Thesis (doctoral)--Universität Greifswald, 1914. / Vita.

Thesis (Ph.D.)--City University of Hong Kong, 2009. / "Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves 88-95)

Thesis (Ph.D)--Aerospace Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Mavris, Dimitri; Committee Member: Costello, Mark; Committee Member: German, Brian. Part of the SMARTech Electronic Thesis and Dissertation Collection.

This work consists of three chapters. In the first chapter, a brief overview is made on the history of the modern kinetic theory of elastic and dilute gases since the early stages of Maxwell and Boltzmann. In addition, I short exposition on the complexities of the theory of granular media is presented. This chapter has the objectives of contextualize the problems that will be studied in the remainder of the document and, somehow, to exhibit the mathematical complications that may arise in the inelastic gases (not present in the elastic theory of gases). The rest of the work presents two self-contained chapters on different topics in the study of the Boltzmann equation. Chapter 2 focuses in studying and extending the propagation of regularity properties of solutions for the elastic and homogeneous Boltzmann equation following the techniques introduced by A. Bobylev in 1997 and Bobylev, Gamba and Panferov in 2002. Meanwhile, chapter 3 studies the existence and uniqueness of the inelastic and inhomogeneous Cauchy problem of the Boltzmann equation for small initial data. A new set of global in time estimates, proved for the gain part of the inelastic collision operator, are used to implement the scheme introduced by Kaniel and Shinbrot in the late 70’s. This scheme, known as Kaniel and Shinbrot iteration, produces a rather simple and beautiful proof of existence and uniqueness of global solutions for the Boltzmann equation with small initial data. / text

Much research has recently been directed at social aggression, which includes subtle and covert behaviors intended to harm the target. Evidence indicates that social aggression is associated with social maladjustment such as peer rejection and internalizing and externalizing problems. Despite increasing interest by researchers on the consequences of this form of aggression, relatively few studies have examined the etiology of social aggression. Previous research has demonstrated that depression and social anxiety may predict social aggression, however little research has examined the role of the family system in contributing to the development of this maladaptive behavior. Using path-analytic techniques, this study examined how family factors (parent-adolescent conflict, positive family relations, and maternal psychological control) affect subsequent social aggression one-year later after controlling for baseline levels of social aggression. Individual symptoms of depression and social evaluative anxiety were also incorporated in the model to determine if the effects of the family variables on later social aggression were mediated by the individual emotional adjustment of a child. Using competing models, this study compared model fit across boys and girls. The stability of social aggression over a 1 year period was also examined using confirmatory factor analysis techniques. Participants included in this study were 497 10- to 14-year-old middle school students. Results suggest that social aggression is a stable and chronic difficulty for boys and girls over a one year period. Positive family relations significantly negatively effected social aggression over the course of a year, above and beyond baseline subsequent levels of social aggression, for girls. Additionally, parent-adolescent conflict, positive family relations, and maternal psychological control were significantly related to baseline levels of social aggression. This study corroborated previous research on the deleterious effects of parent-adolescent conflict, less positive family relations, and maternal psychological control on depressive symptoms for both boys and girls. Additionally, positive family relations were also shown to reduce social evaluative anxiety for both boys and girls. Findings from this study emphasize the need for prevention and intervention efforts directed at the family system for improved adjustment of early adolescents. / text

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In 1990’s, the circumstances of being a contestant on a popular game show were published in a trendy question and answer column in Parade Magazine. If contestant switched from the initial choice to a second choice offer by the host, would the chances of winning the desired prize be increase? The columnist’s response to the reader sparked a good deal of controversy among mathematicians. Shortly after the publication of this answer, articles appeared in various mathematical publications some supporting and some refuting the columnist’s answer. This document reports the results of research into the controversy generated by some of the probability problems used on Let’s Make a Deal game show. Using a variety of approaches and assumption, the author attempts to formulate mathematical proof to explain the correct answer to the contestant’s question, “Should I switch?” / text

Not available / text

published_or_final_version / Public Administration / Master / Master of Public Administration

No description available.