Doctor of Philosophy, University of Toledo, 2006, Mathematics

We study the tangent TG and cotangent bundles T*G of a Lie group G which are also Lie groups. Our main results are to show that on TG the canonical Jacobi ndomorphism field S is parallel with respect to the canonical Lie group connection Lie group and that dually on the cotangent bundle of G the canonical symplectic form is parallel with respect to the canonical connection. We next prove some theorems for Lie algebra extensions in which we can obtain a group representation for the extended algebra from the representation of the lower dimensional algebra. We also determine the Lie algebra of the automorphism group of three well known Lie algebras. Finally we study the Hamilton-Jacobi separability of conformally flat metrics and find a metric, Lagrangian and geodesics for the solvable codimension one nilradical six dimensional Lie Algebras where one exists.

Doctor of Philosophy, The Ohio State University, 2020, Political Science

Do fluctuations in climate spur violence? Across a variety of stakeholders, there is an intuitive expectation that climate factors influence conflict in vulnerable areas. While existing research suggests that there might be a relationship between climate and conflict, the exact linkage between the two remains an open question. Contemporary research in this area suffers from three main gaps: it often uses incomplete measures for climate that generate unreliable results; many studies employ statistical methods that do not accurately model the underlying data structure of the conflict outcome; and most studies use theoretical models of conflict participation that cannot account for variation at the micro-level. To address these gaps, this dissertation leverages spatially disaggregated climate data, original data collected during fieldwork in Uganda, and improved modeling strategies to explore the links between climate and conflict at the macro, meso, and micro levels. I propose a coherent theoretical framework through which we can understand how climate volatility impacts individual decision-making and drive violence. I argue that climate volatility heightens feelings of uncertainty among small-holder farmers; discomfort with feelings of uncertainty pushes individuals to try and seek certainty in a variety of ways. One way to find certainty, although not the only one, is to align with social groups that can offer psycho-social and economic benefits to membership. Armed groups and micro-finance social groups are examples of social groups that benefit from this certainty seeking behavior. Individual efforts to reduce uncertainty results in a larger pool of potential supporters and recruits for social groups, which can lead to the occurrence of violence. As the pace of anthropogenic climate change accelerates and uncertainty increases, a nuanced understanding of the climate-conflict relationship is critical for protecting those most at risk. Clarifying the links between (open full item for complete abstract)

Ph.D., Antioch University, 2017, Leadership and Change

The purpose of this study is to gain knowledge about the relationship between sponsor and sponsee in Al-Anon Family Groups from the perspective of sponsors and sponsees in Al-Anon. The main question guiding my research is: What is the nature and quality of the sponsorship relationship as perceived by sponsors and sponsees? Nineteen men and women were interviewed and shared stories of their experience of being a sponsor and a sponsee in the Al-Anon program. I utilized a holistic-content approach to analyze the date from the interviews. To help situate the findings in current literature a discussion of sponsorship in Alcoholics Anonymous, therapy, mentoring, and other helping groups is provided. The findings suggest that there are similarities between Al-Anon sponsorship and mentoring in that both relationships progress through stages of development. The findings suggest that boundaries are an important aspect of Al-Anon that helps its members to healthily detach from other people. Al-Anon members are motivated to help based on the culture of helping found in the program as seen through its service structure and sponsorship. The leadership that Al-Anon sponsors provide finds connections with several leadership theories including, transformational, servant, relational, and authentic leadership. The electronic version of this dissertation is at AURA: Antioch University and Repository Archive, https://aura.antioch.edu/ and Ohio Link ETD Center, https://etd.ohiolink.edu

MS, University of Cincinnati, 2016, Engineering and Applied Science: Computer Science

Today, large number of companies are migrating to the cloud, leaving behind the concept of maintaining traditional data centers and servers. The main reasons for this migration include reduced capital costs, reduced expenditure on infrastructure and ease of accessibility. With the increasing demand for Cloud Computing and the changing needs of users, a need to make the services on the cloud dynamic in nature is essential. However, dynamic services require constant costly updates and highly meticulous configurations. One such dynamic service offered by Amazon Web Services (AWS) is Auto Scaling Groups (ASGs). With this service, AWS facilitates automatic scale up and scale down on the count of servers (instance resources) based on the ASG policies and conditions set by the users. A small misconfiguration or a build failure associated with the Amazon Machine Image (AMI) could cause the dynamism to occur when not actually needed. Since users are charged for the instances by the hour, unnecessary costs occur even if the usage is for as less as a minute. This situation of unnecessary launch and termination of instances is termed as “flaps” and can be compared to oscillations in signals. To prevent energy dissipation in case of oscillating signals, damping of signals is performed. This is similar to the problem of flapping in ASGs. We have come up with a software called AWS Flap Detector as a solution to this problem. AWS Flap Detector efficiently detects and reports flapping Auto Scaling Groups and paves the way for correction. This in turn helps prevent unnecessary resource allocation and billing.

