Uniqueness of limit cycles for quadratic vector fields

Producción CientíficaThis article deals with the study of the number of limit cycles surrounding a critical point of a quadratic planar vector field, which, in normal form, can be written as x ′ = a1x − y − a3x 2 + (2a2 + a5)xy+a6y 2 , y ′ = x+a1y+a2x 2+(2a3+a4)xy−a2y 2 . In particular, we study the semi-varieties defined in terms of the parameters a1, a2, . . . , a6 where some classical criteria for the associated Abel equation apply. The proofs will combine classical ideas with tools from computational algebraic geometry.Agencia Estatal de Investigación - Fondo Europeo de Desarrollo Regional (grant MTM 2011-22751)Junta de Extremadura (grant GR15055)Ministerio de Economía, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (grant MTM2015-65764-C3-1-P

Vanishing Abelian integrals on zero-dimensional cycles

In this paper we study conditions for the vanishing of Abelian integrals on families of zero-dimensional cycles. That is, for any rational function $f(z)$, characterize all rational functions $g(z)$ and zero-sum integers $\{n_i\}$ such that the function $t\mapsto\sum n_ig(z_i(t))$ vanishes identically. Here $z_i(t)$ are continuously depending roots of $f(z)-t$. We introduce a notion of (un)balanced cycles. Our main result is an inductive solution of the problem of vanishing of Abelian integrals when $f,g$ are polynomials on a family of zero-dimensional cycles under the assumption that the family of cycles we consider is unbalanced as well as all the cycles encountered in the inductive process. We also solve the problem on some balanced cycles. The main motivation for our study is the problem of vanishing of Abelian integrals on single families of one-dimensional cycles. We show that our problem and our main result are sufficiently rich to include some related problems, as hyper-elliptic integrals on one-cycles, some applications to slow-fast planar systems, and the polynomial (and trigonometric) moment problem for Abel equation. This last problem was recently solved by Pakovich and Muzychuk (\cite{PM} and \cite{P}). Our approach is largely inspired by their work, thought we provide examples of vanishing Abelian integrals on zero-cycles which are not given as a sum of composition terms contrary to the situation in the solution of the polynomial moment problem.Comment: 35 pages, 1 figure; one reference added; abstract, introduction and structure change

Optimización de Coeficientes de Absorción para Simulación Numérica Acústica

The following work presents a methodology to optimize the absorption coefficients, conventionally considered as the main input parameters of room acoustical simulators. In the first place a presentation of the main characteristics of the acoustic simulator is made. Next, the procedure that is based on a modified “hill-climbing” approach is detailed. It performs the optimization of the coefficients value in an iterative procedure, which includes the calculation of the acoustic quality parameters (AQPs) with the results of an acoustic simulation of a real room. The AQPs from each simulation are compared with experimental measurements performed in the room, used as a reference for iterative adjustments. Finally, the results of the last iteration show a substantial reduction of the error, showing differences of 5.83% with the AQPs measured in the real room. &nbsp

Adults'Education and Agricultural Innovation: A Social Learning Approach

Social learning processes can be the basis of a method of agricultural innovation that involves expert and empirical knowledge. In this sense, the objective of this study was to determine the effectiveness and sustainability of an innovation process, understood as social learning, in a group of small farmers in the southern highlands of Peru. Innovative proposals and its permanence three years after the process finished were evaluated. It was observed that innovation processes generated are maintained over time; however, new innovations are not subsequently generated. We conclude that adult learning processes and innovation based on social learning are more effective and sustainable; however, the farmers internalization in innovation processes is given longer term

Implementación European Credit Transfer System en un curso de Programación en Ingeniería = European Credit Transfer System implementation in an Introduction to Programming Course for a Mechanical Engineering Degree

