Roofs and Convexity

Roofs and Convexity

Convex roof extensions are widely used to create entanglement measures in quantum information theory. The aim of the article is to present some tools which could be helpful for their treatment. Sections 2 and 3 introduce into the subject. It follows descriptions of the Wootters’ method, of the “subtraction procedure”, and examples on how to use symmetries.

Near convexity, metric convexity, and convexity

It is shown that a subset of a uniformly convex normed space is nearly convex if and only if its closure is convex. Also, a normed space satisfying a mild completeness property is strictly convex if and only if every metrically convex subset is convex. 1 Classical and constructive mathematics The arguments in this paper conform to constructive mathematics in the sense of Errett Bishop. This mea...

Efficient Roof Shapes through Wind Flow and Indoor Temperature, Case Studies: Flat Roofs and Domed Roofs

Convexity and Geodesic Metric Spaces

In this paper, we first present a preliminary study on metric segments and geodesics in metric spaces. Then we recall the concept of d-convexity of sets and functions in the sense of Menger and study some properties of d-convex sets and d-convex functions as well as extreme points and faces of d-convex sets in normed spaces. Finally we study the continuity of d-convex functions in geodesic metr...

Energy savings in buildings or UHI mitigation? Comparison between green roofs and cool roofs

The intensification of the Urban Heat Island effect (UHI) is a problem that involves several fields, and new adequate solutions are required to mitigate its amplitude. The construction sector is strictly related with this phenomenon; in particular, roofs are the envelope components subject to the highest solar irradiance, hence any mitigation strategy should start from them and involve their ap...