Let G he the direct sum of n ≥ 2 copies of the cyclic group, Z , of integers. Let p be a fixed prime and α ≥ 1 a fixed integer. Consider the subgroups, λ , of G of index p[superscript]α in G . Let S be a subset of G. We say S is a stellar set if ax ε S implies (1.1) x,2x,...,ax ε S for any x ε G and any integer a ≥ 1 . Suppose S is a stellar set, p[superscript]α G ∩ S = ∅, and S intersects all the subgroups λ of G of index p[superscript]α in G . We shall show that then |S| ≥ p[superscript]α + P[superscript]α-1. / Science, Faculty of / Mathematics, Department of / Graduate

A series of ab initio calculations has been performed in the Born-Oppenheimer approximation for some electronic states of OH. Wavefunctions and energies are calculated variationally. The form chosen for the wave-function is a finite linear superposition of configurations. Molecular orbitals are formed by Schmidt-orthogonalizing the atomic orbitals, each of which is represented by a single Slater-type orbital. The variational parameters are the coefficients in the linear expansion of the wave-function, and the non-linear parameters [character omitted] of the Slater-type orbitals. Wavefunctions and potential energy curves are given for some of the lower-lying ²Σˉ and ²Σˉ and ²Πstates. One result of note is that the lowest ²Σˉ state is bound. This disagrees with an earlier calculation (Harris and Michels, 1969), but it is in accord with a recent interpretation of the spectrum (Pryce, 1971). / Science, Faculty of / Physics and Astronomy, Department of / Graduate

In order to assess the need to formulate training requirements for practitioners of group therapy in therapeutic milieus attached to the Cape Provincial Hospital service , the organization, theoretical framework and functioning of these therapeutic milieus have been cutline. The group therapy component of the therapeutic milieu programmes and the present training provider to all four psyct1iatric disciplines from whose ranks the co-therapists of the therapy groups nrc dravm have been examined . Within this framework an assessment of the need to provide bath improved training and some consider able training in common for the four psychiatric disciplines involved has been made. Evidence from U1e writer's observations reached during thrills' years or supervision of psychic social work students' group therapy in the therapeutic milieus together with examples from the students I process records has been cited to support the conclusion that these needs do exist. The training requirements have been analysed into four components: the theory, experiential group attcnd~1ce, group therapy practice, supervision. The formulation of a training programme embracing these components is advocated . It is concluded that the training programme 3hould to a great extent be applicable to co-therapists from the different psychiatric disciplines. Finally, a number of proposals as to hm-1 improved c1:1d common training programmes can be evaluated and implemented · have been outlined.

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published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy