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Exercises B

Exercises and solutions in LaTex

Revisión sistemática de la literatura: efecto de los rellenos inyectables en la región periorbitaria

Introducción: El conocimiento actual de la fisiopatología del envejecimiento periorbitario justifica la aplicación de materiales de relleno inyectables, dado que se enfocan en la restauración del volumen perdido en esta zona, convirtiéndose en una excelente alternativa a procedimientos quirúrgicos que remueven el tejido excedente. Sin embargo los efectos y la seguridad de esta naciente tendencia terapéutica aún no se sustentan en una sólida base científica. El objetivo de esta revisión es identificar el material de relleno inyectable más adecuado para el manejo de los defectos volumétricos estéticos de la región periorbitaria. Metodología: Se realizó una búsqueda exhaustiva de los artículos indexados publicados del 1º de enero de 2.000 al 30 de septiembre de 2.013, en diversas bases de datos electrónicas, se seleccionaron catorce publicaciones, se extrajo la información referente a datos demográficos, la intervención, el seguimiento y los desenlaces y se realizó un análisis de 14 estudios que cumplieron los criterios. Resultados: Todos los artículos incluidos poseían un bajo nivel de evidencia y del grado de recomendación. Todos los materiales de relleno se asociaron a altos niveles de satisfacción para el paciente, adecuada mejoría de la apariencia estética y similares efectos colaterales, el ácido hialurónico fue el material de relleno inyectable más utilizado en la región periorbitaria. Discusión: Los materiales de relleno inyectable mejoran los defectos volumétricos estéticos de la región periorbitaria pero es necesaria mayor evidencia para determinar el tipo relleno más apropiado para esta condición.

Enucleación y evisceración en la población pediátrica

Objetivo: Analizar los resultados de 111 pacientes pediátricos sometidos a enucleación o evisceración en la Clínica Barraquer durante 11 años (1990-2000), determinando tipo de corrección realizada y complicaciones asociadas al procedimiento quirúrgico. Métodos: Estudio retrospectivo de las historias clínicas de todos los pacientes menores de 18 años que fueron sometidos a los procedimientos mencionados, obteniendo datos demográficos,diagnóstico, cirugías oftalmológicas asociadas, características de implantes o injertos, seguimiento y complicaciones postoperatorias en todos los pacientes. Resultados: Se realizaron 55 enucleaciones y 56 evisceraciones. Sólo en un caso no se colocó algún implante o injerto. Durante los primeros 4 años del análisis los injertos lipodérmicos correspondían a un 25,45% y los implantes de Nylon a un 72,72% de las correcciones realizadas, mientras que en los últimos 7 años el implante de hidroxiapatita constituyó el 78,57% de los casos intervenidos. En 17 (15,32%) pacientes se observaron complicaciones que requirieron algún tipo de corrección quirúrgica, sin diferencias estadísticamente significativas entre las distintas correcciones utilizadas. Conclusiones: Para la población pediátrica los implantes de hidroxiapatita, además de brindar una excelente reconstrucción de la órbita anoftálmica, mejoran los resultados estéticos y de motilidad. Sin embargo otro tipo de correcciones como los injertos lipodérmicos siguen constituyendo una excelente alternativa en nuestro medio, teniendo en cuenta que sus costos son mucho menores. Aunque se observaron algunas complicaciones con los diferentes tipos de corrección, muy pocas requirieron una nueva intervención quirúrgica. La tasa de complicaciones se incrementa en pacientes de menos edad.

Ecuaciones diferenciales estocásticas con condición final y soluciones de viscosidad de EDPS semilineales de segundo orden

El objetivo de este documento es recopilar algunos resultados clasicos sobre existencia y unicidad ´ de soluciones de ecuaciones diferenciales estocasticas (EDEs) con condici ´ on final (en ingl ´ es´ Backward stochastic differential equations) con particular enfasis en el caso de coeficientes mon ´ otonos, y su cone- ´ xion con soluciones de viscosidad de sistemas de ecuaciones diferenciales parciales (EDPs) parab ´ olicas ´ y el´ıpticas semilineales de segundo orden.

