Thesis (MComm)--Stellenbosch University, 2003. / ENGLISH ABSTRACT: In this dissertation I investigate the class number one problem in function fields. More precisely I give a survey of the current state of research into extensions of a rational function field over a finite field with principal ring of integers. I focus particularly on the quadratic case and throughout draw analogies and motivations from the classical number field situation. It was the "Prince of Mathematicians" C.F. Gauss who first undertook an in depth study of quadratic extensions of the rational numbers and the corresponding rings of integers. More recently however work has been done in the situation of function fields in which the arithmetic is very similar. I begin with an introduction into the arithmetic in function fields over a finite field and prove the analogies of many of the classical results. I then proceed to demonstrate how the algebra and arithmetic in function fields can be interpreted geometrically in terms of curves and introduce the associated geometric language. After presenting some conjectures, I proceed to give a survey of known results in the situation of quadratic function fields. I present also a few results of my own in this section. Lastly I state some recent results regarding arbitrary extensions of a rational function field with principal ring of integers and give some heuristic results regarding class groups in function fields. / AFRIKAANSE OPSOMMING: In hierdie tesis ondersoek ek die klasgetal een probleem in funksieliggame. Meer spesifiek ondersoek ek die huidige staat van navorsing aangaande uitbreidings van 'n rasionale funksieliggaam oor 'n eindige liggaam sodat die ring van heelgetalle 'n hoofidealgebied is. Ek kyk in besonder na die kwadratiese geval, en deurgaans verwys ek na die analoog in die klassieke getalleliggaam situasie. Dit was die beroemde wiskundige C.F. Gauss wat eerste kwadratiese uitbreidings van die rasionale getalle en die ooreenstemende ring van heelgetalle in diepte ondersoek het. Onlangs het wiskundiges hierdie probleme ook ondersoek in die situasie van funksieliggame oor 'n eindige liggaam waar die algebraïese struktuur baie soortgelyk is. Ek begin met 'n inleiding tot die rekenkunde in funksieliggame oor 'n eindige liggaam en bewys die analogie van baie van die klassieke resultate. Dan verduidelik ek hoe die algebra in funksieliggame geometries beskou kan word in terme van kurwes en gee 'n kort inleiding tot die geometriese taal. Nadat ek 'n paar vermoedes bespreek, gee ek 'n oorsig van wat alreeds vir quadratiese funksieliggame bewys is. In hierdie afdeling word 'n paar resultate van my eie ook bewys. Dan vermeld ek 'n paar resultate aangaande algemene uitbreidings van 'n rasionale funksieliggaam oor 'n eindige liggaam waar die van ring heelgetalle 'n hoofidealgebied is. Laastens verwys ek na 'n paar heurisitiese resultate aangaande klasgroepe in funksieliggame.

