Applied Mathematics Commons^™

Symbol Sense And Its Development In Two Computer Algebra System Environments, Brian A. Keller

Dissertations

The purposes of this study were to: (a) explicate the nature of symbol sense, (b) determine the differential effects of two computer algebra system (CAS) environments on students' development of symbol sense, (c) explore differences in symbol sense among students using a CAS and students not using a CAS, and (d) examine students' achievement in calculus with and without the use of a CAS.

Six sections of first-semester calculus at Western Michigan University during the 1992-93 academic year were used in the study. The investigator taught two CAS sections both semesters (n = 41, 34 Fall and n = 35, …

Distances Associated With Subgraphs And Subdigraphs, Steven John Winters

Dissertations

The defining properties of several important subgraphs and subdigraphs rely on the concept of distance in graphs and digraphs. In this dissertation, we investigate many of these subgraphs and subdigraphs.

In Chapter I, we present some preliminary definitions and examples. In addition, many known results are recalled. We then introduce several new induced subgraphs and subdigraphs.

In Chapter n, we investigate the general structure of the center and periphery of a graph. We introduce two new induced subgraphs of the center along with a new induced subgraph of the periphery of a graph in order to study these structures.

For …

Robust Rank-Based Inference Procedures In The Heteroscedastic Linear Model, Sherry L. Dixon

Dissertations

No abstract provided.

Multivariate Quadrature On Mimd Machines With Shared Or Distributed Memory, Ignatios E. Vakalis

Dissertations

For a procedure as numerical integration, of high computational expense which is used extensively in large-scale computations, it is natural to aim at the design of algorithms which can be used on parallel computes. This work deeds with the design of efficient and portable parallel algorithms on MIMD (Multiple Instruction Multiple Data) architectures with shared memory, and on distributed memory systems.

A parallel global adaptive algorithm is presented for multivariate integration over simplex type regions. Process synchronization is achieved through the use of monitors. Macros were developed, for managing the task pool with a heap data structure. Layered over the …

A Critical Examination Of The Use Of Preliminary Tests In Two-Sample Tests Of Location, Kimberly Tucker Perry

Dissertations

The purpose of this dissertation was to explore the appropriateness of testing the equality of two means using either a t test, the Welch test, or the Mann-Whitney-Wilcoxon test for two independent samples based on the results of using two classes of preliminary tests. One class of preliminary tests determines whether the population variances differ, and the other class ascertains if the underlying distributions are symmetric or skewed. The F-ratio test and the Levene test (using the median) were compared as preliminary tests for variance homogeneity; and the DAgostino Sy and the Triples tests were also compared as preliminary tests …

Maximal And Maximum Independent Sets In Graphs, Jiuqiang Liu

Dissertations

A maximal independent set of a graph G is an independent set which is not contained properly in any other independent set of G. An independent set is called maximum if it is of largest cardinality. Denote i(G) to be the number of maximal independent sets of G. These special sets and the parameter i(G) have interested many researchers leading to a number of properties and results. One of these is the determination of the maximum number of maximal independent sets among all graphs of order n, and the external graphs. In this investigation,we develop new properties for …

Transformations Of Graphs And Digraphs, Elzbieta B. Jarrett

Dissertations

Some distances defined on graphs depend on transforming one graph into another. Two of these transformations are edge rotation and edge slide. In this dissertation, extensions and generalizations of these transformations are investigated.

Chapter I begins with some preliminary definitions and known results. Then two types of digraph transformations are introduced and their properties are studied.

Some measures of distance between graphs and distance between digraphs are defined in Chapter II. Also distance graphs and digraphs associated with these measures are introduced. Several known results concerning this topic are generalized and new results are presented.

Chapter III is devoted to …

A Representation Of Chemical Reactions By Labeled Graphs, Héctor Hevia

Dissertations

Graphs can be used to represent the atomic structure of chemical compounds where the vertices of the graph represent the individual atoms and the edges of the graph represent the valence bonds between a pair of atoms. M. A. Johnson (1991) introduced a graph-theoretic way to represent structural changes in chemical compounds. Thus, certain labelings of graphs called transitional labelings can be thought as representing chemical equations. Associated with these labelings, we introduce a new invariant of a graph G called the transitional value of G. The transitional value of a graph G gives an indication of how dramatic a …

Surgical Techniques For Constructing Minimal Orientable Imbeddings Of Joins And Compositions Of Graphs, David L. Craft

Dissertations

The various cases within the proof of the Heawood Map-Coloring Theorem, which established the genus of the complete graphs, utilized various techniques--some for the first time. This activity spurred interest in determining the genus of various other classes of graphs. However, very few generally applicable techniques have been developed, beyond those used in the proof of this famous theorem. Finding genera of arbitrary graphs remains a very difficult problem.

