Revisiting the minimum-norm problem

The design of optimal Magnetic Resonance Imaging (MRI) coils is modeled as a minimum-norm problem (MNP), that is, as an optimization problem of the form min(x is an element of R) parallel to x parallel to, where R is a closed and convex subset of a normed space X. This manuscript is aimed at revisiting MNPs from the perspective of Functional Analysis, Operator Theory, and Banach Space Geometry in order to provide an analytic solution to the following MRI problem: min(psi is an element of R) parallel to psi parallel to(2), where R:= {psi is an element of R-n : parallel to A psi-b parallel to infinity/parallel to b parallel to(infinity) 0, and b is an element of R-m \ {0}.This work has been supported by the Research Grant PGC-101514-B-I00 awarded by the Spanish Ministry of Science, Innovation and Universities and partially funded by ERDF, by the Andalusian Research, Development and Innovation Programme (PAIDI 2020) under the Research Grant PY20_01295, and by the Research Grant FEDER-UCA18-105867 awarded by the 2014-2020 ERDF Operational Programme of the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia. The APCs have been paid by the Mathematics Department of the University of Cadiz

Non-Linear Inner Structure of Topological Vector Spaces

Inner structure appeared in the literature of topological vector spaces as a tool to characterize the extremal structure of convex sets. For instance, in recent years, inner structure has been used to provide a solution to The Faceless Problem and to characterize the finest locally convex vector topology on a real vector space. This manuscript goes one step further by settling the bases for studying the inner structure of non-convex sets. In first place, we observe that the well behaviour of the extremal structure of convex sets with respect to the inner structure does not transport to non-convex sets in the following sense: it has been already proved that if a face of a convex set intersects the inner points, then the face is the whole convex set; however, in the non-convex setting, we find an example of a non-convex set with a proper extremal subset that intersects the inner points. On the opposite, we prove that if a extremal subset of a non-necessarily convex set intersects the affine internal points, then the extremal subset coincides with the whole set. On the other hand, it was proved in the inner structure literature that isomorphisms of vector spaces and translations preserve the sets of inner points and outer points. In this manuscript, we show that in general, affine maps and convex maps do not preserve inner points. Finally, by making use of the inner structure, we find a simple proof of the fact that a convex and absorbing set is a neighborhood of 0 in the finest locally convex vector topology. In fact, we show that in a convex set with internal points, the subset of its inner points coincides with the subset of its internal points, which also coincides with its interior with respect to the finest locally convex vector topology

Convergence Analysis of the Straightforward Expansion Perturbation Method for Weakly Nonlinear Vibrations

There are typically several perturbation methods for approaching the solution of weakly nonlinear vibrations (where the nonlinear terms are "small" compared to the linear ones): the Method of Strained Parameters, the Naive Singular Perturbation Method, the Method of Multiple Scales, the Method of Harmonic Balance and the Method of Averaging. The Straightforward Expansion Perturbation Method (SEPM) applied to weakly nonlinear vibrations does not usually yield to correct solutions. In this manuscript, we provide mathematical proof of the inaccuracy of the SEPM in general cases. Nevertheless, we also provide a sufficient condition for the SEPM to be successfully applied to weakly nonlinear vibrations. This mathematical formalism is written in the syntax of the first-order formal language of Set Theory under the methodology framework provided by the Category Theory

Characterizations of a Banach Space through the Strong Lacunary and the Lacunary Statistical Summabilities

In this manuscript we characterize the completeness of a normed space through the strong lacunary (N-theta) and lacunary statistical convergence (S-theta) of series. A new characterization of weakly unconditionally Cauchy series through N-theta and S-theta is obtained. We also relate the summability spaces associated with these summabilities with the strong p-Cesaro convergence summability space

