I consider the problem of extending certain invariants of subsets of natural numbers to their equivalents for subsets of larger cardinals. The two specific questions I will address are the extension of the off-branch number [Special characters...
A polynomial is a product of distinct cyclotomic polynomials if and only if it is a divisor over [Special characters omitted.] [x ] of xn - 1 for some positive integer n. In this thesis, we will examine two natural questions concerning the divisors...
Constructibility (Set theory). Trees (Graph theory).
This thesis investigates possible initial segments of the degrees of constructibility. Specifically, we completely characterize the structure of degrees in generic extensions of the constructible universe L via forcing with Souslin trees. Then we...
Phase transitions occur in such diverse and important systems as ferromagnets, liquid crystals and the early Universe. The dynamics of phase transitions such as these have been studied for decades, but the analytical models still need a great deal...
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n ≥11), Spin(n) (n = 9, n ≥11), SU (n) (n ≥7), and Sp (n) (n ≥5). The proof breaks into three...
Magnetosphere -- Mathematical models. Magnetic reconnection -- Mathematical models.
In this thesis we present the results of two studies of magnetic reconnection at the dayside magnetopause using the Lyon-Fedder-Mobarry magnetospheric simulation code. The first study examined the global properties of reconnection as a function of...
This dissertation details the use of a new catalog of Galactic bulge field RR Lyrae variables to advance the understanding of the structure of the Milky Way Galaxy. The catalog contains 3667 RR0 Lyrae stars from the eight-year MACHO Project...
This thesis presents two-fluid simulations of forced magnetic reconnection with finite electron inertia in two and three dimensional periodic systems. Reconnection in the system is driven by a spatially localized forcing function, added to the ion...
Electric generators -- Windings. Electric inductors -- Design and construction -- Mathematical models. Electric current converters -- Design and construction -- Mathematical models. Energy dissipation -- Mathematical models.
Magnetic components for high-frequency power conversion applications can have significant losses that compromise the performance of the converter. In particular, winding losses can be large due to high-frequency effects that are difficult to model...