Polynomial Time Algorithms for Multi-Type Branching Processes and Stochastic Context-Free Grammars

We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic polynomial equations in time polynomial in both the encoding size of the system of equations and in log(1/\epsilon), where \epsilon > 0 is the desired additive error bound of the solution. (The model of computation is the standard Turing machine model.) We use this result to resolve several open problems regarding the computational complexity of computing key quantities associated with some classic and heavily studied stochastic processes, including multi-type branching processes and stochastic context-free grammars

An analysis of the electrical circuit of submerged-arc furnaces

Bibliography: leaves 167-174.The measurement of the electrical variables of a submerged-arc furnace is difficult owing to errors in the measurement of electrode-to-bath voltages and the difficulty in maintaining measurement connections to the hot, harsh environment of a furnace. A system is proposed which provides an accurate, reliable measurement of the electrode-to-bath voltages so that the electrical variables of the furnace can be determined. A means for measurement of the arcing conditions under each electrode has also been developed. The measurement system has been used in the examination of the conduction mechanisms occurring in a furnace and this has resulted in a significant improvement in the understanding of the operation. In addition, a method for determination of the lengths of the electrodes has been established. A problem with the measurement system is that it is necessary to make connections in a hot environment and on occasions, when a furnace eruption has occurred, the measurement leads have to be replaced. As a result, an indirect technique for determination of the resistances under each electrode has been developed and used for control of the power distribution in the furnace. The technique is based on an assumption about the relationship between the reactances in the furnace and all measurements are made on the primary side of the furnace transformers where reliable connections can be made

An assessment of financial incentives for encouraging South Africa's domestic solar water heater market

Includes bibliographical references (p. 102-104).SA has a demand for domestic hot water, which is supplied by a number of different technologies. For a number of reasons, including health reasons and versatility, Government has encouraged the demand for electricity to meet domestic requirements. But currently there is a shortage of electricity supply, with negative impacts for the development of SA. Solar water heating (SWH) is a renewable energy technology that could relieve some of the demand for electricity, and the aim of this study is to assess which types of national financial incentive programmes should be implemented in order to encourage the use of SWH systems in households, within the context of SA's energy policy and the current electricity crisis. However, only hybrid SWH technologies were considered, due to a lack of information. A review of literature shows that domestic SWH technology use is uncommon, resulting from households preferring other technologies for reasons of cost and convenience. The modelling of current and hypothetical scenarios of energy consumption for domestic water heating show that the increased use of hybrid SWH technology would benefit SA's sustainable development. A literature review was used to identify the barriers stopping these benefits from being translated into the domestic sector. A literature review of energy policy documents confirmed SA's commitment to sustainable development and introduced a number of developments intended to reduce the barriers to renewable energy technologies. Investment incentives and set-asides were identified as potential financial incentive options for SA. A literature review of the SWH market identified the existing structures and capacity of expertise, and identified options for reducing SWH barriers. A criteria analysis was performed on a set-aside option and investment incentive options, which included a direct subsidy, an income tax deduction, and an interest rate subsidy. The criteria used for this analysis were derived from this study and a report of international experiences, and the analysis provided an assessment of the suitability of each of these financial incentives. The assessment resulted in the recommendation that a direct subsidy programme be implemented, possibly using a system of Tradable Renewable Energy Certificates (TRECs), which could allow for compatibility with developments that could enhance the success of the programme