Translation invariant operators

Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2018, Director: F. Javier Soria de Diego[en] The theory of translation invariant operators is a branch that involves techniques and concepts from a wide variety of fields such as functional analysis, harmonic analysis or Fourier analysis, and whose main goal is to find and describe boundedness conditions and norm estimates on such objects. Its study started to firmly develop around the second half of the last century, thanks to the work of Hörmander, Fefferman, Jodeit, Stein, Marcinkiewicz, and so many others, but it is still a subject of great interest nowadays, not only because of its applications and relations to other fields, such as partial differential equations or summability methods for Fourier coefficients, but also because of the large amount of open questions that the theory still has to answer. For instance, it is not known yet a complete characterization on when such an operator is bounded between two Lebesgue spaces. Maybe that is one of its most surprising aspects: even though its main object of study is a class of operators which are initially defined with a very simple property (namely, commuting with translations), it turns out that this condition gives rise to a rich structure that requires of much more sophisticated tools in order to understand it. The current development of the theory tries to follow that path, using those tools, such as the theory of distributions and Fourier transform, to translate the problem of boundedness of operators to a problem of studying properties of certain functions, which in this context are called multipliers. This is indeed a helpful step, for one can then find symmetry properties on the classes of multipliers of bounded operators between two Lebesgue spaces, and even arrive to the conclusion that when both spaces are actually the same, every multiplier is a bounded function. Yet, starting from a bounded function, finding which of its properties analytical, geometrical,...) might be relevant in order to have a multiplier is a tough task that, as we say, is still barely solved. It is known, for instance, that when the multiplier is a characteristic function of a set, the geometry of the set plays a huge role. The maximum exponent of this fact is probably the, now disproven, multiplier problem for the ball. Even when the geometry of the set gives good boundedness properties (such as the case of a polygon), there is still much work to do on finding sharp constants for the norm of such operators. On the other hand, regularity conditions seem to affect as well, thanks to a couple of results due to Hörmander and Marcinkiewicz. Our goal in this Master’s Thesis is to give an overview of the most relevant as- pects of the theory, starting from the most basic definitions, and ending precisely in the study of Hörmander’s and Marcinkiewicz’s results and the multiplier problem for the ball. Chapters 1 and 2 cover the initial tools that one needs in order to attack this topic, such as the essential elements of the theory of function spaces and distributions, and the definition of translation invariant operators, together with their identification with multipliers and the properties of multipliers’ classes, given mostly by Theorem 2.15. We then move to Chapter 3 in order to review a theory due to Littlewood and Paley about decomposition of functions in the frequency domain using multipliers, which gives estimates on such decompositions in terms of the original function. The idea behind this theory is to extend estimates which are natural on the space of square integrable functions to other spaces of integrable functions, as done in Theorem 3.4. This theory is later used in Chapter 4 to prove the mentioned results of Hörmander and Marcinkiewicz (Theorems 4.2 and 4.5), and we see some applications of these results to multipliers with simple homogeneity properties. Finally, we focus on Chapter 5 to review this influence of geometrical properties on boundedness of this class of operators, where we have exposed Fefferman’s work on the ball multiplier problem. This work, which culminates with the conclusion of Theorem 5.6, represents a nice example on how the theory of translation invariant operators intersects with other seemingly unrelated branches, for it uses a geometrical construction originated around the first half of the past century known as Perron’s tree, which was originally proposed for solving Kakeya’s needle problem

Propuesta innovadora para trabajar la importancia de la alimentación y la actividad física en la salud del alumnado de Primaria.

