The Number of Singularities in the Intersections of Convex Planar Translates

This purpose of this paper is to prove the following result: let phi be a strictly convex, smooth, convex body in the Euclidean plane, if the intersection of n translates of phi has a non-empty interior, and all of the translates contribute to the intersection, then the intersection of these n translates will have exactly n points of singularity along its boundary. Furthermore this result is sharp, in the sense that, removing any one of the assumptions from our statement will render the result unable to hold in general

TEACHING OPTIMAL SWING MECHANICS

An optimal golf swing technique has been proposed that produces a powertul and accurate stroke while minimising the stress on the shoulders and back. However, the teaching of this technique requires specialist knowledge and training to deal with players of different abilities -from the social player to the professional. Teaching methods have been developed that differ considerably from those normally recommended in conventional golf instructio

Illuminating spiky balls and cap bodies

The convex hull of a ball with an exterior point is called a spike (or cap). A union of finitely many spikes of a ball is called a spiky ball. If a spiky ball is convex, then we call it a cap body. In this note we upper bound the illumination numbers of $2$-illuminable spiky balls as well as centrally symmetric cap bodies. In particular, we prove the Illumination Conjecture for centrally symmetric cap bodies in sufficiently large dimensions by showing that any $d$-dimensional centrally symmetric cap body can be illuminated by $<2^d$ directions in Euclidean $d$-space for all $d\geq 20$. Furthermore, we strengthen the latter result for $1$-unconditionally symmetric cap bodies.Comment: 13 pages, 6 figure

Thermal improvement of existing dwellings

This report describes the outcome from a study to determine the impact of energy efficiency measures applied to the Scottish housing stock. Assuming conventional property type classifications, the present performance of the housing stock is quantified using available survey data. Building simulation techniques were then employed to generate a Web-based, decision-support tool for use by policy makers to estimate the impact of deploying energy efficiency measures in different combinations over time. The process of tool formulation is described and an example is given of tool use to identify best-value retrofitting options while taking factors such as future climate change and improved standard of living into account

A multi-criteria performance study of an integrated demand/supply energy system for low and zero carbon technologies within domestic building design

When low carbon and renewable energy (RE) systems are adopted in a building, matching the outputs from RE systems (e.g. photovoltaic, solar collectors, small scale wind turbines and heat pumps) to demand has to be taken into account to fully realise the potential of the hybrid energy system. Considering the varying demand profiles due to different building design options (e.g. orientation, construction types etc), it is necessary to evaluate key technology elements in an integrated context and establish appropriate strategies for simultaneously meeting heating and electricity loads as well as matching demand and supply. This paper presents a new approach to evaluate the interactive effects of low carbon technologies and demand reduction measures in the early design stage of a new building. A case study of a sustainable domestic building project (PLUS 50), was implemented on the basis of the proposed design approach