In this dissertation, we describe two surgical techniques for imbedding graphs. The first construction, called a graphical surface,views an orientable surface as a fattened graph, i.e., vertices become spheres and edges …

Improving Networks Reliability, Jamal H. Nouh

Dissertations

No abstract provided.

Graph Products And Covering Graph Imbeddings, Ghidewon Abay Asmerom

Dissertations

No abstract provided.

On Distance In Graphs And Digraphs, Songlin Tian

Dissertations

One of the most basic concepts associated with a graph is distance. In this dissertation some new definitions of distance in graphs and digraphs are introduced. One principle goal is to extend certain known results involving the standard distance function on graphs to the field of digraphs with an appropriate concept of distance. Several parameters as well as subgraphs and subdigraphs defined in terms of distance are investigated.

Chapter I gives a brief overview of the history of distance and generalized distance in graphs. By presenting a listing of major results in this area, it provides a background for the …

The Enumeration Of Graph Imbeddings, Robert G. Rieper

Dissertations

Graphs can be drawn on surfaces. Here, graphs may have multiple edges or loops (pseudographs), the surfaces are closed orientable 2-manifolds (sphere, torus, etc.) and their generalizations (pseudosurfaces and generalized pseudosurfaces), and the drawings are 2-cell imbeddings. For quite some time it has been known that a connected graph has $\rm \Pi(degree(\upsilon)-1)$! 2-cell imbeddings on surfaces. More detailed information about these imbeddings has been wanting. In addition, many of the imbeddings counted above 'look the same' when all vertex and edge labels are removed. The resulting unlabeled imbeddings are fewer in number and more difficult to enumerate than their labeled …

Enumerating The Orientable 2-Cell Imbeddings Of Complete N-Partite Graphs, Bruce P. Mull

Dissertations

This dissertation develops formulas for the number of congruence classes of maps of complete, complete bi-partite, complete tripartite, and complete n-partite graphs; these congruence classes correspond to unlabeled imbeddings. The method employed for the enumeration is an extension of that used by Mull, Rieper, and White in 1988. We let the automorphism group act on the set of rotations and use Burnside's Lemma to count orbits for these rotations. Compatible permutations are introduced to determine those automorphisms actually contributing to the number of orbits.

The complete n-partite formula is shown to generalize those of the other three families of graphs. …

The Chromatic Sum And Efficient Tree Algorithms, Ewa Kubicka

Dissertations

In Chapter I this concept is introduced. It is shown that computing the chromatic sum is NP-complete. For every natural k the smallest tree which needs k colors to attain its chromatic sum is constructed. It is demonstrated that asymptotically, for each k, almost all trees require more than k colors to achieve their chromatic sums. Also a linear algorithm for a single tree is presented.

In Chapter II three constructions of graphs that require t colors beyond their chromatic number k to achieve their chromatic sum are presented, depending on the ratio ${\rm t}\over{\rm k}$. The order of the …

Measures Of Partial Association Based On Rank Estimates, Sudhakar H. Rao

Dissertations

No abstract provided.

Greatest Common Subgraphs, Grzegorz Kubicki

Dissertations

No abstract provided.

Specified Subgraphs And Subgraph-Defined Parameters In Graphs, Karen S. Holbert

Dissertations

No abstract provided.

Effect Of Computer Graphics Use On Student Understanding Of Calculus Concepts, Charlene E. Beckmann

Dissertations

Student understanding of selected calculus concepts as developed through use of a Cartesian coordinate graphical representation system were investigated. Subjects (N = 163) enrolled in first-semester calculus sections at Western Michigan University participated in one of four treatment conditions: Graphics (G), exposure to a computer-graphically-developed conceptual course; Graphics Plus (G+), exposure to the same course as G subjects plus provision of computer graphics software and related supplemental assignments; Standard 1 (S1), exposure to a graphically-developed, conceptual course; and Standard 2 (S2), exposure to a traditional skill-oriented course.

Two investigations were undertaken. In Investigation 1, comparisons were made between G and …

On Common Subgraphs, Hung Bin Zou

Dissertations

A greatest common (induced) subgraph of graphs G(,1) and G(,2) of equal size is a (an induced) common subgraph (without isolated vertices) of G(,1) and G(,2) having maximum size. For a given graph L, a graph G is locally L if the induced subgraph of the neighborhood of each vertex of G is isomorphic to L (L is called a common link). Several topics concerning these concepts are investigated in this dissertation. An historical background to these topics is given in Chapter I.

Chapter II is devoted to the topic on highly connected unique greatest common subgraphs of graphs. We …

Markovian Multiserver Queueing Systems With Servers In Series, Nancy Jean Boynton

Dissertations

No abstract provided.