• On the coefficients of Drinfeld modular forms of higher rank 

      Basson, Dirk Johannes (Stellenbosch : Stellenbosch University, 2014-04)
      ENGLISH ABSTRACT: Rank 2 Drinfeld modular forms have been studied for more than 30 years, and while it is known that a higher rank theory could be possible, higher rank Drinfeld modular forms have only recently been de ...
    • On the computation of freely generated modular lattices 

      Semegni, Jean Yves (Stellenbosch : Stellenbosch University, 2008-12)
      Please refer to full text for abstract.
    • On the constant reductions of valued function fields and their automorphism groups 

      Razafindramahatsiaro, Tovondrainy Christalin (Stellenbosch : Stellenbosch University, 2015-11-20)
      ENGLISH ABSTRACT : The aim of the project is to investigate properties of the automorphism group of a function field in one variable over an algebraically closed field in relation to its reductions with respect to special ...
    • On the inducibility of rooted trees 

      Dossou-Olory, Audace Amen Vioutou (Stellenbosch : Stellenbosch University, 2018-12)
      ENGLISH ABSTRACT : The density of appearances of a fixed tree in a larger tree is examined for rooted trees without vertices of outdegree 1 (also known as topological trees). Given a topological tree S with k leaves and ...
    • On the Latimer-MacDuffee theorem for polynomials over finite fields 

      Van Zyl, Jacobus Visser (Stellenbosch : University of Stellenbosch, 2011-03)
      ENGLISH ABSTRACT: Latimer & MacDuffee showed in 1933 that there is a one-to-one correspondence between equivalence classes of matrices with a given minimum polynomial and equivalence classes of ideals of a certain ring. ...
    • On the maximum degree chromatic number of a graph 

      Nieuwoudt, Isabelle (Stellenbosch : Stellenbosch University, 2007-12)
      ENGLISH ABSTRACT: Determining the (classical) chromatic number of a graph (i.e. finding the smallest number of colours with which the vertices of a graph may be coloured so that no two adjacent vertices receive the same ...
    • On the numerical evaluation of finite-part integrals involving an algebraic singularity 

      Kutt, H. R. (Helmut Richard) (Stellenbosch : Stellenbosch University, 1975-08)
      ENGLISH ABSTRACT: Some problems of applied mathematics, for instance in the fields of aerodynamics or electron optics, involve certain singular integrals which do not exist classically. The problems can, however, be ...
    • On towers of function fields over finite fields 

      Lotter, Ernest Christiaan (Stellenbosch : University of Stellenbosch, 2007-03)
      Explicit towers of algebraic function fields over finite fields are studied by considering their ramification behaviour and complete splitting. While the majority of towers in the literature are recursively defined by a ...
    • Oriented 123-TQFTs via String-Nets and State-Sums 

      Goosen, Gerrit (Stellenbosch : Stellenbosch University, 2018-03)
      ENGLISH ABSTRACT :In a series of papers Bartlett, Douglas, Schommer-Pries, and Vicary discovered a finite generators-and-relations presentation of the oriented bordism bicategory. This simplifies the task of finding ...
    • Polynomial containment in refinement spaces and wavelets based on local projection operators 

      Moubandjo, Desiree V. (Stellenbosch : Stellenbosch University, 2007-03)
      ENGLISH ABSTRACT: See full text for abstract
    • Properties of graph polynomials and related parameters 

      Misanantenaina, Valisoa Razanajatovo (Stellenbosch : Stellenbosch University, 2017-12)
      ENGLISH ABSTRACT : In this thesis, we investigate various problems related to graph polynomials. We first define two-variable polynomials for rooted trees and specific posets, which are motivated by the Tutte polynomial. ...
    • Random walk hitting times in random trees 

      Oosthuizen, Joubert (Stellenbosch : Stellenbosch University, 2017-12)
      ENGLISH ABSTRACT : The hitting time Hxy, between two vertices x and y of a graph, is the average time that the standard simple random walk takes to get from x to y. We start by giving a recursive formula for higher moments ...
    • Rank matrix cascade algorithm, hermite interpolation 

      Dongmo, Guy Blaise (Stellenbosch : University of Stellenbosch, 2007-12)
      ENGLISH ABSTRACT: (Math symbols have changed) Wavelet and subdivision techniques have developed, over the last two decades, into powerful mathematical tools, for example in signal analysis and geometric modelling. Both ...
    • Refinable functions with prescribed values at the integers 

      Gavhi, Mpfareleni Rejoyce (Stellenbosch : Stellenbosch University, 2012-03)
      ENGLISH ABSTRACT: See full text
    • Refinable vector splines and multi-wavelets with shortest matrix filters 

      Ranirina, Dinna (Stellenbosch : Stellenbosch University, 2018-03)
      ENGLISH ABSTRACT : A widely used class of basis functions in signal analysis is obtained from the dilation and integer shifts of a given (compactly supported) wavelet ψ : R → R, by means of which a (scalar) signal can ...
    • Sensitivity analysis of multilayer neural networks 

      Engelbrecht, Andries Petrus (Stellenbosch : Stellenbosch University, 1999-12)
      ENGLISH ABSTRACT: The application of artificial neural networks to solve classification and function approximation problems is no longer an art. Using a neural network does not simply imply the presentation of a data set ...
    • Solving embedding problems with bounded ramification 

      Ramiharimanana, Nantsoina Cynthia (Stellenbosch : Stellenbosch University, 2016-12)
      ENGLISH ABSTRACT : Given a Galois extension K/K0 of number fields, a finite group G, and an epimorphism α: G→ Gal(K/K0) with solvable kernel, our goal is to embed K into a Galois extension N of K0 with Galois group ...
    • Spectral theory in commutatively ordered banach algebras 

      Muzundu, Kelvin (Stellenbosch : Stellenbosch University, 2012-12)
      ENGLISH ABSTRACT: See full text.
    • Spreading waves of invasive species 

      Ramanantoanina, Andriamihaja (Stellenbosch : Stellenbosch University, 2014-03)
      ENGLISH ABSTRACT: Invasive species are well known to harm economy as well as ecological assets and impair ecosystems functioning around the world. Timely control and management of new incursions of invasive species ...
    • Stochastic visual tracking with active appearance models 

      Hoffmann, McElory Roberto (Stellenbosch : University of Stellenbosch, 2009-12)
      ENGLISH ABSTRACT: In many applications, an accurate, robust and fast tracker is needed, for example in surveillance, gesture recognition, tracking lips for lip-reading and creating an augmented reality by embedding a ...