Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 5 of 5
Full-Text Articles in Entire DC Network
A Paley-Wiener Theorem For All Two And Three-Step Nilpotent Lie Groups., Robert Reeve Park
A Paley-Wiener Theorem For All Two And Three-Step Nilpotent Lie Groups., Robert Reeve Park
LSU Historical Dissertations and Theses
A Paley-Wiener Theorem for all connected, simply-connected two and three-step nilpotent Lie groups is proved. If f $\epsilon \ L\sbsp{c}{\infty}({G}),$ where G is a connected, simply-connected two or three-step nilpotent Lie group such that the operator-valued Fourier transform $\\varphi(\pi)$ = 0 for all $\pi$ in E, a subset of G of positive Plancherel measure, then it is shown that f = 0 a. e. on G. The proof uses representation-theoretic methods from Kirillov theory for nilpotent Lie groups, and uses an integral formula for the operator-valued Fourier transform $\\varphi(\pi)$. It is also shown by example that the condition that G …
Structural Results For Matroids., Sandra Reuben Kingan
Structural Results For Matroids., Sandra Reuben Kingan
LSU Historical Dissertations and Theses
This dissertation solves some problems involving the structure of matroids. In Chapter 2, the class of binary matroids with no minors isomorphic to the prism graph, its dual, and the binary affine cube is completely determined. This class contains the infinite family of matroids obtained by sticking together a wheel and the Fano matroid across a triangle, and then deleting an edge of the triangle. In Chapter 3, we extend a graph result by D. W. Hall to matroids. Hall proved that if a simple, 3-connected graph has a $K\sb5$-minor, then it must also have a $K\sb{3,3}$-minor, the only exception …
Graphs In Number Theory., Leigh Ann Myers
Graphs In Number Theory., Leigh Ann Myers
LSU Historical Dissertations and Theses
In the 1930's L. Redei and H. Reichardt established methods for determining the 4-rank of the narrow ideal class group of a quadratic number field, Q($D\sp{1/2}).$ One of these methods involves determining the number of D-splittings of the discriminant, D, of the number field. Later, this method was revised so that we need only find the rank of a matrix over F$\sb2$. In some cases, these Redei matrices can be viewed as adjacency matrices of graphs or digraphs. In Chapter I we introduce the graphs and matrices mentioned above, the method for finding 4-ranks, and present some preliminary results on …
The Generalized Distributive Law As Tacit Knowledge In Algebra., Juanita Lavall Bates
The Generalized Distributive Law As Tacit Knowledge In Algebra., Juanita Lavall Bates
LSU Historical Dissertations and Theses
The purposes of this study were to investigate theories that explain why common errors of the type ($a \pm b)\sp{c} = a\sp{c} \pm b\sp{c}$ and $\root c \of {a \pm b} = \root c \of {a} \pm \root c \of {b}$ occur in algebra problem solving by novices; and to develop and assess techniques for remediating these errors. The meaning theory of learning (ML), procedural learning theory (PL), and implicit structure learning theory (ISL) are alternative frameworks for the explanation of the errors. The ML theory hypothesizes that experts have rich semantic connections to the procedures and symbols of algebra, …
Generalizations Of The Optimal Control Problem For The Vidale-Wolfe Advertising Model., Richard Dale Edie
Generalizations Of The Optimal Control Problem For The Vidale-Wolfe Advertising Model., Richard Dale Edie
LSU Historical Dissertations and Theses
The purpose of this dissertation is to study two different generalizations of the optimal control problem based on the Vidale-Wolfe Advertising Model. The first problem is an infinite horizon free endpoint one-dimensional version of the Vidale-Wolfe optimal control problem of advertising in time varying markets. A solution is obtained for this problem. Then a thorough proof using the method of dynamic programming is presented to verify that this solution is optimal under reasonable market conditions. The second problem is a finite time fixed endpoint two-dimensional version of the Vidale-Wolfe optimal control problem. Normal optimal trajectories are obtained for this problem. …