Algunas demostraciones del valor de la potencia de un punto con respecto a una circunferencia

Se proponen tres demostraciones sobre el valor de la potencia de un punto con respecto a una circunferencia. La primera utiliza el método de la geometría analítica, y las propiedades de las soluciones de la ecuación de segundo grado. La segunda se basa sólo en el Teorema de Pitágoras. Y, la tercera utiliza el álgebra de vectores. Por último, se da el resultado de la potencia de un punto con respecto a una elipse. Con esto se intenta suplir el hueco en los libros de texto, de nivel de Bachillerato, que no recogen una demostración general sobre la constancia de la potencia del punto con respecto a una circunferencia.

Una propiedad del triángulo isósceles

En este artículo se presenta una interesante propiedad de los triángulos isósceles, usando como apoyo técnicas y propiedades de geometría básica.

Concepciones de los alumnos de secundaria sobre modelos probabilísiticos en las secuencias de resultados aleatorios

Presentamos aquí una investigación sobre concepciones aleatorias en estudiantes de secundaria. Las respuestas de 277 estudiantes de dos grupos, con edades de 14 y 17 años, sirven para identificar las propiedades asociadas a secuencias aleatorias y deterministas. En ellas encontramos la capacidad de los alumnos para reconocer modelos matemáticos subyacentes en las secuencias de los resultados aleatorios y su utilización en los juicios sobre aleatoriedad. Por ellos sugerimos al final algunas implicaciones para la enseñanza de la probabilidad en estos niveles iniciales.

Objetos matemáticos ligados a la regresión en los textos españoles de bachillerato

El objetivo de este trabajo es caracterizar la presentación de la regresión en los libros de texto españoles de Bachillerato. Para ello se analizan y clasifican los campos de problema, procedimientos, conceptos y propiedades asociados a la regresión en dieciséis libros de texto de Bachillerato utilizados en España, ocho de la modalidad de Ciencia y Tecnología, y ocho de la modalidad de Humanidades y Ciencias Sociales. En el caso de los conceptos, se estudia si su definición es operacional, estructural o mediante ejemplo. Los resultados indican que no hay grandes diferencias en la presentación de estos objetos matemáticos en los textos dirigidos a las dos modalidades de Bachillerato. Encontramos variedad del número y tipo de propiedades presentadas, que no se suele incluir la valoración de la bondad de ajuste o la construcción de modelos no lineales. Estos resultados proporcionan criterios para mejorar la presentación de la regresión en los textos de Bachillerato.

Fórmulas electorales basadas en sucesiones de divisores

En este trabajo se realiza un estudio que conduce a la obtención de fórmulas electorales, basadas en sucesiones de divisores, que aseguran una representación proporcional a la hora de asignar los escaños en cada circunscripción. Se ha encontrado una familia de fórmulas a la que pertenecen como casos particulares D’Hondt, StLagüe, Imperiali y el método Danés. De las propiedades matemáticas de las fórmulas obtenidas se deducen ventajas e inconvenientes que va a tener el uso de cada una de ellas.

El teorema de Napoleón

Presentamos seis demostraciones del teorema de Napoleón y de varias propiedades que se derivan de la misma configuración. En las demostraciones recurrimos a la geometría métrica, la geometría analítica, los números complejos, la trigonometría y las isometrías, alternativamente. Algunas de dichas demostraciones –no las propiedades– son originales, otras son el desarrollo de sugerencias esbozadas en distintos textos y otras son adaptaciones de las halladas en los textos.

Algunas equivalencias tipológicas del axioma del extremo superior

En este artículo se presentan cuatro propiedades topológicas del conjunto de los números reales, R, que, evidentemente o no, resultan ser todas equivalentes al Axioma del Extremo Superior (AES).

Teacher attitudes and best practices with ICT faculty Adult Continuing Education in Andalusia

The present paper reports the results of a study aiming to describe the attitudes of teachers in adult continuous education in the Autonomous Community of Andalusia (Spain) towards the use and integration of information and communication technologies (ITC) in the educational centres they work in, while identifying those factors that favour the development of good practice. It is a mixed methods descriptive research, and information collection techniques include a questionnaire and in-depth interviews. A total number of 172 teachers were surveyed, as well as 18 head teachers and coordinators, in adult education. For questionnaire validation the expert judgment technique was used, as they were selected by the «expert competence coefficient» or «K coefficient» procedure. To improve its psychometric properties, construct validity was determined by means of Varimax factor analysis and maximum likelihood extraction (two factors were extracted). Confidence was set by Cronbach's alpha (0.88). The interview guide was also validated by this group of experts. Results point out, on one hand, that teachers hold positive attitudes towards ICT regarding both ICT's role in professional development and their ease of use and access. On the other hand, among the most important factors for ICT-supported good educational practices lies in ICT's capacity to favour personalized work.

