Abstract We give a complete classification of Airy structures for finite-dimensional simple Lie algebras over $${\mathbb {C}}$$ C , and to some extent also {R}}$$ R up isomorphisms gauge transformations. The result is that the only this type which admit any are $$\mathfrak {sl}_2$$ ...

For a plane wave incident on either a Luneburg lens or a modified Luneburg lens, the magnitude and phase of the transmitted electric field are calculated as a function of the scattering angle in the context of ray theory. It is found that the ray trajectory and the scattered intensity are not uniformly convergent in the vicinity of edge ray incidence on a Luneburg lens, which corresponds to the...

Scaling level-spacing distribution functions in the “bulk of the spectrum” in random matrix models of N × N hermitian matrices and then going to the limit N → ∞, leads to the Fredholm determinant of the sine kernel sinπ(x− y)/π(x− y). Similarly a scaling limit at the “edge of the spectrum” leads to the Airy kernel [Ai(x)Ai′(y)−Ai′(x)Ai(y)] /(x − y). In this paper we derive analogues for this Ai...

Although there had been occasional references to the visual aura of migraine even in ancient medicine, little attention was given to the phenomenon until the first half of the nineteenth century when French authors began to describe it. In the medicine of English-speaking countries, apart from a few descriptions, it went largely unnoticed until the British Astronomer Royal, Sir George Airy, des...