Mathematics Commons^™

Image Segmentation By Energy And Related Functional Minimization Methods, Eric Hudson Mason

Dissertations

Effective and efficient methods for partitioning a digital image into image segments, called ¿image segmentation,¿ have a wide range of applications that include pattern recognition, classification, editing, rendering, and compressed data for image search. In general, image segments are described by their geometry and similarity measures that identify them. For example, the well-known optimization model proposed and studied in depth by David Mumford and Jayant Shah is based on an L₂ total energy functional that consists of three terms that govern the geometry of the image segments, the image fidelity (or closeness to the observed image), and the prior …

Detectable Coloring Of Graphs, Henry E. Escuadro

Dissertations

A basic problem in graph theory is to distinguish the vertices of a connected graph from one another in some manner. In this study, we investigate the problemof coloring the edges of a graph in a manner that distinguishes the vertices of the graph. The method we use combines many of the features of previously introduced methods.

Let G be a connected graph of order n ≥ 3 and let c : E (G ) [arrow right] {1,2,...,k } be a coloring of the edges of G (where adjacent edges may be colored the same). For each vertex …

Linear And Log-Linear Models Based On Generalized Inverse Sampling Scheme, Soumi Lahiri

Dissertations

This dissertation explores the development of novel statistical techniques and the applications in modeling rare events using generalized inverse sampling scheme. The Poisson model can be used for independent frequency count data. Also negative binomial and negative multinomial (NMn) models are applicable when there is only one rare category in the population. Here, a new model, based on generalized inverse sampling scheme, is introduced to study several rare events simultaneouly. The generalized inverse sampling scheme is used to study several rare categories of a population. Samples are drawn until a predetermined number of the total of the rare events occur. …

Mathematical Problems Arising In Interfacial Electrohydrodynamics, Dmitri Tseluiko

Dissertations

In this work we consider the nonlinear stability of thin films in the presence of electric fields. We study a perfectly conducting thin film flow down an inclined plane in the presence of an electric field which is uniform in its undisturbed state, and normal to the plate at infinity. In addition, the effect of normal electric fields on films lying above, or hanging from, horizontal substrates is considered. Systematic asymptotic expansions are used to derive fully nonlinear long wave model equations for the scaled interface motion and corresponding flow fields. For the case of an inclined plane, higher order …

Nilpotent Orbits On Infinitesimal Symmetric Spaces, Joseph A. Fox

Dissertations

Let G be a reductive linear algebraic group defined over an algebraically closed field k whose characteristic is good for G. Let [straight theta] be an involution defined on G, and let K be the subgroup of G consisting of elements fixed by [straight theta]. The differential of [straight theta], also denoted [straight theta], is an involution of the Lie algebra [Special characters omitted.] = Lie (G ), and it decomposes [Special characters omitted.] into +1- and -1-eigenspaces, [Special characters omitted.] and [Special characters omitted.] , respectively. The space [Special characters omitted.] identifies with the tangent space at the …

Testing Procedures For Group Sequential Clinical Trials With Multiple Survival Endpoints, Rebecca C. Scherzer

Dissertations

This research gives methods for sequential monitoring of survival data in clinical trials with multiple endpoints. We illustrate the use of marginal proportional hazards models and other survival models with various group sequential methods to test multiple survival endpoints at K interim analyses. To adjust for multiplicity at each interim analysis, we consider and extend methods developed by Tang and Geller (1999), Follmann, et al. (1994), and others. These methods are motivated, compared, and evaluated using survival data from a clinical study and using simulation studies.

A Bayesian Approach To Wireless Location Problems, Ivan Zorych

Dissertations

Several approaches for indoor location estimation in wireless networks are proposed. We explore non-hierarchical and hierarchical Bayesian graphical models that use prior knowledge about physics of signal propagation, as well as different modifications of Bayesian bivariate spline models. The hierarchical Bayesian model that incorporates information about locations of access points achieves accuracy that is similar to other published models and algorithms, but by using prior knowledge, this model drastically reduces the requirement for training data when compared to existing approaches. Proposed Bayesian bivariate spline models for location surpass predictive accuracy of existing methods. It has been shown that different versions …

Influences Of Surfactant On The Breakup Of A Fluid Jet In Viscous Surrounding, Muhammad Irfan Hameed

Dissertations

The effect of insoluble surfactant on the breakup of a fluid jet surrounded by another viscous fluid at low Reynolds number is studied both theoretically and experimentally. Equations governing the evolution of the interface and surfactant concentration are derived using a long wavelength approximation for the case of an inviscid jet and a slightly viscous jet surrounded by a more viscous fluid. These one dimensional partial differential equations governing the evolution of the slender jet are solved numerically for given initial interfacial perturbations and surfactant concentration. It is found that the presence of insoluble surfactant at the interface retards the …

Theory And Algorithms For Swept Manifold Intersections, Yuriy Mileyko

Dissertations

Recent developments in such fields as computer aided geometric design, geometric modeling, and computational topology have generated a spate of interest towards geometric objects called swept volumes. Besides their great applicability in various practical areas, the mere geometry and topology of these entities make them a perfect testbed for novel approaches aimed at analyzing and representing geometric objects. The structure of swept volumes reveals that it is also important to focus on a little simpler, although a very similar type of objects - swept manifolds. In particular, effective computability of swept manifold intersections is of major concern.

