McGovern, Warren W.

Within mathematics, the field of algebra focuses primarily on preserving symmetry and structure within a set. This thesis focuses on a given group G over a (commutative) ring R, referred to as the group ring R[G]. Elements within R[G] are finite formal sums of elements of G with coefficients from R. A class of reduced rings that generalizes integral domains is that of complemented rings. We will discuss new subcategories of complemented rings: semi-complemented and almost complemented rings. Since R[G] is a ring itself, we would like to find when R[G] is complemented or perhaps only semi or almost complemented. We will discuss small examples such as Z2[D3] and Zk[Cn].

This thesis delves into the Fontan cardiovascular procedure, a specialized intervention for congenital heart defects. Through historical analysis, preparatory protocols, statistical data, and long-term effects, this paper offers a comprehensive examination of this surgical procedure. It traces its origins, breakthroughs, and milestones, from diagnosis to detailed planning and execution. With approximately 50,000 worldwide cases, statistical analysis explores success rates and demographics. Recognizing its lifelong impact, the research examines postoperative complications, quality of life, and ongoing healthcare needs. This comprehensive scrutiny extends to long-term implications. Additionally, there is a supplementing website conveniently disseminating insights and factual information about the Fontan procedure, fostering greater understanding and awareness among healthcare professionals and the broader community.

In this thesis, titled “Hotel Pricing Strategies in Miami’s Brickell and Coral Gables Neighborhoods,” various statistical techniques and data analytics were employed to examine the current hotel industry in Miami's Brickell and Coral Gables neighborhoods. The central research question examines the prevalence of dynamic pricing in this hotel sector and attempts to identify the most cost-effective time to book hotel rooms in these neighborhoods. The initial hypothesis sought to be proven or disproven is that dynamic pricing is widely used in the hotel industry, meaning there will be a specific time for cost-effective bookings. Moreover, this thesis sought to uncover how hotels in these neighborhoods set their prices for select dates and attempt to categorize them by revenue management techniques. While the research provides insights into the hotel pricing strategies in Brickell and Coral Gables, it acknowledges its limitations due to the sample size and the duration of data collection. These constraints prevent broad generalizations about Miami's entire hotel market.

This investigation presents a method to quantify the progression of different glaucomatous visual field defects detected in 4 patients with chronic open-angle glaucoma using linear algebra. The patients were followed an average of 4.03 years after developing monocular field loss. Either the left or right eye or both eyes showed progression in field changes. For instance, in patient 2, the presenting left eye had severe vision field loss with a greater progression of deterioration than the right eye. Based on standard automated perimetry using a Humphrey’s Visual Field and Frequency Doubling Technology, a dimensional matrix was created to allow physicians to predict the patient’s future visual field, making these matrices translatable to any process in medicine that can be expressed as a linear map. Future studies can answer questions, such as when the optimal time would be for a patient with glaucoma to transition from medicated eye drops to surgery.

The patellar tendon is a largely avascular tendon with a low metabolic rate.
Repeated strain can cause faster breakdown as opposed to healing, resulting in
patellar tendinopathy. As more becomes known about the condition, it is becoming
clear that new treatments need to be developed. Research has shown that
cryotherapy, anti-inflammatory drugs, and corticosteroid injections, though widely
used, are dated and potentially harmful. Other current treatments include physical
therapy, sclerosing and platelet rich plasma (PRP) injections, shock wave therapy,
and surgery. However, none of these treatments has shown significant effectiveness.
Due to a lack of high quality research and intrinsic limitations, it is difficult to make
a definitive conclusion as to the single best treatment. Based on limited existing
data, it is suspected that the best course of action is likely a combination of
treatments, such as employing eccentric exercise, supplemented with PRP.

Abstract algebra is the study of structure, as represented by a set with operations
acting on the set. One such type of structure is known as a ring. Rings themselves are
abstract objects which may be classi ed. Such classi cations become a large area of
study in ring theory. If every instance of a class of rings satis es the de ning property
for another class and vice versa, then they are equivalient classi cations. However, if
every instance of one class satis es the de ning property of the other ring, yet there is
a counterexample of a ring that satis es the latter, but not the former, the latter ring
is generalization of the former. In this thesis, we present a quick survey of foundational
topics in abstract algebra, and discuss main results about von Neumann regular rings,
complemented rings, and nally, fusible rings. We display a counstruction of a ring
that is fusible, yet not complemented, thus concluding that the class of fusible rings
is a generalization of the class of complemented rings.

Reports of a suspected cancer cluster can be frightening for any community. The source of a cancer cluster is often the primary community concern, but it is inherently difficult to link a cluster with any specific environmental agent. This thesis focuses on aspects of cancer clusters such as the official cancer cluster definition and investigation guidelines given by the Centers for Disease Control and Prevention. It explores “Cancer Clusters in the USA: What do the last twenty years of state and federal investigations tell us?” [1], an article which reviewed publicly available cancer cluster investigation reports from 1990 to 2012, and uses a similar methodology to review investigation reports from 2012 to 2016 in the interest of providing more modern data regarding cancer cluster reports.

Socioeconomic status has profound impact on one’s health. A person is
able to spend more on health and wellness when that person has more
disposable income. Socioeconomic status therefore affects people’s biology over
their lifetime, making them more or less susceptible to chronic illness. This rate
of chronic illness within a population will obviously be related to the life
expectancy of the community. Firstly, this thesis examines socioeconomic status
in Washington, D.C., where there is wide inequality between people living only
miles away. Secondly, this thesis correlates, among the eight wards in
Washington, D.C., the different aspects of socioeconomic status to life
expectancy. In an interdisciplinary manner, this thesis aims to analyze the
disparity in life expectancy in Washington, D.C. and the significant factor that
socioeconomic status plays in one’s biological destiny.

One of the most fundamental aspects of the evolution of spoken language over the course of history is the transformation of its speech sounds. These sound change transformations play an important role in the development of grammatical features such as declensional and conjugational paradigms. These sound changes often occur in highly regular patterns which lend themselves readily to mathematical modeling. Thus, we can construct a list of transformation rules that predict the evolution of words from a parent language to a daughter language to a significant degree of accuracy. This thesis constructs a model expressing these sound changes as a function from a set of words in the parent language to a set of words in the daughter language. This theoretical model is then translated to a practical application in C++ programming, and tested using the evolution of Classical Latin to modern standard Spanish as a sample case study.

With the widespread use of the internet, information regarding medical facilities
and practices has never been easier to obtain. This convenience may often prove
beneficial, but using the internet to research topics regarding one's own health creates a
potential for risks. This research addresses these concerns by studying the annual Honor
Roll list of hospitals, a listing published each year by the U.S. News and World Report
that ranks the best medical facilities in the country. To accomplish this, we aimed to
analyze the relationship between the hospitals listed on the Honor Roll and the mortality
rates of the counties in which each hospital is located. Upon completion of this research,
we were unable to find a significant difference between mortality rates of counties with
Honor Roll hospitals and those without.