Projective Limit Random Probabilities on Polish Spaces

A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be constructed from their finite-dimensional marginals---the most prominent example being the construction of the Dirichlet process from finite-dimensional Dirichlet distributions. This approach is both intuitive and applicable to the construction of arbitrary distributions on M(V), but also hamstrung by a number of technical difficulties. We show how these difficulties can be resolved if the domain V is a Polish topological space, and give a representation theorem directly applicable to the construction of any probability distribution on M(V) whose first moment measure is well-defined. The proof draws on a projective limit theorem of Bochner, and on properties of set functions on Polish spaces to establish countable additivity of the resulting random probabilities.

Gas properties as a limit to gas turbine performance

Although increasing the turbine inlet temperature has traditionally proved the surest way to increase cycle efficiency, recent work suggests that the performance of future gas turbines may be limited by increased cooling flows and losses. Another limiting scenario concerns the effect on cycle performance of real gas properties at high temperatures. Cycle calculations of uncooled gas turbines show that when gas properties are modelled accurately, the variation of cycle efficiency with turbine inlet temperature at constant pressure ratio exhibits a maximum at temperatures well below the stoichiometric limit. Furthermore, the temperature at the maximum decreases with increasing compressor and turbine polytropic efficiency. This behaviour is examined in the context of a two-component model of the working fluid. The dominant influences come from the change of composition of the combustion products with varying air/fuel ratio (particularly the contribution from the water vapour) together with the temperature variation of the specific heat capacity of air. There are implications for future industrial development programmes, particularly in the context of advanced mixed gas-steam cycles.