Pure Mathematics Theses: Recent submissions

Now showing items 11-15 of 64

    • Coincidence and disparity of fractal dimensions 

      Burrell, Stuart Andrew (University of St Andrews, 2021-06-29) - Thesis
      We 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 

      Clayton, Ashley (University of St Andrews, 2020-12-01) - Thesis
      Subdirect 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 

      Howroyd, Douglas Charles (University of St Andrews, 2020) - Thesis
      This 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 

      McDevitt, Matthew (University of St Andrews, 2019-12-03) - Thesis
      Substructure 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 

      Yu, Han (University of St Andrews, 2019-12-03) - Thesis
      In 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 ...