In this dissertation, we begin by presenting the result of F. K. C. Rankin and Swinnerton-Dyer on the location of the zeros of the Eisenstein series for the full modular group in the standard fundamental domain. Their simple but beautiful argument shows that all zeros are located on the lower...
We identify all translation covers among triangular billiards surfaces. Our main tools are the J-invariant of Kenyon and Smillie and a property of triangular billiards surfaces, which we call fingerprint type, that is invariant under balanced translation covers.
The purpose of this study is to develop experimental techniques to
characterize typical interconnect discontinuities, including bends, steps, T
junctions, vias and pads, which are the most commonly encountered
interconnections in high speed digital integrated circuits, hybrid and
monolithic microwave circuits and electronic packages. The time domain
reflection response of...
The question of deep time has been widely debated in the field of American Literature, with scholar Wai Chee Dimock arguing that a deep time perspective puts the chronology of different nations against one another. However, this argument has not adequately addressed the issue of how deep time theories would...
In this note, we generalize recent work of Mizuhara, Sellers, and Swisher that gives a method for establishing restricted plane partition congruences based on a bounded number of calculations. Using periodicity for partition functions, our extended technique could be a useful tool to prove congruences for certain types of combinatorial...
One of the most powerful and life-changing events that can occur in the life of a family is
the death of a child. Researchers who have studied death and bereavement suggest that a
child's death has a dramatic impact on parents. However, little is known about the ways
in which...
We generalize overpartition rank and crank generating functions to obtain k-fold variants, and give a combinatorial interpretation for each. The k-fold crank generating function is interpreted by extending the first and second residual cranks to a natural infinite family. The k-fold rank generating functions generate two families of buffered Frobenius...
The behavior and application of organic semiconductor materials depend strongly on their molecular structure, and molecular interactions. Several studies of intermolecular interactions in functionalized polyacene materials are presented. The degree and onset of aggregation of a functionalized anthradithiophene derivative was studied as a function of concentration in two different host...