McGovern, Warren

Statistics within different modes of health care suggest that inequalities exist between differing racial and ethnic subgroups, with some groups experiencing higher rates of positive health care outcomes as opposed to others. This thesis is a review of different sectors of health care and focuses to determine rates of inequalities between treatment of patients, rates of incidence among disseminating groups and focuses on representation of ethnic and racial minorities and to better illuminate how these problems affect people’s lives. It was found that discrepancies exist between the health care outcomes and incidence between Non-Hispanic White and Asian populations versus Non-Hispanic African, Native American/Alaskan Native, and Hispanic populations, as more negative outcomes and treatment within medicine are associated with the latter.

Symmetries are a driving force in the universe and continue to reveal themselves
the deeper we look. While many undergraduate mathematics students
are introduced to symmetries with group theory, many practical applications
are often overlooked. The application of symmetries provides
deep insights into various problems and can frequently simplify complex
mathematics. Applying symmetries typically requires high-level mathematics
that can be prohibitive for people within other disciplines. As such,
this paper explores how Lie groups, a mathematical structure for representing
symmetries, can be utilized in computing, physics, and control theory
to solve practical problems from within these elds. It also serves as an
introduction to the mathematics necessary to utilize Lie groups.

The familiar definition of differentiability in Real Analysis has a natural analogue in Complex Analysis. In this thesis we will first develop the theory of single-variable complex differentiable functions, focusing on integration. Next, we will explore how the class of complex differentiable functions compares to the class of real differentiable functions. Finally, we will examine several applications of Complex Analysis to problems in Real Analysis.

Before Godel's incompleteness theorems, logicians such as Bertrand Russel and Alfred Whitehead pursued an ideal axiomatic system which would have created a reliable framework to successfully prove or refute every mathematical sentence. Godel proved that such systems can never be created. In fact, Godel's incompleteness theorems establish that axiomatic systems that are complex enough to formulate arithmetic can never generate a proof of all the logical statements that are expressible inside of them. According to the first incompleteness theorem, there are constructible mathematical sentences that can never be proven to be true or false using the axioms and the logical rules of the system. Furthermore, the second incompleteness theorem argues that the consistency of all axiomatic systems which contain Peano or Robinson arithmetic can never be determined using the rules and the proof mechanisms available in the system.

In this thesis I will be using natural language processing techniques, particularly text classification and language modeling with Naïve Bayes, to categorize data from social networks such as Facebook, Twitter, and Instagram in order to optimize the user experience. The categorical classifications will serve as meaningful events that may occur in people’s lives so that the user may essentially filter posts for important content such as anniversaries, birthdays, job promotions, or relocation of friends in an application setting. I will apply the algorithm using the Java programming language and the Eclipse Integrated Development Environment.

A common problem surrounding piezoelectric transducers is matching the highimpedance
active piezoelectric element with a low-impedance load, typically water
or skin. This is a common problem with medical devices [Ali00]. Matching layers
are added in an attempt to gradually decrease the impedance of the active piezoelectric
element down to the impedance of water. If the impedance is not gradually
decreased, acoustic waves are reflected at the boundaries that are proportional to
the impedance mismatch of the two materials. A dual-matching layer transducer is
analyzed, and we attempt to optimize the impedances and thicknesses of the two
matching layers using statistical design of experiments.

Arend Lijphart claims low voter turnout plagues democratic countries because it causes elections to be unrepresentative of the electorate. Therefore, he believes that compulsory voting is the only way to solve this ―unresolved dilemma.‖ Proponents of compulsory voting also argue that increased voter participation has positive effects on a country. This paper will not only evaluate the effects of compulsory voting on certain aspects of citizens’ welfare, but also citizens’ overall satisfaction with their life and government. In order to measure each of these elements, I will look at income equality, level of government corruption, and democracy ranking. I will also use the World Values Survey to compare the feelings of citizens towards their life and government in countries with compulsory voting to those of citizens in countries with voluntary voting. I hypothesize that there will not be significant differences between the two electoral systems.

Determining the minimum rank of a graph has been actively studied in combinatorial matrix theory over the past decade. Given a simple, undirected graph G on n
vertices, the problem is to determine the minimum rank over all real, symmetric
n x n matrices whose nonzero off-diagonal entries occur in the positions corresponding to the edges of G. We use graph decompositions such as cliques, cycles, complete bipartites, etc. to help determine the minimum rank. Our focus rests on decompositions using cliques and clique-stars. We note that cliques and clique-stars have minimum rank of 1 and 2 respectively. Such a decomposition is useful for the set of chordal graphs. A chordal graph is one that does not have an induced k-cycle, k ≥ 4. We use cliques and clique-stars to determine the minimum rank of chordal graphs with either three cliques or one clique and one clique-star in a decomposition. We highlight an example that demonstrates the difficulty of calculating the minimum rank.