Physical Sciences and Mathematics Commons^™

The Maximum Clique Problem: Algorithms, Applications, And Implementations, John David Eblen

Doctoral Dissertations

Computationally hard problems are routinely encountered during the course of solving practical problems. This is commonly dealt with by settling for less than optimal solutions, through the use of heuristics or approximation algorithms. This dissertation examines the alternate possibility of solving such problems exactly, through a detailed study of one particular problem, the maximum clique problem. It discusses algorithms, implementations, and the application of maximum clique results to real-world problems. First, the theoretical roots of the algorithmic method employed are discussed. Then a practical approach is described, which separates out important algorithmic decisions so that the algorithm can be easily …

New Electrochemical And Optical Detection Methods For Biological And Environmental Applications, Royce Nicholas Dansby-Sparks

Doctoral Dissertations

Detection of chromium and vanadium is of interest for biomedical and environmental applications. The two metals have narrow limits between being essential and toxic for humans. Ultra-sensitive techniques have been studied to measure Cr and V at low concentrations found in human blood and environmental samples. Bismuth film and mercury-alloy electrodes have been developed as alternatives to traditional Hg-based electrodes for Cr and V detection. While catalytic adsorptive stripping voltammetry (CAdSV) has been used to detect Cr and V, little is known about the process. The mechanisms of CAdSV have been probed to provide a better understanding of its exceptional …

Mixture Of Factor Analyzers With Information Criteria And The Genetic Algorithm, Esra Turan

Doctoral Dissertations

In this dissertation, we have developed and combined several statistical techniques in Bayesian factor analysis (BAYFA) and mixture of factor analyzers (MFA) to overcome the shortcoming of these existing methods. Information Criteria are brought into the context of the BAYFA model as a decision rule for choosing the number of factors m along with the Press and Shigemasu method, Gibbs Sampling and Iterated Conditional Modes deterministic optimization. Because of sensitivity of BAYFA on the prior information of the factor pattern structure, the prior factor pattern structure is learned directly from the given sample observations data adaptively using Sparse Root algorithm. …

Boron And Titanium(Iv) Halide Mediated Reactions, Michael Patrick Quinn

Doctoral Dissertations

This dissertation summarizes research efforts focused on the use of boron and transition metal halides to form new carbon-carbon and carbon-halide bonds. The boron halide mediated alkyne-aldehyde coupling reaction to generate 1,3,5-triaryl-1,5-dihalo-1,4-dienes was reinvestigated in an attempt to explain the stereochemistry observed during changing of both the mode of addition and the reaction temperature. Either (Z,Z)-1,4-dienes or (Z,E)-1,4-dienes can be the predominant product depending on reaction conditions used. This mechanistic investigation also led to the discovery of several novel reactions. These include the stereoselective preparation of (Z)-3-chloroallylic ethers from the reaction of alkenylboron dichlorides with aryl aldehydes in the presence …

Ads/Cft Correspondence And Hydrodynamics Of Relativistic Heavy Ion Collisions, James Ethan Alsup

Doctoral Dissertations

The experiments performed at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Lab have discovered a state of matter called the strongly coupled quark-gluon plasma (sQGP). The strong coupling has limited the ability of the standard theory to describe such matter, namely Quantum Chromodynamics (QCD). However, string theory's anti-de Sitter/conformal field theory (AdS/CFT) correspondence has provided a new way to study the situation and in an analytical manner. So far, hydrodynamic properties of RHIC's plasma, such as elliptic flow and longitudinal expansion, have been seen to follow from classical supergravity calculations. In this dissertation I discuss some of the …

Hairy Particles: Polymer Brush-Supported Organocatalysts And Asymmetric Mixed Homopolymer Brushes, Xiaoming Jiang

Doctoral Dissertations

This dissertation presents the synthesis and studies of polymer brush-supported organocatalysts and asymmetric mixed homopolymer brushes grafted on particles. The brushes were synthesized from initiator-functionalized particles by surface-initiated “living” radical polymerizations.