The main goal …

Electromagnetic And Acoustic Propagation In Strip Lines And Porous Media, Lin Zhou

Dissertations

Wave propagation in two physical structures is described and analyzed in this dissertation. In the first problem, the propagation of a normally incident plane acoustic wave through a three dimensional rigid slab with periodically placed holes is modeled and analyzed. The spacing of the holes A and B, the wavelength λ and the thickness of the slab L are order one parameters compared to the characteristic size D of the holes, which is a small quantity. Scattering matrix techniques are used to derive expressions for the transmission and reflection coefficients of the lowest mode. These expressions depend only on the …

The Control Of Frequency Of A Conditional Oscillator Simultaneously Subjected To Multiple Oscillatory Inputs, Christina L. Ambrosio

Dissertations

A conditional oscillator is one that requires input to oscillate. An example of such is the gastric mill network of the stomatogastric ganglion of the crab Cancer borealis which requires modulatory input from outside the stomatogastric ganglion and fast input from the pyloric network of the animal in order to become active. This dissertation studies how the frequency of the gastric mill network is determined when it is simultaneously subjected to two different rhythmic inputs whose timing may be mismatched. We derive a mathematical model of the gastric mill network and deduce that the difference in timing between the pyloric …

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 …

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 …

Scattering Matrix Analysis Of Photonic Crystals, Valeriy Lukyanov

Dissertations

Using a scattering matrix approach we analyze and study the scattering and transmission of waves through a two-dimensional photonic crystal which consists of a periodic array of parallel rods with circular cross sections. Without making any assumptions about normal incidence, single mode propagation, and sufficient inter-scatter separation in the direction of propagation, we show how to compute the transmission and reflection coefficients of these periodic structures. The method is based on the computation of a generalized scattering matrix for one column of the periodic structure.

We also develop an analytical method to analyze and to study the scattering and transmission …

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 …

Two High School Teachers’ Initial Use Of Geometers Sketchpad: Issues Of Implementation, Kathryn G. Shafer

Dissertations

This study documents two teachers' instructional practices as they learn and incorporate Geometer's Sketchpad (GSP) activities into their curriculum. The researcher (as a mentor) worked closely with two high school geometry teachers following a case study methodology. As a secondary goal, this study examined the use of a mentor as a professional development model to assist classroom teachers in the learning and implementation of Geometer'sSketchpad. Data were gathered through interviews, surveys, observations, classroom videotape, participant journal entries, as well as researcher field notes.

Results are reported in the areas of goals of instruction, method of instruction, role of the teacher, …

Pitchfork Bifurcations Of Invariant Manifolds, Jyoti Champanerkar

Dissertations

In a parameter dependent, dynamical system, when the qualitative structure of the solutions changes due to a small change in the parameter, the system is said to have undergone a bifurcation. Bifurcations have been classified on the basis of the topological properties of fixed points and invariant manifolds of dynamical systems. A pitchfork bifurcation in R is said to have occurred when a stable fixed point becomes unstable and two new stable fixed points, separated by the unstable fixed point come into existence.

In this thesis, a pitchfork bifurcation of an (in- 1)-dimensional invariant submani-fold of a dynamical system in …

Numerical Simulation Of Microwave Heating Of A Target With Temperature Dependent Electrical Properties In A Single-Mode Cavity, Hoa Kien Tran

Dissertations

This dissertation extends the work done by Hue and Kriegsmann in 1998 on microwave heating of a ceramic sample in a single-mode waveguide cavity. In that work, they devised a method combining asymptotic and numerical techniques to speed up the computation of electromagnetic fields inside a high-Q cavity in the presence of low-loss target. In our problem, the dependence of the electrical conductivity on temperature increases the complexity of the problem. Because the electrical conductivity depends on temperature, the electromagnetic fields must be recomputed as the temperature varies. We then solve the coupled heat equation and Maxwell's equations to determine …

A Gibbs Sampling Approach To Maximum A Posteriori Time Delay And Amplitude Estimations, Michele Picarelli

Dissertations

Research concerned with underwater propagation in a shallow ocean environment is a growing area of study. In particular, the development of fast and accurate computational methods to estimate environmental parameters and source location is desired. In this work, only select features of the acoustic field are investigated, namely, the time delays and amplitudes of individual paths, the signal-to-noise ratio, and the number of multi-path arrivals. The amplitudes and delays contain pertinent information about the geometry associated with the environment of interest. Estimating the time delays and amplitudes of select paths in a manner that is both accurate and time efficient, …

