Physical Sciences and Mathematics Commons^™

Naphthalene-2,3-Dialdehyde: A Synthon To 7,9-Polymethylene-8h-Cyclohepta[B]Naphthalene-8-One And A Study Of Their Aromaticity, Edward O. Crapps

Dissertations

This report describes the synthesis of naphthalene-2,3-dialdehyde, and an analytical method for determining its purity by thin layer chromatography. Subsequently, the dialdehyde was condensed with various cyclic ketones to generate a series of polymethylene bridged naphthotropones. It was found that planarity and aromaticity increase with the size of the methylene bridge, although, the bridge must contain six or more methylene groups for the latter to be true. The claim for aromaticity is supported by NMR and IR data, which indicates the positive charge for a perchlorate cation salt is delocalized over the naphthalene and tropone ring system. Furthermore, from the …

On The Genus Of A Block Design, Joan Marie Rahn

Dissertations

The genus of a design (BIBD or PBIBD) is defined to be the genus of its corresponding hypergraph (objects as vertices, blocks as edges); that is, the genus of the bipartite graph associated with the hypergraph in a natural way. The Euler formula is used to establish a lower bound (gamma) for the genus of a block design. An imbedding of the design of the surface of genus (gamma) is then described by a voltage hypergraph or voltage graph. Use of the lower bound formula leads to a characterization of planar BIBDs. A connection between a block design derived from …

The Chromatic And Cochromatic Number Of A Graph, John Gordon Gimbel

Dissertations

Clearly, there are many ways that one can partition the vertex sets of graphs. In the first chapter of this work I examine the problem of determining, for a given graph, the minimum order of a vertex partition having specified properties. In the remaining chapters I concentrate on partitions of two types--those in which each subset induces an empty graph and those in which each subset induces an empty or a complete graph.

The chromatic number of a graph G is the minimum number of subsets into which V(G) can be partitioned so that each subset induces an empty graph. …

The Relationship Of Self-Concept, Sex, Age, Major, Anxiety, Mathematics Background, And Mathematics Ability To The Level Of Mathematics And Statistical Anxiety Among College Juniors, David John Maysick

Dissertations

Problem. One's choice of career has significant effect upon one's future life in terms of earning potential and social interaction. Mathematics/statistical anxiety and the mathematics avoidance often accompanying such anxiety, can influence career choice, causing otherwise talented people to limit their future. The purpose of this study was to determine from selected variables--particularly self-concept--which, if any, were related to the problem of mathematics and/or statistical anxiety.

Method. The statistical sample used was 350 juniors. Stratification was by degree of mathematics content in subject's major field of study. For the study, subjects had to be in the same major category as …