Dyadic harmonic analysis: Non-doubling and noncommutative aspects

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Matemáticas. Fecha de lectura: 26-05-2015La presente tesis contiene resultados sobre análisis armónico diádico en distintos contextos; proporcionando estimaciones a priori para modelos diádicos de integrales singulares. La exposición de los resultados se divide en tres partes. En la primera se caracterizan las medidas de Borel en R para las cuales la transformada de Hilbert diádica asociada es de tipo débil (1, 1). Sorprendentemente, la clase de medidas obtenida contiene estrictamente a las medidas diádicamente doblantes y está contenida estrictamente en la clase de Borel. Se demuestra además que la clase dual caracteriza el tipo débil (1, 1) del adjunto de la transformada de Hilbert diádica. La herramienta principal es una nueva descomposición de Calderón- Zygmund válida para medidas de Borel generales y de interés independiente. Caracterizaciones análogas del tipo débil (1, 1) para operadores Haar shift multidimensionales son obtenidas en términos de dos sistemas de Haar generalizados y no necesariamente cancelativos. Los paraproductos diádicos y sus adjuntos figuran como casos particulares importantes. Por otro lado, es bien sabido que operadores de Calderón-Zygmund con núcleos matriciales — incluso aquellos con buenas propiedades de tamaño y suavidad o cancelación — carecen de estimaciones en Lp semiconmutativas para p 6= 2. En la segunda parte de la tesis se obtienen estimaciones de tipo débil (1, 1) de operadores perfectamente diádicos y, en general para operadores Haar shift, en términos de una descomposición fila/columna de la función de partida. Se muestra también que operadores de Calderón-Zygmund generales satisfacen estimaciones de tipo H1 ! L1, que junto con estimaciones de tipo L1 ! BMO, implican estimaciones fila/columna en espacios Lp semiconmutativos. El enfoque presentado es aplicable a transformadas de martingala y paraproductos con símbolos no conmutativos, para los que obtenemos estimaciones análogas. La tercera parte está dedicada a la generalización semiconmutativa de los resultados obtenidos en la primera parte. Esto es, a la caracterización del tipo débil (1, 1) de operadores Haar shift definidos en términos de dos sistemas de Haar generalizados adaptados a una medida de Borel y con símbolos conmutativos. Así como en el caso conmutativo, el principal recurso técnico es una versión no conmutativa de la descomposición de Calderón-Zygmund introducida en la primera parteThis thesis is divided into three parts, each presenting results on dyadic harmonic analysis in different settings. More specifically, it provides a priori estimates of dyadic and singular integral operators in the non-doubling and semicommutative frameworks. In Part I we characterize the locally finite Borel measures μ on R for which the associated dyadic Hilbert transform satisfy L1(μ) ! L1,1(μ) estimates. Surprisingly, the class of such measures is strictly bigger than the standard class of dyadically doubling measures and strictly smaller than the whole Borel class. We further show that a dual class characterizes the weak-type (1, 1) of the adjoint of the dyadic Hilbert transform. In higher dimensions, we provide a complete characterization of the weak-type (1, 1) of arbitrary Haar shift operators —cancellative or not—written in terms of two generalized Haar systems, including dyadic paraproducts. The main tool used in Part I is a new Calderón-Zygmund decomposition valid for arbitrary Borel measures which is of independent interest. On the other hand, it is well known that Calderón-Zygmund operators with noncommuting kernels may fail to be Lp bounded in semicommutative Lp spaces for p 6= 2, even for kernels with good size and smoothness properties or having dyadic cancellation properties. In Part II we obtain weak-type (1, 1) estimates for perfect dyadic Calderón-Zygmund operators associated to noncommuting kernels in terms of a row/column decomposition of the input function. Analogous estimates are also proved for arbitrary Haar shift operators. General Calderón-Zygmund operators satisfy H1 ! L1 type estimates. In conjunction with L1 ! BMO type estimates, we get similar row/column Lp estimates. The approach here presented also applies to martingale transforms and paraproducts with noncommuting symbols for which we obtain analogous estimates. In Part III we obtain a complete characterization of the weak-type (1, 1) of commuting Haar shift operators in terms of generalized Haar systems adapted to a Borel measure μ in the semicommutative setting. The main technical tool in our method is a noncommutative Calderón-Zygmund decomposition that generalizes the Calderón-Zygmund decomposition used in the first part

A new approach to optimize the energy efficiency of CO2 transcritical refrigeration plants

