Symmetry, winding number and topological charge of vortex solitons in discrete-symmetry media

We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schr\"odinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance.Comment: 6 pages, 2 figure

Vorticity cutoff in nonlinear photonic crystals

Using group theory arguments, we demonstrate that, unlike in homogeneous media, no symmetric vortices of arbitrary order can be generated in two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry. The only condition needed is that the non-linearity term exclusively depends on the modulus of the field. In the particular case of 2D periodic systems, such as nonlinear photonic crystals or Bose-Einstein condensates in periodic potentials, it is shown that the realization of discrete symmetry forbids the existence of symmetric vortex solutions with vorticity higher than two.Comment: 4 pages, 5 figures; minor changes in address and reference

La cetrería en Cataluña

Treball presentat a l'assignatura de Deontologia i Veterinària Legal (21223

Glycogen synthase kinase-3β negatively regulates group IIA phospholipase A2 expression in human aortic smooth muscle and HepG2 hepatoma cells

AbstractThe present study shows that the IFN-γ-mediated upregulation of secretory phospholipase A2 of group IIA (sPLA2-IIA) in HASMC and HepG2 cells is synergistically increased after simultaneous inhibition of glycogen synthase kinase-3β (GSK-3β) by indirubin-3′-monoxime, 5-iodo or AR-A014418. The effect of GSK-3β inhibition was dose- and time-dependent and can be further augmented by its concomitant incubation with Clostridium difficile toxin B, an inhibitor of small Rho proteins, or H-1152, an inhibitor of Rho-associated kinase. Using AG-490 and caffeic acid phenethyl ester (CAPE), it is further demonstrated that the effect of GSK-3β inhibition on sPLA2-IIA expression depends on Janus kinase-2 and NF-κB-signaling

Forward-backward equations for nonlinear propagation in axially-invariant optical systems

We present a novel general framework to deal with forward and backward components of the electromagnetic field in axially-invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse inhomogeneities. With a minimum amount of approximations, we obtain a system of two first-order equations for forward and backward components explicitly showing the nonlinear couplings among them. The modal approach used allows for an effective reduction of the dimensionality of the original problem from 3+1 (three spatial dimensions plus one time dimension) to 1+1 (one spatial dimension plus one frequency dimension). The new equations can be written in a spinor Dirac-like form, out of which conserved quantities can be calculated in an elegant manner. Finally, these new equations inherently incorporate spatio-temporal couplings, so that they can be easily particularized to deal with purely temporal or purely spatial effects. Nonlinear forward pulse propagation and non-paraxial evolution of spatial structures are analyzed as examples.Comment: 11 page

Car quality improvements and price indices in Spain

(resumen en la version española: 'Mejoras de calidad e indices de precios del automovil en España'

1,3-Bis(3-carboxypropyl)-1H-imidazole

The use of γ-aminobutyric acid (GABA) as a starting material in a multicomponent reaction has resulted in the preparation of the zwitterionic 1,3-bis(3-carboxypropyl)imidazole (bcpim). The synthesis of this imidazole derivative in a one-pot procedure with stoichiometric amounts of the corresponding reagents (formaldehyde, glyoxal, and GABA in a 1:1:2 ratio) has resulted in a straightforward and effective methodology, meaning a significant improvement from a sustainable point of view.This research was funded by Ministerio de Ciencia, Innovación y Universidades (grant number PGC2018-096616-B-I00), Ministerio de Ciencia e Innovación (PID2021-127332NB-I00), Generalitat Valenciana (grant number AICO/2021/013), and the University of Alicante (grant number VIGROB-316)