Mathematical Foundation of a Functional Implementation of the CNF Algorithm

The conjunctive normal form (CNF) algorithm is one of the best known and most widely used algorithms in classical logic and its applications. In its algebraic approach, it makes use in a loop of a certain well-defined operation related to the “distributivity” of logical disjunction versus conjunction. For those types of implementations, the loop iteration runs a comparison between formulas to decide when to stop. In this article, we explain how to pre-calculate the exact number of loop iterations, thus avoiding the work involved in the above-mentioned comparison. After that, it is possible to concatenate another loop focused now on the “associativity” of conjunction and disjunction. Also for that loop, we explain how to calculate the optimal number of rounds, so that the decisional comparison phase for stopping can be also avoided

Optimal Centers’ Allocation in Smoothing or Interpolating with Radial Basis Functions

This work was supported by FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades (Research Project A-FQM-76-UGR20, University of Granada) and by the Junta de Andalucía (Research Group FQM191).Function interpolation and approximation are classical problems of vital importance in many science/engineering areas and communities. In this paper, we propose a powerful methodology for the optimal placement of centers, when approximating or interpolating a curve or surface to a data set, using a base of functions of radial type. In fact, we chose a radial basis function under tension (RBFT), depending on a positive parameter, that also provides a convenient way to control the behavior of the corresponding interpolation or approximation method. We, therefore, propose a new technique, based on multi-objective genetic algorithms, to optimize both the number of centers of the base of radial functions and their optimal placement. To achieve this goal, we use a methodology based on an appropriate modification of a non-dominated genetic classification algorithm (of type NSGA-II). In our approach, the additional goal of maintaining the number of centers as small as possible was also taken into consideration. The good behavior and efficiency of the algorithm presented were tested using different experimental results, at least for functions of one independent variable.Junta de Andalucía-Consejería de Transformación Econímica, Industria, Conocimiento y Universidades A-FQM-76-UGR20Universidad de GranadaEuropean Regional Development FundJunta de Andalucía FQM19

Fitting and filling of 3D datasets with volume constraints using radial basis functions under tension

Acknowledgments This work was supported by FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades (Research Project A-FQM-76-UGR20, University of Granada) and by the Junta de Andalucía (Research Groups FQM-191 and TEP-190). Funding for open access charge: Universidad de Granada / CBUA.Given a dataset of 3D points in which there is a hole, i.e., a region with a lack of information, we develop a method providing a surface that fits the dataset and fills the hole. The filling patch is required to fulfill a prescribed volume condition. The fitting–filling function consists of a radial basis functions that minimizes an energy functional involving both, the fitting of the dataset and the volume constraint of the filling patch, as well as the fairness of the function. We give a convergence result and we present some graphical and numerical examples.FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades (Research Project A-FQM-76-UGR20, University of Granada)Junta de Andalucía (Research Groups FQM-191 and TEP-190)Funding for open access charge: Universidad de Granada / CBU

Multivariate analysis and extraction of parameters in resistive RAMs using the Quantum Point Contact model

A multivariate analysis of the parameters that characterize the reset process in RRAMs has been performed. The different correlations obtained can help to shed light on the current components that contribute in the Low Resistance State (LRS) of the technology considered. In addition, a screening method for the Quantum Point Contact (QPC) current component is presented. For this purpose the second derivative of the current has been obtained using a novel numerical method which allows determining the QPC model parameters. Once the procedure is completed, a whole RS series of thousands of curves is studied by means of a genetic algorithm. The extracted QPC parameter distributions are characterized in depth to get information about the filamentary pathways associated with LRS in the low voltage conduction regime.Spanish Ministry of Economy and Competitiveness TEC2014-52152-C3-2-R , MTM2013-47929-P (also supported by the FEDER program)IMB-CNM Spanish Ministry of Economy and Competitiveness TEC2014-52152-C3-1-R and TEC2014-54906-JIN (supported by the FEDER program)ENIAC Joint Undertaking-PANACHE project.Spanish ICTS Network MICRONANOFAB

Superficies de energía mínima sobre triangulaciones de tipo Powell-Sabin

Presentación y resumen en español, ingés y francésTesis Univ. Granada. Departamento de Matemáticas Aplicada. Leída el 17 de julio de 200

Approximation of 3D trapezoidal fuzzy data using radial basis functions

We present a new methodology to approximate a trapezoidal fuzzy numbers set by using smoothing radial basis functions (RBFs). The methodology uses different error and similarity indices to determine and compare the accuracy of the approximation of the given trapezoidal fuzzy data. For the proposed approximation method a fuzzy radial basis functions type are defined, called fuzzy smoothing radial basis functions under tension. The computation of one of these approximation functions from a given trape-zoidal fuzzy data set is described and some convergence results are proved. Finally, some examples in two-dimensions are given to compare the behavior of the presented method by using the proposed error and similarity indices for different configurations of the fuzzy smoothing radial basis functions under tension.FEDER/Junta de Andalucia-Consejeria de Transformacion Economica, Industria, Conocimiento y Universidades A-FQM-76-UGR20Junta de Andalucia FQM19

Numerical Solution of Linear Volterra Integral Equation Systems of Second Kind by Radial Basis Functions

In this paper we propose an approximation method for solving second kind Volterra integral equation systems by radial basis functions. It is based on the minimization of a suitable functional in a discrete space generated by compactly supported radial basis functions of Wendland type. We prove two convergence results, and we highlight this because most recent published papers in the literature do not include any. We present some numerical examples in order to show and justify the validity of the proposed method. Our proposed technique gives an acceptable accuracy with small use of the data, resulting also in a low computational cost

Acción global de innovación docente en asignaturas de matemáticas para las escuelas técnicas

Se trata de presentar la experiencia global obtenida a partir de la puesta en marcha de las distintas iniciativas y proyectos de innovación docente desarrollados y llevados a cabo por los autores de este trabajo durante cursos sucesivos. Estas nuevas ideas y planteamientos han tenido lugar tanto en el modo de presentación de las clases teóricas, como por el uso de herramientas informáticas y de cálculo adicionales en las clases prácticas con ordenador y de resolución de problemas de Análisis Numérico, así como de otras asignaturas impartidas por nuestro Departamento, en la Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos de la Universidad de Granad