Este proyecto innovador trata de desarrollar las clases de Educación Física con una metodología distinta a la tradicional. La gamificación será la metodología que se llevará a cabo con el objetivo de que el alumnado sea capaz de concienciarse sobre el impacto que tiene en su propia salud mantener unos hábitos de vida saludables, como una buena alimentación, buena higiene postural y corporal y la realización de actividad física diaria de una manera mucho más lúdica que aumente la motivación, la implicación y la diversión. Mantener un estilo de vida saludable es fundamental y es necesario asentar una buena base desde los centros educativos.This innovation project aims to develop Physical Education classes with a different methodology from the traditional one. Gamification will be the methodology used in order to develop in the students the awareness of the impact on their own health by maintaining healthy habits, such as a good health, maintaining healthy lifestyle and good nutrition habits. Also, good postural hygiene, nutrition and daily physical activity in a much more playful way that could increase motivation, involvement and fun. Maintaining a healthy lifestyle is fundamental and it is also necessary to lay a good foundation for a healthy lifestyle from the educational centres

Eficacia de la educación terapéutica en las enfermedades respiratorias crónicas: revisión sistemática.

Antecedentes: La educación en pacientes con enfermedades respiratorias crónicas debe ser un componente básico del tratamiento transdisciplinar de los mismos. Va orientada a que el paciente aprenda las necesidades de cumplir con las indicaciones de los profesionales de la salud y a introducir comportamientos que le ayuden a controlar su enfermedad y mejorar su estado de salud. La heterogeneidad en su forma de aplicación y de las medidas de resultados utilizadas para comprobar la eficacia misma no permite mostrar sus beneficios. Objetivos: Evaluar los métodos y eficacia de las intervenciones educativas en los pacientes con enfermedades respiratorias crónicas en el contexto de los resultados de la salud. Metodología: Se realizó una revisión sistemática. Las búsquedas se hicieron en Abril del año 2013 en las bases de datos Pubmed, Cochrane y Web of Science de ensayos clínicos aleatorios y de revisiones sistemáticas a partir del año 2009 escritos en español, inglés o francés que compararan dos o más intervenciones siendo al menos una de ellas una intervención educativa. Palabras clave: Asma, EPOC, fibrosis quística, educación, autocuidado, eficacia. Resultados: De los 30 ensayos clínicos aleatorios incluidos en esta revisión 3 (10%) fueron de muy alta calidad, 16 (53%) son de alta calidad, y 11 (37%) son de baja calidad. Las intervenciones educativas muestran beneficios estadísticamente significativos respecto al tratamiento habitual que no incluye este tipo de intervenciones. Las intervenciones que incluyen ejercicio físico o ejercicios respiratorios o tienen en cuenta las necesidades previas del paciente son más eficaces en términos de percepción de la calidad de vida pero no producen mejora en cuanto a la función pulmonar. Conclusiones: Tras la realización de la revisión no se puede confirmar la eficacia de la educación terapéutica y se requieren más ensayos clínicos aleatorios con una metodología más rigurosa para evaluar su efectividad.Background: Self Management Education Programs should be considered as a basic feature of multidisciplinary treatment for patients with respiratory diseases, thus meaning the patient needs to be taught on the one hand the need to follow the health professional’s advice and also to develop attitudes that may enable him to have control over his disease so as to improve his physical condition. The way the health professionals have carried out this measure and the efficiency of the survey’s result show there are no benefits in the application of this training. Objective: The assessment of the methods and efficiency of the training applications in patients with chronic respiratory diseases. Methodology: In April 2013 and taking 2009 as a starting point, a search on randomized clinical trials and systematic checkups in English, Spanish and French was carried out in the data bases of Pubmed, Cochrane and Web Science. The search aimed at comparing two or more interventions being at least one of them an educational intervention. Key words: Asthma, COPD, cystic fibrosis, education, self care, efficiency. Results: Out of the 30 randomized controlled trials included in this checkups, 3 (10%) were of a very high quality, 16 (53%) of high quality and 11 (37%) of low quality. The educational interventions show statistically significant benefits in relation to the usual treatment where this kind of interventions are not included. The interventions where physical exercise, respiratory exercises or even where the patient´s needs are taken into account before implementing the educational intervention are more efficient in terms of the person’s perception of his quality of life but there is no improvement regarding the patient’s pulmonary functioning or performance. Conclusions: We cannot prove the benefits of therapeutical education and we find there is a need to carry out more randomized controlled trials with a more accurate methodology in order to assess its effectiveness.Grado en Fisioterapi

Eficacia de la educación terapéutica en las enfermedades respiratorias crónicas: revisión sistemática.

