Physical Sciences and Mathematics Commons^™

Geochemical Differences In Calcic Horizons Due To Parent Material And Anthropogenic Water Input In Southeastern Arizona, Alicia Fischer

Honors Theses

Calcic soil horizons are significant carbon sinks. Yet, despite their abundance in semiarid environments, calcic soils are enigmatic for two reasons: (1) some authors hypothesize that dust input does not, independently, control the geochemical properties of these soils; and (2) few studies have examined how these calcic soils change geochemically with respect to irrigation. A 2017 pilot study used portable x-ray fluorescence (pXRF) on calcic soils in Southeastern Arizona (SEAZ) to address these questions. However, this technology has not been widely employed to evaluate soils. The current study addresses whether pXRF and XRF data obtained from the same soil samples …

Silicon And Tin Substituted Halocyclopropanes: Approaches To New Carbenes And Strained Cyclic Allenes, Noura Srour

Honors Theses

Chloro(trimethylsilyl)carbene and chloro(trimethylstannyl)carbene were generated through photolysis of cyclopropanated phenanthrene precursors which were synthesized in two steps. The photolysis reactions were done in the presence of cis and/or trans-beta-methylstyrene. Though product peaks corresponding to the carbene-alkene adducts were observed in the GCMS, the yields were too low for their isolation and complete characterization. Density functional theory (DFT) calculations were performed on the stereoisomers of the precursor to Chloro(trimethylsilyl)carbene and the carbene itself. Surprisingly, Chloro(trimethylsilyl)carbene’s triplet state was found to be more stable than the singlet at this level of theory.

In a related project, (1-bromo-1a,9b-dihydro-1H-cyclopropa[l]phenanthren-1-yl)trimethylstannane, was …

Mechanism Design, Matching Theory And The Stable Roommates Problem, Yashaswi Mohanty

Honors Theses

This thesis consists of two independent albeit related chapters. The first chapter introduces concepts from mechanism design and matching theory, and discusses potential applications of this theory, particularly in relation to dorm allocations in colleges. The second chapter investigates a subset of the dorm allocation problem, namely that of matching roommates. In particular, the paper looks at the probability of solvability of random instances of the stable roommates game under the condition that preferences are not completely random and exogenous but endogenously determined through a dependence on room choice. These probabilities are estimated using Monte-Carlo simulations and then compared with …

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 …

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 …