University students with disabilities in Universities. A study of their inclusion

Access to higher education has increased among students with disabilities, and universities are adopting different alternatives which must be assessed. The purpose of this study was to identify the situation of a sample of students with disabilities (n=91) who attend a university in Spain, through the design and validation of the “CUNIDIS-d” scale, with satisfactory psychometric properties. The results show the importance of making reasoned curriculum adaptations, adapting teacher training, improving accessibility and involving all the university community. Different proposals were provided which support the social dimension of the EHEA.

Adaptation of a questionnaire to assess the epistemological beliefs of mathematics in secondary school teachers

The objective of the study is to determine the psychometric properties of the Epistemological Beliefs Questionnaire on Mathematics. 171 Secondary School Mathematics Teachers of the Central Region of Cuba participated. The results show acceptable internal consistency. The factorial structure of the scale revealed three major factors, consistent with the Model of the Three Constructs: beliefs about knowledge, about learning and teaching. Irregular levels in the development of the epistemological belief system about mathematics of these teachers were shown, with a tendency among naivety and sophistication poles. In conclusion, the questionnaire is useful for evaluating teacher’s beliefs about mathematics.

Estudio y análisis de eficiencia de un quemador de fuel oil N. 6, con calentamiento del aire de pulverización para un caldero de 300 BPH

La presente tesis está enfocada al análisis estrictamente de la combustión de un quemador de aceite (fuel oil # 6) para un caldero degeneración de vapor de agua de 300 BHP de potencia, el cual para su atomización del combustible usa aire comprimido a 40 PSI de presión y una temperatura que va desde los 15 ºC hasta los 150 ºC según nuestra particular implementación del sistema de calentamiento. El desarrollo emprende desde un marco teórico de los quemadores, sus partes consistentes, el combustible, clasificación, propiedades y características. De manera muy particular nos centramos en el proceso de combustión por cuanto es la parte medular del presente documento, así como generalidades, fundamentos, los elementos y productos, los comportamientos de éstos en la combustión. Además enfocamos conceptos básicos de tipos de combustión. En una forma analítica se establece la ecuación general de la combustión, una evaluación de la energía liberada en el proceso, en base al volumen y composición de lso productos que intervienne en la misma, yademás de la forma de cómo calibrar el equipo o sistema para obtener combustion lo más eficiente posible, sea produciendo energía calorífica más alta posible con el mínimo requerido posible de combustión. Se enfoca en el presente documento un análisis de las relaciones termodinámicas en la combustión como: la entalpía de los elementos como de los productos, las entalpías de formación de los mismos, le energía interna de los gases productos, y de la entropía o irreversibilidades del proceso total de combustión. La determinación del calor generado más la temperatura de llama adiabática son temas fundamentales en el desarrollo del tema, es por lo tanto parte importante del documento. Ya en el análisis experimental se parte del hecho de tener instalado a modo de prueba un intercambiador de calor para calentar el aire de atomización en uncaldero específico, esto es en un caldero de 300 BHP de potencia, de generación de vapor de agua de 100 PSI de presión, en la empresa Tejidos Pintex, y el análisis va enfocado a determinar la efectividad o no de calentar el aire de atomización, y de ser así cuantificar los beneficios del sistema.

Assessing the combined effect of land management and wildfire on runoff and soil erosion in north central Portugal

Strong and sometimes extreme responses in runoff and soil erosion following wildfires have been reported worldwide. However, in the case of North-Central Portugal, little research had been carried out regarding the hydrologic and erosive impacts of several land management activities in recently burnt areas (such as ground preparation, post-fire logging or post-fire mitigation treatments). This study aims to assess post-fire runoff and soil erosion response on Eucalypt and Maritime pine plantations during the first, second and third years following wildfires. The effect of several pre-fire ground preparation operations (ploughed down-slope, contour ploughed and inclined terraces), post-fire logging activities (on both the eucalypt and pine plantations), as well as the application of hydromulch (a post-fire emergency treatment) on overland flow and soil erosion were compared to burnt but undisturbed and untreated areas. The intensive monitoring of runoff, soil erosion and selected soil properties served to determine the main factors involved in post-fire runoff and soil erosion and their spatial and temporal variation. Soil water repellency deserved special attention, due to its supposed important role for overland flow generation. Repeated rainfall simulation experiments (RSE’s), micro-scale runoff plots and bounded sediment fences were carried out and/or installed immediately after the wildfire on seven burnt slopes. Micro-scale runoff plots results under natural rainfall conditions were also compared to the RSE’s results, which was useful for assessing the representativeness of the data obtained with artificial rainfall. The results showed comparable runoff coefficient (20-60%) but lower sediment losses (125-1000 g m-2) than prior studies in Portugal, but especially outside Portugal. Lower sediment losses were related with the historic intensive land use in the area. In evaluating these losses, however, the shallowness and stoniness of the soils, as well as the high organic matter fraction of the eroded sediments (50%) must not be overlooked. Sediment limited erosion was measured in all the ploughed sites, probably due to the time since ploughing (several years). The disturbance of the soil surface cover due to post-fire logging and wood extraction substantially increased sediment losses at both the pine and eucalypt sites. Hydromulch effectiveness in reducing the runoff (70%) and sediment losses (83%) was attributed to the protective high coverage provided by hydromulch. The hydromulch significantly affected the soil cover and other soil properties and these changes also reduced the soil erosion risk. The rainfall amount was the main factor explaining the variance in runoff. However, a shift from rainfall amount to rainfall intensity was detected when either the surface cover or the infiltration capacity (hydrophilic conditions) increased. Sediment losses were controlled by rainfall intensity and surface cover. The role of soil water repellency on runoff generation was not consistent; the overall repellency levels alone were not enough to assess its hydrological impact. Soil water repellency explained runoff generation in the specific-sites model better than in the overall model. Additionally, soil moisture content was a better predictor for soil water repellency than antecedent rainfall. The natural rainfall results confirmed that RSE’s were able to capture the specific sediment losses and its organic matter content as well as the differences between the ploughed and unploughed sites. Repeated RSE’s also captured the seasonal variations in runoff and sediment losses attributed to soil water repellency. These results have implications for post-fire soil erosion modelling and soil conservation practices in the region, or areas with the same land use, climate and soil characteristics. The measured sediment loss, as well as the increasing frequency of ploughing in recently burnt and unburnt eucalypt stands, suggests ploughing is not an effective as a soil conservation measure. Logging activities with less impact are recommended in order to maintain the forest litter protecting the soil surface. Due to its high effectiveness in reducing runoff and soil erosion, hydromulch is recommended for highly sensitive and vulnerable areas.

