Browsing Faculty of Graduate Studies Online Theses by Subject "Mathematics"
Now showing items 1-7 of 7
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ANALYSIS OF CLUSTER AND STRIPE SOLUTIONS IN A ONE-DIMENSIONAL MODEL OF BIOLOGICAL AGGREGATION
(2012-05-28)This thesis studies the model of swarming of organisms in groups or clusters and the solution of the interaction equation in a one dimensional biological swarm model. This process describes the behavior of some animal ... -
A Brief Exploration of Total Colouring
(2017-09-05)A total colouring of a graph is an assignment of colours to the edges and vertices such that adjacent objects receive different colours. In this thesis, we prove partial results towards the Total Colouring Conjecture which ... -
LAR's and PLAR's, during SARS
(2022-08-08)The Weak Lefschetz Property (WLP) of polynomial quotient rings is studied in commutative algebra for the implications it has for a ring's Hilbert function, which is a chief object of study in commutative algebra. As ... -
On the algebraic connectivity of graphs
(2022-04-29)Algebraic connectivity, or the second smallest eigenvalue of the Laplacian matrix, is a well-studied parameter in spectral graph theory. In this thesis, we present new upper bounds and asymptotic estimates for the algebraic ... -
The Root of All Dimensions
(2014-08-21)This thesis aims to resolve the disjunction of ontology and epistemology in Platonist mathematical philosophy. This disharmony results from the assumption of the non-spatiotemporal existence of abstract mathematical entities, ... -
SOME CLASSES OF GENERALIZED CYCLOTOMIC POLYNOMIALS
(2019-12-16)For a positive integer n the nth cyclotomic polynomial can be written as Φn(x)=∏︂(x−e^{2pi k/n} ). k∈(Z/nZ)^{×} When n = p is an odd prime, the nth cyclotomic polynomial has the special form ... -
Zero-Forcing Processes on Proper Interval Graphs and Twisted Hypercubes
(2023-04-22)Zero forcing is a graph infection process where a colour change rule is applied iteratively to a graph and an initial set of vertices, S. If S results in the entire graph becoming infected, we call this set a zero forcing ...
