Physical Sciences and Mathematics Commons^™

Solutions To The LP Mixed Boundary Value Problem In C1,1 Domains, Laura D. Croyle

Theses and Dissertations--Mathematics

We look at the mixed boundary value problem for elliptic operators in a bounded C^1,1(ℝⁿ) domain. The boundary is decomposed into disjoint parts, D and N, with Dirichlet and Neumann data, respectively. Expanding on work done by Ott and Brown, we find a larger range of values of p, 1 < p < n/(n-1), for which the L^p mixed problem has a unique solution with the non-tangential maximal function of the gradient in L^p(∂Ω).

Kronecker's Theory Of Binary Bilinear Forms With Applications To Representations Of Integers As Sums Of Three Squares, Jonathan A. Constable

Theses and Dissertations--Mathematics

In 1883 Leopold Kronecker published a paper containing “a few explanatory remarks” to an earlier paper of his from 1866. His work loosely connected the theory of integral binary bilinear forms to the theory of integral binary quadratic forms. In this dissertation we discover the statements within Kronecker's paper and offer detailed arithmetic proofs. We begin by developing the theory of binary bilinear forms and their automorphs, providing a classification of integral binary bilinear forms up to equivalence, proper equivalence and complete equivalence.

In the second chapter we introduce the class number, proper class number and complete class number as …

Use And Evaluation Of Lidar For Mapping Sinkholes In Royal Spring Groundwater Basin, Fidele Nsonguh Tibouo

Theses and Dissertations--Earth and Environmental Sciences

This study utilizes a digital elevation model of the surface derived from high-resolution LiDAR (Light Detection and Ranging) and aerial-image technologies to map sinkholes in the Royal Spring groundwater basin. Shade-relief maps, with vertical exaggeration, were very helpful in the initial characterization of depressions. Then, aerial-photography sets were likewise helpful in identifying man-made structures such as retention basins, swimming pools, and parking lots, and to identify new sinkholes.

Field checking was necessary to further define depressions into two categories: 1.) potential sinkholes and 2.) probable sinkholes. This study had a lower success rate (50 percent) for identifying sinkholes via LiDAR …

Integrated Geophysical Methods In Investigation Of Claiborne Aquifer Hydrostratigraphy, Jackson Purchase, Kentucky, Marie Cooper

Theses and Dissertations--Earth and Environmental Sciences

Increased groundwater withdrawals associated with agricultural irrigation in the Jackson Purchase have prompted questions related to groundwater availability and sustainability. Key factors in addressing these questions are understanding the extent and variation in thickness of the local hydrostratigraphic system, which is the upper part of the Mississippi Embayment aquifer system. Correlations of 70 gamma-ray well logs, and 49 resistivity logs were made across parts of the Jackson Purchase in Fulton and Hickman Counties in order to delineate the upper Claiborne aquifer and middle Claiborne confining unit. Commercial software (i.e. Petra 3.8.3) was used to generate cross sections, structure and isopach …

Mobility Of Escherichia Coli Within Karst Terrains, Kentucky, Usa, Ashley M. Bandy

Theses and Dissertations--Earth and Environmental Sciences

Bacterial contamination of karst aquifers is a concern as water quality across the globe deteriorates in the face of decreasing water security. This study examined the transport and attenuation of two non-virulent isolates of Escherichia coli in relation to traditional groundwater tracers such as rhodamine WT dye and latex microspheres in two karst regions in Kentucky. Differential movement between the four tracers was observed in both epikarst and karst aquifer traces, with differences in behavior dependent on flow conditions. Attenuation was greater for the bacterial isolate containing the iha gene, compared to the isolate containing the kps gene. Microspheres of …

Denali In A Box: Analog Experiments Modeled After A Natural Setting Provide Insight On Gentle Restraining Bend Deformation, Anne M. Fendick

Theses and Dissertations--Earth and Environmental Sciences

The Mount McKinley restraining bend (MMRB) creates an ~18° left-step in the arcuate surface trace of the dextral Denali Fault in south-central Alaska. Despite being a large, crustal-scale fault, little is understood about the controls on deformation within the MMRB. Similarities between previous wet kaolin analog modeling and the MMRB suggest that the first-order deformation patterns may derive from similar mechanisms. We compare uplift patterns, localization of deformation, formation of new faults, and displacement fields from the analog model and the natural setting to assess the influence of different variables on the overall system. Despite strong rheological heterogeneity in the …

