School of Sciencehttp://hdl.handle.net/10500/27362016-07-28T01:00:02Z2016-07-28T01:00:02ZAlgebraic and multilinear-algebraic techniques for fast matrix multiplicationGouaya, Guy Mathiashttp://hdl.handle.net/10500/201802016-06-03T08:10:17Z2015-01-01T00:00:00ZAlgebraic and multilinear-algebraic techniques for fast matrix multiplication
Gouaya, Guy Mathias
This dissertation reviews the theory of fast matrix multiplication from a multilinear-algebraic point of view, as
well as recent fast matrix multiplication algorithms based on discrete Fourier transforms over nite groups.
To this end, the algebraic approach is described in terms of group algebras over groups satisfying the triple
product Property, and the construction of such groups via uniquely solvable puzzles.
The higher order singular value decomposition is an important decomposition of tensors that retains some of
the properties of the singular value decomposition of matrices. However, we have proven a novel negative result
which demonstrates that the higher order singular value decomposition yields a matrix multiplication algorithm
that is no better than the standard algorithm.
2015-01-01T00:00:00ZNon-resonant microwave absorption studies in SmFeAs(O,F) iron pnictide superconductorOnyancha, Robert Birunduhttp://hdl.handle.net/10500/200322016-03-11T01:00:23Z2015-03-01T00:00:00ZNon-resonant microwave absorption studies in SmFeAs(O,F) iron pnictide superconductor
Onyancha, Robert Birundu
As an electromagnetic response detection technique, non-resonant microwave absorption (NRMA) has been without doubt, one of the fundamental tools in characterizing high temperature superconductors (HTSC). The technique can explicitly give factual information on flux pinning, granularity, magnetization, and detection of iota superconducting phases among many more.
The emergence of iron pnictides superconductors has brought an enormous impact on HTSC field due to their relatively high 𝑇c, high critical fields 𝐵c2, huge critical current density and low anisotropy. Accordingly, they look appealing candidates in industrial applications more especially in high magnetic field applications. As of yet, its electromagnetic response particularly the low field microwave absorption (LFMA) or the non-resonant microwave absorption (NRMA) is relatively unknown.
Consequently, in this work, systematic studies have been done on SmFeAs(O,F), superconductors to determine the low field sweep microwave absorption. Furthermore, effect of varying temperature, microwave power and field modulation amplitude on NRMA line shape have been addressed and the results obtained are compared with NRMA results of cuprates superconductors.
Interestingly, the NRMA line shape has been found to evolve as a function of temperature, microwave power and field modulation amplitude. A structure i.e a broad peak 1 and a narrow peak 2 have been identified. Furthermore, the line shape shows a phase reversal at moderately high microwave power.
This dissertation presents the theoretical background of superconductors, experimental techniques, working principles of the equipments, results, discussions and conclusions. As pertains to the future work, recommendations have been suggested in trying other forms of sample and also different sample materials of iron based superconductors to fully understand the NRMA and ensure a progressive and continuous work in this field. Also, we will carry out extensive studies on critical current density, fluxon dynamics and irreversibility fields on iron-based superconductors by means of NRMA technique.
2015-03-01T00:00:00ZCohomologies on sympletic quotients of locally Euclidean Frolicher spacesTshilombo, Mukinayi Hermenegildehttp://hdl.handle.net/10500/199422016-02-18T11:09:13Z2015-08-01T00:00:00ZCohomologies on sympletic quotients of locally Euclidean Frolicher spaces
Tshilombo, Mukinayi Hermenegilde
This thesis deals with cohomologies on the symplectic quotient of a Frölicher space which is locally diffeomorphic to a Euclidean Frölicher subspace of Rn of constant dimension equal to n. The symplectic reduction under consideration in this thesis is an extension of the
Marsden-Weinstein quotient (also called, the reduced space) well-known from the finite-dimensional smooth manifold case. That is, starting with a proper and free action of a Frölicher-Lie-group on a locally Euclidean Frölicher space of finite constant dimension, we
study the smooth structure and the topology induced on a small subspace of the orbit space. It is on this topological space that we will construct selected cohomologies such as : sheaf cohomology, Alexander-Spanier cohomology, singular cohomology, ~Cech cohomology and de Rham cohomology. Some natural questions that will be investigated are for instance: the impact of the symplectic structure on these di erent cohomologies; the cohomology that will
give a good description of the topology on the objects of category of Frölicher spaces; the extension of the de Rham cohomology theorem in order to establish an isomorphism between the five cohomologies.
Beside the algebraic, topological and geometric study of these new objects, the thesis contains a modern formalism of Hamiltonian mechanics on the reduced space under symplectic and Poisson structures.
2015-08-01T00:00:00ZForecasting annual tax revenue of the South African taxes using time series Holt-Winters and ARIMA/SARIMA ModelsMakananisa, Mangalani P.http://hdl.handle.net/10500/199032016-02-26T12:44:36Z2015-10-01T00:00:00ZForecasting annual tax revenue of the South African taxes using time series Holt-Winters and ARIMA/SARIMA Models
Makananisa, Mangalani P.
This study uses aspects of time series methodology to model and forecast major taxes such as Personal Income Tax (PIT), Corporate Income Tax (CIT), Value Added Tax (VAT) and Total Tax Revenue(TTAXR) in the South African Revenue Service (SARS).
The monthly data used for modeling tax revenues of the major taxes was drawn from January 1995 to March 2010 (in sample data) for PIT, VAT and TTAXR. Due to higher volatility and emerging negative values, the CIT monthly data was converted to quarterly data from the rst quarter of 1995 to the rst quarter of 2010. The competing ARIMA/SARIMA and Holt-Winters models were derived, and the resulting model of this study was used to forecast PIT, CIT, VAT and TTAXR for SARS fiscal years 2010/11, 2011/12 and 2012/13. The results show that both the SARIMA and Holt-Winters models perform well in modeling and forecasting PIT and VAT, however the Holt-Winters model outperformed the SARIMA model in modeling and forecasting the more volatile CIT and TTAXR. It is recommended that these methods are used in forecasting future payments, as they are precise about forecasting tax revenues, with minimal errors and fewer model revisions being necessary.
2015-10-01T00:00:00Z