We investigate the modular properties of a new partition rank, the M-d-rank of overpartitions. In fact this is an infinite family of ranks, indexed by the positive integer d, that gives both the Dyson rank of overpartitions and the overpartition M-2-rank as special cases. The M-d-rank of overpartitions is the...
As dams approach the end of their useful life, there is need to predict where and how accumulated sediment will move following their removal to estimate impacts on aquatic habitat and infrastructure. Flume studies suggest that sediment pulses disperse in place for most dams, but it is hypothesized that a...
In 1956, Alder conjectured an integer partition inequality which generalized Euler’s partition identity, the first Rogers-Ramanujan identity, and a partition identity of Schur. Alder’s conjecture, proved in part by Andrews in 1971, followed by Yee in 2008, and finally completed by Alfes, Jameson, and Lemke Oliver in 2010 states that...
Candidatus Liberibacter solanacearum’ (Lso) is a bacterium that infects solanaceous crops and causes plant decline and yield losses, especially in potato and tomato. Lso is transmitted to these hosts by the potato psyllid (Bactericera cockerelli Sulc) vector. B. cockerelli host plants are not limited to crop plants, but also include...
In 2013, Lemke Oliver created a list of all eta-quotients which are theta functions. Then in 2016, Folsom, Garthwaite, Kang, Swisher, and Treneer utilized this list of ``eta-theta'' functions along with Zwegers's construction of mock theta functions to create a set of mock modular forms which are also quantum modular...
In this dissertation, we consider two problems in number theory, both relating to modular forms. First we consider when a given modular form can be expressed as a quotient in Dedekind's $\eta$ function. Rouse and Webb \cite{RW} have determined the integers $N \leq 500$ such that the graded ring of...
Following the work of Asai, Kaneko, and Ninomiya for Faber polynomials associated to the modular group, and Bannai, Kojima, and Miezaki's partial proof for the case of the Fricke group of level 2, we show that the zeros of certain modular functions for some low-level genus zero groups associated to...
Patients with end-stage renal disease undergoing hemodialysis have a high incidence of oxidative stress-related diseases. This study evaluated oxidative stress and inflammatory markers in patients undergoing hemodialysis before and during vitamin E supplementation. Blood samples were obtained before and after dialysis during two separate dialysis sessions to establish baseline measurements....