Hrvoje Kraljević

Approximate supersymmetries in nuclei

Abstract Dynamical symmetries and supersymmetries for the SU(6) quadrupole phonon model are the same as those of the IBM/IBFM. Here we propose the approximate supersymmetry SU BF (3), with predictions for unique-parity bands in odd nuclei which are in the neighbourhood of the SU(3)-type even nucleus. The persistence of the supersymmetric pattern is investigated in the quadrupole phonon representation; this gives an additional argument for the existence of supersymmetries in nuclei.

Some Landau's type inequalities for infinitesimal generators

SummaryLett ↦ T(t) be a strongly continuous contraction semigroup on a complex Banach space and letA be its infinitesimal generator. We prove that, forx ∈D(A3), the following inequalities hold true: ∥Ax∥3 ⩽ 243/8 ∥x∥2∥A3x∥, ∥A2x∥ ⩽ 24 ∥x∥∥A3x∥2. Ift → T(t) is a contraction group (resp. cosine function) we get the analogous but better inequalities with constants 9/8 and 3 (resp. 81/40 and 72/25) instead of 243/8 and 24. We consider also uniformly bounded semigroups, groups and cosine functions.

A note on nonunitary principal series representations

It is proven in a rather elementary way that any nonunitary principal series representation of a semisimple Lie group G is of finite length, having as a trivial consequence that the set of infinitesimal equivalence classes of quasisimple irreducible representations of G with a given infinitesimal character is finite.

On Landau's theorems

In this paper we give some applications and special cases of a generalization of the Landau’s theorem for Frechet-differentiable functions.