Physical Sciences and Mathematics Commons^™

Counting Number Fields By Discriminant, Harsh Mehta

Theses and Dissertations

The central topic of this dissertation is counting number fields ordered by discriminant. We fix a base field k and let Nd(k,G;X) be the number of extensions N/k up to isomorphism with Nk/Q(dN/k) ≤ X, [N : k] = d and the Galois closure of N/k is equal to G.

We establish two main results in this work. In the first result we establish upper bounds for N_|G| (k,G;X) in the case that G is a finite group with an abelian normal subgroup. Further, we establish upper bounds for the case N _|F| (k,G;X) where G is a Frobenius …

An Ensemble-Based Projection Method And Its Numerical Investigation, Shuai Yuan

Theses and Dissertations

In many cases, partial differential equation (PDE) models involve a set of parameters whose values may vary over a wide range in application problems, such as optimization, control and uncertainty quantification. Performing multiple numerical simulations in large-scale settings often leads to tremendous demands on computational resources. Thus, the ensemble method has been developed for accelerating a sequence of numerical simulations. In this work we first consider numerical solutions of Navier-Stokes equations under different conditions and introduce the ensemblebased projection method to reduce the computational cost. In particular, we incorporate a sparse grad-div stabilization into the method as a nonzero penalty …

What Can Scattered Light Tell You About Your Favorite Magnetic Material?: A Magneto Optical Investigation Of The Magnetic Properties Of Aligned Janus Fiber Agglomerates.Influence Of Dynamic Multiaxial Transverse Loading On Ultrahigh Molecular Weight Polyethylene Single Fiber Failure, Cory John Dolbashian

Theses and Dissertations

Here we seek to take a traditional Magneto Optic Kerr Effect (MOKE) experimental design, useful for local magnetization measurements, and apply it to measuring aligned multiferroic Janus nano fiber agglomerates. In order to achieve this we modify the traditional MOKE geometry by measuring our Kerr rotation from collimated scattered light, rather than the conventional specular reflection. Using various techniques to improve signal to noise ratio (SNR), we extend the application of this scattered MOKE geometry to build families of First Order Reversal Curves (FORC). Using an alternative analysis technique, FORC curves are processed and become a FORC diagram, which is …

Finite Axiomatisability In Nilpotent Varieties, Joshua Thomas Grice

Theses and Dissertations

Study of general algebraic systems has long been concerned with finite basis results that prove finite axiomatisability of certain classes of general algebras. In the 1970’s, Bjarni Jónsson speculated that a variety generated by a finite algebra might be finitely based provided the variety has a finite residual bound (that is, a finite bound on the cardinality of subdirectly irreducible algebras in the variety). As such, most finite basis results since then have had the hypothesis of a finite residual bound. However, Jónsson also speculated that it might be sufficient to replace the finite residual bound with the weaker hypothesis …

Flexible Regression Models For Survival Data, Ennan Gu

Theses and Dissertations

Survival analysis is a branch of statistics to analyze the time-to-event data or survival data. One important feature of survival data is censoring, which means that not all the subjects’ survival time are observed directly. Among all the survival data, right-censored data are the most common type and consist of some exactly observed survival times and some right-censored observations. In this dissertation, we focus on studying flexible regression models for complicated right-censored survival data when the classical proportional hazards (PH) assumption is not satisfied. Flexible semiparametric regression models can largely avoid misspecification of parametric distributions and thus provide more modeling …

Distance Related Graph Invariants In Triangulations And Quadrangulations Of The Sphere, Trevor Vincent Olsen

Theses and Dissertations

The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices. I provide asymptotic upper bounds and sharp lower bounds for the Wiener index of simple triangulations and quadrangulations with given connectivity. Additionally, I make conjectures for the extremal triangulations and quadrangulations which maximize the Wiener index based on computational evidence. If σ(v) denotes the arithmetic mean of the distances from v to all other vertices of G, then the remoteness and proximity of G are defined as the largest and smallest value of σ(v) over all vertices v of G, respectively. …

