Differentiable structures on metric measure spaces: A Primer

This is an exposition of the theory of differentiable structures on metric measures spaces, in the sense of Cheeger and Keith.Comment: 23 page

Locally Collapsed 3-Manifolds

We prove that a 3-dimensional compact Riemannian manifold which is locally collapsed, with respect to a lower curvature bound, is a graph manifold. This theorem was stated by Perelman and was used in his proof of the geometrization conjecture.Comment: Final versio

Symbolic energy estimation model with optimum start algorithm implementation

The drive to reduce carbon emissions and energy utilisation, directly associated with dwellings and to achieve a zero carbon home, suggests that the assessment of energy ratings will have an increasingly prioritised role in the built environment. Created by the Building Research Establishment (BRE), the Standard Assessment Procedure (SAP) is the UK Government’s recommended method of assessing the energy ratings of dwellings. This paper describes a new, simplified dynamic method (hence known as IDEAS – Inverse Dynamics based Energy Analysis and Simulation) of assessing the controllability of a building and its servicing systems. The IDEAS method produces results that are comparable to SAP. An Optimum Start algorithm is explored in this paper to allow heating systems of different responsiveness and size to be integrated into the IDEAS framework. Results suggest that this design approach could enhance the SAP Methodology by the addition of advanced systems controllability and dynamic values

Motor racing, tobacco company sponsorship, barcodes and alibi marketing

Background Sponsorship of Formula One (F1) motor racing, which has been used as an indirect medium of tobacco advertising for several decades, was prohibited by the 2005 European Union Tobacco Advertising Directive. Most F1 tobacco sponsorship of motor racing in the EU has since ceased, with the exception of the Scuderia Ferrari team, which continues to be funded by Philip Morris. In 2007, the Marlboro logo on Ferrari cars and other race regalia was replaced by an evolving ‘barcode’ design, which Ferrari later claimed was part of the livery of the car, and not a Marlboro advertisement. Objective: To determine whether the ‘barcode’ graphics used by Ferrari represent ‘alibi’ Marlboro advertising. Methods Academic and grey literature, and online tobacco industry document archives, were searched using terms relevant to tobacco marketing and motorsport. Results Tobacco sponsorship of F1 motor racing began in 1968, and Philip Morris has sponsored F1 teams since 1972. Phillip Morris first used a ‘barcode’ design, comprising red vertical parallel lines below the word Marlboro on the British Racing Motors F1 car in 1972. Vertical or horizontal ‘barcode’ designs have been used in this way, latterly without the word Marlboro, ever since. The modern ‘barcode’ logos occupied the same position on cars and drivers' clothing as conventional Marlboro logos in the past. The shared use of red colour by Marlboro and Ferrari is also recognised by Philip Morris as a means of promoting brand association between Marlboro and Ferrari. Conclusion The Ferrari ‘barcode’ designs are alibi Marlboro logos and hence constitute advertising prohibited by the 2005 EU Tobacco Advertising Directive

Linear Control Theory with an ℋ∞ Optimality Criterion

This expository paper sets out the principal results in ℋ∞ control theory in the context of continuous-time linear systems. The focus is on the mathematical theory rather than computational methods