Families of periodic horseshoe orbits in the restricted three-body problem

We compute families of symmetric periodic horseshoe orbits in the restricted three-body problem. Both the planar and three-dimensional cases are considered and several families are found.We describe how these families are organized as well as the behavior along and among the families of parameters such as the Jacobi constant or the eccentricity. We also determine the stability properties of individual orbits along the families. Interestingly, we find stable horseshoe-shaped orbit up to the quite high inclination of 17◦

Sentencia de casación respecto de las actuaciones de las administraciones tributarias vinculadas a actos administrativos impugnados judicialmente (Jurisprudencia)

En ocasiones las administraciones tributarias han errado en la comprensión del contenido y alcance de la facultad determinadora. Al constituir una actividad reglada, la determinación tributaria debe observar rigurosamente las normas relativas a materia, oportunidad y competencia. La sentencia materia de la presente recensión se refiere precisamente al ejercicio de la facultad determinadora en lo que hace relación con los actos administrativos que se encuentran impugnados judicialmente. Considerando que uno de los efectos de la judicialización del acto administrativo es abstraerlo de la órbita competencial de la administración tributaria, esta no puede ejercer sobre él ninguna de sus facultades, entre ellas, la verificadora. El criterio de juzgamiento analizado confirma este particular, dejando en claro las consecuencias que la impugnación judicial comporta tanto para los actos administrativos como para la administración tributaria.

Sampling uncertainties in surface radiation budget calculations in RADAGAST

In the Radiative Atmospheric Divergence Using ARM Mobile Facility GERB and AMMA Stations (RADAGAST) project we calculate the divergence of radiative flux across the atmosphere by comparing fluxes measured at each end of an atmospheric column above Niamey, in the African Sahel region. The combination of broadband flux measurements from geostationary orbit and the deployment for over 12 months of a comprehensive suite of active and passive instrumentation at the surface eliminates a number of sampling issues that could otherwise affect divergence calculations of this sort. However, one sampling issue that challenges the project is the fact that the surface flux data are essentially measurements made at a point, while the top-of-atmosphere values are taken over a solid angle that corresponds to an area at the surface of some 2500 km2. Variability of cloud cover and aerosol loading in the atmosphere mean that the downwelling fluxes, even when averaged over a day, will not be an exact match to the area-averaged value over that larger area, although we might expect that it is an unbiased estimate thereof. The heterogeneity of the surface, for example, fixed variations in albedo, further means that there is a likely systematic difference in the corresponding upwelling fluxes. In this paper we characterize and quantify this spatial sampling problem. We bound the root-mean-square error in the downwelling fluxes by exploiting a second set of surface flux measurements from a site that was run in parallel with the main deployment. The differences in the two sets of fluxes lead us to an upper bound to the sampling uncertainty, and their correlation leads to another which is probably optimistic as it requires certain other conditions to be met. For the upwelling fluxes we use data products from a number of satellite instruments to characterize the relevant heterogeneities and so estimate the systematic effects that arise from the flux measurements having to be taken at a single point. The sampling uncertainties vary with the season, being higher during the monsoon period. We find that the sampling errors for the daily average flux are small for the shortwave irradiance, generally less than 5 W m−2, under relatively clear skies, but these increase to about 10 W m−2 during the monsoon. For the upwelling fluxes, again taking daily averages, systematic errors are of order 10 W m−2 as a result of albedo variability. The uncertainty on the longwave component of the surface radiation budget is smaller than that on the shortwave component, in all conditions, but a bias of 4 W m−2 is calculated to exist in the surface leaving longwave flux.

Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?

Estimating surface CO2 fluxes from space-borne dry air mole fraction observations using an Ensemble Kalman filter

We have developed an ensemble Kalman Filter (EnKF) to estimate 8-day regional surface fluxes of CO2 from space-borne CO2 dry-air mole fraction observations (XCO2) and evaluate the approach using a series of synthetic experiments, in preparation for data from the NASA Orbiting Carbon Observatory (OCO). The 32-day duty cycle of OCO alternates every 16 days between nadir and glint measurements of backscattered solar radiation at short-wave infrared wavelengths. The EnKF uses an ensemble of states to represent the error covariances to estimate 8-day CO2 surface fluxes over 144 geographical regions. We use a 12×8-day lag window, recognising that XCO2 measurements include surface flux information from prior time windows. The observation operator that relates surface CO2 fluxes to atmospheric distributions of XCO2 includes: a) the GEOS-Chem transport model that relates surface fluxes to global 3-D distributions of CO2 concentrations, which are sampled at the time and location of OCO measurements that are cloud-free and have aerosol optical depths <0.3; and b) scene-dependent averaging kernels that relate the CO2 profiles to XCO2, accounting for differences between nadir and glint measurements, and the associated scene-dependent observation errors. We show that OCO XCO2 measurements significantly reduce the uncertainties of surface CO2 flux estimates. Glint measurements are generally better at constraining ocean CO2 flux estimates. Nadir XCO2 measurements over the terrestrial tropics are sparse throughout the year because of either clouds or smoke. Glint measurements provide the most effective constraint for estimating tropical terrestrial CO2 fluxes by accurately sampling fresh continental outflow over neighbouring oceans. We also present results from sensitivity experiments that investigate how flux estimates change with 1) bias and unbiased errors, 2) alternative duty cycles, 3) measurement density and correlations, 4) the spatial resolution of estimated flux estimates, and 5) reducing the length of the lag window and the size of the ensemble. At the revision stage of this manuscript, the OCO instrument failed to reach its orbit after it was launched on 24 February 2009. The EnKF formulation presented here is also applicable to GOSAT measurements of CO2 and CH4.

