Applied Mathematics Commons^™

A Comprehensive Uncertainty Analysis And Method Of Geometric Calibration For A Circular Scanning Airborne Lidar, Michael Oliver Gonsalves

Dissertations

This dissertation describes an automated technique for ascertaining the values of the geometric calibration parameters of an airborne lidar. A least squares approach is employed that adjusts the point cloud to a single planar surface which could be either a narrow airport runway or a dynamic sea surface. Going beyond the customary three boresight angles, the proposed adjustment can determine up to eleven calibration parameters to a precision that renders a negligible contribution to the point cloud’s positional uncertainty.

Presently under development is the Coastal Zone Mapping and Imaging Lidar (CZMIL), which, unlike most contemporary systems that use oscillating mirrors …

Dnagents: Genetically Engineered Intelligent Mobile Agents, Jeremy Otho Kackley

Dissertations

Mobile agents are a useful paradigm for network coding providing many advantages and disadvantages. Unfortunately, widespread adoption of mobile agents has been hampered by the disadvantages, which could be said to outweigh the advantages. There is a variety of ongoing work to address these issues, and this is discussed. Ultimately, genetic algorithms are selected as the most interesting potential avenue. Genetic algorithms have many potential benefits for mobile agents. The primary benefit is the potential for agents to become even more adaptive to situational changes in the environment and/or emergent security risks. There are secondary benefits such as the natural …

Understanding Similarity: Bridging Geometric And Numeric Contexts For Proportional Reasoning, Dana Christine Cox

Dissertations

The concept of similarity is uniquely situated at the crossroads of geometric and numerical proportional reasoning. Although studies have documented the existence and nature of student difficulties with this topic, there exists a gap between documented visual insights of younger children and the quantitative inadequacies of older ones. Using a revised version of the Similarity Perception Test followed by 21 clinical interviews, this study investigated the visual and analytical strategies that are used by middle-school students to differentiate and construct similar figures.

New strategies for construction and differentiation were identified, and three overarching conclusions were drawn from the work. First, …

What Allows Teachers To Extend Student Thinking During Whole-Group Discussions, Nesrin Cengiz

Dissertations

Research indicates that extending students' mathematical thinking during whole-group discussions is challenging, even for the most experienced teachers. That is, it is challenging for teachers to help students move beyond their initial mathematical observations and solutions during whole-group discussions. To better understand this phenomena, the teaching of six experienced elementary school teachers, who had been teaching aStandards-based curriculum for several years and had participated in a multi-year professional development project focused on that curriculum, is explored in this study. In particular, two issues are addressed: what it looks like to extend student thinking during whole-group discussions and how …

Measures Of Travers Ability In Graphs, Futaba Okamoto

Dissertations

For a connected graph G of order n ≥ 3 and a cyclic ordering sc : v 1, v2,..., vn, v n+1 = v1 of vertices of G, the number d(sc) is defined by d(sc) = i=1n d(vi, vi +1), where d(vi, vi +1) is the distance between vi and vi+1 in G for 1 ≤ i ≤ n. The Hamiltonian number h(G) and upper Hamiltonian number h +(G) of G are defined as h(G) = min{d(sc)} and h+(G) = max{d(sc)}, respectively, where the minimum and maximum are taken over all cyclic orderings s c of vertices of G. For …

The Fock Space And Related Bergman Type Integral Operators, Ovidiu Furdui

Dissertations

In this thesis we study the boundedness of a general class of integral operators induced by the kernel functions of Fock spaces. More precisely, for a, b, and c real parameters we study the action of [Special characters omitted.] and [Special characters omitted.] on Lp ([Special characters omitted.] ,dv_s ), where dv_s ( z ) = [Special characters omitted.] is the Gaussian probability measure on [Special characters omitted.] . We prove that, when p > 1, respectively p = 1, these operators are bounded if and only if p satisfies a quadratic, respectively a linear, inequality. The …

Structure Preserving Algorithms For Computing The Symplectic Singular Value Decom Position, Archara Chaiyakarn

Dissertations

In this thesis we develop two types of structure preserving Jacobi algorithms for com puting the symplectic singular value decomposition of real symplectic matrices and complex symplectic matrices. Unlike general purpose algorithms, these algorithms produce symplectic structure in all factors of the singular value decomposition.

Our first algorithm uses the relation between the singular value decomposition and the polar decomposition to reduce the problem of finding the symplectic singular value decomposition to th a t of calculating the structured spectral decomposition of a doubly structured m atrix. A Jacobi-like m ethod is developed to compute this doubly structured spectral decomposition. …

Stratification And Domination In Graphs And Digraphs, Ralucca M. Gera

Dissertations

In this thesis we combine the idea of stratification with the one of domination in graphs and digraphs, respectively.

A graph is 2-stratified if its vertex set is partitioned into two classes, where the vertices in one class are colored red and those in the other class are colored blue. Let F be a 2-stratified graph rooted at some blue vertex v . An F -coloring of a graph G is a red-blue coloring of the vertices of G in which every blue vertexu belongs to a copy of F rooted at u . The F -domination number γ …

Global Optimality Conditions In Mathematical Programming And Optimal Control, Pariwat Pacheenburawana

Dissertations

We derive new first-order necessary and sufficient optimality conditions characterizing global minimizers in mathematical programming and optimal controlproblems. These conditions are based on level sets of an objective functional and they do not assume special structure of a problem (convexity, linearity, etc.). For a mathematical programming problem of minimization of a smooth functional on some compact convex set with equality nonlinear constraints, we derive first-order optimality conditions in the form of a generalized Lagrange multiplier rule. This rule should hold for any point from the level set of the objective functional corresponding to a global minimizer. We demonstrate that these …

An Investigation Of Secondary Teachers’ Knowledge Of Rate Of Change In The Context Of Teaching A Standards-Based Curriculum, Jihwa Noh

Dissertations

This study investigated teachers' mathematical content knowledge and pedagogical content knowledge with respect to rate of change in the context of teaching a Standards-based high school mathematics curriculum that emphasizes rate of change as a central theme, the Core-Plus Mathematics Project (CPMP) materials. A framework was designed to provide a comprehensive guide for analyzing different aspects of rate of change knowledge incorporating existing frameworks relative to rate of change, NCTM recommendations described in Curriculum and Evaluation Standards for School Mathematics andPrinciples and Standards for School Mathematics (NCTM, 2000), and research related to pedagogical understanding of rate of change.

Data …

New Graphical Approach On The Analysis Of Experimental Data, Suha Sari

Dissertations

This study presents a new graphical method to identify significant effects in factorial experiments. The proposed methods are obtained for the different cases in which the design can be of full factorial or fractional factorial and the factor levels can be pure or mixed.

We focus on the different decomposition methods, for example orthogonal components system and orthogonal contrast method, to make use of the chisquare plot which requires that the sums of squares are of the same degrees of freedom. Examples and simulations illustrating the different cases of the procedure are presented.

Resolvability In Graphs, Varaporn Saenpholphat

Dissertations

The distance d (u, v ) between two vertices u and v in a connected graph G is the length of a shortest u - v path in G . For an ordered set W = { w1 , w2 , [Special characters omitted.] &cdots; , wk } of vertices in G and a vertex v of G , the code of v with respect to W is the k -vector cW (v ) = (d ( v, w1 ),d (v, w 2 ), [Special characters omitted.] &cdots; , d …

Cost Domination In Graphs, David John Erwin

Dissertations

Let G be a connected graph having order at least 2. A function f : V (G) —> {0 , 1 , . . . , diam G} for which f ( v ) < e(v) for every vertex v of G is a cost function on G. A vertex v with f ( v ) > 0 is an f-dominating vertex, and the set Vj~ = {v 6 V(G) : f(v) > 0} of f-dominating vertices is the f-dominating set. An /-dominating vertex v is said to f-dominate every vertex u with d(n, v) < f(u ), while …

