Class Notes for Math 918: Homological Conjectures, Instructor Tom Marley

This course was an overview of what are known as the “Homological Conjectures,” in particular, the Zero Divisor Conjecture, the Rigidity Conjecture, the Intersection Conjectures, Bass’ Conjecture, the Superheight Conjecture, the Direct Summand Conjecture, the Monomial Conjecture, the Syzygy Conjecture, and the big and small Cohen Macaulay Conjectures. Many of these are shown to imply others. This document contains notes for a course taught by Tom Marley during the 2009 spring semester at the University of Nebraska-Lincoln. The notes loosely follow the treatment given in Chapters 8 and 9 of Cohen-Macaulay Rings, by W. Bruns and J. Herzog, although many other sources, including articles and monographs by Peskine, Szpiro, Hochster, Huneke, Grith, Evans, Lyubeznik, and Roberts (to name a few), were used. Special thanks to Laura Lynch for putting these notes into LaTeX.

Effects of addition of a bird repellent to fish diets on their growth and bioaccumulation

The effects of adding the nonlethal bird repellent methyl anthranilate (MA), at levels of 100 and 1000 mg/kg, to fish feed on the bioaccumulation and growth of juvenile (10 g) hybrid striped bass (Morone chrysops x M. saxatilis) and juvenile (1g) African cichlid fish Aulonocara jacobfreibergi were investigated under laboratory conditions. The bird repellent did not have any effect on the fish growth or survival over a period of 6 weeks. MA residues at low levels of 11.2 ± 2.6 mg/g were found in lipophilic tissues (liver) of MA-fed fish. Control fish, which had no MA added to their diet, had a much lower level of 0.6 ± 0.3 mg/g MA in their liver. Fish muscle was found to contain negligible MA residues, while the outer body surface mucus did not contain any MA. Following a 6-week depuration period, during which the previously MA-fed hybrid striped bass were fed a feed to which no MA was added, the levels of MA residues detected were reduced by one order of magnitude.