Hysteresis, defined as a rate independent memory effect, is a phenomenon that occurs in many physical systems. The effect is sometimes desired, sometimes a nuisance, sometimes catastrophic, but in every case we must understand hysteresis if we are to better understand the system itself. While the study of hysteresis has been conducted by engineers, scientists and mathematicians, the contribution of mathematicians has at times been theoretically sound but impractical to implement. The goal of this work is to use sound mathematical theory to provide practical information on the subject. The Preisach operator was developed to model hysteresis in magnetism. It is based on a continuous linear combination of relay operators weighted by a distribution function μ. A new method for approximating μ in a finite dimensional space is described. Guidelines are given for choosing the “best” finite dimensional space and a “most efficient” training set. Simulated and experimental data are also introduced to demonstrate the utility of this method. In addition, the approximation of singular Preisach measures is explored. The types of singularities investigated are characterized by non-zero initial slopes of reversal curves. The difficulties of finding the “optimal” approximation in this case are detailed as well as a method for determining an approximation “close” to the optimal approximation. / Ph. D.

There are several conditions for applying equal weights as an alternative to least squares weights. Psychometric parallelism, one of the conditions, has been suggested as a necessary and sufficient condition for equal-weights aggregation. The purpose of this study is to investigate the effect of psychometric parallelism among predictors on the efficiency of equal weights and least squares weights. Target correlation matrices with 10,000 cases were simulated so that the matrices had varying degrees of psychometric parallelism. Five hundred samples with six ratios of observation to predictor = 5/1, 10/1, 20/1, 30/1, 40/1, and 50/1 were drawn from each population. The efficiency is interpreted as the accuracy and the predictive power estimated by the weighting methods. The accuracy is defined by the deviation between the population R² and the sample R² . The predictive power is referred to as the population cross-validated R² and the population mean square error of prediction. The findings indicate there is no statistically significant relationship between the level of psychometric parallelism and the accuracy of least squares weights. In contrast, the correlation between the level of psychometric parallelism and the accuracy of equal weights is significantly negative. Under different conditions, the minimum p value of χ² for testing psychometric parallelism among predictors is also different in order to prove equal weights more powerful than least squares weights. The higher the number of predictors is, the higher the minimum p value. The higher the ratio of observation to predictor is, the higher the minimum p value. The higher the magnitude of intercorrelations among predictors is, the lower the minimum p value. This study demonstrates that the most frequently used levels of significance, 0.05 and 0.01, are no longer the only p values for testing the null hypotheses of psychometric parallelism among predictors when replacing least squares weights with equal weights.

Na década de 1990, emergiu uma numerosa literatura abordando os efeitos da confiança interpessoal no crescimento econômico dos países. Teoricamente, a confiança afeta o crescimento econômico por afetar as decisões que envolvem incerteza acerca das ações futuras de outros agentes, como: investimentos, contratações de trabalhadores, inovação, dentre outras. Este trabalho utiliza a metodologia corrente nesta literatura, avaliando o papel da confiança no crescimento econômico em um cross section de países para três períodos, utilizando informações, principalmente, das Penn World Tables, World Values Survey e dados de educação da UNESCO. Aplicando a técnica de least trimmed squares é avaliada a robustez da variável confiança quando se retiram observações aberrantes. Encontra-se que a confiança tem um efeito considerável no crescimento econômico, mesmo quando outliers são removidos. Também são realizados exercícios para a correção de possíveis problemas de endogeneidade da variável de confiança. Além disso, o trabalho analisa os determinantes da confiança individual, utilizando um modelo probit cujas variáveis explicativas são: renda, escolaridade, idade, país, religião, dentre outras. Este exercício também é feito para analisar o caso brasileiro. Encontra-se que a confiança é uma variável que depende mais da sociedade ou do grupo que das características individuais e, para o caso brasileiro, verificou-se que independentemente de gênero, escolaridade ou renda, as pessoas não confiam nos demais. / In the 1990\'s a large number of works came out investigating the effects of interpersonal trust on the economic growth of countries. Theoretically, trust affects economic growth by affecting all decisions that involve uncertainty on future actions of other agents, such as: investments, hire of employees, innovation, among others. This study uses the current literature methodology, tackling the trust importance for economic growth on a cross section of countries for three periods, using informations mainly from the Penn World Tables, World Values Survey and educational data from UNESCO. Applying the least trimmed squares technique it is evaluated the robustness of the trust variable when influential observations are excluded. It is found a remarkable estimated effect of trust on economic growth, even when outliers are removed. Also some studies are made in order to correct for possible endogeneity problems of the trust variable. Moreover, the work analyses the determinants of individual trust, using a probit model with the regressors: income, schooling, age, country, religion, among others. This analysis is also applied for the brazilian case. It is found that trust depends more on the society or group than on individual characteristics and, for the brazilian case, it was observed that, no matter which gender, schooling or income level the person belongs to, people do not trust each other.