The Geostationary Earth Radiation Budget Project

This paper reports on a new satellite sensor, the Geostationary Earth Radiation Budget (GERB) experiment. GERB is designed to make the first measurements of the Earth's radiation budget from geostationary orbit. Measurements at high absolute accuracy of the reflected sunlight from the Earth, and the thermal radiation emitted by the Earth are made every 15 min, with a spatial resolution at the subsatellite point of 44.6 km (north–south) by 39.3 km (east–west). With knowledge of the incoming solar constant, this gives the primary forcing and response components of the top-of-atmosphere radiation. The first GERB instrument is an instrument of opportunity on Meteosat-8, a new spin-stabilized spacecraft platform also carrying the Spinning Enhanced Visible and Infrared (SEVIRI) sensor, which is currently positioned over the equator at 3.5°W. This overview of the project includes a description of the instrument design and its preflight and in-flight calibration. An evaluation of the instrument performance after its first year in orbit, including comparisons with data from the Clouds and the Earth's Radiant Energy System (CERES) satellite sensors and with output from numerical models, are also presented. After a brief summary of the data processing system and data products, some of the scientific studies that are being undertaken using these early data are described. This marks the beginning of a decade or more of observations from GERB, as subsequent models will fly on each of the four Meteosat Second Generation satellites.

Mersenne numbers

These notes have been issued on a small scale in 1983 and 1987 and on request at other times. This issue follows two items of news. First, WaIter Colquitt and Luther Welsh found the 'missed' Mersenne prime M110503 and advanced the frontier of complete Mp-testing to 139,267. In so doing, they terminated Slowinski's significant string of four consecutive Mersenne primes. Secondly, a team of five established a non-Mersenne number as the largest known prime. This result terminated the 1952-89 reign of Mersenne primes. All the original Mersenne numbers with p < 258 were factorised some time ago. The Sandia Laboratories team of Davis, Holdridge & Simmons with some little assistance from a CRAY machine cracked M211 in 1983 and M251 in 1984. They contributed their results to the 'Cunningham Project', care of Sam Wagstaff. That project is now moving apace thanks to developments in technology, factorisation and primality testing. New levels of computer power and new computer architectures motivated by the open-ended promise of parallelism are now available. Once again, the suppliers may be offering free buildings with the computer. However, the Sandia '84 CRAY-l implementation of the quadratic-sieve method is now outpowered by the number-field sieve technique. This is deployed on either purpose-built hardware or large syndicates, even distributed world-wide, of collaborating standard processors. New factorisation techniques of both special and general applicability have been defined and deployed. The elliptic-curve method finds large factors with helpful properties while the number-field sieve approach is breaking down composites with over one hundred digits. The material is updated on an occasional basis to follow the latest developments in primality-testing large Mp and factorising smaller Mp; all dates derive from the published literature or referenced private communications. Minor corrections, additions and changes merely advance the issue number after the decimal point. The reader is invited to report any errors and omissions that have escaped the proof-reading, to answer the unresolved questions noted and to suggest additional material associated with this subject.

High-resolution, unstructured meshes for hydrodynamic models of the Great Barrier Reef, Australia

Accuracy and mesh generation are key issues for the high-resolution hydrodynamic modelling of the whole Great Barrier Reef. Our objective is to generate suitable unstructured grids that can resolve topological and dynamical features like tidal jets and recirculation eddies in the wake of islands. A new strategy is suggested to refine the mesh in areas of interest taking into account the bathymetric field and an approximated distance to islands and reefs. Such a distance is obtained by solving an elliptic differential operator, with specific boundary conditions. Meshes produced illustrate both the validity and the efficiency of the adaptive strategy. Selection of refinement and geometrical parameters is discussed. (c) 2006 Elsevier Ltd. All rights reserved.