Windows And Generalized Drinfeld Kernels, Robert R. Vandermolen

Theses and Dissertations

We develop a generalization of a construction of Drinfeld, first inspired by the Qconstruction of Ballard, Diemer, and Favero. We use this construction to provide kernels for Grassmann flops over an arbitrary field of characteristic zero. In the case of Grassmann flops this generalization recovers the kernel for a Fourier-Mukai functor on the derived category of the associated global quotient stack studied by Buchweitz, Leuschke, and Van den Bergh. We show an idempotent property for this kernel, which after restriction, induces a derived equivalence over any twisted form of a Grassmann flop.

Fundamental Studies Of Bimetallic Model Surfaces And Metal Organic Framework Thin Films, Fathima Sharfa Farzandh

Theses and Dissertations

This work is mainly focused on gaining a fundamental understanding of conventional bimetallic catalysts in order to correlate their macroscopic properties with the observed kinetic properties. This is achieved by synthesizing and studying fundamental model surface analogues of conventional catalysts that are difficult to study due to their complex, ill-defined nature. A wide array of surface science techniques that use ultra-high vacuum (UHV) conditions are readily available for detailed studies that can be conducted on model surfaces. This work focuses on the synthesis and investigation of two fundamental bimetallic catalysts formed via the addition of a second metal to an …

Fundamental Studies Of Bimetallic Model Surfaces And Metal Organic Framework Thin Films, Fathima Sharfa Farzandh

Theses and Dissertations

This work is mainly focused on gaining a fundamental understanding of conventional bimetallic catalysts in order to correlate their macroscopic properties with the observed kinetic properties. This is achieved by synthesizing and studying fundamental model surface analogues of conventional catalysts that are difficult to study due to their complex, ill-defined nature. A wide array of surface science techniques that use ultra-high vacuum (UHV) conditions are readily available for detailed studies that can be conducted on model surfaces. This work focuses on the synthesis and investigation of two fundamental bimetallic catalysts formed via the addition of a second metal to an …

Probing The Interstellar Medium Of Galaxies Using Gravitationally Lensed Sight Lines And The Relevant Atomic Physics, Frances Cashman

Theses and Dissertations

Absorption spectroscopy of gravitationally lensed quasars (GLQs) enables study of spatial variations in the interstellar and/or circumgalactic medium (ISM, CGM) of foreground galaxies. In this work I present observations of 4 GLQs, each with two images separated by 0.8-3.000, that show strong absorbers at redshifts 0.4 abs< 1.3 in their spectra, including some at the lens redshift. The H I Lyman lines were measured in five absorbers using HST-STIS, and metal lines with either the MagE spectrograph or the Sloan Digital Sky Survey. These data, combined with the literature, show no strong correlation between absolute values of differences in NH I, NFe II, or [Fe/H] and sight line separations at absorber redshifts. The measured abundance gradients show a tentative anti-correlation with abundances at galaxy centers.

A study of the lens galaxy foreground to the doubly lensed quasar SBS 0909+532 reveals a large difference in H I and metal column densities between sight lines. Using archival HST-STIS and Keck HIRES spectra, log N _{H I} 18.18 cm−2 and log N _{H I} = 20.38±0.02 cm⁻²were measured, resulting …

A Behavioral And Voltammetric Study Of The Effects Of Pb Exposure In Mice As A Model Of Autism Spectrum Disorder, Brenna Parke

Theses and Dissertations

Despite being a known toxin for several centuries, lead (Pb²⁺) is still utilized in commercial products including leaded gasoline, paint, and modern cosmetics. This presence has caused (Pb²⁺) to pollute the environment, including public drinking water sources. The recent outbreaks of elevated levels of (Pb²⁺) in the drinking water in Flint, Michigan and Washington D.C. have caused large populations to be exposed to the heavy metal for months at a time, raising a public health concern over the implications of widespread, long-term (Pb²⁺) exposure. Young children are most susceptible to the effects …