Polymer brush-supported organocatalysts were designed to combine the advantages of both soluble polymer- (high activity) and crosslinked insoluble polymer-supported catalysts (recyclability). Chapter 1 describes the synthesis of a polymer brush-supported 4-N,N-dialkylaminopyridine (DAAP) catalyst from initiator-functionalized latex particles by surface-initiated nitroxide-mediated radical polymerization (NMRP). The hairy particles efficiently catalyzed the acylation of secondary alcohols and Baylis-Hillman reaction and were recycled  six times with no or negligible decrease in the …

Optimal Control Of Species Augmentation Conservation Strategies, Erin Nicole Bodine

Doctoral Dissertations

Species augmentation is a method of reducing species loss via augmenting declining or threatened populations with individuals from captive-bred or stable, wild populations. In this dissertation, species augmentation is analyzed in an optimal control setting to determine the optimal augmentation strategies given various constraints and settings. In each setting, we consider the effects on both the target/endangered population and a reserve population from which the individuals translocated in the augmentation are harvested. Four different optimal control formulations are explored. The first two optimal control formulations model the underlying population dynamics with a system of ordinary differential equations. Each of these …

A Method To Accomplish The Optimal Control Of Continuous Dynamical Systems With Impulse Controls Via Discrete Optimal Control And Utilizing Optimal Control Theory To Explore The Emergence Of Synchrony., Rachel Natalie Graves

Doctoral Dissertations

This research concerns the development of new optimal control methodologies and applications. In the first chapter we consider systems of ordinary differential equations subject to a restricted number of impulse controls. Examples of such systems include tumor growth, in which case the impulsive control is the administration of medication, and ecological invasion, in which case the impulse control is the release of predator species. Impulse control problems are typically solved via related partial differential equations known as quasi-variational inequalities. We show that these types of impulse control problems can be formulated as a discrete optimal control problems. Furthermore, this formulation …

On Conjectures Concerning Nonassociate Factorizations, Jason A Laska

Doctoral Dissertations

We consider and solve some open conjectures on the asymptotic behavior of the number of different numbers of the nonassociate factorizations of prescribed minimal length for specific finite factorization domains. The asymptotic behavior will be classified for Cohen-Kaplansky domains in Chapter 1 and for domains of the form R=K+XF[X] for finite fields K and F in Chapter 2. A corollary of the main result in Chapter 3 will determine the asymptotic behavior for Krull domains with finite divisor class group.

Elasticity Of Krull Domains With Infinite Divisor Class Group, Benjamin Ryan Lynch

Doctoral Dissertations

The elasticity of a Krull domain R is equivalent to the elasticity of the block monoid B(G,S), where G is the divisor class group of R and S is the set of elements of G containing a height-one prime ideal of R. Therefore the elasticity of R can by studied using the divisor class group. In this dissertation, we will study infinite divisor class groups to determine the elasticity of the associated Krull domain. The results will focus on the divisor class groups Z, Z(p infinity), Q, and general infinite groups. For the groups Z and Z(p infinity), it has …

Development Of Nanomechanical Sensors For Environmental Contaminate Screening Using Protein Functionalized Microcantilevers, Kasey L. Hill

Doctoral Dissertations

The development of real time, label-free biosensors based on ligand-induced nanomechanical responses of microcantilevers (MCs) allows for sensitive and selective detection. High sensitivity is afforded by the MCs small dimensions. Immobilizing biomolecular recognition phases imparts selectivity from bioaffinity interactions. Biological sensors on a MC platform utilize various proteins, such as antibodies and nuclear receptors, which can be used to detect and screen for potential environmental contaminants.

The interaction between contaminants and immobilized receptors induces an apparent surface stress that leads to static bending of the MC, which is monitored by an optical beam bending technique. Biofunctionalized MCs can provide high …

Neutron Scattering Study Of The High Tc Superconductors, Jun Zhao

Doctoral Dissertations

We carried out systematic neutron scattering experiments to investigate the magnetic properties and their relationship to the high-$T_c$ superconductivity, when the materials are tuned from their antiferromagnetic (AF) parent compounds to the superconducting regime.

