In this work we model the historical development of best performances in men's 100, 200, 400 and 800m running events. We suppose that the years best performances are independent random variables with generalized extreme value distribution for minima and that there is a decreasing trend in location. Parameters of the models are estimated by using maximum likelihood techniques. The data of years best performances are missing for some years, we treat them as right censored data that are censored by value of world record valid at that time. Graphic tools used for models diagnostics are adjusted to the censoring. The models we get are used to estimate the ultimate records and to predict new records in next years. At the end of the work we estimate several models describing historical development of years best performances for more events at one time.

Capitis deminutio minima The purpose of my thesis is to analyse the institute called the capitis deminutio minima. In this respect, it is primarily necessary to describe the meaning of the word caput for the understanding of the whole topic. The first chapter deals with the explanation of the above-mentioned term. The caput of a human being has in Roman Law three elements: the status of liberty, of citizenship and of family, and the subdivisions of the first chapter correspond to it. There, the first subchapter focuses on the persons who are free and those who are slaves; the latter were not considered to be legal persons at all. The following subchapter characterises the rights and duties of Roman citizens and the situation of the foreigners. The last subchapter contains basic information about the Roman family and its members, who are divided into two cathegories - the sui iuris and the alieni iuris. At the beginning the text describes the position of the head of the family (the pater familias), and his powers. The following text examines the conditions of those who are subjected to the authority of the pater familias. The last part of the text demonstrates the importance of religion in the daily life, both for the family and the whole society. The second chapter contains the description of the capitis...

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

We describe techniques for fast compression of time series and hierarchical indexing of compressed series based on the assignment of importance levels to the extrema of time series and their derivatives. We formalize the distance functions used in compression and retrieval techniques. We describe retrieval techinques that use the developed compression and indexing techniques for fast retreval of series from a database that match a given pattern.

Šiame darbe atliekami stochastinių minimumų asimptotiniai tyrimai. Įrodomos minimumų ribinės teoremos tuo atveju, kai tiesinis normalizavimas neduoda neišsigimusių ribinių skirstinių, tokiu atveju taikau netiesinį minimumų normalizavimą. Konkretaus skirstinio atveju randamos netiesinės normalizavimo funkcijos, kurių pagalba yra gaunami minimumų klasikiniai ribiniai skirstiniai. Įrodoma Perkėlimo teorema netiesiniam normalizavimui. Darbo tikslai: • ištirti netiesinio normalizavimo reikalingumą; • išanalizuoti netiesinio normalizavimo galimybes minimumų schemoje. Darbo uždaviniai: • parinkti netiesinio normalizavimo funkciją konkretaus skirstinio atveju; • gauti ribinius klasikinius skirstinius, kai minimumai normalizuojami netiesiškai; • įvertinti konvergavimo greitį ribinėse teoremose; • atlikti aproksimavimo paklaidų kompiuterinę analizę. / This paper is the asymptotic analysis of stochastic minima. Proofs of minima limit theorems are provided for cases, when linear normalization does not give non-degenerate limit distributions. In this cases, non-linear minima normalization is used. For a specific distribution, non-linear normalization functions are calculated, which are then used to get classic limit distributions for minima. Objectives: • Examine the necessity of non-linear normalization; • Analyze the possibilities for non-linear normalization in minimum pattern. Tasks: • Choose non-linear normalization function for a specific distribution; • Get classic limit distributions, where minima are normalized non-linearly; • Investigate the rate of convergence within the limit theorems; • Perform computer-based analysis of approximation errors.

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.