This diploma thesis deals with basic features of magic squares and analyses these features with regard to usability during the teaching at elementary schools. Magic squares are known for hundreds years and since then they have changed due to various modifications, from which other kinds were derived. The first part of the thesis is therefore dedicated to the history. Next chapter deals with the construction of magic squares. The following chapters study similar games as Sudoku, Kakuro and Latin squares. The final part of the thesis is dedicated to the usability of magic squares in teaching mathematics. To practice the given topic, the worksheets which are divided according to their difficulty, were created.

Na década de 1990, emergiu uma numerosa literatura abordando os efeitos da confiança interpessoal no crescimento econômico dos países. Teoricamente, a confiança afeta o crescimento econômico por afetar as decisões que envolvem incerteza acerca das ações futuras de outros agentes, como: investimentos, contratações de trabalhadores, inovação, dentre outras. Este trabalho utiliza a metodologia corrente nesta literatura, avaliando o papel da confiança no crescimento econômico em um cross section de países para três períodos, utilizando informações, principalmente, das Penn World Tables, World Values Survey e dados de educação da UNESCO. Aplicando a técnica de least trimmed squares é avaliada a robustez da variável confiança quando se retiram observações aberrantes. Encontra-se que a confiança tem um efeito considerável no crescimento econômico, mesmo quando outliers são removidos. Também são realizados exercícios para a correção de possíveis problemas de endogeneidade da variável de confiança. Além disso, o trabalho analisa os determinantes da confiança individual, utilizando um modelo probit cujas variáveis explicativas são: renda, escolaridade, idade, país, religião, dentre outras. Este exercício também é feito para analisar o caso brasileiro. Encontra-se que a confiança é uma variável que depende mais da sociedade ou do grupo que das características individuais e, para o caso brasileiro, verificou-se que independentemente de gênero, escolaridade ou renda, as pessoas não confiam nos demais. / In the 1990\'s a large number of works came out investigating the effects of interpersonal trust on the economic growth of countries. Theoretically, trust affects economic growth by affecting all decisions that involve uncertainty on future actions of other agents, such as: investments, hire of employees, innovation, among others. This study uses the current literature methodology, tackling the trust importance for economic growth on a cross section of countries for three periods, using informations mainly from the Penn World Tables, World Values Survey and educational data from UNESCO. Applying the least trimmed squares technique it is evaluated the robustness of the trust variable when influential observations are excluded. It is found a remarkable estimated effect of trust on economic growth, even when outliers are removed. Also some studies are made in order to correct for possible endogeneity problems of the trust variable. Moreover, the work analyses the determinants of individual trust, using a probit model with the regressors: income, schooling, age, country, religion, among others. This analysis is also applied for the brazilian case. It is found that trust depends more on the society or group than on individual characteristics and, for the brazilian case, it was observed that, no matter which gender, schooling or income level the person belongs to, people do not trust each other.

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-09-08T12:22:35Z No. of bitstreams: 1 QUADRADOS LATINOS E QUADRADOS MÁGICOS UMA PROPOSTA DIDÁTICA.pdf: 24072473 bytes, checksum: 1d47842f904bd89accec69224c2a3c26 (MD5) / Approved for entry into archive by Fernando Souza (fernandoafsou@gmail.com) on 2017-09-08T13:27:24Z (GMT) No. of bitstreams: 1 QUADRADOS LATINOS E QUADRADOS MÁGICOS UMA PROPOSTA DIDÁTICA.pdf: 24072473 bytes, checksum: 1d47842f904bd89accec69224c2a3c26 (MD5) / Made available in DSpace on 2017-09-08T13:27:24Z (GMT). No. of bitstreams: 1 QUADRADOS LATINOS E QUADRADOS MÁGICOS UMA PROPOSTA DIDÁTICA.pdf: 24072473 bytes, checksum: 1d47842f904bd89accec69224c2a3c26 (MD5) Previous issue date: 2017-03-23 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we study the Latin Squares and the Magic Squares. We explore the mathematical teory and, above all, we study the link between theses objects. We bring the necessary information to support the teacher in the usage of Latin Squares and Magic Squares as content. Our goal is to discuss the usage of games and challenges like didatic tools, and to find a proposal to applicate him in the classroom. / Neste trabalho fizemos uma pesquisa bibliográfica sobre os Quadrados Latinos e os Quadrados Magicos. Mostramos a teoria matematica envolvida e, sobretudo, estudamos a ligação entre esses objetos. Trouxemos as informações necessárias para subsidiar o professor a usar Quadrados Mágicos e Quadrados Latinos como con- teúdos. Nosso objetivo é discutir o uso de jogos e passatempos como ferramenta didática e chegar a uma proposta para utilização desses objetos em sala de aula.

