The group of strong Galois objects associated to a cocommutative Hopf quasigroup

Let H be a cocommutative faithfully flat Hopf quasigroup in a strict symmetric monoidal category with equalizers. In this paper we introduce the notion of (strong) Galois H-object and we prove that the set of isomorphism classes of (strong) Galois H-objects is a (group) monoid which coincides, in the Hopf algebra setting, with the Galois group of H-Galois objects introduced by Chase and Sweedler

Factorization method for difference equations of hypergeometric type on nonuniform lattices

We study the factorization of the hypergeometric-type difference equation of Nikiforov and Uvarov on nonuniform lattices. An explicit form of the raising and lowering operators is derived and some relevant examples are given.Comment: 21 page

Large N and double scaling limits in two dimensions

Recently, the author has constructed a series of four dimensional non-critical string theories with eight supercharges, dual to theories of light electric and magnetic charges, for which exact formulas for the central charge of the space-time supersymmetry algebra as a function of the world-sheet couplings were obtained. The basic idea was to generalize the old matrix model approach, replacing the simple matrix integrals by the four dimensional matrix path integrals of N=2 supersymmetric Yang-Mills theory, and the Kazakov critical points by the Argyres-Douglas critical points. In the present paper, we study qualitatively similar toy path integrals corresponding to the two dimensional N=2 supersymmetric non-linear sigma model with target space CP^n and twisted mass terms. This theory has some very strong similarities with N=2 super Yang-Mills, including the presence of critical points in the vicinity of which the large n expansion is IR divergent. The model being exactly solvable at large n, we can study non-BPS observables and give full proofs that double scaling limits exist and correspond to universal continuum limits. A complete characterization of the double scaled theories is given. We find evidence for dimensional transmutation of the string coupling in some non-critical string theories. We also identify en passant some non-BPS particles that become massless at the singularities in addition to the usual BPS states.Comment: 38 pages, including an introductory section that makes the paper self-contained, two figures and one appendix; v2: typos correcte

Solcore: A multi-scale, python-based library for modelling solar cells and semiconductor materials

Computational models can provide significant insight into the operation mechanisms and deficiencies of photovoltaic solar cells. Solcore is a modular set of computational tools, written in Python 3, for the design and simulation of photovoltaic solar cells. Calculations can be performed on ideal, thermodynamic limiting behaviour, through to fitting experimentally accessible parameters such as dark and light IV curves and luminescence. Uniquely, it combines a complete semiconductor solver capable of modelling the optical and electrical properties of a wide range of solar cells, from quantum well devices to multi-junction solar cells. The model is a multi-scale simulation accounting for nanoscale phenomena such as the quantum confinement effects of semiconductor nanostructures, to micron level propagation of light through to the overall performance of solar arrays, including the modelling of the spectral irradiance based on atmospheric conditions. In this article we summarize the capabilities in addition to providing the physical insight and mathematical formulation behind the software with the purpose of serving as both a research and teaching tool.Comment: 25 pages, 18 figures, Journal of Computational Electronics (2018

Optical archival spectra of blazar candidates of uncertain type in the 3rd^{rd} Fermi Large Area Telescope Catalog

Despite the fact that blazars constitute the rarest class among active galactic nuclei (AGNs) they are the largest known population of associated $\gamma$-ray sources. Many of the $\gamma$-ray objects listed in the Fermi-Large Area Telescope Third Source catalog (3FGL) are classified as blazar candidates of uncertain type (BCUs), either because they show multifrequency behaviour similar to blazars but lacking optical spectra in the literature, or because the quality of such spectra is too low to confirm their nature. Here we select, out of 585 BCUs in the 3FGL, 42 BCUs which we identify as probable blazars by their WISE infrared colors and which also have optical spectra that are available in the Sloan Digital Sky Survey (SDSS) and/or Six-Degree Field Galaxy Survey Database (6dFGS). We confirm the blazar nature of all of the sources. We furthermore conclude that 28 of them are BL Lacs, 8 are radio-loud quasars with flat radio spectrum and 6 are BL Lac whose emission is dominated by their host galaxy