Supersymmetry of the magnetic vortex

The N=2 supersymmetry of the Pauli Hamiltonian in any static magnetic field in the plane combines, for the magnetic vortex, with Jackiw's bosonic $o(2)\times o(2,1)$ symmetry, into an $o(2)\times osp(1/2)$ dynamical supersymmetry.Comment: 4 pages. Originally Tours Preprint no 60/93 (1993). Unpublishe

On Maximal Unbordered Factors

Given a string $S$ of length $n$, its maximal unbordered factor is the longest factor which does not have a border. In this work we investigate the relationship between $n$ and the length of the maximal unbordered factor of $S$. We prove that for the alphabet of size $\sigma \ge 5$ the expected length of the maximal unbordered factor of a string of length~$n$ is at least $0.99 n$ (for sufficiently large values of $n$). As an application of this result, we propose a new algorithm for computing the maximal unbordered factor of a string.Comment: Accepted to the 26th Annual Symposium on Combinatorial Pattern Matching (CPM 2015

Semidirect products and the Pukanszky condition

We study the general geometrical structure of the coadjoint orbits of a semidirect product formed by a Lie group and a representation of this group on a vector space. The use of symplectic induction methods gives new insight into the structure of these orbits. In fact, each coadjoint orbit of such a group is obtained by symplectic induction on some coadjoint orbit of a "smaller" Lie group. We study also a special class of polarizations related to a semidirect product and the validity of Pukanszky's condition for these polarizations. Some examples of physical interest are discussed using the previous methods.Comment: 33 pages, including special macros and fonts (JGPpaper.tex is the source TeX file), to appear in J. Geom. Phys., also available via anonymous ftp or via gopher gopher://cpt.univ-mrs.fr

Fermat Principle for spinning light

Mimicking the description of spinning particles in General Relativity, the Fermat Principle is extended to spinning photons. Linearization of the resulting Papapetrou-Souriau type equations yields the semiclassical model used recently to derive the ``Optical Hall Effect'' (alias the ``Optical Magnus Effect'') for polarized light.Comment: Final revised version, to appear in Phys. Rev. D (Rapid Communication). 5 pages, no figure

Conformal Carroll groups

Conformal extensions of Levy-Leblond's Carroll group, based on geometric properties analogous to those of Newton-Cartan space-time are proposed. The extensions are labelled by an integer $k$. This framework includes and extends our recent study of the Bondi-Metzner-Sachs (BMS) and Newman-Unti (NU) groups. The relation to Conformal Galilei groups is clarified. Conformal Carroll symmetry is illustrated by "Carrollian photons". Motion both in the Newton-Cartan and Carroll spaces may be related to that of strings in the Bargmann space.Comment: 31 pages, no figures. Minor misprints corrected and clarifications added. To be published in J. Phys.