Browsing Pure Mathematics Theses by Issue Date
Now showing items 120 of 49

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 ... 
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 ... 
Some group presentations with few defining relations
(University of St Andrews, 1990)  ThesisWe consider two classes of groups with two generators and three relations. One class has a similar presentation to groups considered in the paper by C.M. Campbell and R.M. Thomas, ‘On (2,n)Groups related to Fibonacci ... 
Semigroups of orderdecreasing transformations
(University of St Andrews, 1992)  ThesisLet X be a totally ordered set and consider the semigroups of orderdecreasing (increasing) full (partial, partial onetoone) transformations of X. In this Thesis the study of orderincreasing full (partial, partial ... 
The construction of finite soluble factor groups of finitely presented groups and its application
(University of St Andrews, 1992)  ThesisComputational group theory deals with the design, analysis and computer implementation of algorithms for solving computational problems involving groups, and with the applications of the programs produced to interesting ... 
Semigroup presentations
(University of St Andrews, 1995)  ThesisIn this thesis we consider in detail the following two fundamental problems for semigroup presentations: 1. Given a semigroup find a presentation defining it. 2. Given a presentation describe the semigroup defined by ... 
Presentations and efficiency of semigroups
(University of St Andrews, 1998)  ThesisIn this thesis we consider in detail the following two problems for semigroups: (i) When are semigroups finitely generated and presented? (ii) Which families of semigroups can be efficiently presented? We also consider ... 
Proof search issues in some nonclassical logics
(University of St Andrews, 1999)  ThesisThis thesis develops techniques and ideas on proof search. Proof search is used with one of two meanings. Proof search can be thought of either as the search for a yes/no answer to a query (theorem proving), or as the ... 
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 ... 
Restricted permutations, antichains, atomic classes and stack sorting
(University of St Andrews, 2003)  ThesisInvolvement is a partial order on all finite permutations, of infinite dimension and having subsets isomorphic to every countable partial order with finite descending chains. It has attracted the attention of some celebrated ... 
On permutation classes defined by token passing networks, gridding matrices and pictures : three flavours of involvement
(University of St Andrews, 20070619)  ThesisThe study of pattern classes is the study of the involvement order on finite permutations. This order can be traced back to the work of Knuth. In recent years the area has attracted the attention of many combinatoralists ... 
Simplicity in relational structures and its application to permutation classes
(University of St Andrews, 20071130)  ThesisThe simple relational structures form the units, or atoms, upon which all other relational structures are constructed by means of the substitution decomposition. This decomposition appears to have first been introduced in ... 
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 ... 
Inhomogeneous selfsimilar sets and measures
(University of St Andrews, 2008)  ThesisThe thesis consists of four main chapters. The first chapter includes an introduction to inhomogeneous selfsimilar sets and measures. In particular, we show that these sets and measures are natural generalizations of ... 
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, ... 
Resonances for graph directed Markov systems, and geometry of infinitely generated dynamical systems
(University of St Andrews, 20090624)  ThesisIn the first part of this thesis we transfer a result of Guillopé et al. concerning the number of zeros of the Selberg zeta function for convex cocompact Schottky groups to the setting of certain types of graph ... 
Intersection problems in combinatorics
(University of St Andrews, 20091130)  ThesisWith the publication of the famous ErdősKoRado Theorem in 1961, intersection problems became a popular area of combinatorics. A family of combinatorial objects is tintersecting if any two of its elements mutually ... 
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 ... 
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 ... 
Stable and multistable processes and localisability
(University of St Andrews, 20100623)  ThesisWe first review recent work on stable and multistable random processes and their localisability. Then most of the thesis concerns a new approach to these topics based on characteristic functions. Our aim is to construct ...