Properties from relativistic coupled-cluster without truncation: hyperfine constants of 25Mg+^{25}{\rm Mg}^+, 43Ca+^{43}{\rm Ca}^+ , 87Sr+^{87}{\rm Sr}^+ and 137Ba+^{137}{\rm Ba}^+

We demonstrate an iterative scheme for coupled-cluster properties calculations without truncating the dressed properties operator. For validation, magnetic dipole hyperfine constants of alkaline Earth ions are calculated with relativistic coupled-cluster and role of electron correlation examined. Then, a detailed analysis of the higher order terms is carried out. Based on the results, we arrive at an optimal form of the dressed operator. Which we recommend for properties calculations with relativistic coupled-cluster theory.Comment: 13 pages, 4 figures, 5 table

Almost ellipsoidal sections and projections of convex bodies

In (1) Dvoretsky proved, using very ingenious methods, that every centrally symmetric convex body of sufficiently high dimension contains a central k-dimensional section which is almost spherical. Here we shall extend this result (Corollary to Theorem 2) to k-dimensional sections through an arbitrary interior point of any convex bod