The Stationary Phase Method for a Wave Packet in a Semiconductor Layered System. The applicability of the method

Using the formal analysis made by Bohm in his book, {\em "Quantum theory"}, Dover Publications Inc. New York (1979), to calculate approximately the phase time for a transmitted and the reflected wave packets through a potential barrier, we calculate the phase time for a semiconductor system formed by different mesoscopic layers. The transmitted and the reflected wave packets are analyzed and the applicability of this procedure, based on the stationary phase of a wave packet, is considered in different conditions. For the applicability of the stationary phase method an expression is obtained in the case of the transmitted wave depending only on the derivatives of the phase, up to third order. This condition indicates whether the parameters of the system allow to define the wave packet by its leading term. The case of a multiple barrier systems is shown as an illustration of the results. This formalism includes the use of the Transfer Matrix to describe the central stratum, whether it is formed by one layer (the single barrier case), or two barriers and an inner well (the DBRT system), but one can assume that this stratum can be comprise of any number or any kind of semiconductor layers.Comment: 15 pages, 4 figures although figure 4 has 5 graph

Modelling the behaviour of microbulk Micromegas in Xenon/trimethylamine gas

We model the response of a state of the art micro-hole single-stage charge amplication device (`microbulk' Micromegas) in a gaseous atmosphere consisting of Xenon/trimethylamine at various concentrations and pressures. The amplifying structure, made with photo-lithographic techniques similar to those followed in the fabrication of gas electron multipliers (GEMs), consisted of a 100 um-side equilateral-triangle pattern with 50 um-diameter holes placed at its vertexes. Once the primary electrons are guided into the holes by virtue of an optimized field configuration, avalanches develop along the 50 um-height channels etched out of the original doubly copper-clad polyimide foil. In order to properly account for the strong field gradients at the holes' entrance as well as for the fluctuations of the avalanche process (that ultimately determine the achievable energy resolution), we abandoned the hydrodynamic framework, resorting to a purely microscopic description of the electron trajectories as obtained from elementary cross-sections. We show that achieving a satisfactory description needs additional assumptions about atom-molecule (Penning) transfer reactions and charge recombination to be made

Estudio empírico sobre la influencia de recursos heurísticos en la resolución de problemas de probabilidad condicionada L0 y L2

Se ha constatado la dificultad de los estudiantes a la hora de resolver problemas de probabilidad condicionada (Cañadas et al., 2011). En general, la complejidad de estos problemas es debida a varios factores: el formato y el orden en el que se presentan los datos, el contexto en el que se plantea el problema, el lenguaje utilizado para expresar los datos condicionales o las herramientas utilizadas en el proceso de resolución. En nuestro estudio nos centraremos en el uso y la influencia de recursos heurísticos, como tablas de contingencia o diagramas de árbol, durante la resolución de un problema de probabilidad condicionada

Smile esthetic evaluation of mucogingival reconstructive surgery

To assess the difference in smile esthetic impact of Coronally Advanced Flap (CAF) with or without the adjunct of a collagen matrix (CMX) used as root coverage procedures. Subjects with esthetic demands showing multiple upper gingival recessions of at least 2 mm, without interproximal attachment loss and cervical abrasion no more than 1 mm were recruited and randomized to CAF plus CMX or CAF alone. The Smile Esthetic Index (SEI) was adopted to quantify the quality of the smile recorded at baseline and 12 months after treatment for each treatment group. In addition, between group difference in the SEI was calculated. 24 Patients were treated and analysed. At baseline, mean gingival recession depths were 2.3 ± 0.7 mm for Test group and 2.6 ± 1.0 mm for Control group. After 1 year, the residual recession depth was 0.3 ± 0.4 mm in the CAF + CMX group and 0.6 ± 0.3 mm in the control group. The SEI at baseline was 8.1 ± 1.0 and 7.9 ± 0.7 for Test and Control group, respectively. The between groups difference at 12 months in SEI was 0.4 (95% C.I. − 0.0 to 0.8, P = 0.0697). Twelve months after treatment, CAF + CMX provided a similar SEI compared to CAF alone and the adjunct of a collagen matrix did not show a different impact on the smile esthetic appearance

Natural or Palatal Positioning of Immediate Post-extraction Implants in the Aesthetic Zone? Five-year Outcomes of a Multicentre Randomised Controlled Trial

