Orientador: Pedro Toniol Cardin / Banca: Edson Donizete de Carvalho / Banca: Wendel Cleber Soares / Resumo: O principal objetivo deste trabalho e fazer um estudo sobre problemas de máximos e mínimos de funções de uma variável no ensino médio. E destinado a professores e alunos de matemática deste nível de ensino. Tem a pretensão de melhorar a compreensão deste tema, muitas vezes s o abordado a nível de funções quadráticas. Serve também como uma aplicação da fórmula de Taylor. Neste trabalho queremos incentivar alunos e professores de matemática ao estudo de máximos e mínimos de funções de uma variável. Resolveremos diversos problemas envolvendo máximos e mínimos de funções polinomiais do 2o grau, utilizando os conceitos básicos de vértice, ponto de máximo, ponto de mínimo. Iremos também mostrar a resolução de problemas de máximos e mínimos que não recaem em uma função quadrática, utilizando o conceito de derivada. Por fim, para estes ultimos problemas, utilizaremos a fórmula de Taylor para aproximar a função obtida por seu polinômio de Taylor de 2a ordem. Encontraremos o valor máximo ou mínimo de tal polinômio usando as ferramentas básicas de função quadrática. De fato, devido a teoria de Taylor, constataremos que o valor otimo obtido no problema e o valor máximo ou mínimo de tal polinômio estarão suficientemente próximos / Abstract: The main goal of this work is to make a study about problems of maxima and minima of functions of one variable in High School. It is intended for teachers and students of mathematics of this level of learning. It intends to improve the understanding of this subject which it is often only addressed to the level of quadratic functions. It also serves as an application of the Taylor formula. In this work we want to encourage students and teachers of mathematics to the study of maxima and minima of functions of one variable. We will solve several problems involving maxima and minima of polynomial functions of the second degree, using the basic concepts of vertex, maximum point, minimum point. We will also show the resolution of problems of maxima and minima that do not lead to a quadratic function, using the derivative concept. Finally, for these last problems, we will make use of the Taylor formula in order to approximate the function obtained by its Taylor polynomial of second order. We will nd the maximum or minimum value of such polynomial by using the basic tools of quadratic function. In fact, due to Taylor theory, we will note that the optimal value obtained in the problem and the maximum or minimum value of such polynomial will be su ciently close / Mestre

Chiu Chun Hung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 112-114). / Abstracts in English and Chinese. / Abstract --- p.i / 論文摘要 --- p.ii / Acknowledgment --- p.iii / List of Figures n --- p.i / List of Tables n --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.4 / Chapter 3 --- Review of the Minimax Model --- p.7 / Chapter 4 --- Portfolio Optimization with Shorting --- p.13 / Chapter 4.1 --- Formulation of Minimax Model with Shorting --- p.13 / Chapter 4.2 --- A Simple Optimal Investment Strategy --- p.14 / Chapter 4.2.1 --- All Assets Are Risk --- p.14 / Chapter 4.2.2 --- Some Assets Are Riskless --- p.31 / Chapter 4.3 --- Tracing Out the Efficient Frontier --- p.34 / Chapter 4.3.1 --- No Riskless Assets Are Involved --- p.34 / Chapter 4.3.2 --- Riskless Assets Are Involved --- p.43 / Chapter 4.4 --- Chapter Summary --- p.44 / Chapter 5 --- Portfolio Optimization with Investment Limit --- p.50 / Chapter 5.1 --- Formulation of Minimax Model with Investment Limit --- p.51 / Chapter 5.2 --- Optimal Solution to POI(λ) --- p.52 / Chapter 5.2.1 --- All Assets Are Risky --- p.52 / Chapter 5.2.2 --- Some Assets Are Riskless --- p.67 / Chapter 5.3 --- Chapter Summary --- p.71 / Chapter 6 --- Numerical Analysis --- p.72 / Chapter 6.1 --- Data Analysis --- p.72 / Chapter 6.2 --- Experiment Description and Discussion --- p.75 / Chapter 6.2.1 --- Short-Selling is Allowed --- p.75 / Chapter 6.2.2 --- Comparison Between the Cases With Short-Selling and Without Short-Selling --- p.77 / Chapter 6.3 --- Chapter Summary --- p.79 / Chapter 7 --- Conclusion --- p.39 / Chapter A --- List of Companies Included in Numerical Analysis --- p.82 / Chapter B --- Graphical Result of Section 6.21 --- p.84 / Chapter C --- Graphical Result of Section 6.22 --- p.93 / Bibliography --- p.112

