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Satellite reflectarray synthesis using the intersection approach by means of algorithms of the alternating generalized projection (AGP) method to avoid trap points with sequential stages of different illuminations is presented. In this scenario, we examine two distinct sets: the set of radiation patterns producible by the reflectarray and the set of radiation patterns which meet the mission’s criteria. These sets are generally non-convex. Therefore, it is expected that conventional algorithms of the method of alternating projections (MAP) converge to trap points (i.e., local minima of the distance between the involved sets). Thus, the AGP method, which takes into account the trap points, has been considered. When large reflectarrays are considered for satellite applications, several trap points can appear, producing oscillatory behavior between several trap points. A mathematical formalism which supports the idea that a reduction in the edge illumination of an antenna involves fewer trap points is described. Thus, the oscillatory behavior can be avoided by using sequential stages in the synthesis process with different edge illumination levels in each stage. In this work, we demonstrate this synthesis technique with sequential stages, using the proposed algorithm to avoid trap points. more...

Species coexistence is a major issue in ecology. We disentangled the role of individual interference when competing in the classical interference competition model. For the first time, we considered simultaneously intra- and inter-species interference by introducing the Beddington–DeAngelis competitive response into the classical competition model. We found a trade-off between intra- and inter-species interference that refines in a sense the well-known balance of intra- and inter-species competition coefficients. As a result, we found that (i) global coexistence is possible for a larger range of values of the inter-/intra-species competition coefficients and contributes to explaining the high prevalence of species coexistence in nature. This feature is exclusively due to intra-species interference. (ii) We found multi-stability scenarios previously described in the literature that can be reinterpreted in terms of individuals interference. more...

Trending topics are often the result of the spreading of information between users of social networks. These special topics can be regarded as rumors. The spreading of a rumor is often studied with the same techniques as in epidemics spreading. It is common that many datasets may not have enough measured variables, so we propose a method for studying the general behavior of the spreaders by selecting estimated variables given by the deterministic model. In order to provide a good approximation, we implemented an adaptive neuro-fuzzy inference system (ANFIS). So, in our numerical experimentations, a deterministic approach using SIR and SIRS models (with delay) for two different topics is used. Thus, the authors just applied the ANFIS model for their application and the deterministic model as the preprocessing input variable. more...

We use the segmented formulation of the Tau method to approximate the solutions of a family of linear and nonlinear neutral delay differential equations a1(t) y'(t) = y(t)[a2(t)] y(t-τ) + a3(t) y'(t-τ) + a4(t)] + a5(t) y(t-τ) + a6(t) y'(t-τ) + a7(t), t ≥ 0 y(t) = Ψ(t), t ≤ 0 which represents, for particular values of ai(t), i=1,7, and τ, functional differential equations that arise in a natural way in different areas of applied mathematics. This paper means to highlight the fact that the step by step Tau method is a natural and promising strategy in the numerical solution of functional differential equations. more...

In this paper we extend the application of the alternating projection algorithm to solve the problem of finding a point in the intersection of n sets (n>=2), which are not all of them convex sets. Here we term such method as alternating generalized projection (AGP) method. In particular, we are interested in addressing the problem of avoiding the so-called trap points, which may prevent an algorithm to obtain a feasible solution in two or more sets not all convex. Some strategies that allow us to reach the feasible solution are established and conjectured. Finally, we present simple numerical results that illustrate the efficiency of the iterative methods considered. more...

This work refers to the analysis, study and resolution of the mathematical problem involved in the design and construction of the cover of a ball, such as the ones used in sports, in order to achieve a ball with optimal roundness and sphericity factors.The design of well distributed ball structures has grown in importance in the last years, most of all in the field of sports, such as soccer. The current trend is directed mainly towards finding a fast ball that will give more dynamism to the game. In order to achieve a greater velocity of the ball during its movement it is important that it has not only an adequate distribution of panels, that give it a greater sphericity, but also that it has a structure that allows for a good distribution of the existing tension between the panels. Starting from an initial design, we define a process of readjustment of the panels in the ball cover, which will lead us to obtain optimal sphericity factors. Then, through a “twisting” process, we can add area to the surface without altering the sphericity factors, and solving the Missing Area Problem (or MAP). Finally, by redefining the final form of the panels, we propose tessellate strategies that will optimize the ball’s spherical structure. more...

Los algoritmos de proyección han evolucionado a partir del algoritmo de proyección alternante propuesto por J. von Neumann en 1933, donde el espacio solución es la intersección de un número finito de subespacios o conjuntos convexos. Investigaciones recientes se han centrado en técnicas para acelerar la convergencia del método y explotar el multiprocesamiento. En este trabajo consideramos el problema de restauración de imágenes. La mayoría de las técnicas desarrolladas para resolverlo han usado algoritmos iterativos; una de ellas consiste en usar proyecciones ortogonales alternantes. Llevamos a cabo una revisión cronológica de las diferentes técnicas en las que se ha aplicado el método de las proyecciones ortogonales alternantes al problema de restauración de imágenes, hasta llegar al enfoque reciente de Combettes (1997-1999), en donde la restauración se basa en el cálculo de proyecciones aproximadas, en lugar de proyecciones exactas. more...

El objetivo del presente estudio fue analizar las herramientas tecnológicas disponibles para mejorar la formación por competencias en la educación a distancia de la Facultad de Ciencias Empresariales en la Universidad Privada Domingo Savio, Bolivia. La investigación fue descriptiva-exploratoria y propositiva, con un diseño no experimental. Los resultados indicaron insuficiencias en el uso del Entorno Virtual de Aprendizaje por parte del profesorado y educandos y no se utilizan de manera pertinente las tecnologías en las actividades docentes. Se comprueba una falta de interés y desmotivación de los educandos el (76%), el 64% de alumnos reconoció que utiliza de manera adecuada las herramientas tecnológicas que se emplean en la docencia. Se resalta la necesidad de capacitación continua del profesorado, ya que el 66% no recibió capacitación adecuada por parte de la universidad que les permita fortalecer los conocimientos y competencias digitales para desarrollar actividades docentes innovadoras en la modalidad a distancia. more...