Physical Sciences and Mathematics Commons^™

Almost Difference Sets In 2-Groups, Xin Yutong

Honors Theses

Difference sets have been studied for decades due to their applications in digital communication, cryptography, algebra, and number theory. More recently, mathematicians have expanded their focus to the field of almost difference sets. Almost difference sets have similar functionalities with difference sets, yet with more potential of finding new constructions. In this paper I will introduce the definitions, properties, and applications of difference sets and almost difference sets, and discuss our effort and results in the exploration of almost difference sets in cyclic and non-cyclic groups.

Aldol Condensations And Nitrile Aldol Reactions Mediated By Trimethylsilyl Trifluoromethanesulfonate, Samuel R. Bottum

Honors Theses

In the presence of excess trimethylsilyl trifluoromethanesulfonate (TMSOTf), ketones and esters undergo aldol addition and dehydration to yield chalcones and cinnamates. This one-pot reaction proceeds through in situ enol silane formation, avoiding the need to pre-form and purify the nucleophile in the Mukaiyama aldol reaction. The stoichiometry of the TMSOTf controls whether the reaction proceeds with simple addition or addition-dehydration. When (trimethylsilyl) acetonitrile is stirred with an aldehyde and TMSOTf, nitrile aldol addition is observed.

Internal Migration Of Foreign-Born In Us: Impacts Of Population Concentration And Risk Aversion, Thin Yee Mon Su

Honors Theses

Internal migration in the US has been declining since the 1990s and research has mostly focused on labor market dynamics and aging population to explain the migration trends. This paper analyzes migration patterns of foreign-born groups in the US from 2000 to 2019. Along with the migration determinants such as education and employment, the paper focuses on population concentration as a factor that shapes foreign-born decisions to relocate in the US. Population concertation is defined to be a measure of how geographically concentrated each foreign-born group is across the US. I find that the likelihood of migrating to another state …

Biasing Medial Axis Rapidly-Exploring Random Trees With Safe Hyperspheres, David Qin

Honors Theses

Motion planning is a challenging and widely researched problem in robotics. Motion planning algorithms aim to not only nd unobstructed paths, but also to construct paths with certain qualities, such as maximally avoiding obstacles to improve path safety. One such solution is a Rapidly-Exploring Random Tree (RRT) variant called Medial Axis RRT that generates the safest possible paths, but does so slowly. This paper introduces a RRT variant called Medial Axis Ball RRT (MABallRRT) that uses the concept of clearance -- a robot's distance from its nearest obstacle -- to efficiently construct a roadmap with safe paths. The safety of …

Fast Medial Axis Sampling For Use In Motion Planning, Hanglin Zhou

Honors Theses

Motion planning is a difficult but important problem in robotics. Research has tended toward approximations and randomized algorithms, like sampling-based planning. Probabilistic RoadMaps (PRMs) are one common sampling-based planning approach, but they lack safety guarantees. One main approach, Medial Axis PRM (MAPRM) addressed this deficiency by generating robot configurations as far away from the obstacles as possible, but it introduced an extensive computational burden. We present two techniques, Medial Axis Bridge and Medial Axis Spherical Step, to reduce the computational cost of sampling in MAPRM and additionally propose recycling previously computed clearance information to reduce the cost of connection in …

Connectiveity And Structures Of Coloring Graphs, Xin Yutong

Honors Theses

Reconfiguration problems have been studied and applied to solve problems in various areas, including Math, Computer Science, and Chemistry. Due to the close relatedness between coloring graphs and reconfiguration problems, the connectivity and structure of coloring graphs give valuable information to a solution set of the corresponding reconfiguration problem. In this paper we will discuss 2--connectedness and cut-vertices of coloring graphs, and forbidden structures on a coloring graph wit cut-vertices.

Nanoparticles As Alternative Ceramic Glaze Colorants, Nathan Dinh

Honors Theses

Metallic nanoparticles, including gold and silver, have been used in wide-ranging applications due to their versatile characteristics. These include catalysis, biosensing, imaging, cancer treatments, and art. Due to the phenomenon called surface plasmon resonance, metallic particles change optical properties when sized in the nanoscale based on their composition, shape, diameters, or aspect ratios. In study, these robust nanoparticle systems are applied as an alternative to traditional bulk metal colorants in ceramic glazes.

In this study, the research goals are two-fold: to understand firing mechanism on the gold nanoparticle size and to develop these processes for wider use by regular artisans. …

Synthesis, Characterization, And Reactivity Of Palladium Proazaphosphatrane Complexes, Adrian D. Matthews

Honors Theses

Palladium-catalyzed cross-coupling reactions provide an efficient pathway to a wide variety of otherwise inaccessible compounds. In this study, the synthesis and reactivity of novel palladium proazaphosphatrane complexes that are believed to be intermediates in C–N cross-coupling reactions are described. Both the fundamental reactivity of these complexes and elementary steps involved in a catalytic process are demonstrated. The catalytic viability of palladium proazaphosphatrane complexes is shown through stoichiometric and catalytic cross-coupling reactions. Our findings support the long-standing hypothesis that proazaphosphatranes are conformationally flexible ligands that stabilize a number of catalytic intermediates.

Design Of New Ruthenium Complexes For Photoactivated Chemotherapy, Lindsey Paul

Honors Theses

Photoactivated chemotherapy (PACT) offers a targeted approach to cancer treatment through selective drug activation. Substitutionally labile ruthenium-based prodrugs undergo ligand-loss when irradiated, producing an unbound ligand and a Ru-aqua complex. We report the synthesis and cytotoxicity of several new ruthenium-centered complexes and their irradiation products for use in PACT. A series of complexes were synthesized in order to study the effects of structural differences on cell viability. Cell viability was tested on T47D human breast cancer cells in the presence of compound to determine cytotoxicity and dose-response. While neither the Rucomplexes nor their ligands demonstrated cytotoxicity, their Ru-aqua dissociation complexes …

Estimating Value-At-Risk Of An Unconventional Portfolio, Elizabeth N. Mejía-Ricart

Honors Theses

Since the 2008 financial crisis, interest rates and bond yields have been low all through the recovery and expansion that followed, and they are still low. As a result, more investors have been attracted to US equities, a space of possibly higher returns. However, these returns come with a potential downside: risk of loss. One of the methods to assess this potential downside is value-at-risk (VaR), which gained momentum in the late 1990s. At the time, the market risk amendment to the 1988 Basle Capital Accord required commercial banks with significant trading activities to put aside capital to cover market …

Computer-Assisted Coloring-Graph Generation And Structural Analysis, Wesley Su

Honors Theses

Graphs are a well studied construction in discrete math, with one of the most common areas of study being graph coloring. The graph coloring problem asks for a color to be assigned to each vertex in a graph such that no two adjacent vertices share a color. An assignment of k colors that meets these criteria is called a k-coloring. The coloring graph Ck(G) is defined as the graph where every vertex represents a valid k-coloring of graph G and edges exist between colorings that di↵er by one vertex. We call graph G the base graph of the k-coloring graph …