Tong Kwong-Bun. / Thesis submitted in: December 2002. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 77-[80]). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- An Overview --- p.1 / Chapter 1.2 --- Tree Search --- p.2 / Chapter 1.2.1 --- Minimax Algorithm --- p.2 / Chapter 1.2.2 --- The Alpha-Beta Algorithm --- p.4 / Chapter 1.2.3 --- Alpha-Beta Enhancements --- p.5 / Chapter 1.2.4 --- Selective Search --- p.9 / Chapter 1.3 --- Construction of Evaluation Function --- p.16 / Chapter 1.4 --- Contribution of the Thesis --- p.17 / Chapter 1.5 --- Structure of the Thesis --- p.19 / Chapter 2 --- The Probabilistic Forward Pruning Framework --- p.20 / Chapter 2.1 --- Introduction --- p.20 / Chapter 2.2 --- The Generalized Probabilistic Forward Cuts Heuristic --- p.21 / Chapter 2.3 --- The GPC Framework --- p.24 / Chapter 2.3.1 --- The Alpha-Beta Algorithm --- p.24 / Chapter 2.3.2 --- The NegaScout Algorithm --- p.25 / Chapter 2.3.3 --- The Memory-enhanced Test Algorithm --- p.27 / Chapter 2.4 --- Summary --- p.27 / Chapter 3 --- The Fast Probabilistic Forward Pruning Framework --- p.30 / Chapter 3.1 --- Introduction --- p.30 / Chapter 3.2 --- The Fast GPC Heuristic --- p.30 / Chapter 3.2.1 --- The Alpha-Beta algorithm --- p.32 / Chapter 3.2.2 --- The NegaScout algorithm --- p.32 / Chapter 3.2.3 --- The Memory-enhanced Test algorithm --- p.35 / Chapter 3.3 --- Performance Evaluation --- p.35 / Chapter 3.3.1 --- Determination of the Parameters --- p.35 / Chapter 3.3.2 --- Result of Experiments --- p.38 / Chapter 3.4 --- Summary --- p.42 / Chapter 4 --- The Node-Cutting Heuristic --- p.43 / Chapter 4.1 --- Introduction --- p.43 / Chapter 4.2 --- Move Ordering --- p.43 / Chapter 4.2.1 --- Quality of Move Ordering --- p.44 / Chapter 4.3 --- Node-Cutting Heuristic --- p.46 / Chapter 4.4 --- Performance Evaluation --- p.48 / Chapter 4.4.1 --- Determination of the Parameters --- p.48 / Chapter 4.4.2 --- Result of Experiments --- p.50 / Chapter 4.5 --- Summary --- p.55 / Chapter 5 --- The Integrated Strategy --- p.56 / Chapter 5.1 --- Introduction --- p.56 / Chapter 5.2 --- "Combination of GPC, FGPC and Node-Cutting Heuristic" --- p.56 / Chapter 5.3 --- Performance Evaluation --- p.58 / Chapter 5.4 --- Summary --- p.63 / Chapter 6 --- Conclusions and Future Works --- p.64 / Chapter 6.1 --- Conclusions --- p.64 / Chapter 6.2 --- Future Works --- p.65 / Chapter A --- Examples --- p.67 / Chapter B --- The Rules of Chinese Checkers --- p.73 / Chapter C --- Application to Chinese Checkers --- p.75 / Bibliography --- p.77

Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2010. / Committee Chair: Earl Barnes; Committee Member: Arkadi Nemirovski; Committee Member: Faiz Al-Khayyal; Committee Member: Guillermo H. Goldsztein; Committee Member: Joel Sokol. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--University of Wisconsin, 1967. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (Ph. D.)--Florida State University, 2006. / Advisor: Kai-Sheng Song, Florida State University, Collee of Arts and Sciences, Dept. of Statistics. Title and description from dissertation home page (viewed Dec. 5, 2006). Document formatted into pages; contains vii, 93 pages. Includes bibliographical references.