Field, Geochronologic, And Geochemical Constraints On Late Precambrian To Early Paleozoic Terrane Accretion In The Southern Appalachian Blue Ridge Province, Emma A. Larkin

Theses and Dissertations--Earth and Environmental Sciences

Xenolith-bearing orthogneiss of Amazonian affinity discovered in the Dellwood quadrangle in the Blue Ridge basement complex represents the oldest crustal component of the southern Appalachians (1.33 – 1.37 Ga: Quinn, 2012). New U-Pb zircon ages for migmatitic paragneiss of the Cartoogechaye terrane exposed in the Dellwood quadrangle reveal two unique detrital zircon age signatures that indicate either a local eastern Laurentian margin source or an exotic source. Detailed mapping, whole rock geochemistry, and U-Pb zircon geochronology were conducted to determine whether this exotic crustal component extends farther south into the Hazelwood 7.5” quadrangle. Lithological similarities exist between paragneisses in the …

Dating Deformation In The Palmer Zone Of Transpression, Central Massachusetts: Temporal Constraints On Models For Progressive Deformation In The Middle Crust, James K. Mcculla

Theses and Dissertations--Earth and Environmental Sciences

The Palmer Zone of Transpression (PZoT) in the Bronson Hill zone of central Massachusetts is an expression of late Paleozoic oblique convergence between Avalonia and Laurentia. The steeply W-dipping, N-S trending PZoT is defined by bounding high strain zones (Mt. Dumplin on west, Central Maine and Conant Brook on east) of opposing shear sense enclosing the Monson orthogneiss. Research was designed to establish the timing of deformation to test the hypothesis that strain in transpressional systems occurs contemporaneously. An understanding of the timing of deformation in this zone could elucidate the mechanisms that formed the zone and contribute to a …

Topics In Logistic Regression Analysis, Zhiheng Xie

Theses and Dissertations--Statistics

Discrete-time Markov chains have been used to analyze the transition of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient states, and death as competing risk. A multinomial logistic regression model is used to estimate the probability distribution in each row of the one-step transition matrix that correspond to the transient states. We investigate some goodness of fit tests for a multinomial distribution with covariates to assess the fit of this model to the data. We propose a modified chi-square test statistic and a score test statistic for the multinomial assumption in each …

On Skew-Constacyclic Codes, Neville Lyons Fogarty

Theses and Dissertations--Mathematics

Cyclic codes are a well-known class of linear block codes with efficient decoding algorithms. In recent years they have been generalized to skew-constacyclic codes; such a generalization has previously been shown to be useful. We begin with a study of skew-polynomial rings so that we may examine these codes algebraically as quotient modules of non-commutative skew-polynomial rings. We introduce a skew-generalized circulant matrix to aid in examining skew-constacyclic codes, and we use it to recover a well-known result on the duals of skew-constacyclic codes from Boucher/Ulmer in 2011. We also motivate and develop a notion of idempotent elements in these …

Inverse Scattering For The Zero-Energy Novikov-Veselov Equation, Michael Music

Theses and Dissertations--Mathematics

For certain initial data, we solve the Novikov-Veselov equation by the inverse scat- tering method. This is a (2+1)-dimensional completely integrable system that gen- eralizes the (1+1)-dimensional Korteweg-de-Vries equation. The method used is the inverse scattering method. To study the direct and inverse scattering maps, we prove existence and uniqueness properties of exponentially growing solutions of the two- dimensional Schrodinger equation. For conductivity-type potentials, this was done by Nachman in his work on the inverse conductivity problem. Our work expands the set of potentials for which the analysis holds, completes the study of the inverse scattering map, and show that …

Statistical Properties Of Pseudorandom Sequences, Ting Gu

Theses and Dissertations--Computer Science

Random numbers (in one sense or another) have applications in computer simulation, Monte Carlo integration, cryptography, randomized computation, radar ranging, and other areas. It is impractical to generate random numbers in real life, instead sequences of numbers (or of bits) that appear to be ``random" yet repeatable are used in real life applications. These sequences are called pseudorandom sequences. To determine the suitability of pseudorandom sequences for applications, we need to study their properties, in particular, their statistical properties. The simplest property is the minimal period of the sequence. That is, the shortest number of steps until the sequence repeats. …

Effects Of Mountaintop Removal Mining On Population Dynamics Of Stream Salamanders, Sara B. Freytag

