Physical Sciences and Mathematics Commons^™

Parametric Polynomials For Small Galois Groups, Claire Huang

Honors Theses

Galois theory, named after French mathematician Evariste Galois in 19th-century, is an important part of abstract algebra. It brings together many different branches of mathematics by providing connections among fields, polynomials, and groups.

Specifically, Galois theory allows us to attach a finite field extension with a finite group. We call such a group the Galois group of the finite field extension. A typical way to attain a finite field extension to compute the splitting field of some polynomial. So we can always start with a polynomial and find the finite group associate to the field extension on its splitting field. …

Algebraic Number Theory And Simplest Cubic Fields, Jianing Yang

Honors Theses

The motivation behind this paper lies in understanding the meaning of integrality in general number fields. I present some important definitions and results in algebraic number theory, as well as theorems and their proofs on cyclic cubic fields. In particular, I discuss my understanding of Daniel Shanks' paper on the simplest cubic fields and their class numbers.

Stable Bromine Isotope Signature Of Bromoform From Enzymatic And Abiotic Formation Pathways And Its Application In Identifying Sources Of Environmental Bromoform In The Damariscotta River, Chengyang Wang

Honors Theses

Bromoform is a major source of atmospheric bromine. Most bromoform is produced by marine organisms including macroalgae and phytoplankton, using the enzyme bromoperoxidase (BPO). Bromoform can also be a byproduct of industrial processes such as water disinfection. Identifying sources of environmental bromoform is still a challenge. A novel technique of using quadrupole mass spectrometry coupled to a gas chromatography (GCqMS) was developed and optimized for Br isotope analyses. The study shows that GCqMS in single ion monitoring (SIM) mode can measure 81Br with precision of around ±0.7‰ (60pmol bromoform injected). This study aims to investigate stable Br isotopes of bromoform …

Raman Spectroscopic And Computational Study Of Hydrogen Bond Interactions Between Guanidine Hydrochloride, Trimethylamine N-Oxide (Tmao), Urea, And Water, Andrew Kamischke

Honors Theses

Proteins are broken down in the body and produce water, CO2, and ammonia as by-products. Ammonia is toxic to cells, making it a priority to be excreted. Urea is the key route for the transportation of ammonia out of the body and is the main component of urine. Guanidine is another important nitrogen-containing molecule that is structural like urea and plays important biological roles in the stabilization of proteins. Guanidine hydrochloride and Urea are known to denature proteins and this functionality continues to be a topic of great interest. Urea and guanidine contain many hydrogen bonding sites and interactions with …

Studies Of Carbonaceous Materials Using Raman Spectroscopy, Cameron L. Smith

Honors Theses

Various carbonaceous materials including graphene, treated biochar, and C60 were studied using Raman spectroscopy with particular attention given to the treatment process and the Raman enhancement methods. Such studies that focus on the treatment process are useful in determining the extent to which the species was affected via shifts in the Raman peaks. Previous collaborations have proven successful when multiple samples were studied and analyzed. The attempt to create a novel Raman enhancement technique via combination of two previously recorded techniques was ultimately unsuccessful but further work is necessary.

Classifying #Metoo Hash-Tagged Tweets By Semantics To Understand The Extent Of Sexual Harassment, Claire Hubacek

Honors Theses

This thesis contains a program that will process tweets from Twitter that use the hashtag "#MeToo" and categorize them by their relevance to the movement, their stance on the movement, and the type of sexual harassment expressed (if applicable). Being able to work with a narrowed set of tweets belonging to a specific category creates the capacity to do more in-depth research and analysis, exploring Twitter as a special platform for discussing these sensitive topics and showing that this online space for expressing personal experiences has delivered unprecedented potential avenues of study. This thesis also contains research into additional solutions …

Investigation Of Vibrational Signatures Of Nitrobenzenes Enhanced By Argyrophilic Interactions, Hailey Reed

Honors Theses

This investigation studies the interactions between various nitroaromatic high energy density materials (HEDMs) and a pair of silver atoms (Ag2). Additionally, we examine the changes in frequency, infrared (IR) intensities, and Raman activities induced by the Ag2 unit as the complexes form. Full geometry optimizations of the isolated HEDM molecules as well as complexes where Ag2 is bound to various argyrophillic sites of these compounds have been carried out along with the corresponding harmonic vibrational frequency computations using the M06-2X density functional with a correlation consistent triple-ζ basis set augmented with diffuse functions on all atoms and a relativistic pseudopotential …