Didactic handbook in visual format fot the practice of specialized translation

La experiencia docente de los participantes en este proyecto ha puesto de relieve la importancia de orientar sus principios didácticos a fomentar la incentivación y el compromiso de los alumnos en el proceso de aprendizaje, así como la explicitación y ordenación de metodologías y materiales, adecuándolos a las necesidades y capacidades del alumno de traducción. De ahí, surge la iniciativa de proporcionar al alumno una metodología práctica bien definida, de carácter progresivo, y sustentada en modelos de análisis de discurso y de análisis traductológico. Según esto, este proyecto se orienta a la creación de material docente para la práctica de la traducción especializada. En concreto se ha diseñado un manual virtual cuyo contenido se presenta mediante vídeos explicativos. Este material audiovisual se ha alojado, junto a los textos, recursos bibliográficos, modelos de análisis, traducciones comentadas, etc., en la plataforma virtual EXA ENOA2, de acceso abierto a los alumnos de la Universidad de Córdoba y con formato html5, para poder acceder a ella desde cualquier dispositivo móvil. El manual, estructurado en cuatro itinerarios (jurídico-económico-administrativo, científico-técnico, humanístico-literario y audiovisual), ofrece un modelo de análisis discursivo específico que permite al alumno detectar y priorizar las especificidades de cada género textual y sus particularidades lingüísticas. Estos análisis se aplican a un corpus bilingüe de textos (FR>ES / EN>ES) seleccionados y explicados por los docentes, de los que se aporta además una traducción al español y su correspondiente análisis traductológico. Este manual proporciona además, a modo de anexo, una selección de recursos documentales, en formato electrónico, de carácter especializado (diccionarios, bases terminológicas, manuales de traducción especializada, etc.) que el alumno puede consultar de modo inmediato o descargarse en su ordenador para futuras consultas. Este material en soporte virtual de acceso abierto pretende configurarse como manual de autoaprendizaje de técnicas de traducción especializada y se constituye como complemento didáctico para el perfeccionamiento de las destrezas de traducción en áreas especializadas, así como la asimilación de una metodología práctica y funcional que permita al alumno optimizar las fases que configuran el proceso traslativo.The teaching experience of the members of this project emphasises the importance of directing teaching principles at encouraging students’ motivation and commitment within the learning process, as well as specifying and classifying methodologies and materials in order to adapt them to the necessities and capabilities of the translation students. This fact gives rise to the initiative to provide students a fully-designed, progressive and practical methodology, which is based on the models for discourse analysis and translation analysis. In this regard, the present project targets the elaboration of teaching materials for the practice of specialised translation. In particular, we have designed a virtual manual whose contents are presented through explanatory videos. These audiovisual contents, together with texts, bibliographical resources, analysis models and commented translations, have been hosted in the EXA ENOA2 virtual platform – with open-access to all students at the University of Córdoba – in html5 format, so it can be accessed from any mobile device. The manual includes four itineraries (legal-economical, scientific-technical, humanistic-literary, and audiovisual). It offers a specific discourse analysis model for each field, helping the student to detect and prioritize the characteristics of each textual genre and their linguistic features. These analysis models are applied to a bilingual corpora (FR/EN) of texts selected and explained by the teachers. Moreover, a Spanish translation and the corresponding translation analysis are provided. The manual also procures an annex including a selection of documentary resources in electronic format – such as dictionaries, termbases, specialized translation guides, etc. – that students can check immediately or download for future consults. This open-access virtual material aims to be a self-learning tool for specialised translation and to be constituted as a teaching complement for further acquisition of translation skills in specialised fields, as well as a practical and functional methodology that enables students to optimise every phase of the translation process

Exact Solutions to the Maxmin Problem max‖Ax‖ Subject to ‖Bx‖≤1

In this manuscript we provide an exact solution to the maxmin problem max ∥ A x ∥ subject to ∥ B x ∥ ≤ 1 , where A and B are real matrices. This problem comes from a remodeling of max ∥ A x ∥ subject to min ∥ B x ∥ , because the latter problem has no solution. Our mathematical method comes from the Abstract Operator Theory, whose strong machinery allows us to reduce the first problem to max ∥ C x ∥ subject to ∥ x ∥ ≤ 1 , which can be solved exactly by relying on supporting vectors. Finally, as appendices, we provide two applications of our solution: first, we construct a truly optimal minimum stored-energy Transcranian Magnetic Stimulation (TMS) coil, and second, we find an optimal geolocation involving statistical variables

The Bishop-Phelps-Bollobás modulus for operators

A modulus for the Bishop–Phelps–Bollobás property for operators (BPBpo) is formerly introduced in the literature that characterizes whether a pair of Banach spaces enjoys the BPBpo and that also provides the best possible value of the BPBpo for a given pair of Banach spaces that enjoys it. We use it also to show that the BPBpo is hereditary to a class of complemented subspaces that strictly includes the M-summands. We also provide an equivalent reformulation of this modulus. Finally, the continuity properties of this modulus are also discussed

