Improved Iterative Solution of Linear Fredholm Integral Equations of Second Kind via Inverse-Free Iterative Schemes

[EN] This work is devoted to Fredholm integral equations of second kind with non-separable kernels. Our strategy is to approximate the non-separable kernel by using an adequate Taylor's development. Then, we adapt an already known technique used for separable kernels to our case. First, we study the local convergence of the proposed iterative scheme, so we obtain a ball of starting points around the solution. Then, we complete the theoretical study with the semilocal convergence analysis, that allow us to obtain the domain of existence for the solution in terms of the starting point. In this case, the existence of a solution is deduced. Finally, we illustrate this study with some numerical experiments.This research was partially supported by a grant of the Spanish Ministerio de Ciencia, Innovacion y Universidades (Ref. PGC2018-095896-B-C21-C22).Gutiérrez, JM.; Hernández-Verón, MÁ.; Martínez Molada, E. (2020). Improved Iterative Solution of Linear Fredholm Integral Equations of Second Kind via Inverse-Free Iterative Schemes. Mathematics. 8(10):1-13. https://doi.org/10.3390/math8101747S113810Argyros, I. K. (1988). On a class of nonlinear integral equations arising in neutron transport. Aequationes Mathematicae, 36(1), 99-111. doi:10.1007/bf01837974Bruns, D. D., & Bailey, J. E. (1977). Nonlinear feedback control for operating a nonisothermal CSTR near an unstable steady state. Chemical Engineering Science, 32(3), 257-264. doi:10.1016/0009-2509(77)80203-0GANESH, M., & JOSHI, M. C. (1991). Numerical Solvability of Hammerstein Integral Equations of Mixed Type. IMA Journal of Numerical Analysis, 11(1), 21-31. doi:10.1093/imanum/11.1.21Anderson, B. D. O., & Kailath, T. (1971). Some Integral Equations with Nonsymmetric Separable Kernels. SIAM Journal on Applied Mathematics, 20(4), 659-669. doi:10.1137/0120065Ezquerro, J. A., & Hernández, M. A. (2004). A modification of the convergence conditions for Picard’s iteration. Computational & Applied Mathematics, 23(1). doi:10.1590/s0101-82052004000100003Amat, S., Ezquerro, J. A., & Hernández-Verón, M. A. (2013). Approximation of inverse operators by a new family of high-order iterative methods. Numerical Linear Algebra with Applications, 21(5), 629-644. doi:10.1002/nla.1917Barikbin, M. S., Vahidi, A. R., Damercheli, T., & Babolian, E. (2020). An iterative shifted Chebyshev method for nonlinear stochastic Itô–Volterra integral equations. Journal of Computational and Applied Mathematics, 378, 112912. doi:10.1016/j.cam.2020.112912Rabbani, M., Das, A., Hazarika, B., & Arab, R. (2020). Existence of solution for two dimensional nonlinear fractional integral equation by measure of noncompactness and iterative algorithm to solve it. Journal of Computational and Applied Mathematics, 370, 112654. doi:10.1016/j.cam.2019.11265

Propagation dynamics of vector Mathieu-Gauss beams

The vector Mathieu-Gauss beams of integer order are examined as the solutions of the vector paraxial wave equation in elliptical coordinates. The propagation of the vector components and the three-dimensional intensity distribution of focused vector Mathieu-Gauss beams are analyzed for a variety of polarizations. Conditions in which the linearly polarized Mathieu-Gauss beams can be approximated by the scalar solutions of the paraxial wave equation are also discussed

Analysis of 222Rn Surface Concentrations in the Basque Country (Spain): A Case Study of Heat Waves

The objective of this study was to characterize radon concentrations registered in the Radiological Surveillance Network of the Basque country in relation to local meteorological parameters, and to determine its behaviour under heatwave events. For this purpose, radon measurements and meteorological parameters from June 2012 to June 2015 were analysed at two sites, Bilbao and Vitoria (northern Spain), in a region characterized by complex orography, causing large temporal and spatial variability in meteorological conditions. Yearly, seasonal, and diurnal cycle differences and similarities were investigated at both sites. The temporal evolution of radon concentration was analysed at both sites during the two heatwave periods officially identified by the State Meteorological Agency (8–11 August 2012 and 17–23 August 2012). The analysis revealed two different patterns of radon concentrations, in terms of both time and intensity, under this synoptic pattern, making it also possible to identify regional transport channels of radon concentrations between the two sites. This set of results evidences the adequate position of both stations to represent the spatial and temporal evolution of radiological variables continuously in this region

Desarrollo de habilidades de modelación y de creación matemática en el contexto de la orientación vocacional