Master of Science, University of Akron, 2010, Mathematics

William Burnside's paqb theorem is a very important result in group theory, which states that any group G of order paqb is solvable. An interesting fact about this theorem is that it was originally proven using techniques from character theory, another branch of algebra. In fact, it was about seventy years before a group-theoretic proof of Burnside's theorem was developed through the work of Goldschmidt, Matsuyama,Bender, and other mathematicians. Their approach to proving the theorem was to show that, in essence, minimally simple groups of size paqb do not exist. Our purpose here is to use various techniques from the group-theoretic proof of Burnside's theorem to establish and prove similar results about minimally simple groups G of arbitrary order.

Master of Science, University of Akron, 2013, Mathematics

Let G be a finite group that is equal to its commutator subgroup, and suppose that G contains an element of order 2 whose centralizer in G is dihedral of 2-power order. We study the cases where this centralizer is dihedral of order 8, 16, 32, 64, 128, or 256. It is true in each case that this centralizer is a Sylow 2-subgroup of G. We then use character-theoretic techniques to generate a list of possibilities for the order of G. In the process of generating this list of possible orders, we prove several results about the structure of our group under consideration. We then strengthen the original hypotheses to require G to be non-abelian simple, and we use the results proved about the structure of G to eliminate all possible orders such that there is no non-abelian simple group of that order.

Bachelor of Arts (BA), Ohio University, 2024, Environmental Studies

Spring Break Sisters is a professional project led by Ohio University undergraduate students to provide a Spring Break Camp to Athens County girls aged 11-14. The inaugural camp ran from March 11th-15th, 2024, at ARTS/West. The camp themes were community, self-care, and empowerment. During the week, ten people participated in an educational nature walk, guest speakers, nature poetry, and the creation of 2 community-themed murals, now on display in the Athens Community Center. The camp was possible through a partnership with Athens, Arts, Parks, and Recreation and by a $5,000 experiential education award from the Center for Advising, Career, and Experiential Learning.

PHD, Kent State University, 2024, College of Arts and Sciences / Department of Mathematical Sciences

The commuting graph of a group is a graph whose vertices are the noncentral elements of the group, and two vertices are connected in the commuting graph if the elements commute. We first investigate the commuting graph of finite, solvable A-groups, groups whose Sylow subgroups are abelian. We determine when the commuting graph of a solvable A-group will be connected and prove that, when connected, the diameter of the commuting graph will be at most 6. Next, we briefly turn our attention to commuting graphs of p-groups, where p is a prime. We build off work that established there was no universal upper bound on the diameter of the commuting graph by constructing a family of p-groups whose commuting graphs have increasing diameters. Lastly, we define the cyclic graph of a group to be the graph whose vertices are the nontrivial elements of a group, and two vertices are connected in the cyclic graph if the elements generate a cyclic subgroup. We investigate the cyclic graph of a finite, solvable A-group and establish an upper bound for the diameter. More specifically, if Z(Gi), where Gi is the i-th term in the derived series, we establish that when the deleted enhanced power graph is connected, it will have diameter at most 6+4i. For A-groups of derived length 2, we prove an even stronger bound of 8 for the diameter.

Doctor of Business Administration (D.B.A.), Franklin University, 2024, Business Administration

This research study explores how employee resource groups (ERGs) impact individual employee voice behaviors. The study is grounded in the spiral of silence theoretical framework (Codington-Lacerte, 2020; Noelle-Neumann, 1974), with the concepts of psychological safety, social identity, social exchange, and self-efficacy explored as mediating factors. The study consists of a qualitative, single case study at an organization that recently established ERGs. Seventeen employees were interviewed, representing eleven of the organization's twelve ERGs. Results from the study support the application of the spiral of silence theoretical framework at the individual employee level. Thematic analysis was used to identify themes in the data, which demonstrate that ERGs impact individual voice behaviors through building relationships, creating cultural change, and empowering individuals.