Antecedentes: La educación en pacientes con enfermedades respiratorias crónicas debe ser un componente básico del tratamiento transdisciplinar de los mismos. Va orientada a que el paciente aprenda las necesidades de cumplir con las indicaciones de los profesionales de la salud y a introducir comportamientos que le ayuden a controlar su enfermedad y mejorar su estado de salud. La heterogeneidad en su forma de aplicación y de las medidas de resultados utilizadas para comprobar la eficacia misma no permite mostrar sus beneficios. Objetivos: Evaluar los métodos y eficacia de las intervenciones educativas en los pacientes con enfermedades respiratorias crónicas en el contexto de los resultados de la salud. Metodología: Se realizó una revisión sistemática. Las búsquedas se hicieron en Abril del año 2013 en las bases de datos Pubmed, Cochrane y Web of Science de ensayos clínicos aleatorios y de revisiones sistemáticas a partir del año 2009 escritos en español, inglés o francés que compararan dos o más intervenciones siendo al menos una de ellas una intervención educativa. Palabras clave: Asma, EPOC, fibrosis quística, educación, autocuidado, eficacia. Resultados: De los 30 ensayos clínicos aleatorios incluidos en esta revisión 3 (10%) fueron de muy alta calidad, 16 (53%) son de alta calidad, y 11 (37%) son de baja calidad. Las intervenciones educativas muestran beneficios estadísticamente significativos respecto al tratamiento habitual que no incluye este tipo de intervenciones. Las intervenciones que incluyen ejercicio físico o ejercicios respiratorios o tienen en cuenta las necesidades previas del paciente son más eficaces en términos de percepción de la calidad de vida pero no producen mejora en cuanto a la función pulmonar. Conclusiones: Tras la realización de la revisión no se puede confirmar la eficacia de la educación terapéutica y se requieren más ensayos clínicos aleatorios con una metodología más rigurosa para evaluar su efectividad.Background: Self Management Education Programs should be considered as a basic feature of multidisciplinary treatment for patients with respiratory diseases, thus meaning the patient needs to be taught on the one hand the need to follow the health professional’s advice and also to develop attitudes that may enable him to have control over his disease so as to improve his physical condition. The way the health professionals have carried out this measure and the efficiency of the survey’s result show there are no benefits in the application of this training. Objective: The assessment of the methods and efficiency of the training applications in patients with chronic respiratory diseases. Methodology: In April 2013 and taking 2009 as a starting point, a search on randomized clinical trials and systematic checkups in English, Spanish and French was carried out in the data bases of Pubmed, Cochrane and Web Science. The search aimed at comparing two or more interventions being at least one of them an educational intervention. Key words: Asthma, COPD, cystic fibrosis, education, self care, efficiency. Results: Out of the 30 randomized controlled trials included in this checkups, 3 (10%) were of a very high quality, 16 (53%) of high quality and 11 (37%) of low quality. The educational interventions show statistically significant benefits in relation to the usual treatment where this kind of interventions are not included. The interventions where physical exercise, respiratory exercises or even where the patient´s needs are taken into account before implementing the educational intervention are more efficient in terms of the person’s perception of his quality of life but there is no improvement regarding the patient’s pulmonary functioning or performance. Conclusions: We cannot prove the benefits of therapeutical education and we find there is a need to carry out more randomized controlled trials with a more accurate methodology in order to assess its effectiveness.Grado en Fisioterapi

Confirmation of symmetrical distributions of clinical attachment loss and tooth loss in a homogeneous Mexican adult male population