This paper proposes a model-free real-time optimization and control strategy for CO2 transcritical refrigeration plants that assures covering the cooling demand and continuous tracking of conditions for maximum efficiency. Our approach obtains the feedback with only three measurements, and controls the opening degree of a backpressure valve and the speed of the compressor. The strategy minimizes the power consumption of the compressor instead of maximizing the coefficient of performance, which avoids several sensors, and we demonstrate mathematically that both approaches are equivalent. We implemented the strategy with an algorithm that includes two independent auto tuned controllers, one devoted to regulate the high-pressure and another to regulate the outlet temperature of the secondary fluid of the evaporator. It also incorporates a real time perturb and observe procedure to locate online the optimum high-pressure that minimizes the compressor power consumption. The paper presents the experimental evaluation of the control strategy, verifying the stable operation of the algorithm and the energy optimization of the plant

Rules of tissue packing involving different cell types: human muscle organization

Natural packed tissues are assembled as tessellations of polygonal cells. These include skeletal muscles and epithelial sheets. Skeletal muscles appear as a mosaic composed of two different types of cells: the “slow” and “fast” fibres. Their relative distribution is important for the muscle function but little is known about how the fibre arrangement is established and maintained. In this work we capture the organizational pattern in two different healthy muscles: biceps brachii and quadriceps. Here we show that the biceps brachii muscle presents a particular arrangement, based on the different sizes of slow and fast fibres. By contrast, in the quadriceps muscle an unbiased distribution exists. Our results indicate that the relative size of each cellular type imposes an intrinsic organization into natural tessellations. These findings establish a new framework for the analysis of any packed tissue where two or more cell types exist.España, Gobierno BFU2011-2573

Multilevel multiphase space vector PWM algorithm with switching state redundancy

Multilevel multiphase technology combines the benefits of multilevel converters and multiphase machines. Nevertheless, new modulation techniques must be developed to take advantage of multilevel multiphase converters. In this paper, a new space vector pulsewidth modulation algorithm for multilevel multiphase voltage source converters with switching state redundancy is introduced. As in three-phase converters, the switching state redundancy permits to achieve different goals like extending the modulation index and reducing the number of switchings. This new algorithm can be applied to the most usual multilevel topologies; it has low computational complexity, and it is suitable for hardware implementations. Finally, the algorithm was implemented in a field-programmable gate array, and it was tested by using a five-level five-phase inverter feeding a motor.Ministerio de Educación y Ciencia | Ref. ENE2006-0293

Multilevel multiphase space vector PWM algorithm

In the last few years, interest in multiphase converter technology has increased due to the benefits of using more than three phases in drive applications. Besides, multilevel converter technology permits the achievement of high power ratings with voltage limited devices. Multilevel multiphase technology combines the benefits of both technologies, but new modulation techniques must be developed in order to take advantage of multilevel multiphase converters. In this paper, a novel space vector pulsewidth modulation (SVPWM) algorithm for multilevel multiphase voltage source converters is presented. This algorithm is the result of the two main contributions of this paper: the demonstration that a multilevel multiphase modulator can be realized from a two-level multiphase modulator, and the development of a new two-level multiphase SVPWM algorithm. The multiphase SVPWM algorithm presented in this paper can be applied to most multilevel topologies; it has low computational complexity and it is suitable for hardware implementations. Finally, the algorithm was implemented in a low-cost field-programmable gate array and it was tested in a laboratory with a real prototype using a five-level five-phase inverter.Ministerio de Educación y Ciencia | Ref. ENE2006-0293

Height cohorts and district of residence in the city of Madrid during the 20th century

