The elasticity of demand is about occupancy, not prices: building European demand curves based on occupancy elasticity

The peak congestion of the European grid may create significant impacts on system costs because of the need for higher marginal cost generation, higher cost system balancing and increasing grid reinforcement investment. The use of time of use rates, incentives, real time pricing and other programmes, usually defined as Demand Side Management (DSM), could bring about significant reductions in prices, limit carbon emissions from dirty power plants, and improve the integration of renewable sources of energy. Unlike previous studies on elasticity of residential electricity demand under flat tariffs, the aim of this study is not to investigate the known relatively inelastic relationship between demand and prices. Rather, the aim is to assess how occupancy levels vary in different European countries. This reflects the reality of demand loads, which are predominantly determined by the timing of human activities (e.g. travelling to work, taking children to school) rather than prices. To this end, two types of occupancy elasticity are estimated: baseline occupancy elasticity and peak occupancy elasticity. These represent the intrinsic elasticity associated with human activities of single residential end-users in 15 European countries. This study makes use of occupancy time-series data from the Harmonised European Time Use Survey database to build European occupancy curves; identify peak occupancy periods; draw time use demand curves for video and TV watching activity; and estimate national occupancy elasticity levels of single-occupant households. Findings on occupancy elasticities provide an indication of possible DSM strategies based on occupancy levels and not prices.

Anodic polarization curves revisited

An experiment published in this Journal has been revisited and it is found that the curve pattern of the anodic polarization curve for iron repeats itself successively when the potential scan is repeated. It is surprising that this observation has not been reported previously in the literature because it immediately brings into question the long accepted and well-known explanations involving a passive film. A qualitative and plausible explanation is provided from surprisingly simple principles for this new finding. Some important pedagogic conclusions have been derived from this work. It is noteworthy that the somewhat complicated phenomenon can be simply explained, thus providing two important lessons to students. First, even well-accepted scientific work studying simple processes may be incomplete and worthy of further study, and second, such processes may be explained simply at the undergraduate level. The contents of the paper also confirm that presenting curricular contents in a new and more correct manner is beneficial, interesting, and that research in curricular contents represents one of the important forms of educational research.

Uniqueness of signature for simple curves

We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two dimensional closed curve with finite p-variation, 1≤p<2, are in fact moments of its winding number. This relation allows us to prove that the signature series of a class of simple non-smooth curves uniquely determine the curves. This implies that outside a Chordal SLEκ null set, where 0<κ≤4, the signature series of curves uniquely determine the curves. Our calculations also enable us to express the Fourier transform of the n-point functions of SLE curves in terms of the expected signature of SLE curves. Although the techniques used in this article are deterministic, the results provide a platform for studying SLE curves through the signatures of their sample paths.

Simple piecewise geodesic interpolation of simple and Jordan curves with applications

We explicitly construct simple, piecewise minimizing geodesic, arbitrarily fine interpolation of simple and Jordan curves on a Riemannian manifold. In particular, a finite sequence of partition points can be specified in advance to be included in our construction. Then we present two applications of our main results: the generalized Green’s theorem and the uniqueness of signature for planar Jordan curves with finite p -variation for 1⩽p<2.