Physical Sciences and Mathematics Commons^™

Solving The Yang-Baxter Matrix Equation, Mallory O. Jennings

Honors Theses

The Yang-Baxter equation is one that has been widely used and studied in areas such as statistical mechanics, braid groups, knot theory, and quantum mechanics. While many sets of solutions have been found for this equation, it is still an open problem. In this project, I solve the Yang-Baxter matrix equation that is similar in format to the Yang-Baxter equation. I try to solve the corresponding Yang-Baxter matrix equation, ������=������, where X is an unknown ������ matrix, and ��=[0����0] or [0−��−��0], by using the Jordan canonical form to find infinitely many solutions.

Investigating The Effects Of Decreased Ph On The Intertidal Shore Crab, Hemigrapsus Nudus, Avni Gandhi

Honors Theses

Ocean acidification has emerged as an issue for marine organisms, due to increased levels of CO2 in the atmosphere. In particular, invertebrates with calcium carbonate exoskeletons seem to be at risk. Our research investigates the potential effect of decreased pH on the weight of Hemigrapsus nudus, a species of intertidal crab found in Northern California. Over a 6 week period, crabs were maintained in individual containers with recirculating chilled seawater at 12.7°C. The control aquaria was maintained at 8.1 pH, while the experimental aquaria averaged a pH of 7.5. Crabs were weighed at two week intervals, preliminary information shows the …

Epoch, Latitude And Star Positions From Hipparchus’ Commentary, Irene Vargas-Salazar

Honors Theses

No abstract provided.

Paleoecological Analysis Of The Clayton Formation (Paleocene) Near Malvern, Arkansas, Brenna J. Hart

Honors Theses

The Clayton Formation is a section of the Midway Group immediately above the Cretaceous-Paleogene boundary that contains marine fossils from the Paleocene Epoch. The formation is composed of glauconitic sand, clay, marl, and limestone. Fossils within the formation commonly occur in clay or are concentrated in conglomeratic lag lenses. To assess paleoecology of the region during the Paleocene, the Clayton Formation was sampled for fossil content at a distinctly visible exposure along Interstate 30 near Malvern, Arkansas, that was excavated as part of a landslide mitigation project. Complimentary sites were sampled nearby along the Ouachita River and behind a shopping …

Synthesis Of Polythioether Nanoparticles Via Thiol-Alkene/Alkyne Photopolymerization In Miniemulsion, Susan E. Walley

Honors Theses

Emulsion-based processes – such as miniemulsion polymerizations – provide well-studied synthetic routes to polymer nanomaterials. Miniemulsion polymerizations are characterized as aqueous dispersions of small, narrowly distributed monomer droplets created through high shear and stabilized against Ostwald ripening/collisional degradation by addition of an appropriate surfactant and costabilizer. In this work, thiol–alkene/alkyne photopolymerization in miniemulsion is demonstrated as a simple, rapid, and one-pot synthetic approach to polythioether nanoparticles with tuneable particle size and clickable functionality. Nanoparticles with mean particle diameters ranging from 45 nm to 200 nm were synthesized through simple modifications to the miniemulsion formulation and processing parameters. Facile access to …

Kinetic Study Of Conjugated Polymer Packing And Agglomeration, Skye R. Travis

Honors Theses

Although organic electronic materials are flexible, cheap to fabricate, and molecularly tunable, their performance has generally been less efficient than that of their inorganic counterparts. Chemical doping has been attempted as a method to increase the efficiency of organic materials. During this process, an organic material, typically a conjugated polymer, is exposed to an oxidant/reductant, called a dopant. Electron transfer between host polymer and dopant molecules increases the charge carrier density in the doped host material, making it a more efficient conductor. The effects of doping using 2,3,5,6-tetrafluoro-tetracyanoquinodimethane (F4TCNQ) on low molecular weight poly(3-hexylthiophene-2,5-diyl) (LMW P3HT) in varying ratios of …

Synthesis Of A Thermally Reversible Cross-Linked System Using Electrophilic Cleavage/Functionalization Of Poly(Isobutylene-Co-Isoprene), Savannah H. Steadman

