The Morse-Sard theorem revisited

Let $n, m, k$ be positive integers with $k=n-m+1$. We establish an abstract Morse-Sard-type theorem which allows us to deduce, on the one hand, a previous result of De Pascale's for Sobolev $W^{k,p}_{\textrm{loc}}(\mathbb{R}^n, \mathbb{R}^m)$ functions with $p>n$ and, on the other hand, also the following new result: if $f\in C^{k-1}(\mathbb{R}^n, \mathbb{R}^m)$ satisfies $$\limsup_{h\to 0}\frac{|D^{k-1}f(x+h)-D^{k-1}f(x)|}{|h|}<\infty$$ for every $x\in\mathbb{R}^n$ (that is, $D^{k-1}f$ is a Stepanov function), then the set of critical values of $f$ is Lebesgue-null in $\mathbb{R}^m$. In the case that $m=1$ we also show that this limiting condition holding for every $x\in\mathbb{R}^n\setminus\mathcal{N}$, where $\mathcal{N}$ is a set of zero $(n-2+\alpha)$-dimensional Hausdorff measure for some $0<\alpha<1$, is sufficient to guarantee the same conclusion.Comment: We corrected some misprints and made some changes in the introductio

Thermal switching of the scattering coefficients of terahertz surface plasmon polaritons impinging on a finite array of subwavelength grooves on semiconductor surfaces

8 págs.; 8 figs.; 1 tab. ; PACS number s : 73.20.Mf, 78.68. m, 65.40. b, 41.20.JbWe present a theoretical framework that allows us to investigate the scattering of terahertz surface plasmon polaritons (SPP's) by arrays of subwavelength grooves and ridges on semiconductors. The formulation is based on the reduced Rayleigh equation resulting upon imposing an impedance boundary condition. Guided by approximate estimations of the broadening with temperature of the first gap in the SPP dispersion relation in the case of indium antimonide samples with rectangular grooves, numerical calculations are carried out to determine the spectral dependence of all the SPP scattering channels (reflection, transmission, and radiation) in the immediate vicinity of that gap. The thermally induced switching of the SPP reflection and transmission nearby the lower SPP band edge is investigated as a function of groove parameters (size and number); near-field intensity maps are also presented. We thus shed light on the SPP scattering and switching physical mechanisms, thereby providing the most suitable experimental configurations. © 2006 The American Physical Society.This work was supported in part by the Spanish “Ministerio de Educación y Ciencia” Grant Nos. BFM2003-0427 and FIS2004-0108 and “Comunidad de Madrid” Grant MICROSERES and by the European Union Grant HPRN-CT- 2002-00206. The work of J.G.R. was supported by the “Stichting voor Fundamenteel Onderzoek der Materie” FOM, which is financially supported by the “Nederlandse Organisatie voor Wetenschappelijk Onderzoek” NWO.Peer Reviewe

Optical scattering resonances of single and coupled dimer plasmonic nanoantennas

The optical resonances of individual plasmonic dimer antennas are investigated using confocal darkfield spectroscopy. Experiments on an array of antennas with varying arm lengths and interparticle gap sizes show large spectral shifts of the plasmon modes due to a combination of geometrical resonances and plasmon hybridization. The resonances of the coupled-dimer antennas are considerably broadened compared to those of single nanorods, which is attributed to a superradiant damping of the coupled antenna modes. The scattering spectra are compared with electrodynamic model calculations that demonstrate both the near-field and far-field characteristics of a half-wave antenna

Resultados en la cirugía de revisión de la artroplastia de rodilla con aporte de aloinjerto óseo