We observed resonance mode in the electron doped cuprate Nd$_{1.85}$Ce$_{0.15}$CuO$_4$, demonstrating that the resonance is a general phenomenon in cuprate superconductors regardless of hole- or electron-doping. In Pr$_{0.88}$LaCe$_{0.12}$CuO$_4$, the local susceptibility displays two distinct energy scales that are broadly consistent with the bosonic modes revealed by scanning tunneling microscopy experiments. These results indicate the presence of very strong electron spin excitations couplings in electron doped cuprates. …

Theoretical Models For Wall Injected Duct Flows, Tony Saad

Doctoral Dissertations

This dissertation is concerned with the mathematical modeling of the flow in a porous cylinder with a focus on applications to solid rocket motors. After discussing the historical development and major contributions to the understanding of wall injected flows, we present an inviscid rotational model for solid and hybrid rockets with arbitrary headwall injection. Then, we address the problem of pressure integration and find that for a given divergence free velocity field, unless the vorticity transport equation is identically satisfied, one cannot find an analytic expression for the pressure by direct integration of the Navier-Stokes equations. This is followed by …

Radial Heterogeneity And Surface Properties Of Columns Used In High Performance Liquid Chromatography, Jude A. Abia

Doctoral Dissertations

The radial heterogeneity of some columns used in high performance liquid chromatography (HPLC) was investigated using an on-column microelectrochemical amperometric detector. Such a detector allowed the recording of the elution profiles at different spatial positions throughout the column exit cross-section. From this, we obtain information about the radial distribution of the mobile phase velocity, column efficiency, and analyte concentration. In all cases, the results obtained show that the spatial distribution of the mobile phase velocity does not follow a piston-flow behavior but exhibits radial heterogeneity with differences not exceeding 5% between the center and wall regions of any column. The …

A New Screening Methodology For Mixture Experiments, Maria Weese

Doctoral Dissertations

Many materials we use in daily life are comprised of a mixture; plastics, gasoline, food, medicine, etc. Mixture experiments, where factors are proportions of components and the response depends only on the relative proportions of the components, are an integral part of product development and improvement. However, when the number of components is large and there are complex constraints, experimentation can be a daunting task. We study screening methods in a mixture setting using the framework of the Cox mixture model [1]. We exploit the easy interpretation of the parameters in the Cox mixture model and develop methods for screening …

Investigations Of The Dynamical Response In Solids By Time-Dependent Density-Functional Theory, Qinghong Kou

Doctoral Dissertations

The present dissertation studies a joint theoretical-experimental investigation of the dynamical structure factor of wide-gap insulators, using lithium-fluoride as a prototype. Ground-state (energy bands and electron densities) was calculated using Linear Augmented Plane Wave (LAPW) method and local density approximation (LDA) of density functional theory (DFT). Ab-initio principal is applied to obtain a realistic description of the band structure, which is central to the current research in the condensed matter physics. Dynamical response function has been evaluated within time-dependent density functional theory (DFT) with an adiabatic approximation (TDLDA), for the exchange-correlation kernel. Our TDLDA spectra contain one adjustable parameter: a …

Newly-Developed Nanostructured Microcantilever Arrays For Gas-Phase And Liquid-Phase Sensing, Zhou Long

Doctoral Dissertations

The microcantilever (MC) has become a common transducer for chemical and biological sensing in gas phase and liquid phase during recent years. MC sensors provide superior mass sensitivity by converting weak chemical and biological stimuli into high mechanical response. Moreover, other advantages such as small size, low cost and array format have made MCs more attractive than other comparable sensors.

Selectivity in MC sensors can be enhanced by creating a differentially functionalized MC array (MCA) with responsive phases (RPs). A well-designed array should incorporate RPs exhibiting a variety of possible interactions with the analytes, and a specific analyte should induce …

Carleson-Type Inequalitites In Harmonically Weighted Dirichlet Spaces, Gerardo Roman Chacon Perez

Doctoral Dissertations

Carleson measures for Harmonically Weighted Dirichlet Spaces are characterized. It is shown a version of a maximal inequality for these spaces. Also, Interpolating Sequences and Closed-Range Composition Operators are studied in this context.

