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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.

In this work, it is of interest to study the effects of thrombocytosis and microvascular anastomosis to that of vascular thrombosis. Here the splenectomy is used to the experimental subjects to have caused thrombocytosis first and later have the microvascular anastomsis on the divided vessel. Observations on different variables which may be related to vascular thrombosis are obtained during the three stages of the experiments, there are pre-splenectomy, post-splenectomy but before vascular division, and after the vascular anastomsis. These variables include platelet number, RBC count, Nitric oxide(nitrite and nitrate), femoral artery perfusion unit, hematocrit, reticulated-platelet number, and activated-platelets(p-selectin, CD62p). The experimental units are divided into thrombocysis group and control group. Basic statistical analysis are performed first to see the differences between the two groups for the above mentioned variables, and later try to use the profile analysis in multivariate analysis to understand the changes of these variables in different stages as well as their possible relationships with the cause of vascular thrombosis. Finally, classical regression and robust regression analysis for finding outliers are also used to see whether certain characteristics of those outliers have something to do with vascular thrombosis.

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Thesis (M.S.)--University of North Carolina Wilmington, 2008. / Title from PDF title page (viewed May 27, 2009) Includes bibliographical references (p. 22-24)