Les systèmes intelligents sont de plus en plus présents dans notre société à l’instar des systèmes de surveillance et de protection de sites civils ou militaires. Leur but est de détecter les intrus et remonter une alarme ou une menace à un opérateur distant. Dans nos travaux, nous nous intéressons à de tels systèmes avec comme objectif de gérer au mieux la qualité de l’information présentée à l’opérateur en termes de fiabilité et précision. Nous nous concentrons sur la modalité image en vue de gérer des détections à la fois incertaines et imprécises de façon à présenter des objets fiables à l’opérateur.Pour préciser notre problème nous posons les contraintes suivantes. La première est que le système soit modulaire, l’une des briques (ou sous-fonctions) du système étant la détection de fragments correspondant potentiellement à des objets. Notre deuxième contrainte est alors de n’utiliser que des informations issues de la géométrie des détections fragmentaires : localisation spatiale dans l’image et taille des détections. Une menace est alors supposée d’autant plus importante que les détections sont de tailles importantes et temporellement persistantes.Le cadre formel choisi est la théorie des fonctions de croyance qui permet de modéliser des données à la fois imprécises et incertaines. Les contributions de cette thèse concernent la représentation des objets en termes de localisation imprécise et incertaine et le filtrage des objets.La représentation pertinente des informations est un point clé pour les problèmes d’estimation ou la prise de décision. Une bonne représentation se reconnaît au fait qu’en découlent des critères simples et performants pour résoudre des sous-problèmes. La représentation proposée dans cette thèse a été valorisée par le fait qu’un critère d’association entre nouvelles détections (fragments) et objets en construction, a pu être défini d’une façon simple et rigoureuse. Rappelons que cette association est une étape clé pour de nombreux problèmes impliquant des données non étiquettées, ce qui étend notre contribution au-delà de l’application considérée.Le filtrage des données est utilisé dans de nombreuses méthodes ou algorithmes pour robustifier les résultats en s’appuyant sur la redondance attendue des données s’opposant à l’inconsistance du bruit. Nous avons alors formulé ce problème en termes d’estimation dynamique d’un cadre de discernement contenant les ‘vraies hypothèses’. Ce cadre est estimé dynamiquement avec la prise en compte de nouvelles données (ou observations) permettant de détecter deux principaux types d’erreurs : la duplication de certaines hypothèses (objets dans notre application), la présence de fausses alarmes (dues au bruit ou aux fausses détections dans notre cas).Pour finir nous montrons la possibilité de coupler nos briques de construction des objets et de filtrage de ces derniers avec une brique de suivi utilisant des informations plus haut niveau, telle que les algorithmes de tracking classiques de traitement d’image.Mots clés: théorie des fonctions des croyances, association de données, filtrage. / Intelligent systems are more and more present in our society, like the systems of surveillance and civilian or military sites protection. Their purpose is to detect intruders and present the alarms or threats to a distant operator. In our work, we are interested in such systems with the aim to better handle the quality of information presented to the operator in terms of reliability and precision. We focus on the image modality and we have to handle detections that are both uncertain and imprecise in order to present reliable objects to the operator.To specify our problem, we consider the following constraints. The first one is that the system is modular; one subpart of the system is the detection of fragments corresponding potentially to objects. Our second constraint is then to use only information derived from the geometry of these fragmentary detections: spatial location in the image and size of the detections. Then, a threat is supposed all the more important as the detections have an important size and are temporally persistent.The chosen formal framework is the belief functions theory that allows modeling imprecise and uncertain data. The contributions of this thesis deal with the objects representation in terms of imprecise and uncertain location of the objects and object filtering.The pertinent representation of information is a key point for estimation problems and decision making. A representation is good when simple and efficient criteria for the resolution of sub problems can be derived. The representation proposed has allowed us to derive, in a simple and rigorous way, an association criterion between new detections (fragments) and objects under construction. We remind that this association is a key step for several problems with unlabelled data that extends our contribution beyond of the considered application.Data filtering is used in many methods and algorithms to robustify the results using the expected data redundancy versus the noise inconsistency. Then, we formulated our problem in terms of dynamic estimation of a discernment frame including the 'true hypotheses'. This frame is dynamically estimated taking into account the new data (or observations) that allow us to detect two main types of errors, namely the duplication of some hypotheses (objects in our application) and the presence of false alarms (due to noise or false detections in our case).Finally, we show the possibility of coupling our sub-functions dealing with object construction and their filtering with a tracking process using higher level information such as classical tracking algorithm in image processing.Keywords: belief functions theory, data association, filtering.

For many enterprises, brand extension has played an important role in the new products developement and brand strategy. By using brand extension, corporation could reduce costs and effectivly gain their reputation while they sell new products. Recently, certain reserch about brand extension have shown that the key factor of successful brand extension lies in the connection between consumer brand extension and parent brand, the more related of the brands and the products, the higher of the effect of brand extension. In addition, self-construals also make effects in understanding the effects of brand extensions. In this study, we form the concept from this base and would like to exam the further extension effect of brand concept and the distance of each case. Also, we would like to testify how would different self-construals of consumer products works while they evaluate the products and try to examine their influence to consumer through advertising techniques by the extension of self-construals and product reviews. In this study, we use really existed brand as our studing case ,"Nike", "Adidas" and "New balance". We would like to explore the different brand extension degree lie in several types of consumer self-construals from the case. In this study, based on attitude function theory, we form the questions toward advertising manipulation of different attitudes inoder to explore whether consumer self-construals affect cognition, and thus affect the extension of consumer product evaluation. The results indicate that, in general, different types of consumer self-construals for evaluation of the product from the extension make significant difference in distance extension products. When the parent brand as a functional brand concept, no matter the distance or distance extension products, self-construals on the extension of product evaluation is not significant. The study also find that different attitude affects advertising strategy for the consumer, and have no significant effects for self-construals. In addition, they can not affect the extension of product evaluation.

<p>Molecular electronics is envisioned as a possible next step in device miniaturization. It is usually taken to mean the design and manufacturing of electronic devices and applications where organic molecules work as the fundamental functioning unit. It involves the easurement and manipulation of electronic response and transport in molecules attached to conducting leads. Organic molecules have the advantages over conventional solid state electronics of inherent small sizes, endless chemical diversity and ambient temperature low cost manufacturing.</p><p> In this thesis we investigate the switching and conducting properties of photochromic dithienylethene derivatives. Such molecules change their conformation in solution when acted upon by light. Photochromic molecules are attractive candidates for use in molecular electronics because of the switching between different states with different conducting properties. The possibility of optically controlling the conductance of the molecule attached to leads may lead to new device implementations.</p><p> The switching reaction is investigated with potential energy calculations for different values of the reaction coordinate between the closed and the open isomer. The electronic and atomic structure calculations are performed with density functional theory (DFT). It is concluded that there is a large potential energy barrier separating the open and closed isomer and that switching between open and closed forms must involve excited states. </p><p>The conducting properties of the molecule inserted between gold leads is calculated within the Non Equilibrium Green Function theory. The transmission function is calculated for the two isomers with different basis sizes for the gold contacts, as well as the electrostatic potential, for finite applied bias voltages. We conclude that a Au 6s basis give qualitatively the same result as a Au spd basis close to the Fermi level. The transmission coefficient at the Fermi energy is around 10 times larger in the closed molecule compared to the open. This will result in a large difference in conductivity. It is also found that the large difference in conductivity will remain for small applied bias voltages. The results are consistent with earlier work.</p>