On The Irreducibility Of The Cauchy-Mirimanoff Polynomials, Brian C. Irick

Doctoral Dissertations

The Cauchy-Mirimanoff Polynomials are a class of polynomials that naturally arise in various classical studies of Fermat's Last Theorem. Originally conjectured to be irreducible over 100 years ago, the irreducibility of the Cauchy-Mirimanoff polynomials is still an open conjecture.

This dissertation takes a new approach to the study of the Cauchy-Mirimanoff Polynomials. The reciprocal transform of a self-reciprocal polynomial is defined, and the reciprocal transforms of the Cauchy-Mirimanoff Polynomials are found and studied. Particular attention is given to the Cauchy-Mirimanoff Polynomials with index three times a power of a prime, and it is shown that the Cauchy-Mirimanoff Polynomials of index …

Schubert Numbers, Masato Kobayashi

Doctoral Dissertations

This thesis discusses intersections of the Schubert varieties in the flag variety associated to a vector space of dimension n. The Schubert number is the number of irreducible components of an intersection of Schubert varieties. Our main result gives the lower bound on the maximum of Schubert numbers. This lower bound varies quadratically with n. The known lower bound varied only linearly with n. We also establish a few technical results of independent interest in the combinatorics of strong Bruhat orders.

Computational Circle Packing: Geometry And Discrete Analytic Function Theory, Gerald Lee Orick

Doctoral Dissertations

Geometric Circle Packings are of interest not only for their aesthetic appeal but also their relation to discrete analytic function theory. This thesis presents new computational methods which enable additional practical applications for circle packing geometry along with providing a new discrete analytic interpretation of the classical Schwarzian derivative and traditional univalence criterion of classical analytic function theory. To this end I present a new method of computing the maximal packing and solving the circle packing layout problem for a simplicial 2-complex along with additional geometric variants and applications. This thesis also presents a geometric discrete Schwarzian quantity whose value …

Fractions Of Numerical Semigroups, Harold Justin Smith

Doctoral Dissertations

Let S and T be numerical semigroups and let k be a positive integer. We say that S is the quotient of T by k if an integer x belongs to S if and only if kx belongs to T. Given any integer k larger than 1 (resp., larger than 2), every numerical semigroup S is the quotient T/k of infinitely many symmetric (resp., pseudo-symmetric) numerical semigroups T by k. Related examples, probabilistic results, and applications to ring theory are shown.

Given an arbitrary positive integer k, it is not true in general that every numerical semigroup S is the …

On Calculating Residuated Approximations And The Structure Of Finite Lattices Of Small Width, Wu Feng

Doctoral Dissertations

The concept of a residuated mapping relates to the concept of Galois connections; both arise in the theory of partially ordered sets. They have been applied in mathematical theories (e.g., category theory and formal concept analysis) and in theoretical computer science. The computation of residuated approximations between two lattices is influenced by lattice properties, e.g. distributivity.

In previous work, it has been proven that, for any mapping f : L → [special characters omitted] between two complete lattices L and [special characters omitted], there exists a largest residuated mapping ρf dominated by f, and the notion of "the shadow …

Accurate And Stable Numerical Methods For Solving Micro Heat Transfer Models In An N-Carrier System In Spherical Coordinates, Di Zhao

Doctoral Dissertations

Energy exchange between electrons and phonons in metal provides the best example in describing non-equilibrium heating during the ultrafast transient. In times comparable to the thermalization and relaxation time of electrons and phonons, which are in the range of a few to several tens of picoseconds, heat continuously flows from hot electrons to cold phonons through mutual collisions. Consequently, electron temperature continuously decreases whereas phonon temperature continuously increases until thermal equilibrium is reached. Tien developed the well-known parabolic two-step model for describing the non-equilibrium heating in the electron-phonon system in 1992, and Tzou developed the parabolic model for the non-equilibrium …