Bayesian Analysis Of Binary Diagnostic Tests And Panel Count Data, Chunling Wang

Theses and Dissertations

This dissertation mainly explores several challenging topics that arise in diagnostic tests and panel count data in the Bayesian framework. Binary diagnostic tests, particularly multiple diagnostic tests with repeated measures and diagnostic procedures with a large number of raters, are studied. For panel count data, most traditional methods only handle panel count data for a single type of recurrent event. In this dissertation, we primarily focus on the case with multiple types of recurrent events.

In Chapter 1, an introduction to the binary diagnostic tests data and panel count data is presented and related literature works are briefly reviewed. To …

An Equivariant Count Of Nodal Orbits In An Invariant Pencil Of Conics, Candace Bethea

Theses and Dissertations

Enumerative geometry studies the number of geometric objects in a given class satisfying specific geometric conditions. For example, we can ask how many conics in the plane pass through four points. One such example is a specific case of Göttsche’s conjecture, stated in (Göttsche 1998): given a pencil of conics in P2 C, how many curves in the pencil have nodal singularities? The answer is three as long as the defining conics of the pencil are general. The conjecture was proved in full generality by Y. Tzeng in 2010 in (Tzeng 2012), and another proof exists due to Kool, Shende, …

An Overlay Architecture For Pattern Matching, Rasha Elham Karakchi

Theses and Dissertations

Deterministic and Non-deterministic Finite Automata (DFA and NFA) comprise the fundamental unit of work for many emerging big data applications, motivating recent efforts to develop Domain-Specific Architectures (DSAs) to exploit fine-grain parallelism available in automata workloads.

This dissertation presents NAPOLY (Non-Deterministic Automata Processor Over- LaY), an overlay architecture and associated software that attempt to maximally exploit on-chip memory parallelism for NFA evaluation. In order to avoid an upper bound in NFA size that commonly affects prior efforts, NAPOLY is optimized for runtime reconfiguration, allowing for full reconfiguration in 10s of microseconds. NAPOLY is also parameterizable, allowing for offline generation of …

Mechanistic Investigations Of Isothiourea Catalyzed Silylations Of Secondary Alcohols Using Reaction Progress Kinetic Analysis, Brandon Kane Redden

Theses and Dissertations

The primary focus of this research is in expanding the knowledge and scope of the asymmetric silylation of alcohols. Since it was discovered in 2011 that chiral isothioureas can selectively silylate alcohols through kinetic resolution reactions, the Wiskur group has been working to increase the applications of the methodology. Understanding the kinetics behind the mechanism of the reaction is fundamental in the designing both improved kinetic resolutions and other silylation methodology. Chapter 2 focuses on using reaction progress kinetic analysis to monitor silylations of secondary alcohols with thiourea catalysts in real time using in situ IR to determine the rate …

Chemistry Of A Biscarborane Dithiol And Its Nickel (Ii) Complex, Tyler Hemingway

Theses and Dissertations

Neutral biscarborane dithiol and its anionic dithiolate form were successfully synthesized and structurally characterized. The C–C intracluster bond lengths were found to be responsive to the electron density on the cluster. Introduction of two thiol groups on biscarborane led to the significant increase of intracluster C–C bond lengths compared to those of unsubstituted biscarborane. Furthermore, the anionic dithiolate form had even longer C–C cluster bonds. This comparison shows electronic effect of substituents attached to carbon atoms of biscarborane on the strength of its C–C bonds. Additionally, a novel Ni complex was obtained using this dithiolate as a ligand. This complex …

Development Of Natural Product-Derived Cationic Polymers For Biomaterial Applications, Moumita Sharmin Jui

Theses and Dissertations

In this thesis, multicyclic natural products and metallocene-containing polymers were synthesized for biomedical applications.