The sewing operation is an integral component of both Geometric Function Theory and Conformal Field Theory and in this thesis we explore the interplay between the two fields. We will first generalize Huang's Geometric Sewing Equation to the quasi-symmetric case. That is, given specific maps g(z) and f^{-1}(z), we show the existence of the sewing maps F_{1}(z) and F_{2}(z). Second, we display an algebraic procedure using convergent matrix operations showing that the coefficients of the Conformal Welding Theorem maps F(z) and G(z) are dependent on the coefficients of the map phi(z). We do this for both the analytic and quasi-symmetric cases, and it is done using a special block/vector decomposition of a matrix representation called the power matrix. Lastly, we provide a partial result: given specific maps g(z) and f^{-1}(z) with analytic extensions, as well as a particular analytic map phi(z), it is possible to provide a method of determining the coefficients of the complementary maps.

The sewing operation is an integral component of both Geometric Function Theory and Conformal Field Theory and in this thesis we explore the interplay between the two fields. We will first generalize Huang's Geometric Sewing Equation to the quasi-symmetric case. That is, given specific maps g(z) and f^{-1}(z), we show the existence of the sewing maps F_{1}(z) and F_{2}(z). Second, we display an algebraic procedure using convergent matrix operations showing that the coefficients of the Conformal Welding Theorem maps F(z) and G(z) are dependent on the coefficients of the map phi(z). We do this for both the analytic and quasi-symmetric cases, and it is done using a special block/vector decomposition of a matrix representation called the power matrix. Lastly, we provide a partial result: given specific maps g(z) and f^{-1}(z) with analytic extensions, as well as a particular analytic map phi(z), it is possible to provide a method of determining the coefficients of the complementary maps.

The paper examines the extent to which the prestige value of a retiree’s former occupation increases the likelihood that they will make a transition into volunteering after retirement. Following social production function theory, we assume that when a person retires, the prestige value attached to their former occupation fades. The fact that volunteering has the character of a collective good provides the opportunity to gain social prestige to offset the loss of occupational prestige. However, the extent of the incentive to volunteer will be distributed unequally across occupations: the higher the former occupational prestige value, the higher the perceived loss of prestige after retirement. Thus, doing a job with high prestige value increases the incentive to volunteer in retirement. This assumption is tested, using data taken from the German Socio-Economic Panel (GSOEP) 1992-2013. The sample contains 1,631 workers and 589 retirees, 278 of whom transitioned into volunteering during the observation window. Based on Kaplan-Meier-Failure-Estimates and complementary log-log hazard models, findings show a positive effect of occupational prestige on the transition into volunteering. Thus, the loss of high occupational prestige can be compensated by the social prestige associated with volunteering. Formal volunteering in retirement follows, albeit to a lesser extent, the logic of the occupational social strata.

The objectives of this work are to discuss multiscale models that are used to characterize the constitutive relations of the granular composite materials with dual functions. This is accomplished by the use of ab initio methods to obtain the constitutive relations of the structural energetic materials without conducting tests. First, it is necessary to study the quantum many body problem to quantitatively determine the internal energy of the material when subjected to different strain conditions. It is impossible to obtain an exact solution to the quantum many body problem that is modeled by the Schrödinger's equations with the current technology. It is possible to solve these equations approximately by the density functional theory which yields only energies at absolute 0ºK. Thus it becomes necessary to add both the lattice thermal contributions and electron thermal contribution. Then, resulting energy is used to bridge to the continuum level and obtain the constitutive equations. This is the procedure that is used in this work. The issues of the constitutive equations form the focus of this thesis. More specifically, the scope of the thesis is further restricted to analyze the constitutive equations of specific mixtures of nickel, aluminum with PTFE or Teflon as the binder. It is to be noted that the equations of state forms only a part of the complete constitutive relationships. This thesis presents solutions to the following problems: (1) Determination of the thermodynamically complete equation of state of the binder and the energetic material PTFE or Teflon, from ab initio methods based on the density functional theory. (2) Determination of the equations of state of the granular composite or the mixture of nickel, aluminum and PTFE from ab initio methods. (3) Determination of the complete constitutive equation of aluminum, from ab initio methods, under conditions of finite deformations, with principle of objectivity, material symmetry conditions and polyconvexity of the strain energy. All results are compared to test results whenever they are available.

Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2005. / Includes bibliographical references (leaves 112-113).

Proefschrift Rijksuniversiteit Groningen. / Met lit.opg. - Met samenvatting in het Nederlands.