Let b(K) denote the minimal number of smaller homothetical copies of a convex body K ⊂ R, n ≥ 2, covering K. For the class B of belt bodies, which is dense in the set of all convex bodies (in the Hausdorff metric), 3 · 2 is known to be an upper bound on b(K) if K is different from a parallelotope. We will show that (except for all parallelotopes and two particular cases, each satisfying b(K) = ...

let r be a commutative noetherian ring. we study the behavior of injectiveand at dimension of r-modules under the functors homr(-,-) and -×r-.

Abstract In this perspective we discuss recent theoretical and experimental concepts giving a route to better understanding of conventional unconventional pairing mechanisms between opposite-spin fermions arising in one-dimensional mesoscopic systems. With special attention, focus on the problem detectability correlations particles. We argue that state-of-the-art experiments with few ultracold ...