Los autores documentan en este artículo el proceso de adaptación a una metodología acorde con los créditos ECTS dentro de una asignatura de introducción a la Programación de ordenadores para ingenieros, equiparable a la que existe en los primeros cursos de las ingenierías superiores de corte más industrial (Ingeniería Industrial, Ingeniería de Caminos, Canales y Puertos, Ingeniería Aeronáutica, Ingeniería de Minas e Ingeniería Naval y Oceánica). Para ese proceso de adaptación se han tomado como referencia los modelos de madurez del proceso (CMM) de Ingeniería del Software y se han adaptado estos modelos, sustituyendo los procesos de elaboración de software por los formativos. Se documenta el proceso tratando de que éste sea repetible y sobre todo evaluable por agentes externos. Mientras que la mayoría de las experiencias de adaptación se centran en cuestiones relativas a la cuantificación del esfuerzo realizado por los estudiantes, en este caso se ha querido aprovechar esta oportunidad para realizar una transformación metodológica profunda, incorporando la evaluación a toda la intervención educativa. Se describe con detalle el tipo de evaluación realizada, la cual contempla la realización de un portafolio, el trabajo en grupo, la ponderación explícita de la participación y que no excluye por principio la posibilidad de aprobar sólo mediante un examen final. Se presentan resultados comparativos respecto a cursos anteriores, y correlaciones entre la evaluación ECTS y la basada simplemente en el examen. Los resultados son interesantes y sugieren que estamos cerca de completar el nivel Definido en la escala CMM. In this article, a process of adaptation to an ECTS-type methodology is documented in the context of an introductory programming course for mechanical engineers, similar to the one that exists in the initial years of more industrially-oriented engineering degrees (civil engineering, construction engineering, aeronautical engineering, mining engineering, and naval architecture and offshore engineering). For this adaptation process,Capability Maturing Models (CMM) from Software Engineering have been taken as moulds, adapting them by substituting software elaboration processes by pedagogical ones.The process is documented in a way that can be replicated and assessed by external consultants.While the majority of the ECTS adaptation experiences focus on quantifying the students' efforts, in this case, the authors have taken advantage of this opportunity to perform a profound methodological transformation, incorporating the assessment to the whole learning-teaching activity. The assessment technique is described in detail and it comprises the compiling of a portfolio, group work and explicit student participation assessment. It does not exclude on principle the possibility of passing simply via a final exam. Comparative results with previous academic years are presented, as well as correlations between ECTS assessment and marks based on the final exam. Results are interesting, suggesting we are not far from completing the CMM defined level

Gallium nanoparticles colloids synthesis for UV bio-optical sensors

F. Nucciarelli, I. Bravo, L. Vázquez, E. Lorenzo, J. L. Pau, "Gallium nanoparticles colloids synthesis for UV bio-optical sensors", SPIE Optics + Optoelectronics Proc. SPIE 10231 (16 May 2017) Copyright 2017 Society of Photo Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited. Proceedings of the Optical Sensors Conference (Prague, Czech Republic) doi: https://doi.org/10.1117/12.2265883A new method for the synthesis of colloidal gallium nanoparticles (Ga NPs) based on the thermal evaporation of Ga on an expendable aluminum zinc oxide (AZO) layer is presented here. The growth of AZO layers was investigated on different substrates at room temperature and 300 °C. By means of physical evaporation process, nanoparticles were deposited with a distribution ranging from 10 nm to 80 nm in diameter. A study of their endurance in acidic environment was carried out in order to assure the NPs shape and size stability during the etching process. Smaller particles start to disappear between 1h and 2h immersion time in a pH=1 solution, while bigger particles reduce their dimension. The NPs were dispersed in tetrahydrofuran (THF) organic solvent and optically characterized, showing strong UV absorption with a band centered at 280 nm. The colloids size distribution of as-evaporated samples was compared with the distribution obtained in droplets of the solution after drop-casting. By Dipole Discrete Approximation simulations, a close relationship between the UV absorption and the NPs with diameter smaller than ∼40 nm was found. Because of the gallium oxide (Ga1-xOx) outer shell that surrounds the Ga NPs, an enhancement of their hydrophobicity occurs. Hence, the low agglomeration state between NPs in tetrahydrofuran allows to obtain narrow absorption band in the optical spectrumWe are also grateful to the international PROMIS project, framed in the Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 641899. This research is supported by the MINECO (CTQ2014-53334-C2-2-R and MAT2016-80394-R) and Comunidad de Madrid (NANOAVANSES ref. S2013/MIT-3029) Projec