Prior knowledge about the possible characteristics of demand and supply is vital in the planning and operation of economically sustainable isolated rural power systems. System modelling and simulation is one of the tools that can be used in planning and assessing the performance of these systems. This thesis is presenting a Monte Carlo simulation methodology for modelling, simulating and analysing the performance of isolated rural electricity markets applicable in developing countries. The definitions of possible power system operators managing these markets are introduced based on different economic objectives of operating the systems. The two system operators considered in the thesis are: altruistic and profit maximising operators. The concept used to define types of isolated rural electricity markets is combining the definitions of operators and the possible combinations of power supply options (purely thermal or hybrid system). It is anticipated that the rural electricity markets under consideration comprise of uncertainties in demand and supply (both demand and generation are modelled as random variables from assumed or estimated probability distributions). Demand is price sensitive and modelled as a product of two random variables, relative demand and peak demand. The price sensitivity of demand is shown by representing peak demand using an economic price-demand function. The parameters (price sensitivity and demand factor) of this function are modelled as random variables which reflect the randomness of consumers’ preferences. The simulation algorithm is based on the theory of correlated sampling, in order to compare the performance of systems under different operators. The thesis introduces the concept of nested Monte Carlo simulation to be able manage the simulation of different operators subjected to the same market conditions. The performance of electricity markets is assessed by analysing three parameters (tariffs, profit and reliability), which are random variables presented using probability distributions in form of duration curves. The methodology is tested on a theoretical case study system using load data obtained from a rural community in Africa.  The case study illustrates how to use the model, preparation of the input variables and how to use the output to estimate and assess the possible performance of isolated rural power systems under different power system operators. It is anticipated that the proposed methodology can be used by researchers, planners and academia as a tool for planning, estimating and assessing the performance of rural power systems in isolated areas of developing countries

Inbound tour operators play a key role in sustainable tourism development, as they are centrally positioned in the distribution chain and provide the link between the supply and demand of tourism products and services. Embedded in this position, inbound tour operators can put pressure on their suppliers to operate more sustainably, while educating their customers on sustainable tourism practices, and influencing consumers’ decision-making before the purchasing of tourism products and services. Inbound tour operators can further implement sustainable tourism practices as part of their business operations. To date, little research has focussed on inbound tour operators’ contribution to sustainable tourism development, especially in a developing country context. Sustainable inbound tour operators can also become certified by a sustainable tourism certification programme to showcase their commitment to sustainability. Various studies have highlighted the history, benefits and issues related to certification programmes, but few studies have investigated the perspective that inbound tour operators have towards sustainable tourism certification programmes. Making use of a qualitative research approach, in-depth interviews were conducted with 22 South African inbound tour operators to investigate and identify the sustainable tourism practices currently being adopted within their organisations. Content analysis was used to analyse the data. The findings produced a list of sustainable tourism practices currently being adopted by inbound tour operators in South Africa. This study proposes that sustainable tourism organisations should become certified by a national or global sustainable tourism certification programme, to prove that they are truly operating sustainably, thus decreasing the effects of greenwashing. In addition, the certification of tourism organisations can assist inbound tour operators in identifying truly sustainable suppliers, fostering the development of a sustainable supply chain management strategy. / Dissertation (MCom)--University of Pretoria, 2020. / Tourism Management / MCom / Unrestricted

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A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa, in ful lment of the requirements for the degree of Masters of Science. May 27, 2015. / Abstract The unsteady three-dimensional ow of a thin slender rivulet of incompressible Newtonian uid down an inclined porous plane is investigated. The leak-o velocity is not speci ed in the model but is determined in the process of deriving the invariant solution. A second order nonlinear partial di erential equation in two spatial variables and time and containing the leak-o velocity is derived for the height of the thin slender rivulet. Using Lie group analysis it is found that the partial di erential equation can be reduced in two steps to an ordinary di erential equation provided the leak-o velocity satis es a rst order linear partial di erential equation in three variables. An exact analytical solution with a dry patch in the central region is derived for a special leak-o velocity. Two models are considered, one with the leak-o velocity proportional to the height of the rivulet and the other with leak-o velocity proportional to the cube of the height. Numerical solutions are obtained for the height of the rivulet using a shooting method which also determines the two-dimensional boundary of the rivulet on the inclined plane. The e ect of uid leak-o on the height and width of the rivulet is investigated numerically and compared in the two models. The conservation laws for the partial di erential equation with no uid leak-o are investigated. Two conserved vectors are derived, the elementary conserved vector and a new conserved vector. The Lie point symmetry of the partial di erential equation associated with each conserved vector is obtained. Each associated Lie point symmetry is used to perform a double reduction of the partial di erential equation, but the solutions obtained are not physically signi cant.

Continued fractions have been extensively studied in number theoretic ways. In this text we will consider continued fraction expansions with partial quotients that are in Z = f x : x 2 Zg and where = 2 cos( q ); q 3 and with 1 < < 2. These continued fractions are expressed as the composition of M obius maps in PSL(2;R), that act as isometries on H2, taken at 1. In particular the subgroups of PSL(2;R) that are studied are the Hecke groups G . The Modular group is the case for q = 3 and = 1. In the text we show that the Hecke groups are triangle groups and in this way derive their fundamental domains. From these fundamental domains we produce the v-cell (P0) that is an ideal q-gon and also tessellate H2 under G . This tessellation is called the -Farey tessellation. We investigate various known -continued fractions of a real number. In particular, we consider a geodesic in H2 cutting across the -Farey tessellation that produces a \cutting sequence" or path on a -Farey graph. These paths in turn give a rise to a derived -continued fraction expansion for the real endpoint of the geodesic. We explore the relationship between the derived -continued fraction expansion and the nearest - integer continued fraction expansion (reduced -continued fraction expansion given by Rosen, [25]). The geometric aspect of the derived -continued fraction expansion brings clarity and illuminates the algebraic process of the reduced -continued fraction expansion.

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The Harris-Venkatesh conjecture posits a relationship between the action of derived Hecke operators on weight-one modular forms and Stark units. We prove the full Harris-Venkatesh conjecture for all CM dihedral weight-one modular forms. This reproves results of Darmon-Harris-Rotger-Venkatesh, extends their work to the adelic setting, and removes all assumptions on primality and ramification from the imaginary dihedral case of the Harris-Venkatesh conjecture. This is done by introducing the Harris-Venkatesh period on cuspidal one-forms on modular curves, introducing two-variable optimal modular forms, evaluating GL(2) × GL(2) Rankin-Selberg convolutions on optimal forms and newforms, and proving a modulo-ℓᵗ comparison theorem between the Harris-Venkatesh and Rankin-Selberg periods. Furthermore, these methods explicitly describe local factors appearing in the constant of proportionality prescribed by the Harris-Venkatesh conjecture. We also look at the application of our methods to non-dihedral forms.

In this paper, we examine the conjecture of Avner Ash, Darrin Doud, David Pollack, and Warren Sinnott relating Galois representations to the mod p cohomology of congruence subgroups of the general linear group of n dimensions over the integers. We present computational evidence for this conjecture (the ADPS Conjecture) for the case n = 3 by finding Galois representations which appear to correspond to cohomology eigenclasses predicted by the ADPS Conjecture for the prime p, level N, and quadratic nebentype. The examples include representations which appear to be attached to cohomology eigenclasses which arise from D8, S3, A5, and S5 extensions. Other examples include representations which are reducible as sums of characters, representations which are symmetric squares of two-dimensional representations, and representations which arise from modular forms, as predicted by Jean-Pierre Serre for n = 2.

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