Duisburg, Essen, Universiẗat, Diss., 2005.

After an introduction to Brownian motion, Hausdorff dimension, nonstandard analysis and Loeb measure theory, we explore the notion of a nonstandard formulation of Hausdorff dimension. By considering an adapted form of the counting measure formulation of Lebesgue measure, we find that Hausdorff dimension can be computed through a counting argument rather than the traditional way. This formulation is then applied to obtain simple proofs of some of the dimensional properties of Brownian motion, such as the doubling of the dimension of a set of dimension smaller than 1/2 under Brownian motion, by utilising Anderson's formulation of Brownian motion as a hyperfinite random walk. We also use the technique to refine a theorem of Orey and Taylor's on the Hausdorff dimension of the rapid points of Brownian motion. The result is somewhat stronger than the original. Lastly, we give a corrected proof of Kaufman's result that the rapid points of Brownian motion have similar Hausdorff and Fourier dimensions, implying that they constitute a Salem set. / Mathematical Sciences / D. Phil. (Mathematical Sciences)

After an introduction to Brownian motion, Hausdorff dimension, nonstandard analysis and Loeb measure theory, we explore the notion of a nonstandard formulation of Hausdorff dimension. By considering an adapted form of the counting measure formulation of Lebesgue measure, we find that Hausdorff dimension can be computed through a counting argument rather than the traditional way. This formulation is then applied to obtain simple proofs of some of the dimensional properties of Brownian motion, such as the doubling of the dimension of a set of dimension smaller than 1/2 under Brownian motion, by utilising Anderson's formulation of Brownian motion as a hyperfinite random walk. We also use the technique to refine a theorem of Orey and Taylor's on the Hausdorff dimension of the rapid points of Brownian motion. The result is somewhat stronger than the original. Lastly, we give a corrected proof of Kaufman's result that the rapid points of Brownian motion have similar Hausdorff and Fourier dimensions, implying that they constitute a Salem set. / Mathematical Sciences / D. Phil. (Mathematical Sciences)

No description available.

Universiẗat, Diss., 2003--München.

No description available.

L’objet de ce travail est l’utilisation de certains formalismes non classiques (analyses non standard, analyses constructives) afin de proposer des bases théoriques nouvelles autour des problèmes de discrétisations d’objets continus. Ceci est fait en utilisant un modèle discret du système des nombres réels appelé droite d’Harthong-Reeb ainsi que la méthode arithmétisation associée qui est un processus de discrétisation des fonctions continues. Cette étude repose sur un cadre arithmétique non standard. Dans un premier temps, nous utilisons une version axiomatique de l’arithmétique non standard. Puis, dans le but d’améliorer le contenu constructif de notre méthode, nous utilisons une autre approche de l’arithmétique non standard découlant de la théorie des Ω-nombres de Laugwitz et Schmieden. Cette seconde approche amène à une représentation discrète et multi-résolution de fonctions continues.Finalement, nous étudions dans quelles mesures, la droite d’Harthong-Reeb satisfait les axiomes de Bridges décrivant le continu constructif. / The aim of this work is to introduce new theoretical basis for the discretization of continuous objects using non classical formalisms. This is done using a discrete model of the continuum called the Harthong-Reeb line together with the related arithmetization method which is a discretisation process of continuous functions. This study stands on a nonstandard arithmetical framework. Firstly, we use an axiomatic version of nonstandard arithmetic. In order to improve the constructive content of our method, the next step is to use another approach of nonstandard arithmetic deriving from the theory of Ω-numbers by Laugwitzand Schmieden. This second approach leads to a discrete multi-resolution representation of continuous functions. Afterwards, we investigate to what extent the Harthong-Reeb line fits Bridges axioms of the constructive continuum.

Univ., Diss.--Cambridge, 1991. / Literaturverz. S. [133] - 138.

This research focuses on training bundles, nonstandard work arrangement and their relationship in high-tech industry, and the conclusions are listed as follows, 1. Training bundles and training effectiveness Training practicability has a positive impact on employee productivity, company profitability, innovation and reduction of employee turnover rates. Training institutionalization has a positive impact on employee productivity and company profitability. Rather than reducing employee turnover rates, training has the greater positive impact on employee productivity. Furthermore, larger organizations have higher level of training practicability. 2. Nonstandard work arrangement in high-tech industry As the data showed, over 80% companies ever had nonstandard work arrangement in 2002, and in the companies that had such arrangement, fixed-term hires and subcontractors were mostly used. To adjust for business fluctuations and reduce administrative workload are first two reasons why companies use nonstandard work arrangement. Limited head count and personnel cost saving are also important factors to hire nonstandard workers. In particular, cost saving is the most important factor for companies to use subcontractors. About the occupational structure, most nonstandard workers are either present in the position of administration or production. Only subcontractors are most present in the service occupations such as janitors, cleaners or caterers. With regard to personnel cost saving, compare to using dispatched workers, part-time workers and fixed-term hires are more helpful to reduce the personnel cost. 3. Training bundles and nonstandard work arrangement The result indicates that the level of training bundles can not be the determinant of using nonstandard work arrangement. Besides, we found that organization size has a positive effect on using nonstandard work arrangement, fixed-term hires, dispatched workers and subcontractors.

L'objet de ce travail est l'utilisation de certains formalismes non classiques (analyses non standard, analyses constructives) afin de proposer des bases théoriques nouvelles autour des problèmes de discrétisations d'objets continus. Ceci est fait en utilisant un modèle discret du système des nombres réels appelé droite d'Harthong-Reeb ainsi que la méthode arithmétisation associée qui est un processus de discrétisation des fonctions continues. Cette étude repose sur un cadre arithmétique non standard. Dans un premier temps, nous utilisons une version axiomatique de l'arithmétique non standard. Puis, dans le but d'améliorer le contenu constructif de notre méthode, nous utilisons une autre approche de l'arithmétique non standard découlant de la théorie des Ω-nombres de Laugwitz et Schmieden. Cette seconde approche amène à une représentation discrète et multi-résolution de fonctions continues.Finalement, nous étudions dans quelles mesures, la droite d'Harthong-Reeb satisfait les axiomes de Bridges décrivant le continu constructif.