Let X = {X(x): x ∊ 𝕊N} be a real-valued, centered Gaussian random field indexed on the N -dimensional unit sphere 𝕊N. Approximations to the excursion probability ℙ{supx∊𝕊N X(x) ≥ u}, as →∞, are ...

They may not know it, but grocers face some of the most difficult questions in mathematics when stacking produce each day. Four centuries ago, the astronomer and mathematician Johannes Kepler guessed ...

Opting to build the Death Star in the shape of a sphere may not have been classic Star Wars villain Darth Vader's wisest move, according to math teacher Ben Orlin. He investigates this burning ...

In 1948, Hendrik Casimir predicted that a generalized version of van der Waals forces would arise between two metal plates due to quantum fluctuations of the electromagnetic field. These forces become ...

This is a preview. Log in through your library . Abstract We give an extensive discussion of sphere-preserving maps defined on subdomains of Euclidean n-space, and their relationship to Möbius maps ...