Univ., Diplomarbeit, 2008--Frankfurt (Main). / Übers. des Hauptsacht.: A universal central limit theorem for the distance of two balls in random split trees.

Univ. der Bundeswehr, Diss., 1993--Hamburg. / Gedruckt auch im VDI-Verlag, Düsseldorf (Fortschritt-Berichte VDI : Reihe 7, Strömungstechnik ; Bd. 240, ISBN 3-18-144007-8) erschienen.

Techn. Hochsch., Diss., 2004--Aachen.

In the presented work, we study several basis systems satisfying certain spatial/spectral localization conditions on the unit sphere and the ball embedded in Euclidean space of dimension $d\geq2$. For the spherical setup, we investigate some properties of the Hardy-Hodge decomposition for locally supported fields, and propose a multi-scale basis system that is suitable for modeling the Hardy components of such spherical vector fields and allows a simple mapping between the Hardy spaces. In the case of the solid ball, we revisit the Slepian spatiospectral concentration problems for the spherical Fourier-Jacobi, spherical Fourier-Bessel, as well as the multivariate algebraic polynomial systems. We investigate the bimodal distribution phenomena of the eigenvalues of concentration operators and give an asymptotic characterization of the Shannon number for these setups, which lay a foundation for the utilization of associated Slepian bases and localized spectral analysis.

Um das Fließverhalten von Granulaten in dünnwandigen Metallsilos auch mikroskopisch detailliert beschreiben zu können, ist es wichtig, beide Kontaktpartner (Granulat und elastische Wand) detailliert abbilden zu können. Granulate können vereinfacht als Kugeln betrachtet werden, weswegen die Diskrete-Elemente-Methode (DEM) hierfür geeignet ist. Die elastische Verformung der Metallwand kann mit Hilfe der Finiten-Elemente-Methode (FEM) berechnet werden. Ziel dieser Arbeit ist es, eine Simulation zu entwickeln, welche für beide Kontaktpartner eine gemeinsame Simulationsumgebung schafft. Dabei sollen zu Beginn einfache Beispiele für den Kontakt von Granulat und Festkörperstrukturen erarbeitet werden, die verschiedene Lastfälle abdecken. Um die Simulationsergebnisse bewerten zu können, sollen die Beispiele so gewählt werden, dass die Simulationen analytisch oder numerisch validiert werden können.

This dissertation seeks to provide a plausible alternative to the consensus interpretation of Jesus' "do not judge" teaching in Matt 7:1-5. While the overwhelming majority of recent interpreters understand "do not judge" (7:1) and its concurrent sayings such as "take the log out of your own eye" (7:5) to promote a non-judgmental attitude, this monograph seeks to situate this block of teaching within a Jewish second-Temple judicial setting. To this end, an overview of the judicial system during the second Temple era is provided, after which it is argued that Matt 7:1-5 is the Matthean Jesus' halakhic, midrashic comment upon the laws for just legal judging in Lev 19:15-18, 35-36 by which he prophetically criticizes unjust legal judging. Jesus' brother James takes up this teaching in Jas 2:1-13, using it to exhort Jewish Christian leaders who judge cases within Diaspora synagogues/churches. Such an alternative interpretation of Jesus' "do not judge" teaching in Matt 7:1-5 matches well other passages in Matthew which likewise speak of judicial, brotherly conflict such as 5:21-26 and 18:15-35. Some early Christian writers who quote or allude to Matt 7:1-5 reflect a judicial understanding of these verses as well, often relating Matt 7:1-5 to Lev 19:15-18, 35-36 and/or drawing parallels between Matt 7:1-5 and one or more of the NT judicial texts which, this thesis argues, is related to it (Matt 5:21-26, 18:15-35; Jas 2:1-13).