Now showing items 1-6 of 6
On the theory and examples of group extensions.
The work described in this dissertation was largely motivated by the aim of producing a survey on the theory of group extensions. From the broad scope of the theory of group extensions we single out two aspects to discuss, ...
The paradigms of mechanics : a symmetry based approach.
An overview of the historical developments of the paradigms of classical mechanics, the free particle, oscillator and the Kepler problem, is given ito (in terms of) their conserved quantities. Next, the orbits of the three ...
Noether's theorem and first integrals of ordinary differential equations.
The Lie theory of extended groups is a practical tool in the analysis of differential equations, particularly in the construction of solutions. A formalism of the Lie theory is given and contrasted with Noether's theorem ...
Parameters related to fractional domination in graphs.
The use of characteristic functions to represent well-known sets in graph theory such as dominating, irredundant, independent, covering and packing sets - leads naturally to fractional versions of these sets and corresponding ...
Ermakov systems : a group theoretic approach.
The physical world is, for the most part, modelled using second order ordinary differential equations. The time-dependent simple harmonic oscillator and the Ermakov-Pinney equation (which together form an Ermakov system) ...