Measures on effect algebras

We study measures defined on effect algebras. We characterize real-valued measures on effect algebras and find a class of effect algebras, that include the natural effect algebras of sets, on which σ-additive measures with values in a finite dimensional Banach space are always bounded. We also prove that in effect algebras the Nikodym and the Grothendieck properties together imply the Vitali-Hahn-Saks property, and find an example of an effect algebra verifying the Vitali-Hahn-Saks property but failing to have the Nikodym property. Finally, we define the concept of variation for vector measures on effect algebras proving that in effect algebras verifying the Riesz Decomposition Property, the variation of a finitely additive vector measure is a finitely additive positive measure

Exact Solutions to the Maxmin Problem max parallel to Ax parallel to Subject to parallel to Bx parallel to <= 1

In this manuscript we provide an exact solution to the maxmin problem max parallel to Ax parallel to subject to parallel to Bx parallel to <= 1, where A and B are real matrices. This problem comes from a remodeling of max parallel to Ax parallel to subject to min parallel to Bx parallel to, because the latter problem has no solution. Our mathematical method comes from the Abstract Operator Theory, whose strong machinery allows us to reduce the first problem to max parallel to Cx parallel to subject to parallel to x parallel to <= 1, which can be solved exactly by relying on supporting vectors. Finally, as appendices, we provide two applications of our solution: first, we construct a truly optimal minimum stored-energy Transcranian Magnetic Stimulation (TMS) coil, and second, we find an optimal geolocation involving statistical variablesSpanish Ministry of Science, Innovation and Universities - FEDE

El Aprendizaje y Servicio como herramienta para laaplicación de los objetivos de Salud Pública en el colectivode personas mayores

Introduction: Elderly are making more use of health services and exhibit a high consumption of medicines. This is associated with a difficulty in treatment compliance and with a greater risk of adverse reactions. The aim of this project is to evaluate the knowledge and handling of medicines in a group of elderly community centers. &nbsp; Material and methods: This study is part of a Learning and Service Project (LSP) between the Complutense University of Madrid (UCM) and Coslada Town Council. The students designed and elaborated a survey of 32 items and interviewed the elderly volunteers (N=366) during the period of Nov-Dec (2019). After collecting the information, a descriptive analysis stratified by sex was carried out. &nbsp; Results: The average age of participants was 70.7 years, with a majority of women (70.2%). More than two thirds perceived their quality of life to be between very good and good, with this perception being slightly higher in women. Participants take an average of 3.4 medicines and 10% forgot medication intake. Even though most of them are independent and autonomous when it comes to taking their medication, 38% use a reminder method. &nbsp; Conclusion: The group of elderly people in Coslada stands out for its highly perceived quality of life and knowledge of their therapeutic management. The LSP is a unique opportunity to directly extrapolate the knowledge of Public Health to a reality and social need.Introducción: Las personas mayores recurren con más frecuencia a los servicios sanitarios.&nbsp; El elevado consumo de medicamentos dificulta el cumplimiento terapéutico en este colectivo asociándose a un mayor riesgo de reacciones adversas. El objetivo de este proyecto es evaluar el conocimiento y manejo de los medicamentos en un grupo de personas que acuden a los centros de mayores. Material y métodos: Este estudio se enmarca en un proyecto de Aprendizaje y Servicio (ApS) entre la Universidad Complutense de Madrid (UCM) y el Ayuntamiento de Coslada. Los estudiantes diseñaron y elaboraron una encuesta de 32 ítems y entrevistaron a las personas mayores voluntarias (N=366) durante el periodo de Nov-Dic (2019). Tras la recogida de la información, se llevó a cabo un análisis descriptivo estratificado por sexo. Resultados: La edad media de los encuestados fue de 70,7 años, siendo mayoritariamente mujeres (70,2%). Más de dos tercios, percibe su calidad de vida entre muy buena y buena, siendo esta percepción ligeramente superior en mujeres. Los encuestados toman una media de 3,4 medicamentos y un 10% afirmo olvidar alguna toma. Pese a que la mayoría una independencia y autonomía a la hora de consumir la medicación, un 38% recurre a un método recordatorio. Conclusión: El colectivo de personas mayores de Coslada destaca por su alta calidad de vida percibida y conocimiento del manejo terapéutico. El ApS es una oportunidad única de extrapolación directa de conocimientos de Salud Pública a una realidad y necesidad socia