There are roof shapes and ratios that maximize heat retainment and energy efficiency and, interestingly, ancient Italian architects and builders seemed to know it, too.

ELLIE: And if you want to really get into it, be sure to grab a pen and paper so you can make notes and try out equations ... work done. We cover work done in much more detail in our Bitesize ...

In this article, our focus lies on a Schrödinger equation incorporating a Hardy term. To identify the global minimizers of the functional I under a mass constraint, we ...