Doctor of Education , University of Dayton, 2024, Educational Administration

Minorities working at predominantly white institutions (PWI) of higher education face many challenges. One critical challenge is feeling a sense of belonging (SoB) in their organization. In this qualitative study six members of ERG's at a large PWI in the Midwest were interviewed. Participants varied, in race, gender, age, and role at the University. Three themes emerged which were identity, belonging, and University support. The findings revealed that ERG membership does have a significant impact on the (SoB) for minority staff. The recommended action steps focus on the theme of University support in the forms of funding, access to information, acknowledgment of the voluntary efforts of staff, and informing new and existing staff of the existence of ERG's.

Master of Sciences, Case Western Reserve University, 2021, EECS - Computer and Information Sciences

We prove some new results regarding binary and n-ary totally symmetric and medial (TSM) quasigroups and explore their applications to cubic curves and cryptography. We first generalize to the n-ary case Etherington's result that a product in binary TSM quasigroup is symmetric in factors whose depths differ by a multiple of 2 in the corresponding product tree. We then demonstrate that there are an equal number of the four following labeled structures over any finite set: abelian groups, n-ary abelian groups, TSM quasigroups, and n-ary TSM quasigroups. Next we explore applications of quasigroups in cryptography and discuss how our maps between abelian groups, TSM quasigroups, and n-ary TSM quasigroups can be used to generate and easily calculate products in quasigroups for use in cryptosystems. Finally, we discuss the TSM quasigroup of points on a cubic curve and prove some properties of iterated squaring in prime-order TSM quasigroups.

Doctor of Philosophy, The Ohio State University, 2020, Political Science

This dissertation presents an exploration of anxiety for politics distinct from previous study in political psychology. Previous studies report on anxiety's potential to mobilize the electorate. Anxiety has been shown to bring political activation, to help sustain the collective action needed for civic and political participation, to increase willingness for compromise, to encourage political learning, and to increase trust in experts. But for many, the political world underlies much of their anxiety. Consider members of marginalized groups, many of whom are chronically taxed by politics, which can rewire neural networks in the brain and which leaves them with less available mental bandwidth to conduct themselves civically and politically. Taken together, I predict members of marginalized groups respond differently to anxiety than members of non-marginalized groups. While non-marginalized persons can muster their cognitive resources to channel anxiety into action, the precarious situations of many marginalized people merits devoting their cognitive resources elsewhere, leaving them demobilized by their anxiety. In Chapter 2 I lay bare this theory and annotate specific hypotheses. In Chapter 3 I launch a preregistered survey experiment to test my theory among a sample of Black subjects, White subjects, and Hispanic subjects, on welfare and off. Findings offer support for a heterogeneous understanding of anxiety's effects. Higher levels of anxiety caused the marginalized to be less likely to express an interest in voting than the non-marginalized. Furthermore, the interactive effect of race and welfare status inhibited participation the most among the intersectionally marginalized. In Chapter 4 I offer robustness tests for my hypotheses, testing for moderated mediation in particular. In Chapter 5 I conclude by discussing the broad implications of my findings, how government and politics can foster anxiety among the masses, but in particular the negative consequences i (open full item for complete abstract)

PHD, Kent State University, 2019, College of Arts and Sciences / Department of Mathematical Sciences

For a p-group G and an irreducible character χ of G, the codegree of χ is given by |G:ker(χ)|/χ(1). We investigate the relationship between the codegrees and nilpotence class of p-groups. If the set of codegrees of the irreducible characters of G has order 4, and G either has coclass at most 3, largest character degree p2, or |G:G'|=p2, then the nilpotence class of G is at most 4. Similar conditions exist which guarantee the existence of p2 as a codegree of G. If |G|=pn then cod(G) contains all powers of p up to pn-1 if and only if G satisfies one of three cases in which G has maximal class or nilpotence class at most 2. We find families of maximal class groups which have consecutive p-power codegrees.