Theses and Dissertations--Forestry and Natural Resources

Mountaintop removal mining (MTR) is a notorious stressor of stream ecosystems in the Central Appalachians. Valley fills (VF) lead to reduced occupancy, abundance, and species richness of stream salamanders. Multiple factors may be responsible for these reductions, but specifically habitat fragmentation and degradation may reduce colonization rates and increase local extinction rates. From 2013-2015, repeated counts of salamanders were conducted in stream reaches impacted by MTR/VF and compared to counts in reference reaches to answer the question: do stream salamander population dynamics differ between stream reaches impacted by MTR/VF and reference stream reaches? I also investigated dynamics of stream habitat …

The Bourgain Spaces And Recovery Of Magnetic And Electric Potentials Of Schrödinger Operators, Yaowei Zhang

Theses and Dissertations--Mathematics

We consider the inverse problem for the magnetic Schrödinger operator with the assumption that the magnetic potential is in C^λ and the electric potential is of the form p₁ + div p₂ with p₁, p₂ ∈ C^λ. We use semiclassical pseudodifferential operators on semiclassical Sobolev spaces and Bourgain type spaces. The Bourgain type spaces are defined using the symbol of the operator h²Δ + hμ ⋅ D. Our main result gives a procedure for recovering the curl of the magnetic field and the electric potential from the Dirichlet to Neumann …

Information-Theoretic Secure Outsourced Computation In Distributed Systems, Zhaohong Wang

Theses and Dissertations--Electrical and Computer Engineering

Secure multi-party computation (secure MPC) has been established as the de facto paradigm for protecting privacy in distributed computation. One of the earliest secure MPC primitives is the Shamir's secret sharing (SSS) scheme. SSS has many advantages over other popular secure MPC primitives like garbled circuits (GC) -- it provides information-theoretic security guarantee, requires no complex long-integer operations, and often leads to more efficient protocols. Nonetheless, SSS receives less attention in the signal processing community because SSS requires a larger number of honest participants, making it prone to collusion attacks. In this dissertation, I propose an agent-based computing framework using …

Stratigraphic, Geochemical, And Well Log Analysis Of The Wolfcamp-D Unconventional Play In The Central Midland Basin, Texas, Patrick Thomas Ryan

Theses and Dissertations--Earth and Environmental Sciences

This M.S. thesis utilizes diverse subsurface datasets from the central Midland Basin, a recently reinvigorated petroleum producing region, to better understand the depositional history of the prospective Wolfcamp-D interval. An integrated set of methods were applied to ~320 ft of drill core from Midland County (Texas). Elemental chemostratigraphy collected via x-ray fluorescence highlights the pervasive fine-scale variability in the stratigraphy of the core, and aided in the classification of three different mudrock facies types. Organic-rich, siliceous mudrocks are cyclically interbedded with aluminum-rich mudrocks and carbonates throughout the Wolfcamp-D. Trace metal correlations with total organic carbon indicate slow bottom-water recharge from …

Lattice Qcd Calculation Of The Momentum Fraction Carried By Quarks In The Nucleon, And The Roper Puzzle, Mingyang Sun

Theses and Dissertations--Physics and Astronomy

This thesis is concerned with the lattice QCD calculation of the momentum fraction carried by quarks in the nucleon. Particularly, the strange quark contribution, (x)_s, is calculated, as well as the ratio of the strange (x) to that of u/d in the disconnected insertion which will be useful in constraining the global fit of parton distribution functions at small x. The disconnected insertion is known to be hard to calculate on the lattice. We adopt the overlap fermion action on several 2 + 1 flavor domain-wall fermion ensembles with a light sea quark mass which corresponds to pion …

Analyzing The Geo-Dependence Of Human Face Appearance And Its Applications, Mohammad T. Islam

Theses and Dissertations--Computer Science

Human faces have been a subject of study in computer science for decades. The rich of set features from human faces have been used in solving various problems in computer vision, including person identification, facial expression analysis, and attribute classification. In this work, I explore the human facial features that depend on the geo-location using a data- driven approach. I analyze millions of public domain images to extract the geo-dependent human facial features and explore their applications. Using various machine learning and statistical techniques, I show that the geo-dependent features of human faces can be used to solve the image …

Probing Physical Conditions In The Crab Nebula With Emission Line Analysis, Xiang Wang

Theses and Dissertations--Physics and Astronomy

We present a range of steady-state photoionization simulations, corresponding to different assumed shell geometries and compositions, of the unseen postulated rapidly expanding outer shell to the Crab Nebula. The properties of the shell are constrained by the mass that must lie within it, and by limits to the intensities of hydrogen recombination lines. In all cases the photoionization models predict very strong emission from high ionization lines that will not be emitted by the Crab’s filaments, alleviating problems with detecting these lines in the presence of light scattered from brighter parts of the Crab. The NIR [Ne VI] λ 7.652 …