Associative Pattern Mining For Supervised Learning, Harpreet Singh

Doctoral Dissertations

The Internet era has revolutionized computational sciences and automated data collection techniques, made large amounts of previously inaccessible data available and, consequently, broadened the scope of exploratory computing research. As a result, data mining, which is still an emerging field of research, has gained importance because of its ability to analyze and discover previously unknown, hidden, and useful knowledge from these large amounts of data. One aspect of data mining, known as frequent pattern mining, has recently gained importance due to its ability to find associative relationships among the parts of data, thereby aiding a type of supervised learning known …

A Study Of The Growth And Structure Of Chromium And Iron Oxide Films On Pd(001) Using X-Ray Photoelectron Diffraction And Low Energy Electron Diffraction, Tina Dhekial-Phukan

Doctoral Dissertations

"In this study, attempts were made to grow well-ordered chromium- and iron-oxide films on a Pd(001) surface, and two sample preparation techniques, the multilayer and the sequential growth techniques, were used to grow these transition metal oxide films. The study is a part of a larger project that aims to look into the interaction between metal substrates and the overlayers grown on them. Previous studies of oxide films on Ag(001) resulted in the growth of 4-fold and 3-fold symmetry oxide structures from the multilayer and sequential growth techniques respectively. The present investigation's goal was to study how the growth of …

Ground Penetrating Radar Investigations In Upper Kama Potash Mines, Oleg N. Kovin

Doctoral Dissertations

"An understanding of the structure and state of the rock mass surrounding underground openings in the potash mines is critically important for safe mining, planning the methods of extraction of an orebody, and preventing the influx of ground water. Continuous common offset ground penetrating radar (GPR) data were acquired in the potash mine operated by the Joint Stock Company (JSC) "Silvinit" (Russia) as part of an investigation of both pre-existing fractures exposed by mine workings and other anomalous geological structures. During the course of GPR investigation, the electrical properties of salt-bearing units were determined, site-specific data acquisition techniques and object-oriented …

Capillary Electrophoresis Of Pteridines In Urine And Plants And Quantification Of Pharmaceutical And Personal Care Products In Missouri Waste Water, Stephen E. Gibbons

Doctoral Dissertations

"Capillary electrophoresis (CE) is a powerful technique that separates molecules based on their respective charge and hydrodynamic size. The major advantages of CE are high separation efficiency, small sample volume requirements, simple to no sample preparation and often organic solvents are not required for the separation.

The work presented in this dissertation utilized capillary electrophoresis for the analysis two different classes of compounds in different matrices. The first project investigated pteridines in urine and plants. The second project investigated pharmaceutical and personal care products (PPCP's) in Missouri waste water.

As cancer continues to be one of the top three causes …

A Study Of Synchronization Of Nonlinear Oscillators: Application To Epileptic Seizures, Daisuke Takeshita

Doctoral Dissertations

"This dissertation focuses on several problems in neuroscience from the perspective of nonlinear dynamics and stochastic processes. The first part concerns a method to visualize the idea of the power spectrum of spike trains, which has an educational value to introductory students in biophysics. The next part consists of experimental and computational work on drug-induced epileptic seizures in the rat neocortex. In the experimental part, spatiotemporal patterns of electrical activities in the rat neocortex are measured using voltage-sensitive dye imaging. Epileptic regions show well-synchronized, in-phase activity during epileptic seizures. In the computational part, a network of a Hodgkin-Huxley type neocortical …

Deadlock Detection And Dihomotopic Reduction Via Progress Shell Decomposition, David Andrew Cape

Doctoral Dissertations

"Deadlock detection for concurrent programs has traditionally been accomplished by symbolic methods or by search of a state transition system. This work examines an approach that uses geometric semantics involving the topological notion of dihomotopy to partition the state space into components, followed by an exhaustive search of the reduced state space. Prior work partitioned the state-space inductively; however, this work shows that a technique motivated by recursion further reduces the size of the state transition system. The reduced state space results in asymptotic improvements in overall runtime for verification. Thus, with efficient partitioning, more efficient deadlock detection and eventually …