Multifractal behavior of polynomial Fourier series

We prove non-trivial upper and lower bounds for the "Spectrum of Singularities" of Fourier Series with polynomial frequencies. The Spectrum of Singularities of a function f gives the Hausdorff dimension of the set of points with a given H\"older exponent for f.Comment: 36 pages, 2 figures. Submitted for publicatio

Fourier series in BMO with number theoretical implications

This is a post-peer-review, pre-copyedit version of an article published in Mathematische Annalen. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00208-019-01882-9We introduce an elementary argument to bound the BMO seminorm of Fourier series with gaps giving in particular a sufficient condition for them to be in this space. Using finer techniques we carry out a detailed study of the series ∑n-1e2πin2x providing some insight into how much this BMO Fourier series differs from defining an L∞ functionThe authors are partially supported by the MTM2017-83496-P Grant of the MICINN (Spain) and the first author and the second author are also supported by “Severo Ochoa Programme for Centres of Excellence in R&D” (SEV-2015-0554

Multifractal behavior of polynomial Fourier series

We study the spectrum of singularities of a family of Fourier series with polynomial frequencies, in particular we prove that they are multifractal functions. The case of degree two was treated by S. Jaffard in 1996. Higher degrees require completely different ideas essentially because harmonic analysis techniques (Poisson summation) are useless to study the oscillation at most of the points. We introduce a new approach involving special diophantine approximations with prime power denominators and fine analytic and arithmetic aspects of the estimation of exponential sums to control the Hölder exponent in thin Cantor-like set

Decision-making Tools and Memetic Algorithms in Management and Linear Programming Problems

Operational Research uses a set of tools based on scientific research principles to achieve rational and meaningful management decisions. This article tries to give solution to a highly complex Linear Programming problem by using Simplex method, Solver and a hybrid prototype which combines the theories of Genetic Algorithms with a new local search heuristic technique. Hybridization of these two techniques is becoming known as Memetic Algorithm. Additionally, this article tries to present different techniques to support management decision-making, with the intention of being used increasingly in the business environment sustaining, thus, decisions by mathematics or artificial intelligence and not only by experience.quantitative management; quantitative methods; decision-making; linear programming; operational research; heuristics; hybrid methods; memetic algorithms.

ISO 9001: 2008 y la investigación de la satisfacción del cliente

La norma ISO 9001:2008 requiere en su claúsula "8.2.1. Satisfacción del cliente" que la empresa para poder certificarse debe realizar el seguimiento de la información relativa a la percepción del cliente. Además permite que ese seguimiento pueda realizarse no sólo con encuestas sino con diferentes métodos. A priori aparenta ser un campo donde las empresas de investigación comercial podrían ser contratadas por su especialización. Sin embargo los autores de este artículo hemos auditado un total de 123 Pymes en el País Vasco y Navarra a lo largo del pasado año 2009 y sorprendemente ninguna empresa externalizaba esta investigación. ¿Por qué

Algoritmos meméticos en problemas de investigación operativa

En este artículo se plantea la resolución de un problema de Investigación Operativa utilizando PHPSimplex (herramienta online de resolución de problemas de optimización utilizando el método Simplex), Solver de Microsoft Excel y un prototipo híbrido que combina las teorías de los Algoritmos Genéticos con una técnica heurística de búsqueda local. La hibridación de estas dos técnicas es conocida como Algoritmo Memético. Este prototipo será capaz de resolver problemas de Optimización con función de maximización o minimización conocida, superando las restricciones que se planteen. Los tres métodos conseguirán buenos resultados ante problemas sencillos de Investigación Operativa, sin embargo, se propone otro problema en el cual el Algoritmo Memético y la herramienta Solver de Microsoft Excel, alcanzarán la solución óptima. La resolución del problema utilizando PHPSimplex resultará inviable. El objetivo, además de resolver el problema propuesto, es comparar cómo se comportan los tres métodos anteriormente citados ante el problema y cómo afrontan las dificultades que éste presenta. Además, este artículo pretende dar a conocer diferentes técnicas de apoyo a la toma de decisiones, con la intención de que se utilicen cada vez más en el entorno empresarial sustentando, de esta manera, las decisiones mediante la matemática o la Inteligencia Artificial y no basándose únicamente en la experiencia.KUTXA; Vicerrectorado de Campus de Gipuzkoa de la UPV/EH

D8.6 OPTIMAI commercialization and exploitation strategy

Deliverable D8.6 OPTIMAI commercialization and exploitation strategy 1 st version is the first version of the OPTIMAI Exploitation Plan. Exploitation aims at ensuring that OPTIMAI becomes sustainable well after the conclusion of the research project period so as to create impact. OPTIMAI intends to develop an industry environment that will optimize production, reducing production line scrap and production time, as well as improving the quality of the products through the use of a variety of technological solutions, such as Smart Instrumentation of sensors network at the shop floor, Metrology, Artificial Intelligence (AI), Digital Twins, Blockchain, and Decision Support via Augmented Reality (AR) interfaces. The innovative aspects: Decision Support Framework for Timely Notifications, Secure and adaptive multi-sensorial network and fog computing framework, Blockchain-enabled ecosystem for securing data exchange, Intelligent Marketplace for AI sharing and scrap re-use, Digital Twin for Simulation and Forecasting, Embedded Cybersecurity for IoT services, On-the-fly reconfiguration of production equipment allows businesses to reconsider quality management to eliminate faults, increase productivity, and reduce scrap. The OPTIMAI exploitation strategy has been drafted and it consists of three phases: Initial Phase, Mid Phase and Final Phase where different activities are carried out. The aim of the Initial phase (M1 to M12), reported in this deliverable, is to have an initial results' definition for OPTIMAI and the setup of the structures to be used during the project lifecycle. In this phase, also each partner's Individual Exploitation commitments and intentions are drafted, and a first analysis of the joint exploitation strategies is being presented. The next steps, leveraging on the outcomes of the preliminary market analysis, will be to update the Key Exploitable Results with a focus on their market value and business potential and to consolidate the IPR Assessment and set up a concrete Exploitation Plan. The result of the next period of activities will be reported in D8.7 OPTIMAI commercialization and exploitation strategy - 2nd version due at month 18 (June 2022