A Systematic Study Of The Effect Of Spin-Orbit Interaction On Properties Of Tetravalent And Pentavalent Iridate Compounds, Jasminka Terzic

Theses and Dissertations--Physics and Astronomy

Previous studies of iridates have shown that an interplay of strong SOI, Coulomb interaction U, Hund’s rule coupling and crystalline electric fields result in unexpected insulating states with complex magnetic states. The novel J_eff =1/2 insulating state first observed in Sr₂IrO₄ is a direct consequence of such an intriguing interplay and is one of the central foci of this dissertation study.

The work presented here consists of three projects: (1) Effects of Tb doping on Sr₂IrO₄ having tetravalent Ir⁴⁺(5d⁵) ions; (2) Emergence of unexpected magnetic states in double-perovskite (Ba …

Physical And Electronic Properties Of Nanoscale 2d Materials, Mathias J. Boland

Theses and Dissertations--Physics and Astronomy

There is a great push towards reducing the size scale of both electronic components and machines. Two dimensional materials, such as graphene, are ideal candidates towards this push, as they are naturally atomically thin. In the case of nanoscale machines, the mechanical properties of the material surfaces become increasingly important. The use of laminar materials, such as graphene and MoS₂, to modify the surface properties, yet maintain nanoscale topographical features, are very attractive. Towards this goal, we have investigated the surface properties of MoS₂ at the nanoscale using Lateral Force Microscopy (LFM). In these investigations, we measure …

Evaluating A Bystander Intervention Program On Reproductive Coercion: Using Quasi-Experimental Design Strategies To Address Methodologic Issues In Randomized Community Prevention Trials, Catherine P. Starnes

Theses and Dissertations--Epidemiology and Biostatistics

Community (or cluster) randomized trials are trials in which communities or groups of individuals (clusters) are randomized to receive the intervention of interest. Community randomized trials frequently more closely resemble a natural experiment than a randomized controlled trial (RCT) following intervention allocation. In particular, the effects of non-compliance can pose methodologic challenges in estimating the intervention effect which may require a quasiexperimental approach in order to minimize bias.

The motivating example to illustrate these issues is the Green Dot High School (GDHS) study. The GDHS study was a longitudinal, cluster-randomized controlled trial designed to assess the effectiveness of a bystander …

Towards An Understanding Of Pharmacologically Induced Intracellular Changes In Nicotinic Acetylcholine Receptors: A Fluorescence Microscopy Approach, Ashley M. Loe

Theses and Dissertations--Chemistry

Upregulation of nicotinic acetylcholine receptors (nAChRs) is a well-documented response to chronic nicotine exposure. Nicotinic acetylcholine receptors are pentameric ligand-gated ion channels consisting of alpha (α2-10) and beta (β2-4) subunits. Nicotine, an agonist of nAChRs, alters trafficking and assembly of some subtypes of nAChRs, leading to an increase in expression of high sensitivity receptors on the plasma membrane. These physiological changes in nAChRs are believed to contribute to nicotine addiction, although the mechanism of these processes has not been resolved. Recently, many studies have converged on the idea that nicotine induces upregulation by an intracellular mechanism. In this dissertation, expression …

Effects Of Epichloë Coenophiala−Tall Fescue Symbiosis On Plant-Microbe-Soil Interactions In A Temperate Pasture, Lindsey C. Slaughter

Theses and Dissertations--Plant and Soil Sciences

Plants interact in myriad ways with microorganisms to influence ecosystem processes such as nutrient cycling, which can regulate ecosystem response to global change. One important plant-microbe symbiosis occurs between cool-season grasses and asexual fungal Epichloë endophytes, such as tall fescue (Schedonorus arundinaceus) and Epichloë coenophiala. Because the common toxic strain of the endophyte (CTE) harms grazing livestock, non-livestock toxic endophyte (NTE) strains have been developed and are increasingly deployed in pastures. Little is known about how these symbioses impact other plant-microbe interactions and microbe-mediated soil processes in grassland ecosystems. I conducted three studies to determine how E. …

Development Of A Semi-Automated Methodology For Discriminating Between Natural And Manmade Seismic Events Using The Oiink Seismic Array, Paul Rodriguez Asihama

