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...
The present thesis is focused on developing a better understanding of factors driving disease biology and overall risk using cancers of the bladder and breast as model systems. As no single approach was likely to unravel the complexities of these...
The Euler '-function and Carmichael -function are extremely important in modern number theory, and much work has been devoted to studying the distribution and arithmetic properties of the values of each function. One interesting unresolved question...
In Chapter 2 we look at the distribution of permutation statistics in the context of pattern-avoiding permutations. The first part of this chapter deals with a recursively defined bijection of Robertson [37] between 123- and 132-avoiding...
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...
In this thesis we look at several problems that lie in the intersection between combinatorial and multiplicative number theory. A common theme of many of these problems are estimates for and properties of the smooth numbers, those integers not...
Partially ordered sets and permutations are combinatorial structures having vast applications in theoretical computer science. In this thesis, we study various computational and algorithmic problems related to these structures. The first chapter of...
Brain mapping via EEG activation is a useful tool of basic neuroscience, and has wide clinical applications as well. The mapping is achieved by means of Event Related Potentials (ERPs), task-related changes in EEG time series. The methodology of...
Social networks -- Mathematical models. Social networks -- Computer simulation. Dynamics. Social sciences -- Network analysis -- Methodology.
Detecting the significance of relationships between people is a complicated and difficult task. This is especially true when these relationships are intermixed with hundreds of different mundane and ordinary interactions that are simply background...
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...