Made available in DSpace on 2015-04-09T12:28:28Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-09-22Bitstream added on 2015-04-09T12:47:21Z : No. of bitstreams: 1 000809210.pdf: 459385 bytes, checksum: dab92fb8cd81e57ec76cb5ce64b983e9 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O principal objetivo deste trabalho e fazer um estudo sobre problemas de máximos e mínimos de funções de uma variável no ensino médio. E destinado a professores e alunos de matemática deste nível de ensino. Tem a pretensão de melhorar a compreensão deste tema, muitas vezes s o abordado a nível de funções quadráticas. Serve também como uma aplicação da fórmula de Taylor. Neste trabalho queremos incentivar alunos e professores de matemática ao estudo de máximos e mínimos de funções de uma variável. Resolveremos diversos problemas envolvendo máximos e mínimos de funções polinomiais do 2o grau, utilizando os conceitos básicos de vértice, ponto de máximo, ponto de mínimo. Iremos também mostrar a resolução de problemas de máximos e mínimos que não recaem em uma função quadrática, utilizando o conceito de derivada. Por fim, para estes ultimos problemas, utilizaremos a fórmula de Taylor para aproximar a função obtida por seu polinômio de Taylor de 2a ordem. Encontraremos o valor máximo ou mínimo de tal polinômio usando as ferramentas básicas de função quadrática. De fato, devido a teoria de Taylor, constataremos que o valor otimo obtido no problema e o valor máximo ou mínimo de tal polinômio estarão suficientemente próximos / The main goal of this work is to make a study about problems of maxima and minima of functions of one variable in High School. It is intended for teachers and students of mathematics of this level of learning. It intends to improve the understanding of this subject which it is often only addressed to the level of quadratic functions. It also serves as an application of the Taylor formula. In this work we want to encourage students and teachers of mathematics to the study of maxima and minima of functions of one variable. We will solve several problems involving maxima and minima of polynomial functions of the second degree, using the basic concepts of vertex, maximum point, minimum point. We will also show the resolution of problems of maxima and minima that do not lead to a quadratic function, using the derivative concept. Finally, for these last problems, we will make use of the Taylor formula in order to approximate the function obtained by its Taylor polynomial of second order. We will nd the maximum or minimum value of such polynomial by using the basic tools of quadratic function. In fact, due to Taylor theory, we will note that the optimal value obtained in the problem and the maximum or minimum value of such polynomial will be su ciently close

Made available in DSpace on 2015-05-15T11:46:08Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-08-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work presents a research on problems of maxima and minima of the Euclidean geometry. Initially we present some preliminary results followed by statements that in essence use basic concepts of geometry. Below are some problems of maximizing area and minimizing perimeter of triangles and convex polygons, culminating in a proof of the isoperimetric inequality for polygons and review the general case. Solve some classical problems of geometry that are related to outliers and present other problems as proposed. / Este trabalho apresenta uma pesquisa sobre problemas de máximos e mínimos da Geometria Euclidiana. Inicialmente apresentamos alguns resultados preliminares seguidos de suas demonstrações que em sua essência usam conceitos básicos de geometria. Em seguida apresentamos alguns problemas de maximização de área e de minimização de perímetro em triângulos e polígonos convexos, culminando com uma prova da desigualdade isoperimétrica para polígonos e comentário do caso geral. Resolvemos alguns problemas clássicos de geometria que estão relacionados com valores extremos e apresentamos outros como problemas propostos.

Trends in streamflow extremes at a regional scale linked to the possible influences of four major oceanic-atmospheric oscillations are analyzed in this study. Oscillations considered include: El Niño Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), Atlantic Multidecadal Oscillation (AMO), and North Atlantic Oscillation (NAO). The main emphasis is low flows in the South-Atlantic Gulf region of the United States. Several standard drought indices of low flow extremes during two different phases (warm/positive and cool/negative) of these oscillations are evaluated. Long-term streamflow data at 43 USGS sites in the region from the Hydro-Climatic Data Network that are least affected by anthropogenic influences are used for analysis. Results show that for ENSO, low flow indices were more likely to occur during La Niña phase; however, longer deficits were more likely during El Niño phase. Results also show that for PDO (AMO), all (most) low flow indices occur during the cool (warm) phase. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2015. / FAU Electronic Theses and Dissertations Collection

Nie Xiaofeng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 52-56). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- A Minimax Model and Its CAPM --- p.9 / Chapter 2.1 --- Model Formulation --- p.9 / Chapter 2.2 --- Efficient Frontier --- p.11 / Chapter 2.3 --- Market Portfolio --- p.15 / Chapter 2.4 --- CAPM of Minimax Model --- p.22 / Chapter 3 --- "A Revised Minimax Model with Downside Risk, and Its CAPM" --- p.28 / Chapter 3.1 --- Model Formulation --- p.28 / Chapter 3.2 --- Efficient Frontier --- p.30 / Chapter 3.3 --- Market Portfolio and CAPM --- p.38 / Chapter 4 --- Numerical Analysis --- p.43 / Chapter 4.1 --- Efficient Frontiers --- p.43 / Chapter 4.1.1 --- Input Data --- p.45 / Chapter 4.1.2 --- Efficient Frontiers --- p.45 / Chapter 4.2 --- Monthly Rate of Return Comparison --- p.47 / Chapter 5 --- Summary --- p.50 / Bibliography --- p.52