incentive to retire in a DC (NDC) scheme is influenced by engaging private information on life expectancy. This is an important question since the decisions made under the two scenarios, optimizing using the private life expectancy or the cohort average made available by the pension provider, create different welfare and financial outcomes. The analytical framework is a standard life-cycle model, accounting for monetary gain from work and non-monetary gain from leisure. The unique feature here is that the individual life expectancy is an explicit driver of disutility of work. The theoretical result is that prevailing private information of a longer-than-average life expectancy can lead to both advancing and delaying retirement, depending on other factors determining utility. The numerical example using Swedish data proves the theoretical results and suggests a rather small average impact on the choice of retirement by engaging private information of life expectancy. / Essay 4:   Pensions in the increasingly popular Notional Defined Contribution (NDC) Pay-as-You-Go Schemes are granted based on cohort-specific life expectancy, regardless socioeconomic differences. This risks perverse intra-generational and unintended inter-generational transfers. This paper introduces an alternative with separate annuity pools for different socioeconomic classes. Using unique Swedish data and the Swedish NDC pension system as an example, the analysis shows a significant gap in life expectancy between socioeconomic classes defined by occupation. In the Swedish context, this implies a perverse transfer of 5% of the pension capital from the manual workers to the non-manual workers, which can be abolished by using the group plan. In addition, the group plan also lessens the risk of inter-generational transfers resulting from the gap in life expectancy.