Inequalities and majorisations for the Riemann-Stieltjes integral on time scales

We prove dynamic inequalities of majorisation type for functions on time scales. The results are obtained using the notion of Riemann-Stieltjes delta integral and give a generalization of [App. Math. Let. 22 (2009), no. 3, 416--421] to time scales.Comment: Submitted 30-Apr-2009; revised 15-Feb-2010; accepted 24-Mar-2010; for publication in Math. Inequal. App

The formal theory of pricing and investment for electricity.

The Thesis develops the framework of competitive equilibrium in infinite-dimensional commodity and price spaces, and applies it to the problems of electricity pricing and investment in the generating system. Alternative choices of the spaces are discussed for two different approaches to the price singularities that occur with pointed output peaks. Thermal generation costs are studied first, by using the mathematical methods of convex calculus and majorisation theory, a.k.a. rearrangement theory. Next, the thermal technology, pumped storage and hydroelectric generation are studied by duality methods of linear and convex programming. These are applied to the problems of operation and valuation of plants, and of river flows. For storage and hydro plants, both problems are approached by shadow-pricing the energy stock, and when the given electricity price is a continuous function of time, the plants' capacities, and in the case of hydro also the river flows, are shown to have definite and separate marginal values. These are used to determine the optimum investment. A short-run approach to long-run equilibrium is then developed for pricing a differentiated good such as electricity. As one tool, the Wong-Viner Envelope Theorem is extended to the case of convex but nondifferentiable costs by using the short-run profit function and the profit-imputed values of the fixed inputs, and by using the subdifferential as a multi-valued, generalised derivative. The theorem applies readily to purely thermal electricity generation. But in general the short-run approach builds on solutions to the primal-dual pair of plant operation and valuation problems, and it is this framework that is applied to the case of electricity generated by thermal, hydro and pumped-storage plants. This gives, as part of the long-run equilibrium solution, a sound method of valuing the fixed assets-in this case, the river flows and the sites suitable for reservoirs

Majorisation Inequalities for Stieltjes Integrals

Inequalities of the majorisation type for convex functions and Stieltjes integrals are given. Applications for some particular convex functions of interest are also pointed out

Majorisation inequalities for Stieltjes integrals

Inequalities of the majorisation type for convex functions and Stieltjes integrals are given. Applications for some particular convex functions of interest are also presented