Honors Theses

Multifunctional polyisobutylenes (PIBs) are of great academic and commercial interest. Current methods to create these materials currently utilize prohibitively expensive synthetic strategies. Recently, Storey et al. reported a novel method for the synthesis of multifunctional PIB which is more commercially viable than the current methods. For this research, the material produced via this technique was utilized to create a thermally reversible crosslinked system using Diels-Alder chemistry. To achieve this, a bromide-functional polyisobutylene obtained via electrophilic cleavage and functionalization of butyl rubber was split into two portions and further functionalized. The first portion of the bromide-functional PIB was reacted with furfuryl …

Type 1a Supernova Models And Galactic Chemical Evolution, Spencer Henning

Honors Theses

Multiple models of type Ia supernovae are discussed, as well as the properties of white dwarf formation, electron degeneracy pressure, nucleosynthesis, and galactic chemical evolution (GCE). A GCE computer model is used to produce nuclear abundance data corresponding to Chandra (W7) and sub-Chandra (WDD2) type Ia supernovae models for Ca, Sc, Ti, V, Cr, and Mn nuclei. Overall, a trend was found indicating that the WDD2 model had greater [x/Fe] abundance values than the W7 model at the end time of the model. Additionally, each model fit within total observed data, but observed data filtered to highlight white dwarf stars …

Extraction Studies Of Toxic Multiply Charged Oxoanions From Aqueous Media Using Nanojars, Hartman Christian

Honors Theses

In this paper, the potential of nanojars as extracting agents of chromate and arsenate from aqueous media into a non-polar organic medium is investigated. Nanojars are a class of compounds that consist of multiple [cis-CuII(μ-OH)(μ-pz)]n cyclic polymerization isomers (n = 6, 8, 9, 10, 12, 14; pz = pyrazolato anion) that form from self-assembly reactions around a multiply-charged oxoanion core with capping counterions to render an overall neutral complex. This incarcerates the anion, preventing it from escaping the complex without the use of any covalent bonding, making it a potentially highly effective and unique extracting agent. We have concluded that …

How To Plan, Budget, Write, And Implement A Student Sustainability Grant, Annalisa Wilder

Honors Theses

The Student Sustainability Grant program was created to give students valuable grant writing experience and to promote a culture of sustainability on Western Michigan University’s campus. Despite the enormous opportunity that this program provides, few students apply for the grants with their sustainable ideas. Even fewer students are able to fully complete the projects, research, and initiatives that receive funding. In order to help increase the number of grants that are fully implemented and to provide students interested in writing a grant with a useful resource, this guide was created. This ‘how-to manual’ provides an undergraduate student’s perspective on the …

The Technological Revolution And Data Science, Leslie Walcott

Honors Theses

What was once only depicted in science fiction is now a reality: computers are taking jobs from humans. As technology improves, automation is transforming the workplace. They say a “fourth industrial revolution” is inevitable within the next ten years. In the industrial revolution, the jobs lost were unskilled laborers, such as coal miners, textiles manufacturers, or cotton workers. There was no argument for whether or not a machine could do the jobs more efficiently--it was fact. The term technological unemployment means the loss of jobs caused by technological change. The headline, “Factory workers replaced by automation,” is not particularly startling …

The Regularity Lemma And Its Applications, Elizabeth Sprangel

Honors Theses

The regularity lemma (also known as Szemerédi's Regularity Lemma) is one of the most powerful tools used in extremal graph theory. In general, the lemma states that every graph has some structure. That is, every graph can be partitioned into a finite number of classes in a way such that the number of edges between any two parts is “regular." This thesis is an introduction to the regularity lemma through its proof and applications. We demonstrate its applications to extremal graph theory, Ramsey theory, and number theory.

