Neste trabalho mostramos o importante teorema de Merkurjev- Suslin para o caso de 2-torção, seguindo o artigo [Mer06], que afirma que, para qualquer corpo F de característica diferente de 2, a 2-torção \'IND.2 Br\'(F) do grupo de Brauer de F é gerada pelas classes de álgebras de quatérnions / In this work we show the important theorem of Merkurjev- Suslin for 2-torsion, following the paper [Mer06], which states that for any field F of characteristic not 2 the 2-torsion \'IND. 2 Br\'(F) of the Brauer Group of F is generated by the quaternion algebra classes

This thesis presents the results of an investigation into the representation theory of the alternating and dihedral groups and explores how their irreducible representations can be distinguished with the use of class sums.

In this thesis, we present a new class of algorithms that determine fast Fourier transforms for a given finite group G. These algorithms use eigenspace projections determined by a chain of subgroups of G, and rely on a path algebraic approach to the representation theory of finite groups developed by Ram (26). Applying this framework to the symmetric group, Sn, yields a class of fast Fourier transforms that we conjecture to run in O(n2n!) time. We also discuss several future directions for this research.

A discrete Fourier transform, or DFT, is an isomorphism from a group algebra to a direct sum of matrix algebras. An algorithm that efficiently applies a DFT is called a fast Fourier transform, or FFT. The concept of a DFT will be introduced and examined from both a general and algebraic perspective. We will then present and analyze a specific FFT for the symmetric group.

Thesis (M.Sc.(Physics)) --University of Limpopo, 2006 / Platinum group minerals are abundant in South Africa. Platinum is of great significance in catalytic applications and many other medical and pharmaceutical industries. Our studies of PtSb2 and PtBi2 were carried out using Density Functional Techniques, including LDA and GGA methods. We investigated the pressure dependences of lattice parameters and bond lengths of the materials. All these properties were shown to decrease with increasing pressure, in a linear fashion. Other features that were studied are the electronic properties like density of states (DOS) and optical properties to determine the type of material being studied. A set of interatomic potentials has been derived for the study of bulk and surface properties of PtSb2 using the GULP code (General Utility Lattice Program). These potentials have proved to be reliable since they reproduced bulk properties of PtSb2 such as lattice parameters and elastic constants. As there are no experimental studies on surfaces we have been able, for the first time, to calculate surface energies for the low index surfaces and found out that the most stable surface is the {100} Sb terminated one, with the energy of 0.933 J.m-2 and the least stable is the {111} Sb terminated surface with the energy of 2.586 J.m-2.

Thesis (MSc (Clinical Psychology) ) -- University of Limpopo, 2012. / The Clinical Psychology training programme at the University of Limpopo (Medunsa Campus) is contextualized within the theoretical paradigm of the General Systems Theory. The main focus during the first block of training is on equipping trainees with a person-centered stance and the necessary skills that go with it such as empathy, unconditional positive regard and congruence and also to develop a frame of reference in the trainees which is suitable to form a basis as a therapist. Thus training within this context is experiential. The aim of this study was to explore the subjective emotional experiences of the Msc1-Clinical Psychology trainees at the University of Limpopo (Medunsa Campus) during their first block of training. The research was conducted through qualitative interviews with the trainees shortly after being exposed to the first block of training. The sample size consisted of five trainees of the 2011 Masters in Clinical Psychology training programme at Medunsa Campus. Interviews were analysed in accordance with qualitative methodology through thematic analysis. Finally, an attempt was made to discuss and integrate the research findings into which the strengths and limitations of the study and future recommendations were made. Results from this study indicated that trainees during their first block of training experienced different challenges which are not only emotional but mental as well as academic in nature. Moreover, it became evident that trainees further experienced challenges in their social contexts such as families and relationships outside the training context.

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The 2-groups of coclass 1 are widely known and James (in 1975) looked at the 2-groups of coclass 2. Development of the p-group generation algorithm implemented by O'Brien at ANU enabled group presentations to be provided for the 2-groups of coclass 3 by Newman and O'Brien for groups of order up to 223. Newman and O'Brien (in 1999) conjectured the number of descendants of 2n for all n. They introduced the concept of a family, with each family related to a different pro-p-group and the concept of a sporadic p-group, a p-group external to any family. They found 1782 sporadic 2-groups with order at most 214. The 70 families of 2-groups of coclass 3 can be further split according to their period, a measure of the repetitive structure of the families. Newman and O'Brien conjectured that these families had periods of 1, 2 or 4. This thesis examines the 2-groups of coclass 3 contained in families with period 1 and shows that the number of descendants conjectured by Newman and O'Brien is correct. Furthermore the presentation of all groups contained in period 1 families is provided and shown to be correct.