Hemos realizado un estudio retrospectivo de 12 pacientes (13 rodillas) intervenidos entre 1975 y 2001 de revisión de prótesis de rodilla utilizando aloinjerto óseo, valorando el resultado funcional y clínico. La edad media fue de 62 años. La indicación primaria fue de gonartrosis primaria en 8 casos (9 rodillas), artrosis postraumática en 1 caso y 2 casos de artritis reumatoide. Los defectos óseos fueron clasificados utilizando la clasificación del Anderson Orthopedic Institute Research. Se utilizó aloinjerto de forma fragmentada en 11 casos y de forma estructural en 2. El seguimiento medio fue de 69 meses. En la valoración clínica se utilizó la escala de la Knee Society; la evaluación radiográfica evaluó la existencia de integración del injerto en el huésped. Los 2 casos de artritis reumatoide presentaron infección profunda protésica y que necesitaron de una artrodesis como solución definitiva. El resto de pacientes mostró unos resultados satisfactorios con buena integración del injerto al huésped. La utilización de aloinjerto fragmentado y estructural en la cirugía de revisión protésica de rodilla resuelve de manera satisfactoria la presencia del defecto óseo, aunque en enfermos con algú tipo de inmunopresión, el elevado riesgo de infección profunda en cirugía de revisión nos obliga a extremar las precauciones.We have carried out a retrospective study of 12 patients (13 knees) treated between 1975 and 2001 after failed total knee arthroplasty (TKA), by means of revision surgery using bone allograft. The mean age was of 62 years. The primary indication was degenerative osteoarthritis in 8 cases (9 knees), postraumatic osteoarthritis in 1 case and rheumatoid artritis in 2 cases. The bony defects were classified according to the Anderson's Orthopedic Institute classification. Fragmented allograft was used in 11 cases and structural allograft in 2. The mean follow-up time was of 69 months. Outcome was evaluated through functional and clinical result. For the clinical evaluation the scale of the Knee Society was used; the radiographic evaluation assessed the degree of integration of the graft. The 2 cases of rheumatoid artritis presented deep infection of the TKA that required an arthrodesis for definitive solution. The rest of patients showed satisfactory results with good integration of the bone graft. The use of fragmented and structural allograft in revision surgery of failed TKA solves in a satisfactory way the presence of bony defects, although in patients with some degree of inmunosupression the high risk of deep infection forces to extreme the cautions

Artroplastia de rodilla infectada: Revisión del tratamiento y valoración de resultados

La infección de la artroplastia total de rodilla representa su complicación local más temida con una incidencia actual entre el 1-5%. Se ha realizado un estudio retrospectivo del tratamiento empleado en 16 artroplastias de rodilla infectadas (3,1%) en los últimos seis años entre 516 artroplastias realizadas en ese mismo periodo de tiempo valorando la ausencia de infección asó como la evaluación de la rodilla tanto funcional mediante las escalas de la Knee Society como subjetiva del paciente mediante una escala analógica visual en función del tratamiento empleado. En todos los casos se erradicó al final del seguimiento aunque los resultados variaron en función del tratamiento. Los mejores resultados lo obtuvieron las infecciones agudas en las que se realizó un desbridamiento precoz o una revisión en 1 tiempo. La revisión en 2 tiempos obtuvo buenos resultados en infecciones tardía aunque fracasó cuando se realizó en infecciones hematógenas y agudas. La artrodesis se utilizó ante el fracaso de otras técnicas obteniendo resultados regulares. La artroplastia de resección obtuvo malos resultados en todos los casos.Infection of knee arthroplasty in the most local ugly complication with an incidence of 1 to 5%. We retrospectively studied 16 infected knee arthroplasties out of of 516 primary artrhoplasties performed in our department the last 6 years (3.1%), evaluating the absence of infection and the functional knee with the Knee Society Score. Subjective assessment was made using a visual analog scale. At the end of the follow-up the cases were free of infection although results changed depending on treatment performed. Best results were found on acute infections, in which early debridement or one-stage revision were performed. Two-stage revision obtained good results on late infections although it failed when it was attempted on hematogeneus and acute infections. Arthrodesis was done in cases where other techniques failed obtaining fair results. Resection arthroplasty obtained poor results in all cases

Fractura de estrés en la infancia: consideraciones diagnósticas sobre 9 casos

Las fracturas de estrés son lesiones que suelen estar en relación con ciclos repetidos de carga sobre un hueso normal sometido a un exceso de solicitaciones mecánicas o bien sobre un hueso con menor resistencia. Se presenta una revisión de 9 casos de fractura de estrés tratadas en el Hospital Infantil Miguel Servet de Zaragoza, en los últimos 10 años, con resultado de 5 niños y 4 niñas, con una edad media de 10,11 años (rango: 5-14). El tiempo de diagnóstico medio fue 17,6 días (rango: 1-92), y las localizaciones más frecuentes fueron los metatarsianos, la tibia y el cuello femoral. Solo dos de los casos estaban relacionados con la práctica deportiva. Todos presentaron clínica de dolor y alteración de la marcha. En uno de ellos se realizó un diagnóstico inicial de sospecha de sarcoma de Ewing. Todos fueron tratados de forma conservadora. El tiempo de seguimiento medio fue 23,92 meses (rango: 2-96).Stress fractures are injuries that are often related to repeated cycles of loading on a normal bone subjected to excessive mechanical stress, as well on a bone of less resistance. We present a review of 9 cases of stress fracture treated at Children's Hospital Miguel Servet in Zaragoza, in the last 10 years, resulting in 5 boys and 4 girls, mean age 10,11 years (3-14). Mean time for diagnosis was 17,6 days (1-92), and the most frequent location was metatarsals, tibia and femoral neck. Only two of the cases were related to sports. All of them presented clinical pain and abnormal gait. One patient received a suspect initial diagnosis of Ewing sarcoma. All were treated conservatively. The mean follow up was 23.92 months (2-96)