Dynamical Systems Associated With Particle Flow Models : Theory And Numerical Methods, Roman V. Samulyak

Dissertations

A new class of integro - partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of infinite-dimensional dynamical systems models) on the Newtonian equations of motion of a many-particle system incorporating widely used inelastic particle-particle force formulas. By using Taylor series expansions, these models can be approximated by a system of partial differential equations of the Navier-Stokes type. Solutions of the new models for granular flows down inclined planes and in vibrating beds are compared with known experimental and …

Microwave Heating Of Fluid/Solid Layers : A Study Of Hydrodynamic Stability And Melting Front Propagation, John Gilchrist

Dissertations

In this work we study the effects of externally induced heating on the dynamics of fluid layers, and materials composed of two phases separated by a thermally driven moving front. One novel aspect of our study is in the nature of the external source, which is provided by the action of microwaves acting on dielectric materials. The main challenge is to model and solve systems of differential equations, which couple fluid dynamical motions (the Navie- Stokes equations for nonisothermal flows) and electromagnetic wave propagation (governed by Maxwell's equations).

When an electromagnetic wave impinges on a material, energy is generated within …

A Generalization Of Cayley Graphs For Finite Fields, Dawn M. Jones

Dissertations

A central question in the area of topological graph theory is to find the genus of a given graph. In particular, the genus parameter has been studied for Cayley graphs. A Cayley graph is a representation of a group and a fixed generating set for that group. A group is said to be planar if there is a generating set which produces a planar Cayley graph. We say that a group is toroidal if there is a generating set that produces a toroidal Cayley graph and if there are no generating sets which produce a planar Cayley graph. Characterizations for …

Perturbed Hamiltonian System Of Two Parameters With Several Turning Points, Myeong Joon Ann

Dissertations

No abstract provided.

Diffusive And Wavelike Phenomena In Thermal Processing Of Materials, John A. Pelesko

Dissertations

Contemporary materials science abounds with novel processing methods. Devices such as lasers, microwave sources, and electron beam guns, provide unprecedented control over the deposition of energy within a material. The modern materials scientist has the ability to deposit energy volumetrically, to precisely control the location of energy deposition within a material, and to deposit energy in extremely short intervals of time. While making possible numerous thermal processing methods, these devices also push the limits of our understanding of the response of materials to energy deposition. In order to optimize and control these processing methods, it becomes necessary to further our …

Domination In Digraphs, Lisa Hansen

Dissertations

No abstract provided.

A Robust Estimate For An Autoregressive Time Series, Jeffrey Terpstra

Dissertations

A weighted rank-based estimate for estimating the parameter of an auto-regressive time series is considered. When the weights are constant, the estimate is equivalent to using Jaeckel’s estimate and Wilcoxon scores. The estimate can be shown to be asymptotically normal at rate y/n. In a linear regression setting this estimate has the desired properties of a continuous totally bounded influence function and a positive breakdown point. It is shown via examples and Monte Carlo that these properties are preserved in an autoregressive time series setting.

Integrity Of Digraphs, Robert Charles Vandell

Dissertations

The vertex-integrity of a digraph D, denoted I(D), is defined to be the minimum over aIII subsets X of the vertex set of D for the quantity IXI + m(D - X), w here IXI is the number of vertices in X and m(D - X) is the maximum order of a strong component in the digraph D - X. In a like manner, the arc-integrity of the digraph D, denoted I’(D), is defined to be the minimum over all subsets Y of the arc set of D for the quantity IYI + m(D - Y), where IYI is the …

Probability Polynomials For Cubic Graphs In The Framework Of Random Topological Graph Theory, Esther Joy Tesar

Dissertations

Topological graph theorists study the imbeddings of graphs on surfaces (spheres with handles). Some interesting questions in the field are on w hat surfaces can a graph be 2 -cell imbedded and how m any such imbeddings are there on each surface. The study of these and related questions is called Enumerative Topological Graph Theory. Random Topological Graph Theory uses probability models to study the 2-cell imbeddings. It generalizes the results from Enumerative Topological Graph Theory (which is the uniform case, p= 1/2) to an arbitrary probability p.

