Thesis--Uppsala. / Includes bibliographical references.

Thesis--Uppsala. / Includes bibliographical references.

Thesis--Friedrich-Wilhelms-Universität in Breslau, 1914. / Cover-title. Lebenslauf.

Thesis--Universität Leipzig. / Lebenslauf.

Thesis--Friedrich-Wilhelm-Universität zu Breslau, 1916. / Cover title. Lebenslauf. Bibliographical foot-notes.

Thesis--Friedrich-Wilhelms-Universität zu Breslau. / Cover title. Lebenslauf.

Thesis--Georg August-Universität zu Göttingen. / Lebenslauf. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

In Chapter 2 we develop the concept of total orthogonality. A number of necessary conditions are derived. Necessary and sufficient conditions for total orthogonality are obtained for 2-groups and for split extensions of elementary abelian 2-groups. A complete description is given for totally orthogonal groups whose character degrees are bounded by 2. Brauer's problem is reduced for Frobenius groups to the corresponding problems for Frobenius kernels and complements. In Chapter 3 classes of examples are presented illustrating the concepts and results of Chapter 2. It is shown, in particular, that 2-Sylow subgroups of finite reflection groups, and of alternating groups, are totally orthogonal.

Random processes are monitored over space and time by a network of stations distributed across a spatial region. Researchers have developed several analysis techniques to model the random process. Some of them require assumptions on the spatio-temporal variability of the process. An alternative method to analyze spatio-temporal data that does not require any assumption on the variance-covariance matrix is the Empirical Orthogonal Functions (EOF) model. The spatial distribution of the network sites influences the accuracy of the prediction results obtained by the EOF model. Researchers have proposed different methods to address this problem. We propose a model, the design-based EOF model, that incorporates information on the spatio-temporal variability of the process captured by the sampling design used to establish the network. The theoretical development of the model and an application are presented. We also consider the inclusion of auxiliary information into the design-based EOF model with the purpose of interpolating the process to unvisited sites. Interpolation results from the design-based EOF model are illustrated by considering a real data set and compared to spatial interpolation results obtained by using ordinary kriging. With the desire of making the design-based EOF model accessible to those monitoring programs that did not use a sampling probability design to establish the monitoring network, we consider two approaches that provide proper weights to be used in the model. / Graduation date: 2000