Erratum to “Hardy-Bohr positivity”

Spherical Reflection Positivity and the Hardy-littlewood-sobolev Inequality

The well-known functions on R , f(x) = c(b + |x − a|2)−p, where a ∈ R , b > 0 and c > 0, appear as the optimizers in some classical functional inequalities, notably the Hardy-Littlewood-Sobolev (HLS) inequality and its dual, the Sobolev inequality. Given their ubiquity, these functions must be endowed with some special property, and this was identified by Y. Y. Li and M. J. Zhu [21]. It is the ...

Erratum to: Armentum: a hybrid direct search optimization methodology

In the original publication of this article unfortunately the co-authors were omitted. The two co-authors are displayed now.

Erratum

Bohr-Sommerfeld Rules to All Orders

The goal of this paper is to give a rather simple algorithm which computes the Bohr-Sommerfeld quantization rules to all orders in the semi-classical parameter h for a semi-classical Hamiltonian Ĥ on the real line. The formula gives the highorder terms in the expansion in powers of h of the semi-classical action using only integrals on the energy curves of quantities which are locally computabl...

Learned to Stop Worrying and Love Bohr

To celebrate the 60th birthday of Charles H. Bennett I (1) publicly announce my referee reports for the original dense coding and telepor-tation papers, (2) present a very economical solution to the Bernstein-Vazirani problem that does not even hint at interference between multiple universes, and (3) describe how I inadvertently reinvented the Copen-hagen interpretation in the course of constru...