Browsing Pure Mathematics Theses by Title
Now showing items 120 of 39

Adventures in applying iteration lemmas
(University of St Andrews, 20130628)  ThesisThe word problem of a finitely generated group is commonly defined to be a formal language over a finite generating set. The class of finite groups has been characterised as the class of finitely generated groups that ... 
Aspects of order and congruence relations on regular semigroups
(University of St Andrews, 1983)  ThesisOn a regular semigroup S natural order relations have been defined by Nambooripad and by Lallement. Different characterisations and relationships between the Nambooripad order J, Lallement's order λ and a certain relation ... 
Cayley automaton semigroups
(University of St Andrews, 20150626)  ThesisLet S be a semigroup, C(S) the automaton constructed from the right Cayley graph of S with respect to all of S as the generating set and ∑(C(S)) the automaton semigroup constructed from C(S). Such semigroups are ... 
Classification and enumeration of finite semigroups
(University of St Andrews, 20100623)  ThesisThe classification of finite semigroups is difficult even for small orders because of their large number. Most finite semigroups are nilpotent of nilpotency rank 3. Formulae for their number up to isomorphism, and up ... 
A commutative noncommutative fractal geometry
(University of St Andrews, 2010)  ThesisIn this thesis examples of spectral triples, which represent fractal sets, are examined and new insights into their noncommutative geometries are obtained. Firstly, starting with Connes' spectral triple for a nonempty ... 
Constructing 2generated subgroups of the group of homeomorphisms of Cantor space
(University of St Andrews, 2017)  ThesisWe study finite generation, 2generation and simplicity of subgroups of H[sub]c, the group of homeomorphisms of Cantor space. In Chapter 1 and Chapter 2 we run through foundational concepts and notation. In Chapter 3 we ... 
Dimension and measure theory of selfsimilar structures with no separation condition
(University of St Andrews, 20151130)  ThesisWe introduce methods to cope with selfsimilar sets when we do not assume any separation condition. For a selfsimilar set K ⊆ ℝᵈ we establish a similarity dimensionlike formula for Hausdorff dimension regardless of any ... 
Dimension theory and fractal constructions based on selfaffine carpets
(University of St Andrews, 20131129)  ThesisThe aim of this thesis is to develop the dimension theory of selfaffine carpets in several directions. Selfaffine carpets are an important class of planar selfaffine sets which have received a great deal of attention ... 
Dimension theory of random selfsimilar and selfaffine constructions
(University of St Andrews, 20170623)  ThesisThis thesis is structured as follows. Chapter 1 introduces fractal sets before recalling basic mathematical concepts from dynamical systems, measure theory, dimension theory and probability theory. In Chapter 2 we give ... 
Directed graph iterated function systems
(University of St Andrews, 20111130)  ThesisThis thesis concerns an active research area within fractal geometry. In the first part, in Chapters 2 and 3, for directed graph iterated function systems (IFSs) defined on ℝ, we prove that a class of 2vertex directed ... 
Dots and lines : geometric semigroup theory and finite presentability
(University of St Andrews, 20150626)  ThesisGeometric semigroup theory means different things to different people, but it is agreed that it involves associating a geometric structure to a semigroup and deducing properties of the semigroup based on that structure. ... 
Endomorphisms of Fraïssé limits and automorphism groups of algebraically closed relational structures
(University of St Andrews, 20121130)  ThesisLet Ω be the Fraïssé limit of a class of relational structures. We seek to answer the following semigroup theoretic question about Ω. What are the group Hclasses, i.e. the maximal subgroups, of End(Ω)? Fraïssé limits for ... 
Ends of semigroups
(University of St Andrews, 2013)  ThesisThe aim of this thesis is to understand the algebraic structure of a semigroup by studying the geometric properties of its Cayley graph. We define the notion of the partial order of ends of the Cayley graph of a semigroup. ... 
Finiteness conditions for unions of semigroups
(University of St Andrews, 20130628)  ThesisIn this thesis we prove the following: The semigroup which is a disjoint union of two or three copies of a group is a Clifford semigroup, Rees matrix semigroup or a combination between a Rees matrix semigroup and a ... 
Flatness, extension and amalgamation in monoids, semigroups and rings
(University of St Andrews, 1986)  ThesisWe begin our study of amalgamations by examining some ideas which are wellknown for the category of Rmodules. In particular we look at such notions as direct limits, pushouts, pullbacks, tensor products and flatness in ... 
Generalized Bernstein polynomials and total positivity
(University of St Andrews, 1999)  Thesis"This thesis submitted for Ph.D. degree deals mainly with geometric properties of generalized Bernstein polynomials which replace the single Bernstein polynomial by a oneparameter family of polynomials. It also provides ... 
Generating "large" subgroups and subsemigroups
(University of St Andrews, 2016)  ThesisIn this thesis we will be exclusively considering uncountable groups and semigroups. Roughly speaking the underlying problem is to find “large” subgroups (or subsemigroups) of the object in question, where we consider ... 
Generating uncountable transformation semigroups
(University of St Andrews, 2009)  ThesisWe consider naturally occurring, uncountable transformation semigroups S and investigate the following three questions. (i) Is every countable subset F of S also a subset of a ﬁnitely generated subsemigroup of S? If so, ... 
Generation problems for finite groups
(University of St Andrews, 20111130)  ThesisIt can be deduced from the Burnside Basis Theorem that if G is a finite pgroup with d(G)=r then given any generating set A for G there exists a subset of A of size r that generates G. We have denoted this property B. A ... 
The geometry of selfaffine fractals
(University of St Andrews, 2008)  ThesisIn this thesis we study the dimension theory of selfaffine sets. We begin by introducing a number of notions from fractal geometry, in particular, dimensions, measure properties and iterated functions systems. We give ...