Background/purpose To ascertain whether or not clinical attachment loss and tooth loss are present with similar severity and prevalence across the two sides of the mouth in a homogeneous sample of urban male adults. Materials and methods A cross-sectional study was carried out on 161 policemen (a largely homogeneous group in terms of ethnic background, socioeconomic status, sex, occupation, and medical/dental insurance) in Campeche, Mexico. Periodontal examinations were undertaken using the Florida Probe System in a dental chair by one trained and standardized examiner (kappa ≥ 0.60) to determine clinical attachment loss and tooth loss. We examined six sites in all teeth present in the mouth (a maximum of 168 sites, no third molars). Because of correlated data between observations, McNemar (for tooth loss) and Wilcoxon (for attachment loss) signed-rank tests were used to compare right and left sites within the same patient. Results The mean age was 38.4 ± 11.0 years. The mean number of teeth present was 24.4 ± 4.6; the mean number of periodontal sites/person was 146.7 ± 27.8. All P values were ≥ 0.05 (except for attachment loss in the upper first premolars), suggesting that there were no statistically significant differences between the right and left sides for the frequency of presentation of these two conditions. Conclusion Tooth loss and attachment loss measurements largely resemble each other on both sides of the mouth

Evaluation of leakages effects in the water supply system of Moratalla (Spain). Póster

One of the risk management requirements is the assessment of the effect of each kind of possible failure. In water supply systems, the most common failures are the pipe leakages. Most leakages can be modelled as orifices in a pipe [1]. At this paper, a leakage pattern is defined for each of the 300 pipes in Moratalla’s water supply system. That leakage pattern is defined as an orifice whose diameter length is 1/10 of the pipe diameter. Epanet-Octave is a GNU Octave wrapper that makes easy and vector oriented the use of EPANET ToolKit. Epanet-Octave library has been used to carry out a simulation for each pipe which may have a leakage. Each simulation lasts a whole simulated day to include leakage effects for the different pressures and demands that happen during the day. Then, the results are summarised by using an index which weights the negative effect of the leakages. Usually leakages are evaluated mainly by the energy waste in pumping that water [2-3]. In this case, the suggested index accounts for leakage flow rates, water quality deterioration and service deterioration. Leakage flow rates effects are included through the maximum leakage flow rate (in time) and its average value, which in this case is proportional to the energy cost used in other works as the system distributes the water from the reservoirs to customers by gravity. Water quality deterioration is evaluated by the presence of negative pressures around the orifice. Finally, service deterioration is measured through the water that would be supplied below the regulated minimum pressure. This weighted index, which is shown in figure 1, can be used, together with other non-hydraulic factors like pipe-age or pipe-material, to prioritise the maintenance and even the replacement of pipes according to a risk management strategy

Alejandra Pizarnik: un surrealismo propio

Esta investigación tiene como objetivo construir una poética de Alejandra Pizarnik, para esto explora la relación de la autora con el surrealismo y reconstruye otras fuentes o lecturas, especialmente hispanoamericanas, que aparecen en la obra de la poeta y que, por lo tanto, establecen ideas y herramientas que fueron usadas, apropiadas y modificadas por Pizarnik, que junto con sus ideas particulares sobre el acto poético permiten la creación de una obra única y muy importante dentro de la literatura latinoamericana y universal. La escritura de Pizarnik muestra no solo una voluntad por convertir toda la realidad en poesía, sino que es también una crítica a la cultura, la literatura y fundamentalmente al lenguaje. Esta propuesta significa el sacrificio de la poeta, su fragmentación, su disolución en la palabra, con el objetivo de encontrar la libertad absoluta y una nueva forma de expresión. Alejandra, a través de una serie de destrucciones sucesivas, busca crear una palabra ausente, un vocablo cercano a una lengua natural que revela el contenido sexual latente dentro de cada signo y que además muestra que todo lenguaje es insuficiente y esconde una trampa: siempre es imposible decir

Análisis diacrónico de la recepción literaria de la generación decapitada, el modernismo en el Ecuador.

Esta investigación propone el análisis diacrónico de la recepción de la obra de los poetas modernistas ecuatorianos, La Generación Decapitada, entre 1890 y 1930, es decir una década antes de la aparición del círculo modernista quiteño y las tres primeras décadas de vida de los textos de la generación. Para realizar esta tarea se usará como sustento teórico la Estética de la recepción literaria, que permitirá identificar cómo fueron interpretados los textos y cómo influyeron estas interpretaciones al ubicar a los cuatro poetas de la generación, Ernesto Noboa, Humberto Fierro, Arturo Borja y Medardo Ángel Silva, dentro de la historia de la literatura ecuatoriana