Doctor of Philosophy (Ph.D.), Bowling Green State University, 2017, Mathematics

Quasiconformal mappings were first utilized by Grotzsch in the 1920's and then later named by Ahlfors in the 1930's. The conformal mappings one studies in complex analysis are locally angle-preserving: they map infinitesimal balls to infinitesimal balls. Quasiconformal mappings, on the other hand, map infinitesimal balls to infinitesimal ellipsoids of a uniformly bounded eccentricity. The theory of quasiconformal mappings is well-developed and studied. For example, quasiconformal mappings on Euclidean space are almost-everywhere differentiable. A result due to Pansu in 1989 illustrated that quasiconformal mappings on Carnot groups are almost-everywhere (Pansu) differentiable, as well. It is easy to show that a biLipschitz map is quasiconformal but the converse does not hold, in general. There are many instances, however, where globally defined quasiconformal mappings on Carnot groups are biLipschitz. In this paper we show that, under certain conditions, a quasiconformal mapping defined on an open subset of a Carnot group is locally biLipschitz. This result is motivated by rigidity results in geometry (for example, the theorem by Mostow in 1968). Along the way we develop background material on geometric group theory and show its connection to quasiconformal mappings.

Doctor of Philosophy, The Ohio State University, 1974, Graduate School

Doctor of Philosophy, The Ohio State University, 2016, Mathematics

In this dissertation, we study the action dimension of general Artin groups. Please review the abstract in the dissertation to see a complete abstract.

PHD, Kent State University, 2014, College of Arts and Sciences / Department of Mathematical Sciences

Let G be a finite group and let cd(G) be the set of irreducible character degrees of G. The character degree graph Δ(G) of G is the graph whose set of vertices is the set of primes dividing an element of cd(G), with an edge between p and q if pq divides some element of cd(G). We say G is almost simple provided S ≤ G ≤ Aut(S) for some simple group S, which is the socle of G, Soc(G). Here we determine the character degree graphs of almost simple groups whose socle is one of PSL3(q), PSU3(q2), or Sz(q). We also discuss Δ(G) for almost simple G with other socles.

Doctor of Philosophy, The Ohio State University, 2013, Mathematics

We study deformations of discrete groups generated by linear re ections and associated geometric structures on orbifolds via cohomology of Coxeter groups with coecients in the adjoint representation associated to a discrete representation. We completely describe a cochain complex that computes this cohomology for an arbitrary discrete re ection group and, as a consequence of this description, give a vanishing theorem for cohomology in dimensions greater than 2. As an application, we discuss some situations in which the cohomology vanishes in dimension 2 as well. In particular, we are able to give a proof of a recent result of Choi and Lee on deforming a certain class of hyperbolic orbifolds through non-hyperbolic projective structures in cohomological language and give some insight into how the result can be extended.

Master of Science in Mathematics, Youngstown State University, 2011, Department of Mathematics and Statistics

In 1961 Roger W. Carter proved a theorem about solvable groups similar to Sylow's theorem. He proved that if a group is solvable then it always contains a nilpotent, self-normalizing subgroup called a Carter subgroup, and that all such subgroups are conjugate to each other by an element of the group. The objective of this thesis is to present a proof of Carter's theorem.

Master of Science in Mathematics, Youngstown State University, 2011, Department of Mathematics and Statistics

The Classification of Finite Simple Groups was a prominent goal of algebraists. The Classification Theorem was complete in 1983 and many textbooks from the 1980s include detailed proofs and explorations of many aspects of this subject. For example, J.J. Rotman devotes an entire chapter to the Mathieu groups [13]. It seems that there is still disagreement amongst mathematicians as to whether the Classification Theorem should be deemed thorough or without major error. Looking into the entire Classification Theorem would be a huge undertaking, so in this paper we are discussing only the five sporadic Mathieu groups. Looking at these small sporadic simple groups opened up a discussion of transitivity and k-transitivity. In addition to traditional abstract algebra material, this paper explores a relationship between the five sporadic Mathieu groups and the combinatorial Steiner Systems. Included in this discussion is the relationship of M24 with the Binary Golay Code. This thesis ends in a proof of the simplicity of the Mathieu Groups. The proof of the simplicity of M11 and M23 which was developed by R. Chapman in his note, An elementary proof of the Mathieu groups M11 and M23 makes the preliminary theorems to the simplicity proof in J.J. Rotman's book look much less perfunctory [2],[13]. This raises the question of whether there could possibly be a more succinct proof of the simplicity of M12, M22 and M24.