One of the earliest results (1955) in the theory of derivations is the celebrated
theorem of I. M. Singer and J. Wermer [14] which asserts that every bounded
derivation on a commutative Banach algebra has range contained ...
Let G be a graph and D a set of vertices such that every vertex in G is in D or adjacent to at least one vertex in D. Then D is called a dominating set of G and the smallest cardinality of such a dominating set of G is ...
Domination in graphs is now well studied in graph theory and the literature on this
subject has been surveyed and detailed in the two books by Haynes, Hedetniemi, and
Slater [45, 46]. In this thesis, we continue the study ...
The aim of this thesis is to investigate the topic of edge-colourings of graphs in the
context of hereditary graph properties. We particularly aim to investigate analogues
of reducibility, unique factorization and some ...
Entanglement is a quantum resource with applications in quantum communication
as well as quantum computing amongst others. Since quantum entanglement
is such an abstract concept numerous mathematical measures exist. ...
Keywords: entanglement, complexity, entropy, measurement
In chapter 1 the basic principles of communication complexity are introduced.
Two-party communication is described explicitly, and multi-party
communication ...
In this study we consider the problem ofestiniating the slope in the simple linear errors-in-variables model. There are two different types of relationship that can he specified in the errors-in-variables model: one that ...
In Chapter 1, we consider the relevant theory pertaining to graphs and digraphs
that will be used in the study of flows in networks. Warshall’s algorithm for
reachability is also considered since it will allow us to ...
The aim of the thesis is to develop game-theoretic techniques for dealing with common
problems in model theory, mainly that of showing logical equivalence between structures,
and to illustrate the effectiveness of the ...
In this thesis we investigate generalized chromatic numbers in the context of hereditary
graph properties. We also investigate the general topic of invariants of graphs as well as
graph properties.
In Chapter 1 we give ...
Important ideas from dynamical systems theory and the restricted three-body
problem are introduced. The intention is the application of dynamical systems
theory techniques to the restricted three-body problem to better ...
The creation of smooth interpolating curves and surfaces is an important
aspect of computer graphics. Trigonometric interpolation in the form of the
Fourier transform has been a popular technique. For computer graphics, ...
The basis for this study rests upon the question whether typical human reasoning is reliant upon the application of formal inference rules or not. Two major approaches on this topic, formal logic and mental model theory, ...
Explicit schemes for integrating ODEs and time–dependent partial differential
equations (in the method of lines–MoL–approach) are very well–known
to be stable as long as the maximum sizes of their timesteps remain below
a ...
In this thesis, the ranks of many types of regular and strongly regular graphs are
determined. Also determined are ranks of regular graphs under unary operations: the line
graph, the complement, the subdivision graph, ...
Die leerder met Wiskunde sukkel omdat hy nie 'n metode het om Wiskunde te leer nie. Groot druk word op die onderwyser geplaas, want hy moet nou vir die leerder leer hoe
om Wiskunde te leer. Die vraag ontstaan of daar 'n ...