Entre las habilidades más difíciles de lograr por el matemático figuran las de modelación y creación. La impartición por profesores universitarios de una asignatura para la enseñanza media superior, plantea la necesidad de formalizar un conjunto de ejercicios que se corresponden con las temáticas: inferencia, ecuaciones, problemas con ecuaciones, cálculos algebraicos, geometría y técnicas matemáticas, por lo que se concibió la tipología de los ejercicios en correspondencia con los procedimientos típicos de los métodos de la matemática para desarrollar las citadas habilidades. Resultó funcional establecer la tipología, pues permite la apropiada ampliación de la ejercitación en el contexto requerido. La Orientación Vocacional en el preuniversitario debe procurar desarrollar los intereses cognoscitivos, conocimientos y habilidades relacionados con las diferentes áreas del saber, mediante una asignatura y las demás actividades que se realizan en el proceso formativo.Una de las actividades que se ha concebido desde el curso 2014-2015 es la atención a la asignatura Matemática en el currículo de los grados décimo y onceno, destinada a despertar motivación y entrenar habilidades matemáticas, impartida por profesores universitarios

New Approaches for Teaching Soil and Rock Mechanics Using Information and Communication Technologies

Soil and rock mechanics are disciplines with a strong conceptual and methodological basis. Initially, when engineering students study these subjects, they have to understand new theoretical phenomena, which are explained through mathematical and/or physical laws (e.g. consolidation process, water flow through a porous media). In addition to the study of these phenomena, students have to learn how to carry out estimations of soil and rock parameters in laboratories according to standard tests. Nowadays, information and communication technologies (ICTs) provide a unique opportunity to improve the learning process of students studying the aforementioned subjects. In this paper, we describe our experience of the incorporation of ICTs into the classical teaching-learning process of soil and rock mechanics and explain in detail how we have successfully developed various initiatives which, in summary, are: (a) implementation of an online social networking and microblogging service (using Twitter) for gradually sending key concepts to students throughout the semester (gradual learning); (b) detailed online virtual laboratory tests for a delocalized development of lab practices (self-learning); (c) integration of different complementary learning resources (e.g. videos, free software, technical regulations, etc.) using an open webpage. The complementary use to the classical teaching-learning process of these ICT resources has been highly satisfactory for students, who have positively evaluated this new approach.This work has been developed in the framework of the RECLAND Project. It has been funded by the European Union under Lifelong Learning Programme, Erasmus Programme: Erasmus Multilateral Projects, 526746-LLP-1-2012-1-ES-ERASMUS-EMCR, MSc Programme in Climate Change and Restoration of Degraded Land

Experimental study on the motion of solids around an isolated bubble rising in a vertically vibrated fluidized bed

The motion of solids around isolated bubbles rising in a vertically vibrated pseudo-2D bed is experimentally studied in this work by combining Digital Image Analysis (DIA) and Particle Image Velocimetry (PIV). The bed material is Geldart B spherical particles. Different vibration amplitudes and frequencies are applied to the bed vessel while the bed is fluidized with air at minimum fludization conditions and isolated bubbles are sequentially injected in the bed. An averaging of bubbles method is presented and used to statistically characterize the average motion of solids around the bubbles. The results show that the presence of a bubble in the system perturbs the cyclic compression and expansion behavior of the bed bulk and, in particular, influences the velocity of the expansion wave front traveling upwards the bed. Analogously, the motion of solids around the bubble and, specially, in the bubble wake region, are strongly affected by the cyclic compression and expansion of the bed bulk. However, direct comparisons of the experimental results with the Davidson & Harrison potential flow model reveal that this model is still applicable for the prediction of the solids velocity around the bubble in a vertically vibrated fluidized bed

Neutrino events within muon bundles at neutrino telescopes

This work was partially supported by the Spanish Ministry of Sci-ence, Innovation and Universities (PID2019-107844GB-C21/AEI/10.13039/501100011033) and by the Junta de Andalucia, Spain (FQM 101, SOMM17/6104/UGR, P18-FR-1962, P18-FR-5057) . MGG acknowledges a grant from Programa Operativo de Empleo Juvenil (Junta de Andalucia) . The work of GHT has been funded by the program Es-tancias Postdoctorales en el Extranjero 2019-2020 of CONACYT, Mexico. GHT also acknowledges Prof. Pablo Roig for partial support through Catedra Marcos Moshinsky (Fundacion Marcos Moshinsky) . Funding for open access charge: Universidad de Granada/CBUA.The atmospheric neutrino flux includes a component from the prompt decay of charmed hadrons that becomes significant only at E >= 10 TeV. At these energies, however, the diffuse flux of cosmic neutrinos discovered by IceCube seems to be larger than the atmospheric one. Here we study the possibility to detect a neutrino interaction in down-going atmospheric events at km3 telescopes. The neutrino signal will always appear together with a muon bundle that reveals its atmospheric origin and, generically, it implies an increase in the detector activity with the slant depth. We propose a simple algorithm that could separate these events from regular muon bundles.Spanish Ministry of Science, Innovation and Universities PID2019-107844GB-C21/AEI/10.13039/501100011033Junta de Andalucia European Commission FQM 101- SOMM17/6104/UGR- P18-FR-1962- P18-FR-5057Junta de AndaluciaProgram Es-tancias Postdoctorales en el Extranjero 2019-2020 of CONACYT, MexicoUniversidad de Granada/CBUACatedra Marcos Moshinsky (Fundacion Marcos Moshinsky