Ab initio study of the influence of nanoscale doping inhomogeneities in the phase separated state of La1−x_{1-x}Cax_{x}MnO3_3

The chemical influence in the phase separation phenomenon that occurs in perovskite manganites is discussed by means of ab initio calculations. Supercells have been used to simulate a phase separated state, that occurs at Ca concentrations close to the localized to itinerant crossover. We have first considered a model with two types of magnetic ordering coexisting within the same compound. This is not stable. However, a non-isotropic distribution of chemical dopants is found to be the ground state. This leads to regions in the system with different effective concentrations, that would always accompany the magnetic phase separation at the same nanometric scale, with hole-rich regions being more ferromagnetic in character and hole-poor regions being in the antiferromagnetic region of the phase diagram, as long as the system is close to a phase crossover.Comment: 8 pages, 7 figures, 1 tabl

Morphological Description of Frontal EEG Interictal and Ictal Discharges in an Adult Cohort of 175 Patients

EEG morphology; Electroencephalography; Frontal lobe seizuresMorfología EEG; Electroencefalografía; Convulsiones del lóbulo frontalMorfologia EEG; Electroencefalografia; Convulsions del lòbul frontalClinical and electroencephalogram (EEG) features in frontal lobe epilepsy (FLE) vary considerably among patients, making the diagnosis a challenge. The objective of this study was to describe interictal and ictal EEG activity, identifying variables that could help to differentiate and diagnose frontal lobe epilepsy cases. A prospective cross-sectional study from patients with frontal interictal epileptiform discharges (IED) referred to the Vall d’Hebron University Hospital (Barcelona, Spain) after a clinical event compatible with epileptic seizures was designed. The interictal and ictal activity were analyzed to provide a detailed EEG description of the cases, using different statistical analyses. The morphological seizure pattern at the ictal onset remained globally unchanged over time in seizures arising from the frontal lobe for each patient. Isolated sharp waves were the most frequent waveforms in the expression of IED. Frontal lobe seizures are frequently short and sometimes appear grouped in clusters within the same recording. Often the ictal expression of the electrical activity in frontal lobe seizure is subtle and challenging to interpret. A description of the main findings is summarized to identify seizures arising from the frontal lobe and avoid false negatives findings in EEG interpretations.This research received no external funding

El estilo de aprendizaje y su relación con la educación entre pares

The objectives of this work are: to diagnose the Learning Style (LS) of the students of compulsory secondary education (ESO), to know their perception of the peer tutoring and to analyze the relationship between the students’ LS and peer tutoring. The empirical study was conducted with students from all courses of the ESO in 6 school centers in Spain. Data collection was performed using two instruments: the CHAEA and a questionnaire designed by the team of research on peer tutor. In the results it is found that the students´LS is predominantly reflective, students consider the figure of the peer tutor right for learning, and the largest significant differences were found between the active Style and peer tutor.Los objetivos de esta investigación son: diagnosticar el Estilo de Aprendizaje (EA) del alumnadode la Educación Secundaria Obligatoria (ESO), conocer la percepción de este alumnado sobre la figura del compañero tutor, y analizar la relación entre el EA del alumnado y la figura del compañero tutor. Se plantean como hipótesis que no existen diferencias entre los Estilos de Aprendizaje del alumnado y las características del compañero tutor. El estudio empírico se llevó a cabo con estudiantes de todos los cursos de la ESO en 6 Centros en España. La recogida de datos se realizó con dos instrumentos: el CHAEA y un cuestionario diseñado por el propio equipo de investigación sobre compañero tutor. En los resultados se comprueba que el EA del alumnado es predominantemente reflexivo, que los alumnos consideran la figura del compañero tutor adecuada para su aprendizaje, y las mayores diferencias significativas se encuentran entre el Estilo activo y el compañero tutor