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.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1969. / Vita. Typescript. 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.

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A research report submitted to the Faculty of Science of the University of the Witwatersrand, in partial fufillment of the degree of Master of Science, Johannesburg 1991. / Orthogonal polynomials have had a long history. They have featured in the work of Legendre on planetary motion, continued fractions of Stieltjes, mechanical quadrature of Gauss etc. After the publication of 'Orthogonal Polynomials' by Gabor Szego in 1938 relatively little was published on orthogonal polynomials. This changed in the 1970's when increased interest in approximation theory brought about by the incredible upsurge in the use of the computer in the sciences occurred. [Abbreviated Abstract. Open document to view full version] / MT2017

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

This is a research on orthogonal complementary codes, including complete complementary codes, super complementary codes, and generalized pairwise complementary code(GPC code). I discuss the properties of orthogonal complementary codes by the generation of orthogonal matries and realize its auto-correlation and cross-correlation are perfect. Apply orthogonal complementary codes on direct-sequence spreading system and offset stacked spreading system. In these two kinds of transmission, orthogonal complementary codes have the ideal auto-correlation and cross-correlation by way of direct-sequence spreading system, so it can solve multipath interference and multi-access interference effectively. While in offset stacked spreading system, orthogonal complementary codes have ideal cross-correlation. Modulating the offset chip time of offset stacked spreading properly can also solve multipath interference effectively. Moreover, GPC code keeps sub-ideal auto-correlation and cross-correlation, and it forsakes its ideal property to exchange for spreading codes with more users. In Chapter 2, we start to introduce complete complementary codes and its property to resist interferences in different transmission. Chapter 3 is the introduction of super complementary codes and its property to resist interferences in different transmission. Chapter 4 is the introduction of GPC code. We explain that GPC code forsakes its ideal property to exchange for spreading codes with more users. Chapter 5 is the introduce multi-rate orthogonal complementary codes and use 2D OVSF to suport different transmission speed.

In the past when we use the FDTD method to analyze electromagnetic problems, it has to properly discretize the structure and time, then analyze by C code. Before analyzing microstrip structures, we have to calculate and draw the distribution of structure on the grid paper. In order to increase the efficiency of drawing structure and coding, we design a GUI that it can draw and discretize the structure properly. This GUI can generate the most appropriate grid size for the user, reduce the distortion. Then, when we are coding the FDTD analysis program according to the output file, we can replace the parts of setting structure and material parameters with reading data and retain the parts of FDTD algorithm and absorbing boundary condition.

Thesis (doctoral)--Kgl. Universität Breslau, 1912. / Cover title. Vita.