Master of Science / Department of Statistics / Nora Bello / Ordered categorical responses are frequently encountered in many disciplines. Examples of interest in agriculture include quality assessments, such as for soil or food products, and evaluation of lesion severity, such as teat ends status in dairy cattle. Ordered categorical responses are characterized by multiple categories or levels recorded on a ranked scale that, while apprising relative order, are not informative of magnitude of or proportionality between levels. A number of statistically sound models for ordered categorical responses have been proposed, such as logistic regression and probit models, but these are commonly underutilized in practice. Instead, the ordinary least squares linear regression model is often employed with ordered categorical responses despite violation of basic model assumptions. In this study, the inferential implications of this approach are investigated using a simulation study that evaluates robustness based on realized Type I error rate and statistical power. The design of the simulation study is motivated by applied research cases reported in the literature. A variety of plausible scenarios were considered for simulation, including various shapes of the frequency distribution and different number of categories of the ordered categorical response. Using a real dataset on frequency of antimicrobial use in feedlots, I demonstrate the inferential performance of ordinary least squares linear regression on ordered categorical responses relative to a probit model.

Extensive testing is performed when a new aircraft is developed. Flight testing is costly and time consuming but there are aspects of the process that can be made more efficient. A program that estimates aerodynamic parameters during flight could be used as a tool when deciding to continue or abort a flight from a safety or data collecting perspective. The algorithm of such a program must function in real time, which for this application would mean a maximum delay of a couple of seconds, and it must handle telemetric data, which might have missing samples in the data stream. Here, a conceptual program for real-time estimation of aerodynamic parameters is developed. Two estimation methods and four methods for handling of missing data are compared. The comparisons are performed using both simulated data and real flight test data. The first estimation method uses the least squares algorithm in the frequency domain and is based on the chirp z-transform. The second estimation method is created by adding boundary terms in the frequency domain differentiation and instrumental variables to the first method. The added boundary terms result in better estimates at the beginning of the excitation and the instrumental variables result in a smaller bias when the noise levels are high. The second method is therefore chosen in the algorithm of the conceptual program as it is judged to have a better performance than the first. The sequential property of the transform ensures functionality in real-time and the program has a maximum delay of just above one second. The four compared methods for handling missing data are to discard the missing data, hold the previous value, use linear interpolation or regard the missing samples as variations in the sample time. The linear interpolation method performs best on analytical data and is compared to the variable sample time method using simulated data. The results of the comparison using simulated data varies depending on the other implementation choices but neither method is found to give unbiased results. In the conceptual program, the variable sample time method is chosen as it gives a lower variance and is preferable from an implementational point of view.

This master thesis will investigate one solution to the problem issues with nested stochastic simulation arising when the future value of a portfolio need to be calculated. The solution investigated is the Least-squares Monte-Carlo method, where regression is used to obtain a proxy function for the given portfolio value. We will further investigate how to generate an optimal regression function that minimizes the number of terms in the regression function and reduces the risk of overtting the regression.

Numerical simulations are presented for three dimensional viscous incompressible free shear flows. The numerical method is based on solving the vorticity equation using Vortex-In-Cell method. In this method, the vorticity field is discretized into a finite set of Lagrangian elements (particles) and the computational domain is covered by Eulerian mesh. Velocity field is computed on the mesh by solving Poisson equation. The solution proceeds in time by advecting the particles with the flow. Second order Adam-Bashford method is used for time integration. Exchange of information between Lagrangian particles and Eulerian grid is carried out using the M’4 interpolation scheme. The classical inviscid scheme is enhanced to account for stretching and viscous effects. For that matter, two schemes are used. The first one used periodic remeshing of the vortex particles along with fourth order finite difference approximation for the partial derivatives of the stretching and viscous terms. In the second scheme, derivatives are approximated by least squares polynomial. The novelty of this work is signified by using the moving least squares technique within the framework of the Vortex-in-Cell method and implementing it to a three dimensional temporal mixing layer. Comparisons of the mean flow and velocity statistics are made with experimental studies. The results confirm the validity of the present schemes. Both schemes also demonstrate capability to qualitatively capture significant flow scales, and allow gaining physical insight as to the development of instabilities and the formation of three dimensional vortex structures. The two schemes show acceptable low numerical diffusion as well.