Theses and Dissertations--Earth and Environmental Sciences

Broadband waveforms from the Ozark, Indiana, Illinois, Kentucky temporary seismic array OIINK, a Flexible Array in the EarthScope project, were used to develop routines to identify and remove mine blast events from a database of local events and preserve the infrequent, small, natural earthquakes. The approach taken was to first create a database of all seismic events that were detected by the OIINK Seismic Array. False-detections, events detected from outside of the project area (approx. 302 thousand square km), and known (i.e. cataloged) local earthquake were also removed. The remaining in the database were local unknown events. During the Phase …

Modeling, Learning And Reasoning About Preference Trees Over Combinatorial Domains, Xudong Liu

Theses and Dissertations--Computer Science

In my Ph.D. dissertation, I have studied problems arising in various aspects of preferences: preference modeling, preference learning, and preference reasoning, when preferences concern outcomes ranging over combinatorial domains. Preferences is a major research component in artificial intelligence (AI) and decision theory, and is closely related to the social choice theory considered by economists and political scientists. In my dissertation, I have exploited emerging connections between preferences in AI and social choice theory. Most of my research is on qualitative preference representations that extend and combine existing formalisms such as conditional preference nets, lexicographic preference trees, answer-set optimization programs, possibilistic …

Use Of Laboratory Geophysical And Geotechnical Investigation Methods To Characterize Gypsum Rich Soils, Raghava A. Bhamidipati

Theses and Dissertations--Civil Engineering

Gypsum rich soils are found in many parts of the world, particularly in arid and semi-arid regions. Most gypsum occurs in the form of evaporites, which are minerals that precipitate out of water due to a high rate of evaporation and a high mineral concentration. Gypsum rich soils make good foundation material under dry conditions but pose major engineering hazards when exposed to water. Gypsum acts as a weak cementing material and has a moderate solubility of about 2.5 g/liter. The dissolution of gypsum causes the soils to undergo unpredictable collapse settlement leading to severe structural damages. The damages incur …

Ecology Of Two Reintroduced Black Bear Populations In The Central Appalachians, Sean Mccarthy Murphy

Theses and Dissertations--Animal and Food Sciences

Reintroduced populations are vulnerable to demographic and environmental stochasticity, deleterious genetic effects, and reduced population fitness, all of which can increase extinction probability. Population viability is principle to determining the status of reintroduced populations and for guiding management decisions. To attempt to reestablish black bear (Ursus americanus) populations in the central Appalachians, two reintroductions using small founder groups occurred during the 1990s in the Big South Fork area along the Kentucky-Tennessee border (BSF) and in the Jefferson National Forest along the Kentucky-Virginia border (KVP). My objectives were to estimate demographic and genetic parameters, and to evaluate long-term viability …

Lithostratigraphic And Geochemical Characterization Of The Upper Pennsylvanian ‘Wolfcamp D’ Shale, Midland Basin (Usa): Implications For Paleoenvironments And Unconventional Petroleum Reserviors, Patrick W. Baldwin

Theses and Dissertations--Earth and Environmental Sciences

An integrated stratigraphic analysis of a ~350 ft drill core from Upton County (Texas) has revealed pervasive variability of several key siliciclastic and carbonate lithofacies in vertical section, where organic-rich siliceous mudrock beds alternate with aluminum-rich mudrocks and calcareous gravity flow deposits. Sediment chemistry, especially major and trace elements derived from x-ray fluorescence, captures this variability with high sensitivity. The high frequency chemostratigraphic variability appears to be cyclic, and it is interpreted to represent the first example of deep-water Late Pennsylvanian cyclothems for the Midland Basin. Positive trace metal (Mo, Cr) correlations to total organic carbon and gamma ray response …

Deuterium And Oxygen-18 Diffusion In A Confined Aquifer: A Numerical Model Of Stable Isotope Diffusion Across Aquitard-Aquifer Boundaries, Benjamin J. Currens

Theses and Dissertations--Earth and Environmental Sciences

The stable isotopes ²H and ¹⁸O, combined with noble gases and radioisotopes (e.g., ³H, ¹⁴C, ³⁶Cl), are used to infer groundwater age and climate during recharge. Flow regimes within low-velocity flowpaths and long residence times could allow an aquitard-aquifer diffusive flux to alter isotope abundance. Consequently, the diffusion of isotopes (e.g., ¹⁴C, ²H and ¹⁸O) between aquifers and confining layers needs to be considered in such conditions. In this study, COMSOL Multiphysics was used to determine if diffusion of ¹⁸O (and ²H by proxy) from a bounding aquitard could explain …