Chapter 1 describes the overall background, the recent development of natural product-based antimicrobial biomaterial and metallocene containing polymer for biomedical application. Afterward, the primary research objectives of my research are illustrated.

In chapter 2, a multicyclic natural product derived guanidine-based facially amphiphilic homopolymers and copolymers were synthesized. Cholic acid is one of the bile acid derivatives used to prepare facially amphiphilic moieties. A neutral polyethylene glycol (PEG) component was used to prepare copolymers with cholic acid. Reversible-addition fragmentation chain transfer (RAFT) polymerization technique was used to …

Gel Permeation Chromatography Purification And Surface Chemistry Of Technologically Relevant Colloidal Quantum Dots, Adam Roberge

Theses and Dissertations

Semiconductor quantum dots have received extensive research interest due to the size tunable band gap, large extinction coefficient, and ease of synthesis. These nanocrystals possess large surface to volume ratios and the chemistry at the surface of the nanocrystal greatly influences the resultant optoelectronic properties. Therefore, after synthesis, purification of the quantum dot samples to remove synthetic by-products that may alter these properties is of great importance. Gel permeation chromatography (GPC), a form of size exclusion chromatography, has been shown to reproducibly purify CdSe quantum dots. This work focuses on the expansion of purification by gel permeation chromatography to other …

Multivariate Joint Models And Dynamic Predictions, Md Akhtar Hossain

Theses and Dissertations

The joint modeling of longitudinal and time-to-event data is an active area of statistical research that has received a lot of attention. The standard joint models, referred to as univariate joint models, allow simultaneous modeling of a single longitudinal outcome and a single time-to-event under an assumption of independent censoring. The majority of the joint modeling research in the last two decades has focused on extending and improving the univariate joint models. While many of the practical applications involve data on multivariate longitudinal outcomes and multiple timeto- events possibly informatively censored by some other terminal time-to-event, the developments of joint …

An Examination Between Neighborhood Characteristics And Alzheimer’S Disease And Related Dementias And Caregiver Mental Health In South Carolina, Mohammad Jahirul Islam

Theses and Dissertations

Carboranes are of topical interest due to their unique structures and applications in the fields of catalysis, polymers, material sciences and supramolecular chemistry. Icosahedral closo-dicarbadodecaboranes are remarkably robust three-dimensional boron-carbon clusters with two slightly acidic C-H bonds. Moreover, coordinatively unsaturated transition-metal complexes containing C-functionalized ortho-carborane are considered as potential catalysts for activation of small molecules.

Recently, we reported the synthesis of a pyridine-backbone pincer complex {(C₅H₃N)(C₂B₁₀H₁₀)₂}Ni(CH₃CN) (1) in which two C-functionalized ortho-carborane clusters act as the arms of the pincer ligand. The complex …

A Machine Learning Based Approach To Accelerate Catalyst Discovery, Asif Jamil Chowdhury

Theses and Dissertations

Computational catalysis, in contrast to experimental catalysis, uses approximations such as density functional theory (DFT) to compute properties of reaction intermediates. But DFT calculations for a large number of surface species on variety of active site models are resource intensive. In this work, we are building a machine learning based predictive framework for adsorption energies of intermediate species, which can reduce the computational overhead significantly. Our work includes the study and development of appropriate machine learning models and effective fingerprints or descriptors to predict energies accurately for different scenarios. Furthermore, Bayesian inverse problem, that integrates experimental catalysis with its computational …

Structural, Functional And Immunological Studies Of Group 1 And 2 House Dust Mite And Profilin Allergens For The Development Of Allergen Specific Diagnostics And Immunotherapy, Anyway B. Kapingidza

