Physical Sciences and Mathematics Commons^™

Analysis And Treatment Of Emerging Polar Contaminants, Daniel E. Connors

Electronic Theses and Dissertations

Two major classes of polar compounds have recently become a major focus as sources of contamination of water systems. Pharmaceuticals and personal care products (PPCPs) enter water through wastewater streams, and many of these compounds survive current wastewater treatment processes. High production volume chemicals (HPVCs), defined as chemicals produced in excess of one million pounds per year have numerous entries into surface and drinking waters due to their ubiquity. The commonality between many of these compounds is their polarity, which makes them water-soluble.

While both PPCPs and HPVCs have been entering into the environment for decades, advances in analyte detection …

Permutation Patterns, Reduced Decompositions With Few Repetitions And The Bruhat Order, Daniel Alan Daly

Electronic Theses and Dissertations

This thesis is concerned with problems involving permutations. The main focus is on connections between permutation patterns and reduced decompositions with few repetitions. Connections between permutation patterns and reduced decompositions were first studied various mathematicians including Stanley, Billey and Tenner. In particular, they studied pattern avoidance conditions on reduced decompositions with no repeated elements. This thesis classifies the pattern avoidance and containment conditions on reduced decompositions with one and two elements repeated. This classification is then used to obtain new enumeration results for pattern classes related to the reduced decompositions and introduces the technique of counting pattern classes via reduced …