Pure Mathematics Theses: Recent submissions
Now showing items 11-15 of 64
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Coincidence and disparity of fractal dimensions
(University of St Andrews, 2021-06-29) - ThesisWe investigate the dimension and structure of four fractal families: inhomogeneous attractors, fractal projections, fractional Brownian images, and elliptical polynomial spirals. For each family, particular attention is ... -
Subdirect products of free semigroups and monoids
(University of St Andrews, 2020-12-01) - ThesisSubdirect products are special types of subalgebras of direct products. The purpose of this thesis is to initiate a study of combinatorial properties of subdirect products and fiber products of semigroups and monoids, ... -
On the regularity dimensions of measures
(University of St Andrews, 2020) - ThesisThis body of work is based upon the following three papers that the author wrote during his PhD with Jonathan Fraser and Han Yu: [FH20, HY17, How19]. Chapter 1 starts by introducing many of the common tools and notation ... -
Orderings on words and permutations
(University of St Andrews, 2019-12-03) - ThesisSubstructure orderings are ubiquitous throughout combinatorics and all of mathematics. In this thesis we consider various orderings on words, as well as the consecutive involvement ordering on permutations. Throughout ... -
Assouad type dimensions and dimension spectra
(University of St Andrews, 2019-12-03) - ThesisIn the first part of this thesis we introduce a new dimension spectrum motivated by the Assouad dimension; a familiar notion of dimension which, for a given metric space, returns the minimal exponent α ≥ 0 such that for ...