Cohomological Finiteness Properties of Groups

PhD thesis concerning cohomological finiteness conditions of infinite discrete groups. Much of the material in this thesis has also appeared in arXiv:1311.7629, arXiv:1310.6262, arXiv:1311.6156, and arXiv:1207.1597.Comment: PhD Thesis, University of Southampton, 178 pages, 1 figur

Applications of symmetries and conservation laws to the study of nonlinear elasticity equations

Mooney-Rivlin hyperelasticity equations are nonlinear coupled partial differential equations (PDEs) that are used to model various elastic materials. These models have been extended to account for fiber reinforced solids with applications in modeling biological materials. As such, it is important to obtain solutions to these physical systems. One approach is to study the admitted Lie symmetries of the PDE system, which allows one to seek invariant solutions by the invariant form method. Furthermore, knowledge of conservation laws for a PDE provides insight into conserved physical quantities, and can be used in the development of stable numerical methods. The current Thesis is dedicated to presenting the methodology of Lie symmetry and conservation law analysis, as well as applying it to fiber reinforced Mooney-Rivlin models. In particular, an outline of Lie symmetry and conservation law analysis is provided, and the partial differential equations describing the dynamics of a hyperelastic solid are presented. A detailed example of Lie symmetry and conservation law analysis is done for the PDE system describing plane strain in a Mooney-Rivlin solid. Lastly, Lie symmetries and conservation laws are studied in one and two dimensional models of fiber reinforced Mooney-Rivlin materials

Xenophobia: A crime against humanity and its attendant implications on human rights

Migrants across the globe often experience discrimination, exploitation and human rights violations such as xenophobic attacks. Xenophobic attacks have left thousands of foreigners dead and injured with their properties destroyed as well. This paper examines the various human rights violations perpetrated by xenophobes on migrants. It discusses xenophobia, its forms, basis and world cases. It explores xenophobia as a crime against humanity and the duty of states in protecting migrants. It highlights the various migrants’ rights instruments and in conclusion, it puts forward amongst other recommendations that the provisions of Article 7 of the Rome Statute of the International Criminal Court should be enlarged to provide for xenophobia as a crime against humanity.Keywords: Xenophobia, Duty of State, Crime against Humanity, Migrants, Rights, Alien

Quasi-automorphisms of the infinite rooted 2-edge-coloured binary tree

We study the groupQV , the self-maps of the infinite 2-edge coloured binary tree which preserve the edge and colour relations at cofinitely many locations. We introduce related groups QF , QT , zQ T , and zQV , prove that QF , zQ T , and zQV are of type F1, and calculate finite presentations for them. We calculate the normal subgroup structure of all 5 groups, the Bieri-Neumann-Strebel-Renz invariants of QF , and discuss the relationship of all 5 groups with other generalisations of Thompson's groups.</p