A set S of vertices in a graph G is a paired dominating set if every vertex of G is adjacent to a vertex in S and the subgraph induced by S contains a perfect matching (not necessarily as an induced subgraph). The minimum cardinality of a paired dominating set of G is the paired domination number of G. This chapter presents a survey of the major results on paired domination with an emphasis on bounds for the paired domination number.

With the proliferation of computers into homes and businesses and the explosive growth rate of the Internet, the ability to conduct secure electronic communications and transactions has become an issue of vital concern. One of the most prominent systems for securing electronic information, known as RSA, relies upon the fact that it is computationally difficult to factor a "large" integer into its component prime integers. If an efficient algorithm is developed that can factor any arbitrarily large integer in a "reasonable" amount of time, the security value of the RSA system would be nullified. The General Number Field Sieve algorithm is the fastest known method for factoring large integers. Research and development of this algorithm within the past five years has facilitated factorizations of integers that were once speculated to require thousands of years of supercomputer time to accomplish. While this method has many unexplored features that merit further research, the complexity of the algorithm prevents almost anyone but an expert from investigating its behavior. We address this concern by first pulling together much of the background information necessary to understand the concepts that are central in the General Number Field Sieve. These concepts are woven together into a cohesive presentation that details each theory while clearly describing how a particular theory fits into the algorithm. Formal proofs from existing literature are recast and illuminated to clarify their inner-workings and the role they play in the whole process. We also present a complete, detailed example of a factorization achieved with the General Number Field Sieve in order to concretize the concepts that are outlined. / Master of Science

This work is an experimental study of the effect of impinging distance on the heat transfer from a cylinder to turbulent isothermal and non-isothermal jets. The isothermal jet is discharged horizontally at the same temperature as the ambient air while the non-isothermal jet is discharged vertically upwards and vertically downwards at a temperature colder than the ambient air. Temperature measurements are made on a heated cylinder using an infrared (IR) camera at five equal impinging distances ranging from Z/d =4 to Z/d=20 and the distributions of the local Frossling numbers are determined. The overall decrease in the average Frossling numbers of the cylinder impinged by the isothermal jet and the cold jets was 25 % and 40% respectively. The peak values of average Frossling number for the isothermal and the cold jets occurred at Z/d=8 and Z/d=4 respectively. The Stagnation Frossling number and the normalized jet centerline velocity for the isothermal and the cold jets were found to be very close to each other at all impinging distances indicating that the effect of buoyancy is negligible in the range of jet temperatures and distances used in the experiment. / Master of Science

This paper discusses the concepts in algebraic and analytic number theory used in the proofs of Dirichlet's and Cheboterev's density theorems. It presents special cases of results due to the latter theorem for which greatly simplified proofs exist. / Master of Science

The aim of this paper is to exhibit analogs in Number Theory of certain well known theorems and methods of the Theory of Equations.

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published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

published_or_final_version / Mathematics / Master / Master of Philosophy

This dissertation investigates syntactic and semantic agreement in Czech, French, Latvian, Persian, Romanian, Russian, Serbian/Croatian, and Turkish. When more than one target agrees with a controller with a mismatch between its form and meaning, different patterns of agreement are attested: uniform syntactic agreement (e.g. these/*this pants are/*is cute), uniform semantic agreement (e.g. this aircraft is fast/ these aircraft are fast), and mixed agreement (e.g. this/*these committee has/have decided in British English). Diverse agreement patterns are shown to arise through an interaction of three components of agreement: different types of agreement controllers, different types of agreement targets, and the Agreement Marking Principle (Wechsler and Hahm to appear). A distinction between CONCORD, INDEX, and semantic agreement features is adopted (Wechsler and Zlatic 2003). Agreement controllers are specified for different phi-features in CONCORD and INDEX. The types of agreement targets differ in whether they are sensitive to the CONCORD or INDEX features of their controllers. The relation between controllers and targets is governed by the Agreement Marking Principle, which states that an agreement target checks for a feature of its controller, but the target defaults to semantics when its controller lacks the feature. For example, the noun committee in British English is specified for singular in CONCORD but lacks number in INDEX, and thus a CONCORD target (e.g. a demonstrative determiner) agrees in singular syntactically, whereas an INDEX target (e.g. a finite verb) defaults to semantics because it fails to find an INDEX number feature specified for the controller. This research focuses on agreement with polite second person plural pronouns across languages. Such pronouns are plural but can refer politely to a single addressee. All languages discussed exhibit syntactic agreement on finite verb targets when the controller is a polite plural pronoun, while other types of target vary across languages in how they agree. This generalization is explained by two factors: pronouns possess INDEX features and finite verbs are necessarily INDEX targets if they are specified for the person feature, which only belongs to INDEX. A Hybrid Pronoun generalization, which encompasses all types of hybrid pronouns, is supported by evidence from Indo-European and non-Indo-European languages. / text

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