Computational Investigation On Electronic Structures And Properties Of 4,6-Bis(Nitroimino)-1,3,5-Triazinan-2-One: An Insensitive Munitions Compound, Katarina M. Pittman

Honors Theses

In order to minimize unintentional detonation, current munitions research has focused on the development of chemical compounds that are insensitive to external stimuli whilst maintaining their effectiveness. While these compounds, known as high performance in- sensitive munitions compounds, are promising in terms of potency and stability, their envi- ronmental impacts have either not been fully understood or are yet to be investigated. In the present research, we have performed a computational chemistry investigation on electronic structures and properties of an insensitive munition compound 4,6-bis(nitroimino)-1,3,5- triazinan-2-one (DNAM). The Density Functional Theory using the B3LYP and M06- 2X functionals and MP2 methodology …

Electrocatalytic Oxygen Reduction Studies On Gold Nanoparticles, Leigh Sumner

Honors Theses

After determining that the size of nanoclusters can be tuned such that they have a precise formula much like a chemical compound, much is still not known about nanoclusters, their properties, and how they interact if core size, ligand, and even environment is changed. One such mystery is how does the size of the nanoparticle tune its ability as a catalyst. As it is known that nanoparticles possess unique properties, studies have begun to look towards nanoclusters as catalysts for alternative forms of energy. Therefore, determining how size affects the ability of a nanoparticle catalyst becomes a very important question. …

Purification Protocol Development And Analysis Of Binding Properties Of Calmodulin Collagen-Like Protein, Patrick P. Boddie

Honors Theses

Calmodulin is an intensely studied, intracellular, calcium-binding protein that is involved in diverse physiological processes. When bound to calcium, calmodulin undergoes a conformational change that allows it to bind specific target peptides with high affinity, one being the calmodulin binding region of myosin light chain kinase, herein called M13. This high affinity, calcium dependent association has made it a desirable choice for use in a biomaterial for drug delivery for non-steroidal anti- inflammatory drugs (NSAIDs). Two artificial genes have been designed by our lab for use in the proposed biomaterial: calmodulin collagen-like protein (CCLP), a construct composed of two calmodulin …

Post-Translational Modification Of Hypoxia-Inducible Factor Proteins By O-Linked -N-Acetylglucosamine In Breast Cancer Cells, Sean Williamson

Honors Theses

One of the hallmarks of cancer is its ability to adapt its metabolism to survive and thrive despite needing to overcome significant energy barriers and low oxygen settings in order to do so. The hypoxia-inducible factor proteins (HIFs) play important roles in the processes in which cancer fulfills these requirements. The O-linked -N-acetylglucoseamine (O-GlcNAc) can be attached to cellular proteins through O-glycosylation, and is thus considered a potential target for anticancer mechanisms. HIFs are composed of (HIF-1 and HIF-2, respectively) and subunits. This research found that O-GlcNAc is able to attach to and modify the HIF proteins. This was accomplished …

Energetics And Vibrational Signatures Of Nucleobase Argyrophilic Interactions, Suhwan Paul Lee

Honors Theses

This study investigates the interactions of both purine (adenine and guanine) and pyrimidine (cytosine, thymine, and uracil) nucleobases with a pair of silver atoms (Ag2). Full geometry optimizations were performed on several structures of each nucleobase/Ag2 complex and the corresponding isolated monomers using the M06-2X density functional theory (DFT) method with a correlation consistent triple-ζ basis set augmented with diffuse functions on all atoms and a relativistic pseudopotential on Ag (aug-cc-pVTZ for H, C, N, and O and aug-cc-pVTZ-PP for Ag; denoted aVTZ). Harmonic vibrational frequency computations indicate that each optimized structure corresponds to a minimum on the M06-2X/aVTZ potential …

Heterobifunctional Linear Dendritic Block Co-Polymers (Ldbcs) As Multifunctional Carriers For Targeted Drug Delivery, William Rieger

