Affine semigroups having a unique Betti element

We characterize affine semigroups having one Betti element and we compute some relevant non-unique factorization invariants for these semigroups. As an example, we particularize our description to numerical semigroups.Comment: 8 pages, 1 figure. To appear in Journal of Algebra and its Application

Helico-conical optical beams self-heal

An optical beam is said to be self-healing when, distorted by an obstacle, the beam corrects itself upon propagation. In this letter, we show through experiments supported by numerical simulations, that Helico-conical optical beams (HCOBs) self-heal. We observe the strong resilience of these beams with different types of obstructions, and relate this to the characteristics of their transverse energy flow.Comment: 4 pages, 5 figure

Three-sublattice Skyrmion crystal in the antiferromagnetic triangular lattice

The frustrated classical antiferromagnetic Heisenberg model with Dzyaloshinskii-Moriya (DM) interactions on the triangular lattice is studied under a magnetic field by means of semiclassical calculations and large-scale Monte Carlo simulations. We show that even a small DM interaction induces the formation of an Antiferromagnetic Skyrmion crystal (AF-SkX) state. Unlike what is observed in ferromagnetic materials, we show that the AF-SkX state consists of three interpenetrating Skyrmion crystals (one by sublattice), and most importantly, the AF-SkX state seems to survive in the limit of zero temperature. To characterize the phase diagram we compute the average of the topological order parameter which can be associated to the number of topological charges or Skyrmions. As the magnetic field increases this parameter presents a clear jump, indicating a discontinuous transition from a spiral phase into the AF-SkX phase, where multiple Bragg peaks coexist in the spin structure factor. For higher fields, a second (probably continuous) transition occurs into a featureless paramagnetic phase.Comment: 8 pages, 8 figure

Supergroup BF action for supergravity

General relativity can be formulated as a SU(2) BF-theory with constraints, as has been shown, by Pleba\'nski. The cosmological constant term can be obtained from the constraint term, following from the consistency of the equations of motion, as recently shown by Krasnov. We consider an $OSp(2|1)$ invariant, supergravity extension of this theory, for which the consistency of the equations of motion and the constraints contribute as well to the cosmological constant terms of Townsend's supergravity. The Kalb-Ramond invariance is shortly discussed.Comment: 14 page