Theses and Dissertations

Group 1 and 2 house dust mites (HDM) allergens elicit IgE response in more than 80% of sensitized individuals. These allergens affect 10-30% of the world’s population. Prolonged inhalation of low doses of allergens (microgram amounts inhaled over months or years) by genetically predisposed individuals leads to the induction of a Th2-type immune response induced by allergen-specific immunoglobulin E (IgE) produced by plasma cells resulting in allergic diseases like asthma, atopic dermatitis, and rhinitis. Group 1 and 2 HDM allergens, in particular, are associated with the development of the aforementioned allergic diseases. The goal of this research was to characterize …

Rationality Questions And The Derived Category, Alicia Lamarche

Theses and Dissertations

This document is roughly divided into four chapters. The first outlines basic preliminary material, definitions, and foundational theorems required throughout the text. The second chapter, which is joint work with Dr. Matthew Ballard, gives an example of a family of Fano arithmetic toric varieties in which the derived category is able to detect the existence of k-rational points. More succinctly, we show that if X is a generalized del Pezzo variety defined over a field k, then X contains a k-rational point (and is in fact k-rational, that is, birational to Pnk ) if and only if Db(X) admits a …

Two Inquiries Related To The Digits Of Prime Numbers, Jeremiah T. Southwick

Theses and Dissertations

This dissertation considers two different topics. In the first part of the dissertation, we show that a positive proportion of the primes have the property that if any one of their digits in base 10, including their infinitely many leading 0 digits, is replaced by a different digit, then the resulting number is composite. We show that the same result holds for bases b 2 {2, 3, · · · , 8, 9, 11, 31}.

In the second part of the dissertation, we show for an integer b ≥ 5 that if a polynomial ƒ( x) with non-negative coefficients …

Investigating The Role Of Iron-Sulfur Signaling In Yeast Transcriptional Regulation, Malini Gupta

Theses and Dissertations

As an essential cofactor in a myriad of cellular processes, uptake and mobilization of iron must be tightly controlled. Iron homeostasis in fungi involves balancing iron uptake and storage with iron utilization to achieve adequate, non-toxic levels of this essential nutrient. Extensive work in the non-pathogenic yeasts Saccharomyces cerevisiae and Schizosaccharomyces pombe have uncovered unique iron regulation networks for each organism that control iron metabolism via distinct molecular mechanisms. The activities of all fungal iron-sensing transcription factors characterized to date are regulated via iron-sulfur cluster signaling.

In Saccharomyces cerevisiae, expression of iron uptake, utilization and storage genes is primarily regulated …

Connections Between Extremal Combinatorics, Probabilistic Methods, Ricci Curvature Of Graphs, And Linear Algebra, Zhiyu Wang

Theses and Dissertations

This thesis studies some problems in extremal and probabilistic combinatorics, Ricci curvature of graphs, spectral hypergraph theory and the interplay between these areas. The first main focus of this thesis is to investigate several Ramsey-type problems on graphs, hypergraphs and sequences using probabilistic, combinatorial, algorithmic and spectral techniques:

• The size-Ramsey number Rˆ(G, r) is defined as the minimum number of edges in a hypergraph H such that every r-edge-coloring of H contains a monochromatic copy of G in H. We improved a result of Dudek, La Fleur, Mubayi and Rödl [ J. Graph Theory 2017 ] on the size-Ramsey number …

Synthesis And Design Of Novel Polymer Grafted Nanoparticles Relevant To Drug Delivery Vehicles For Biomedical Application, Maan Abduldiyem Hassan Al-Ali

Theses and Dissertations

The modification of inorganic nanoparticles with organic polymer chains has become a significant field of study for the engineering of advanced nanocomposite materials. This dissertation presents the design, synthesis, and characterization of novel polymer grafted silica nanoparticles as new strategies to combat bacterial resistance. Described herein is the synthesis of monomers that have been graft polymerized onto silica nanoparticles that can be used as a delivery drug vehicle for biomedical applications. The polymerization of these monomers was performed via reversible addition-fragmentation chain transfer (RAFT) polymerization. The molecular design of the RAFT agents that are attached to the surfaces of the …