Sum-Defined Colorings In Graphs, James Hallas

Honors Theses

There have been numerous studies using a variety of methods for the purpose of uniquely distinguishing every two adjacent vertices of a graph. Many of these methods have involved graph colorings. The most studied colorings are proper colorings. A proper coloring of a graph G is an assignment of colors to the vertices of G such that adjacent vertices are assigned distinct colors. The minimum number of colors required in a proper coloring of G is the chromatic number of G. In our work, we introduce a new coloring that induces a (nearly) proper coloring. Two vertices u and …

Karst Sub-Basin Delineation Via Dye Trace Study Near Turnhole Bend, Mammoth Cave National Park, Jake Tholen

Honors Theses

Establishing watershed boundaries is a critical stage in understanding the local water cycle. Drainage basins are typically identified by topographic divides; water flows to successively lower locations along the most direct path available. The karst terrain in Mammoth Cave National Park, however, presents additional challenges in identifying the boundaries of these basins. Underground drainages in the form of caves or conduits often do not correspond with surface topography. These passages can redirect water far from the most immediate surface release.

A dye trace study is designed to identify flow paths from the surface to springs along the Green River. Three …

Fluorescence Analysis Of Pamam Dendrimers, Ansel Nam

Honors Theses

Despite their lack of conjugation, polyamidoamine (PAMAM) dendrimers are intrinsically fluorescent, and this fluorescent is somewhat manipulable through altering the dendrimer's solvent. This level of fluorescence is dependent on a number of the dendrimer's qualities: the pH of the solvent, the mass percent concentration of the dendrimer in solvent, and the generation size of the dendrimer. In past studies, fluorescent intensity increased as generation size increased and pH decreased. Thus, this research project will attempt to replicate those results as well as further analyze the efficiency of fluorescence of PAMAM dendrimer in comparison to fluorescein.

War Gaming Applications For Achieving Optimum Acquisition Of Future Space, Karel Marshall

Honors Theses

In 2014, the federal government spent nearly half a trillion dollars on contractor projects. The Department of Defense wants to develop an algorithm to optimize the acquisition of new technologies. This project makes us of game theory, probability and statistics, non-linear programming and mathematical models to model negotiations between governmental agencies and private contractors. If focuses on generating the optimum solution and its corresponding acquisition strategy for different contract types. This project culminates in a collection of MATLAB (MathWorks) programs and the newly developed strategy shows strong convergence to Nash equilibrium values and successful selection of optimum solutions.

Molecular Mass Of L-Arginine-Based Potentially Carcinogenic Heterocyclic Amines, Irene S. Hwang

Honors Theses

Investigation of cancer-inducing molecules in cooked foods has led to the discovery of mutagenic heterocyclic amines (HCAs) in meat. The amino acids creatin(in)e and L-phenylalanine form the precursors for these HCAs. Recent research here at Andrews University have found similar mutagenic HCAs produced from plant-based proteins when L-arginine, rather than creatin(in)e, is substituted in high temperature reactions (simulated cooking) with L-phenylalanine. Our research focused on developing HPLC methods to isolate individual candidates that are then screened for mutagenicity via the Ames test. Mass spectroscopy methods were also developed to identfy the molecular structure of these lead mutagenic L-arginine-based HCAs.

The Effects Of Structural Modification Of The Wing Helix Domain Of Pria On Bacterial Dna, Erich Auer

Honors Theses

During a cell’s life it must copy itself or face death. For the cell to form a new copy it must replicate its DNA, this DNA is the blueprint for the essential components of the cell. The replication process does not always go to completion, which is necessary for the cell to survive, so there are mechanisms to keep the replication process running smoothly. In bacteria, PriA is used to restart replication after damage to the DNA. By looking at the structure of PriA we can start to determine how exactly it works with the damaged DNA and restart the …

Optimized Multilayered Thermal Emitters For Photovoltaic, Lighting, And Countermeasure Technologies, Simón G. Lorenzo

Honors Theses

No abstract provided.

Synthesis Of Β-Methyl-L-Cysteine As A Model For A Β-Methyl-D-Cysteine Building Block For Incorporation Into Microbisporicins, Elora C. Doskey

Honors Theses

No abstract provided.