Honors Theses

Despite current research towards applications of polymeric drug delivery systems (DDSs) in biomedical research, significant limitations—specifically in synthetic accessibility, bio compatibility, and principles of molecular self-assembly—have been discerned. To address these drawbacks, we will investigate the synthesis and characterization of heterobifunctional linear-dendritic block copolymers (LDBCs), which combine the advantageous properties of both linear and dendritic blocks to afford nanomaterials with superior mechanical properties. Our LDBC systems contain two differing functional constituents, namely a hydrophilic polyamidoamine (PAMAM) dendron covalently linked to a hydrophobic polyester (polylactic acid, or PLA), and can self-assemble to form nanoparticles of various morphologies that serve as the …

Automating The Calculation Of Hilbert-Kunz Multiplicities And F-Signatures, Gabriel Johnson

Honors Theses

We describe an application written to automate a calculation for the mathematical research of Dr. Spiroff of University of Mississippi & Dr. Enescu of Georgia State University. This work represents a way to overcome the barriers of the mathematical calculations in obtaining theoretical results.

Assessing Specificity Of Indazole Derivatives As Inhibitors To Cyp2e1, Hannah Hart

Honors Theses

Metabolism of drugs in the human body can yield both desirable and undesirable results. Some of these side-effects are due to drug-drug interactions, drug-diet interactions, or lack of drug specificity. The enzymes that drugs attack are structurally selective and complex; therefore, many drugs are very general in structure and could possibly react with a variety of enzymes. Indazole has been used as a backbone for several drugs as it has the general structure that may react with most P450s. To determine a derivative, or a group of derivatives, of indazole that may be reactive only with cytochrome P450 2El (CYP2El), …

Presence And Potential Sources Of Pharmaceutical And Personal Care Product Chemicals In Messalonskee Lake, Alyssa T. Kullberg

Honors Theses

Pharmaceuticals and personal care product chemicals (PPCPs) represent a large group of contaminants that are mostly not regulated in surface or drinking water and whose presence and environmental and health impacts are poorly understood. We investigated the presence and potential sources of 18 PPCPs in Messalonskee Lake. We collected samples four times over the summer of 2017 at 13 sites around the lake. Samples were tested for PPCPs using liquid chromatography-tandem mass spectrometry. We detected five out of the 18 PPCPs we tested for at the ng/L level: caffeine, 1,7-dimethylxanthine, acetaminophen, sulfachloropyridazine, and amphetamine. PPCPs showed a significant positive correlation …

On Spectral Theorem, Muyuan Zhang

Honors Theses

There are many instances where the theory of eigenvalues and eigenvectors has its applications. However, Matrix theory, which usually deals with vector spaces with finite dimensions, also has its constraints. Spectral theory, on the other hand, generalizes the ideas of eigenvalues and eigenvectors and applies them to vector spaces with arbitrary dimensions. In the following chapters, we will learn the basics of spectral theory and in particular, we will focus on one of the most important theorems in spectral theory, namely the spectral theorem. There are many different formulations of the spectral theorem and they convey the "same" idea. In …

Calcic Paleosols In A Stratigraphic Context From Quaggasfontein, Eastern Cape Province, South Africa: Correlations In The Wapadsberg Pass Area And Implications For Late Permian Climate, Kaci B. Kus

Honors Theses

The Karoo Basin, South Africa, contains a reportedly continuous stratigraphic record spanning the terrestrial vertebrate extinction event equated with the Permian-Triassic boundary (PTB) in the marine record. The current hypothesis links this major loss in biodiversity and vertebrate turnover to a global change in climate towards aridification. Rapid climate change is interpreted to be reflected in continental rocks by a changeover from (1) greenish (Permian) to reddish (Triassic) mudrock, (2) a transition in the river architectures from meandering to braided regimes, and (3) wetland to calcic-bearing paleosols. Here, we present geochemical results on a 1.3-meter calcic paleoVertisol interval found ~34 …

Analysis Of A Custom Support Vector Machine For Photometric Redshift Estimation And The Inclusion Of Galaxy Shape Information, Evan Jones, J. Singal

Honors Theses

Aims. We present a custom support vector machine classification package for photometric redshift estimation, including comparisons with other methods. We also explore the efficacy of including galaxy shape information in redshift estimation. Support vector machines, a type of machine learning, utilize optimization theory and supervised learning algorithms to construct predictive models based on the information content of data in a way that can treat different input features symmetrically, which can be a useful estimator of the information contained in additional features beyond photometry, such as those describing the morphology of galaxies.

Methods. The custom support vector machine package we have …