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

Representaciones gráficas. Una estrategia didáctica en el planteamiento y resolución de problemas de probabilidad

Este artículo es el reporte del taller sobre técnicas y estrategias gráficas para la resolución de problemas de probabilidad, llevado a cabo en el Relme 25 celebrado en la Cd. de Camaguey, Cuba, bajo objetivos didácticos que abordan la enseñanza aprendizaje de la probabilidad en el nivel superior. Para ello se seleccionaron y presentaron para su análisis diversos tipos de problemas con el fin de presentar las técnicas apropiadas para su solución. Se contó con la participación de profesores y estudiantes en la construcción colectiva de los significados, a partir de una situación didáctica representada por el planteamiento de problemas de probabilidad que requieren diferentes estrategias en la búsqueda de soluciones. Siguiendo recomendaciones de la Teoría de situaciones didácticas de Brousseau (1997)

Estrategias didácticas para la construcción de conocimientos estadísticos

En este trabajo de investigación se presenta una guía de aprendizaje construida para utilizar una diversidad de herramientas tecnológicas y matemáticas como parte de una estrategia didáctica, estructurada en función de las necesidades de los estudiantes, donde se cuenta con una variedad de problemas contextuales y factibles, considerando una sociedad en crisis y cuya repercusión se proyecta en el proceso educativo. En la aplicación de ésta, se puede apreciar el hecho de la intencionalidad para utilizar las herramientas, las construcciones de conceptos estadísticos, la motivación del trabajo en equipo y los argumentos presentados por los estudiantes para dar significado a la media aritmética y la noción de variabilidad; como logran darle sentido a la toma de decisiones en forma empírica, basados en los efectos que presenta la inestabilidad de los datos

Risk Communication in Thailand: A Case Study in Rayong Province

This project investigates communication strategies used to convey petrochemical pollution, HIV/AIDS, and motorcycle accident risks in Rayong, Thailand. Our goal was to characterize risk communication in Rayong to provide suggestions for improving risk communication in Rayong and Thailand. We accomplished this goal through interviews with government officials, civil-societies, academic researchers, and Rayong province residents. We identified successful strategies from other countries to develop recommendations, which we present regarding improving information flows, tailoring of information, collaboration among stakeholders, and building trust

Periodic skyrmionic textures via conformal cartographic projections

We find periodic skyrmionic textures via conformal cartographic projections that map either an entire spherical parameter space or a hemisphere onto every regular polygon that provides regular tessellations of the plane. These maps preserve the sign of the Skyrme density throughout the entire space. We implement these textures in the polarization state of a laser beam, and demonstrate that paraxial fields where a periodic texture preserving the sign of the Skyrme density is implemented in the polarization state distribution unavoidably exhibit zeros

A Bilevel Approach to Optimal Price-Setting of Time-and-Level-of-Use Tariffs

Time-and-Level-of-Use (TLOU) is a recently proposed pricing policy for energy, extending Time-of-Use with the addition of a capacity that users can book for a given time frame, reducing their expected energy cost if they respect this self-determined capacity limit. We introduce a variant of the TLOU defined in the literature, aligned with the supplier interest to prevent unplanned over-consumption. The optimal price-setting problem of TLOU is defined as a bilevel, bi-objective problem anticipating user choices in the supplier decision. An efficient resolution scheme is developed, based on the specific discrete structure of the lower-level user problem. Computational experiments using consumption distributions estimated from historical data illustrate the effectiveness of the proposed framework

Vortex breakdown in a water-spout flow

The numerical study of the steady axisymmetric air-water flow in a vertical sealed cylinder, driven by the rotating top disk, describes topological transformations as the rotation intensifies. The air meridional flow (AMF) and swirl induce meridional motions of opposite directions in water. For slow (fast) rotation, the effect of AMF (swirl) dominates. For very fast rotation, large-scale regions of clockwise meridional circulation in air and water are separated by a thin layer of anticlockwise circulation adjacent to the interface in water. This pattern develops for other fluids as well. Physical reasoning behind the flow evolution is provided