Mixing Enhancement By Dual Speed Rotating Stirrer, Arnaud Goullet

Dissertations

Stirring is a well-known means of fluid mixing due to the emergence of complex patterns in the flow, even at low Reynolds numbers. In this work, we consider a stirrer rotating along a circular trajectory at constant speed. The fluid flow, considered incompressible, inviscid and two dimensional (in a circular container), is modeled by a point vortex model consisting of a vortex rotating in a circular container at constant angular speed. The mixing problem is addressed by considering the Hamiltonian form of the advection equations formulated in a frame of reference moving with the vortex. The dynamics of passive fluid …

Nonlinear Long-Wave Interfacial Stability Of Two-Layer Gas-Liquid Flow, Tetyana Segin

Dissertations

The flow of two immiscible viscous fluids in a thin inclined channel is considered, in either a cocurrent or countercurrent regime. Following the air-water case, which is found in a variety of engineering systems, we allow the upper fluid to be either compressible or incompressible. The disparity of the length scales and the density and viscosity ratios of the two fluids is exploited through a lubrication approximation of the conservation of mass and the Navier-Stokes equations. As a result of this long-wave theory, a coupled nonlinear system of partial differential equations is obtained that describes the evolution of the interfacial …

How Secondary School Mathematics Teachers Construct An Understanding Of "Appropriate Use" Of Graphing Calculators In The Context Of Collegial Inquiry, Marcia L. Weller Weinhold

Dissertations

No abstract provided.

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.

Fully Nonlinear Interfacial Waves In A Bounded Two-Fluid System, Lyudmyla Leonidivna Barannyk

Dissertations

We study the nonlinear flow which results when two immiscible inviscid incompressible fluids of different densities and separated by an interface which is free to move and which supports surface tension, are caused to flow in a straight infinite channel. Gravity is taken into consideration and the velocities of each phase can be different, thus giving rise to the Kelvin-Helmholtz instability. Our objective is to study the competing effects of the Kelvin-Helmholtz instability coupled with a stably or unstably stratified fluid system (Rayleigh-Taylor instability) when surface tension is present to regularize the dynamics. Our approach involves the derivation of two-and …

Optimization For Source Localization And Geoacoustic Inversion In Underwater Acoustics, Urmi Ghosh-Dastidar

Dissertations

Matched-field inversion techniques are widely used for source localization and geoacoustic parameter estimation. These inversion methods correlate the received data with modeled data and find the model parameters which provide the maximum correlation. However, when a large number of unknown parameters is involved, many modeled data need to be generated and correlated with the observed data and thus, matched-field inversion can be computationally intensive. An optimization process applied to matched-field inversion is often required to accelerate the inversion process.

In this work, tabu is applied to matched-field inversion for source localization and environmental parameter estimation. Tabu is a global optimization …

Multiobjective Optimal Control Problems With Endpoint And State Constraints, Kirsty J. Eisenhart

Dissertations

In this thesis we consider nonsmooth multiobjective optimal control problems in terms of a general preference on [Special characters omitted.]. The optimal control problems considered involve differential inclusion, endpoint constraints and state constraints. No convexity assumption is needed on the differential inclusion. Examples of common preferences are given, and the idea of approximating a preference is introduced. Euler-Lagrange necessary conditions and a form of the maximum principle are developed for closed preferences (and those that can be approximated by closed preferences) in terms of the limiting subdifferential. As a consequence, this is the first result in the literature for lexicographical …

Closed-Loop Control Of Vortex Shedding By Means Of Lorentz Force, Xiaoyun Sun

Dissertations

When an incompressible fluid flows past a circular cylinder, vortex shedding occurs as soon as the Reynolds number exceeds about 40. Vortex shedding is usually undesirable, as it generates a significant increase in drag, as well an oscillating lift force on the cylinder leading to cross-stream structural vibrations. Flow control to either delay the appearance of vortex shedding or fully suppress it has attracted much attention during the last decade. The focus of this dissertation is to control vortex shedding from a circular cylinder by applying an external electromagnetic field. As in previous works, the latter is generated by electrodes …

Separable Preference Orders, Jonathan K. Hodge

Dissertations

Whenever a decision-maker must express simultaneously his or her preferences on several possibly related issues, the existence of interdependence among these preferences can lead to collective decisions that are unsatisfactory or even paradoxical. Intuitively, an individual’s preferences are said to be separable on a subset of issues if they do not depend on the choice of alternatives for issues outside the subset. Here we explore from a mathematical standpoint the properties of separable and nonseparable preference orders. We begin by formulating a general model of multidimensional preferences and we formally introduce the notions of separability and noninfluentiality. We study the …

Nonlinear Interfacial Stability Of Core-Annular Film Flows In The Presence Of Surfactants, Said A. Kas-Danouche

Dissertations

This work is an analytical and computational study of the nonlinear interfacial instabilities found in core-annular flows in the presence of surfactants. Core-annular flows arise when two immiscible fluids (for example water and oil) are caused to flow in a pipe under the action of ail axial pressure gradient. In one typical type of flow regime, the fluids arrange themselves so that the less viscous (e.g. water) lies in the region of high shear near the pipe wall, with the more viscous fluid occupying the core region. Tech nologically, this arrangement provides an advantage since the highly viscous fluid is …