We study the model where the sample space consists of all labeled, …

Step Domination In Graphs, Kelly Lynne Schultz

Dissertations

One of the major areas in Graph Theory is domination in graphs. It is this area with which this dissertation deals, with the primary emphasis on step domination in graphs.

In Chapter 1 we present some preliminary definitions and examples. In addition, a background of the area of domination is presented. We then introduce the concepts that lead to step domination.

In Chapter II we formally define the concept of step domination and give several examples. We determine the minimum number of vertices needed in a step domination set for many classes of graphs. We then explore step domination for …

Asymptotic Diagonalizations Of A Linear Ordinary Differential System, Feipeng Xie

Dissertations

No abstract provided.

Semi-Strongly Regular Graphs And Generalized Cages, Cong Fan

Dissertations

Two well-known classes of graphs, strongly regular graphs and cages, have been studied extensively by many researchers for a long period of time. In this dissertation, we mainly deal with semi-strongly regular graphs, a class of graphs including all strongly regular graphs, and (r, g, t)-cages, a generalization of the usual cage concept.

Chapter I introduces the two new concepts: semi-strongly regular graphs and generalized (r, g, t)-cages, gives necessary conditions for the existence of semi-strongly regular graphs and some interesting properties regarding common neighbors of pairs of vertices, and shows connections between these two new concepts and the old …

High Breakdown Rank-Based Estimates For Linear Models, William H. Chang

Dissertations

No abstract provided.

The Theory And Applications Of Stratified Graphs, Reza Rashidi

Dissertations

Physical design is one of several stages in the design of a VLSI chip. In this stage, the specifications of an electrical circuit are converted into a geometrical model. Problems concerning the physical design stage can often be studied by means of graphs. The problems encountered here are routing problems and concern placement of vertices, which represent wires, into layers. All this gives rise to a class of graphs whose vertices are partitioned into classes. Such graphs are called stratified graphs. In this dissertation, we formally define stratified graphs, study their properties, and investigate various algorithmic problems related to these …

A Bootstrap Method To Analyze An Intervention Model With Autoregressive Error Terms, Scott D. Mcknight

Dissertations

The analysis of a particular time-series intervention model involving lag one autoregressive (AR(1)) error terms is the focus of this dissertation. The method of ordinary least squares, and several two stage procedures that are commonly used to analyze this intervention model are examined. The two stage Cochrane-Orcutte, Durbin, and generalized least squares procedures each requires estimation of the AR(1) parameter in stage one before hypothesis testing about the intervention parameters can be performed in stage two. Using Monte Carlo experiments we show that the AR(1) estimates commonly used in these procedures are poor and consequently the stage two hypothesis tests …

Isospectral Graphs And The Expander Coefficient, Ian Campbell Walters Jr.

Dissertations

The expander coefficient of a graph is a parameter that is utilized to quantify the rate at which information is spread throughout a graph. The eigenvalues of the Lapladan of a graph provide a bound for the expander coefficient of the graph. In this dissertation, we construct many pairs of isospectral graphs with different expander coefficients.

In Chapter I, we define the problem and present some preliminary definitions. We then introduce two constructions that are related to graph composition and that may be employed to produce cospectral and isospectral graphs.

In Chapter II, we investigate the connectivity of and distance …

Comparisons Of Several Medians In A Lognormal K-Sample Context Where Some Data May Be Left-Censored, Stavros Costa Pouloukas

Dissertations

No abstract provided.