PURPOSE. To evaluate whether there is a difference in aesthetic outcomes when positioning immediate post-extractive implants in the “central” position (where the natural tooth would be in relation to adjacent teeth/implants) as opposed to roughly 3 mm more pala-tally. MATERIALS AND METHODS. Just after tooth extraction, 20 patients requiring one single immediate maxillary post-extraction implant, from second premolar to second premolar, were randomly allocated to receive one implant positioned in either the natural “central” position (central group; 10 patients), or about 3 mm more palatally (palatal group; 10 pa-tients) according to a parallel-group design at two different centres. When needed, sites were reconstructed, and bone-to-implant gaps were filled with granules of anorganic bovine bone and covered by resorbable collagen barriers. Implants were left submerged for 4 months and rehabilitated with provisional crowns, replaced after 4 months by definitive metal-ceramic crowns. Patients were followed up to 5 years after loading. Outcome measures were: crown and implant failures; complications; aesthetics, assessed using the pink aesthetic score (PES); peri-implant marginal bone level changes; and patient satisfaction, recorded by blinded assessors. RESULTS. Three patients from each group dropped out within 3 years after loading. Five years after loading, there were no significant differences between the two groups in median PES score, assessed by a blind assessor, (central: 10 [IQR: 5.5], palatal: 8.5 [IQR: 6.75], median difference =-1.0; 95% CI:-7.0 to 4.0; P = 0.571); median bone level (central: 0.45 mm [IQR: 1.76], palatal: 0.45 mm [IQR: 1.93], median difference = 0 mm; 95% CI:-1.7 to 3.0; P = 1.000); bone level changes (central: 0.15 mm [IQR: 0.70], palatal:-0.05 mm [IQR: 1.23], median difference =-0.20 mm; P = 0.471); implant failures (one in each group, 14%, difference in proportion = 0.00; 95% CI:-0.39 to 0.39; P = 1.000); or complications (two palatal group patients and one central group patient, difference in proportion = 0.14; 95% CI:-0.28 to 0.52; P = 1.000). Furthermore, patients from both groups were equally satisfied with both function and aesthetics (both P = 0.699). CONCLUSIONS. These preliminary results suggest that positioning of immediate post-ex-traction implants 3 mm more palatally may not, in fact, improve aesthetics; however, the sample size of the present study was very limited, and larger trials are therefore required to confirm or refute these findings

Propuesta didáctica para explorar la representación de funciones de dos variables a través de la modelización con iPads

En esta comunicación presentamos una propuesta didáctica dirigida a alumnos de 4º de ESO. Los alumnos actuarán como investigadores para resolver la pregunta: ¿Cómo se propaga el sonido en el aula? Para obtener el modelo matemático asociado al problema, tomarán datos reales usando el iPad® como sonómetro mediante la aplicación Decibel Ultra Pro. El interés de esta tarea es la exploración de conceptos relacionados con las funciones de dos variables, en particular, la representación cartesiana tridimensional asociada a estas funciones. El material diseñado se puso en práctica en una experiencia realizada con un grupo natural de alumnos de 4º de ESO, el análisis de ésta nos permitirá describirlo de forma práctica

Hypersensitivity in molar incisor hypomineralization: Superficial infiltration treatment

To date, there are no standardized protocols available in the literature for hypersensitivity treatment in molar incisor hypomineralization (MIH) patients. The aim of this study was to evaluate the efficacy of erosion\u2013infiltration treatments with resin in children with a strong hypersensitivity and also to develop a minimally invasive diagnostic\u2013therapeutic pathway for young MIH patients. Patients with clinical signs of MIH were enrolled according to international guidelines. A total of 42 patients (8\u201314 years old) with sensitivity of at least one molar and patients with post eruptive enamel fractures, but without dentin involvement or cavitated carious lesions were selected. A single superficial infiltration treatment with ICON (DMG, Germany) was performed with a modified etching technique. Sensitivity was tested with the Schiff Scale and Wong Baker Face Scale and was repeated at 12 months follow\u2010up. All patients reported lower sensitivity values at the end of the treatment. Significant differences of sensitivity according to the Schiff scale were reported between T0 and all subsequent follow\u2010ups, p < 0.05. The treatment of erosion infiltration with ICON resin is a minimally invasive preventive treatment that significantly improves the problem of hypersensitivity in permanent molars with MIH

Impact of erroneous examples on fourth-grade students’ word-problem-solving proficiency using an intelligent tutoring system

Work supported by Spanish administrations under projects PGC2018-096463-B-I00, AICO/2021/019, SBPLY/19/180501/000278, and FPU19/03857, and FEDER