1.

Proper holomorphic embeddings into Stein manifolds with the density property

We prove that a Stein manifold of dimension $d$ admits a proper holomorphic embedding into any Stein manifold of dimension at least $2d+1$ satisfying the holomorphic density property. This generalizes classical theorems of Remmert, Bishop and Narasimhan pertaining to embeddings into complex Euclidean spaces, as well as several other recent results.

COBISS.SI-ID: 17810265

2.

Groups in which every non-abelian subgroup is self-centralizing

We study groups having the property that every non-abelian subgroup contains its centralizer. We describe various classes of infinite groups in this class, and address a problem of Berkovich regarding the classification of finite $p$-groups with the above property.

COBISS.SI-ID: 17738329

3.

Curvature approximation of circular arcs by low-degree parametric polynomials

In this paper some new methods for curvature approximation of circular arcs by low-degree Bézier curves are presented. Interpolation by geometrically continuous $(G^1)$ parametric polynomials is considered. All derived approximants are given explicitly and are therefore practically applicable. Moreover, obtained results indicate that $G^1$ biarcs with at least $G^1$ continuity at the junction have smaller curvature error as parametric polynomial counterparts of the same degree. It is also shown that all considered methods provide optimal asymptotic approximation order.

COBISS.SI-ID: 17724505