Synthesis Of Bis(Quinoxalino) Ligand For The Removal Of Transition Metal Contamination, Alexander J. Farmer

Honors Theses

Transition metal contamination is a constant concern both in the environment and in chemical reaction mixtures. One proposed solution, is the use of peraza-crown macrocycles to selectively bind and remove transition metals. The aim of our project is to determine the novel synthesis of bis(quinoxalino) peraza-crown macrocycles for use as ligands to bind to transition metals. Our proposed molecules incorporate the rigid quinoxaline subunit into an aza-crown macrocycle which can improve binding properties. The synthesis route is novel and overcomes several limitations of the existing methods of aza-crown macrocycle preparation. We have designed the synthesis in such a way that …

Extending Uniqueness Implies Existence Results To Fractional Differential Equations, Tyler Masthay

Honors Theses

In 1967, Andrzej Lasota and Zdzisław Opial proved that under sufficient conditions, uniqueness of solutions for boundary value problems for a second-order ordinary differential equation implies their existence. Lloyd Jackson and Keith Schrader then proved an extension of this result for boundary value problems of third order. In proving the third-order case, this compactness theorem is applied as a key part of the proof. It states that under sufficient conditions, uniform boundedness of a sequence of solutions on a compact domain implies existence of a subsequence which converges uniformly with respect to its zeroth, first, and second derivatives. We present …

Preparation, Analysis And Derivatization Of Benzotris(Thiazole) Triamine, Jonathan Patrick Peter Alessi

Honors Theses

Multiple fields are areas of active research where organic materials hold considerable promise, such as thermoelectrics or photovoltaics. In an effort to design and prepare a new system which would exhibit a set of promising features such as high thermal stability, high degree of planarity, rigid skeleton and strong electron accepting properties, we have undertaken the preparation and characterization of benzotrithiazole and its derivatives. Our work has led to a reproducible and scalable protocol for the generation of one particular structure: benzo[1,2-d:3,4-d':5,6-d"]tris(thiazole)-2,5,8-triamine. We have also conducted further attempts to functionalize this structure, leading to other derivatives of the target compound.

Effects Of Increased Sedimentation On Carbon Accumulation Of Salt Marsh Benthic Biofilms, Abbey Hotard

Honors Theses

No abstract provided.

Effects Of Timber Harvest On Avian Abundance And Diversity, Mckenzie Brandon

Honors Theses

No abstract provided.

Influence Of Nutrient Availability And Sediment Supply On Productivity Of Spartina Patens, Shannon Matzke

Honors Theses

No abstract provided.

Capturing Omni-Stereo Panoramas Within Unreal Engine 4, Evan Preslar

Honors Theses

No abstract provided.

Holographic Scaling In Newtonian Gravity, Emma Machado

Honors Theses

Many high school and college students are required to take physics, but few actually learn to discover the mysteries of the field, because they are too busy trying to memorize equations and solve "plug and chug" style problems. Looking into the calculations and equations of physics, a holography can be seen within the subject. This holography can be discovered and made accessible to general physics students, by studying the duality that exists between Electricity and Gravity. Furthermore, the concept of mass in physics (M_ADM) can be calculated, within this holography, for various black holes along with the …

Identity Theft: A Look Into Preventing Decades Of Damages, Mallory Monaco

Honors Theses

Each year identity theft victimizes more people, taking their time, money, and feeling of financial and physical security. Despite its ongoing presence in the news and media, this fraud is too often treated in a reactive manner. Due to the lack of prevention of identity theft, its negative consequences range from damaging one’s credit score for decades to cases of medical identity theft incorrectly altering a patient’s medical records and causing potentially life threatening complications. This thesis examines four major types of identity theft, including medical identity theft, credit card fraud, consumer data breaches, and the identity theft associated with …

Elliptic Curve Cryptography And Quantum Computing, Emily Alderson

Honors Theses

In the year 2007, a slightly nerdy girl fell in love with all things math. Even though she only was exposed to a small part of the immense field of mathematics, she knew that math would always have a place in her heart. Ten years later, that passion for math is still burning inside. She never thought she would be interested in anything other than strictly mathematics. However, she discovered a love for computer science her sophomore year of college. Now, she is graduating college with a double major in both mathematics and computer science.

This nerdy girl is me. …