OBJECTIVE: in recent decades, an interesting literature has accumulated regarding the biological living standard in Spain at the end of the 19th Century and during the 20th Century. Adult height has been one of the most studied variables, specifically its temporal change at the national and provincial levels, the impact of the Civil War and the subsequent dictatorship, and the differences between urban and rural areas. We want to contribute to this general overview with the presentation of a project about an intra-urban perspective of the city of Madrid. METHODS: We present the stature data of the male population of two Madrid districts, Salamanca and Vallecas, for the period 1936-1986 (year of measurement). RESULTS: In these years, height increased by 5.58 cm, from 166.40 to 171.98 cm, with significant differences observed between both districts as well as a simultaneous decrease of that difference, for those born in 1915 and 1953 from 3.09 to 1.2 cm. The negative effect of the Civil War and the years of autarky are also observed in this urban sample. CONCLUSION: Considering these data together with those available for other demographic and socioeconomic variables, before and after the period studied, we can conclude that the division by districts represents an effective stratification in the biological living standard of the population of the city of Madrid. These results constitute a first intra-urban approximation using height to the debate on inequality and biological living standards in Spain during the 20th Century.Objetivo: en las últimas décadas se ha acumulado una interesante bibliografía sobre los niveles biológicos de vida en España a finales del siglo xix y durante el siglo xx. La talla ha sido una de las variables más estudiadas: su cambio a nivel nacional y provincial, el impacto de la Guerra Civil y de la posterior dictadura y las diferencias entre las áreas urbanas y las rurales. Queremos contribuir a este panorama general con este trabajo, una perspectiva intraurbana de la ciudad de Madrid. Métodos: presentamos el análisis comparativo del cambio temporal en la talla de los madrileños de los distritos de Salamanca y de Vallecas correspondientes al periodo 1936-1986. Resultados: en esos años, la talla total se incrementó en 5,58 cm, pasando de 166,40 a 171,98 cm, aunque se observan diferencias significativas entre ambos distritos; diferencias que se reducen (de 3,09 a 1,2 cm) entre Salamanca y Vallecas para los nacidos en 1915 y 1953, respectivamente. También se observa el efecto negativo de la Guerra Civil y de los años de autarquía. Conclusión: considerando estos primeros datos, junto a los disponibles para otras variables demográficas y socioeconómicas previas y posteriores al periodo estudiado, podemos considerar que la división por distritos representa una estratificación efectiva en los niveles biológicos de vida dentro de la ciudad de Madrid. Estos resultados constituyen una primera aproximación intraurbana con la talla al debate sobre la desigualdad y los niveles de vida en España durante el siglo xxLa publicación de este trabajo ha sido sufragada con fondos del proyecto HAR2016- 76814-C2-2-P del Ministerio de Economía, Industria y Competitividad (MINECO-FEDER-UE

Determination of plantar pressure in people who use orthoses of the foot

[Abstract] Objective: to know the transfer of static plantar pressures and body weight distribution through the lower limbs that occur in people with and without the use of orthoses of different densities and influence in other areas of the foot. Material and Methods: 32 people participated through non-probability convenience sampling in a quasi-experimental study in which self-reported data were recorded, the determination of plantar pressure, and body weight distribution. Results: 64 feet were studied, showing no difference between the medium pressure and the forefoot without orthoses of 5 mm and 10 mm. Decrease in average pressure and percentage of body weight, both statistically significant, with hindfoot orthoses 10 mm was observed. Conclusions: Given the current evidence for the prescribing and use of foot orthoses is limited, designed to improve the functionality and prevent the onset of disease and foot deformities, these results highlight the need to prescribe orthotics 10 mm when needed to relieve pressure on the backfoot, not seeing the average pressure increased nor diminished in other areas of the foo

Plasmas Granulares

Los plasmas granulares son gases total o parcialmente ionizados que, además de iones electrones y átomos neutros, contienen partículas sólidas con carga eléctrica. Dichas partículas cargadas, de tamaño mesoscópico, dan lugar a nuevos fenómenos colectivos con una dinámica característica. Este tipo de plasmas aparecen en sistemas físicos tan diversos como son los reactores de fusión por confinamiento magnético, los sistemas de procesado de semiconductores o en medios astrofísicos. Se presenta una breve introducción divulgativa a esta nueva rama de la física de plasmas que ha tenido un desarrollo espectacular en los últimos años, haciendo énfasis en su carácter multidisciplina

Actuador con mecanismo de rigidez variable y par umbral

Número de publicación: ES2387228 A1 (18.09.2012) También publicado como: ES2387228 B2 (05.02.2013) Número de Solicitud: Consulta de Expedientes OEPM (C.E.O.) P201200712 (29.06.2012)Actuador con mecanismo de rigidez variable y par umbral, del tipo de los utilizados en articulaciones de revolución de brazos robóticos y que pueden modificar su rigidez. El actuador incorpora un motor (1) que se encarga de controlar la posición de equilibrio del eslabón de salida (13). El mecanismo contiene un resorte (18) y una palanca (12). La rigidez del mecanismo puede ser modificada variando la posición de esta palanca (12) mediante un motor (14). Dicha rigidez determina el valor del giro entre la posición de la polea (2) solidaria al eje de salida del motor (1) y la posición del eslabón (13). Dos tensores (5) y (6) permiten modificar la precarga de dos cables (3) y (4) respectivamente, de forma que el mecanismo no entra en funcionamiento hasta que no se ha sobrepasado un cierto valor de par sobre la articulación.Universidad de Almerí