Hackmanite-The Natural Glow-in-the-Dark Material

"Glow-in-the-dark" materials are known to practically everyone who has ever traveled by airplane or cruise ship, since they are commonly used for self-lit emergency exit signs. The green afterglow, persistent luminescence (PeL), is obtained from divalent europium doped to a synthetic strontium aluminate, but there are also some natural minerals capable of afterglow. One such mineral is hackmanite, the afterglow of which has never been thoroughly investigated, even if its synthetic versions can compete with some of the best commercially available synthetic PeL materials. Here we combine experimental and computational data to show that the white PeL of natural hackmanite is generated and controlled by a very delicate interplay between the natural impurities present. The results obtained shed light on the PeL phenomenon itself thus giving insight into improving the performance of synthetic materials

Exact essential norm of generalized Hilbert matrix operators on classical analytic function spaces

We compute the exact value of the essential norm of ageneralized Hilbert matrix operator acting on weightedBergman spaces Apv and weighted Banach spaces H∞v ofanalytic functions, where v is a general radial weight. Inparticular, we obtain the exact value of the essential normof the classical Hilbert matrix operator on standard weightedBergman spaces Apα for p > 2 + α, α ≥ 0, and on Korenblumspaces H∞α for 0 < α < 1. We also cover the Hardy spaceHp, 1 < p < ∞, case. In the weighted Bergman space case, theessential norm of the Hilbert matrix is equal to the conjecturedvalue of its operator norm and similarly in the Hardy spacecase the essential norm and the operator norm coincide. Wealso compute the exact value of the norm of the Hilbert matrixon H∞wα with weights wα(z) = (1 − |z|)α for all 0 < α < 1. Also in this case, the values of the norm and essential normcoincide