Department of Mathematical Sciences
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Nevanlinna Theory and Rational Values of Meromorphic Functions
(Stellenbosch : University of Stellenbosch, 2019-04)ENGLISH ABSTRACT: In this thesis, we are concerned with the problem of counting algebraic points of bounded height and degree on graphs of certain transcendental holomorphic and meromorphic functions. Adopting a Nevanlinna ... -
A simple ecological model captures the transmission pattern of COVID-19 outbreak in China
(BioMed Central, 2020)Background The rapid spread of the 2019 novel coronavirus disease (COVID-19), initially reported in the city of Wuhan in China, and quickly transmitted to the entire nation and beyond, has become an international ... -
Near-vector spaces constructed from near domains
(Miskolci Egyetemi Kiado, 2018)In this paper we prove some new results on near-vector spaces and near domains and give a first application of the nearring of quotients with respect to a multiplicative set, namely we construct a new class of near-vector ... -
Why does not the leaf weight-area allometry of bamboos follow the 3/2-power law?
(Frontiers Media, 2018)The principle of similarity (Thompson, 1917) states that the weight of an organism follows the 3/2-power law of its surface area and is proportional to its volume on the condition that the density is constant. However, the ... -
Spatial segregation facilitates the coexistence of tree species in temperate forests
(MDPI, 2018)Competition between plants has an important role during the natural succession of forest communities. Niche separation between plants can reduce such interspecific competition and enable multispecies plant to achieve ... -
Calibrating a stochastic SIR-model to simulated data using different calibration methods : a tutorial & comparison of methods
(Stellenbosch : Stellenbosch University., 2020-04)ENGLISH ABSTRACT: Mathematical models have helped researchers identify and quantify trends in observed data, which is especially useful in the field of epidemiology. Fitting models to data enhances the credibility of ... -
Drinfeld modular forms of higher rank from a lattice-oriented point of view
(Stellenbosch : Stellenbosch University., 2020-04)ENGLISH ABSTRACT: Please refer to full text for abstract -
Comparison of old and new algorithms for s,t -network reliability
(Stellenbosch : Stellenbosch University., 2020-04)ENGLISH ABSTRACT: Network reliability is the probability of an operative path connecting the source s with the terminal t. s, t-network reliability problems have been proven to be #P-complete. In this thesis we present ... -
Torsion bounds for Drinfeld modules with complex multiplication
(Stellenbosch : Stellenbosch University., 2020-04)ENGLISH ABSTRACT: The main objective of the present thesis is to prove an analogue for Drinfeld modules of a theorem due to Clark and Pollack. The cardinality of the group of K-rational torsion points of an elliptic curve ... -
Influence of rotation on transversely isotropic piezoelectric rod coated with a thin film
(Polish Academy of Sciences, 2018)In this paper, the influence of rotation on axisymmetric waves of a piezoelectric rod coated with a thin film is studied using constitutive form linear theory elasticity and piezo-electric equations. Potential functions ... -
On the distribution of subtree orders of a tree
(University of Primorska, 2018)We investigate the distribution of the number of vertices of a randomly chosen subtree of a tree. Specifically, it is proven that this distribution is close to a Gaussian distribution in an explicitly quantifiable way if ... -
Upscaling biodiversity : estimating the species–area relationship from small samples
(Ecological Society of America, 2018)The challenge of biodiversity upscaling, estimating the species richness of a large area from scattered local surveys within it, has attracted increasing interest in recent years, producing a wide range of competing ... -
Drivers of species turnover vary with species commonness for native and alien plants with different residence times
(Ecological Society of America, 2018)Communities comprising alien species with different residence times are natural experiments allowing the assessment of drivers of community assembly over time. Stochastic processes (such as dispersal and fluctuating ... -
Weighing evidence
(Author retain copyright, 2019-12)Often different pieces of evidence of different degrees of credibility are submitted in legal proceedings. Then a court “weighs” the evidence and arrives at a conclusion. But how should evidence be weighed? The use of ... -
Explicit bound on Siegel zeros of imaginary quadratic fields
(Stellenbosch : Stellenbosch University, 2019-12)ENGLISH ABSTRACT: Please refer to full text for abstract. -
Weighted centrality, and a further approach to categorical commutativity
(Stellenbosch : Stellenbosch University, 2019-12)ENGLISH ABSTRACT: We investigate weighted commutators, that is, weighted subobject commutator and weighted normal commutator, as well as commutators in the sense of Huq, Higgins, Ursini and Smith, which are all special ... -
Concrete foundations of the theory of Noetherian forms
(Stellenbosch : Stellenbosch University, 2019-12)ENGLISH ABSTRACT: This thesis concerns certain investigations in abstract algebra that bring together the ideas of the category of algebraic structures and the lattice of substructures. A central notion in such investigation ... -
Contributions to the theory of Beidleman near-vector spaces
(Stellenbosch : Stellenbosch University, 2019-12)ENGLISH SUMMARY: (Please refer to the abstract on the full text for symbols that did not translate well into this abstract). The study of nearfields was started in 1905 by L.E. Dickson. This thesis is a first step toward ... -
On a generalisation of k-Dyck paths
(Stellenbosch : Stellenbosch University, 2019-12)ENGLISH ABSTRACT: (Refer to full text abstract for symbols that did not transfer correctly). We consider a family of non-negative lattice paths consisting of the step set f(1; 1); (1;k)g called k-Dyck paths, which are ... -
On spanning sets and generators of near-vector spaces
(Scientific and Technological Research Council of Turkey, 2018)In this paper we study the quasi-kernel of certain constructions of near-vector spaces and the span of a vector. We characterize those vectors whose span is one-dimensional and those that generate the whole space.
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