In this thesis, we consider several problems relating to cyclic subgroups of the group [mathematical equation]. Each element of [mathematical equation] has a unique representative in one of the two intervals [mathematical equation] and...
Polynomials. Finite fields (Algebra). Algebraic functions. Number theory.
The ring of univariate polynomials over a finite field shares many foundational arithmetic properties with the ring of rational integers. This similarity makes it possible for many problems in elementary number theory to be translated 'through the...
Let K be the function field over a finite field of odd order, and let H be a definite quaternion algebra over K. If Α is an order of level M in H , we define theta series for each ideal I of Α using the reduced norm on H. Using harmonic analysis...
Metal ions. Binding sites (Biochemistry) -- Thermodynamics. Metalloenzymes. Cellular control mechanisms. Thermometric titration. Calorimetry.
The chemistry of biology is complex and there is a great deal that is not understood. A fundamental understanding of biochemical reactions is important to aid in the identification of undiscovered reactions and is critical to fully appreciate the...
We start by introducing avoidance coupling of Markov chains, with an overview of existing results. We then introduce and motivate a new notion, uniform coupling. We show that the only Markovian avoidance coupling on a cycle is of this type, and...
We consider a problem of information overload: the conflict between vast amounts of data available in electronic form and inadequate tools for finding relevant information. To alleviate this problem we look at the information organization:...
Spectral theory is the subfield of differential geometry which provided the solution to Kac''s famous question, "Can you hear the shape of a drum?" That is, can we use the Laplace spectrum of a manifold to draw conclusions about its geometry or...
In this thesis we study 1=k-geodesics, those closed geodesics that minimize on any subinterval of length L=k, where L is the length of the geodesic. These curves arise as critical points of the uniform energy, a function introduced in Morse theory...
This thesis investigates the embedding theory of orders in central simple algebras, placing a particular emphasis on the role that the phenomenon known as selectivity plays in the theory. Although the notion of selectivity is completely algebraic,...
The accelerated expansion of space in the Universe has been known for two decades. However, finding a plausible theory that describes this expansion is more difficult: Taking general relativity for granted requires us to stipulate the existence of...
Predictive control. Adaptive control systems -- Design. Airplanes -- Control systems.
A direct method to design data-based model predictive controllers is presented. The design method uses system identification techniques to identify model predictive controller gains directly from a set of excitation input and disturbance corrupted...