Open Access. Powered by Scholars. Published by Universities.®

Digital Commons Network

Open Access. Powered by Scholars. Published by Universities.®

Mathematics

University of Tennessee, Knoxville

Doctoral Dissertations

Theses/Dissertations

2001

Articles 1 - 2 of 2

Full-Text Articles in Entire DC Network

An Individual-Based Approach To Population Dynamics With Applications To Sockeye Salmon And Iteroparous Organisms, Cynthia Moira Krohn Aug 2001

An Individual-Based Approach To Population Dynamics With Applications To Sockeye Salmon And Iteroparous Organisms, Cynthia Moira Krohn

Doctoral Dissertations

Individual-based models have been used to study the population dynamics of semelparous and iteroparous organisms. The rst model, developed for sockeye salmon ( On-corhynchus nerka), was based on the physiology of the individual and incorporated into a population model via a McKendrick-von Foerster type partial di
erential equation. Cycles of population abundance historically found in the Fraser River system were recreated through model simulations. Explanations for the appearance of the cycling were investigated and tested. The results showed that density- and size-dependent mortality were not necessary for cycling to appear, however their inclusion or exclusion in combination with the type …


Generalizations Of The Zero-Divisor Graph Of A Ring, Shane Patrick Redmond May 2001

Generalizations Of The Zero-Divisor Graph Of A Ring, Shane Patrick Redmond

Doctoral Dissertations

Let R be a commutative ring with 1, and let Z(R) denote the set of zero­divisors of R. We define an undirected graph Γ(R) with vertices Z(R)* = Z(R) - {0}, where distinct vertices x and y of R are connected if and only if xy = 0. This graph is called the zero-divisor graph of R. We extend the definition of the zero-divisor graph to a noncommutative ring in several ways. Next, given a commutative ring R and ideal Ι of R, we introduce the notion of an …