Las santas reliquias en Europa y la tilma americana: la imaginación histórica en la Nueva España

Los sucesos históricos y culturales en ambos lados del Atlántico durante el siglo XVI tuvieron un punto de confluencia en la representación simbólica del manto de Verónica en el teatro misionero y, poco después, en la legendaria tilma guadalupana. La versión en náhuatl del auto de La destruyción de Jerusalem, de origen valenciano, y la conocida historia aparicionista que tuvo lugar posteriormente adquieren un desarrollo elocuente y polisémico a lo largo de la Colonia, entreverándose con la hipótesis de la llegada a América del apóstol Santo Tomás. En estas tradiciones, la representación simbólica sirve para llenar lo que la ideología occidental consideraba una tabula rasa: la historia y la cultura propias del mundo americano. No obstante, la cultura prehispánica ha aportado sus propios contenidos significativos al manto o tilma maravillosa. Con sus propiedades curativas y su contenido cristiano, la tilma se convierte en un signo de identidad entre Europa y América. Para los europeos, prueba de verdadera fe, para los criollos, autoafirmación, y para los indios, permanencia del tiempo mítico.

Development of chitosan packaging films with carvacrol and grape seed extract as antimicrobial and antioxidant agents

In order to produce packaging films with a broad spectrum of action on microorganisms, the effect of two antimicrobial (AM) to be included in the films, carvacrol and GSE were studied separately on different microorganisms. Carvacrol was more effective against the grampositive bacteria than against the gram-negative bacterium. GSE was not effective against yeast. Subsequently, a search for optimal combinations of carvacrol, GSE and the addition of chitosan (as a third component with film forming properties) was carried out. Response surface analysis showed several synergetic effects and three optimal AM combinations (OAMC) were obtained for each microorganism. The experimental validation confirmed that the optimal solutions found can successfully predict the response for each microorganism. The optimization of mixtures of the three components, but this time, using the same concentration for all microorganisms, was also studied to obtain an OAMC with wide spectrum of activity. The results of the response surface analysis showed several synergistic effects for all microorganisms. Three OAMC, OAMC-1, OAMC-2, OAMC-3, were found to be the optimal mixtures for all microorganisms. The radical scavenging activity (RSA) of the different agents was then compared with a standard antioxidant (AOX) BHT, at different concentrations; as also at the OAMC. The RSA increased in the following order: chitosan

Avaliação da satisfação do utente na comunicação com os profissionais de saúde construção e validação de um instrumento

A satisfação do utente na comunicação com profissionais de saúde é um indicador de qualidade dos serviços ou instituições. Na literatura não encontramos instrumentos padronizados e validados, que avaliem a satisfação do utente na comunicação com os profissionais de saúde. O presente estudo tem como objetivo construir e validar um instrumento para avaliar a satisfação do utente na comunicação com os profissionais de saúde. Desenvolvemos este estudo em três ciclos. Um primeiro, revisão da literatura, para identificar dimensões e itens da comunicação interpessoal na saúde. No segundo ciclo, conduzimos um método de Delphi modificado em três rondas, com recurso à plataforma informática de questionários Survey Monkey, no qual participou um painel de 25 peritos; estabelecemos como critério mínimo de retenção para a ronda seguinte os itens que recebessem 70% do consenso por parte do painel. Após as três rondas, obtivemos um instrumento com seis dimensões comunicacionais (comunicação verbal, comunicação não verbal, empatia, respeito, resolução de problemas e material de apoio), vinte e cinco itens específicos, e mais seis dimensões genéricas, que avaliam cada uma das dimensões. No terceiro ciclo avaliamos as características psicométricas, em termos de sensibilidade, validade do construto e fidelidade, numa amostra de 348 participantes. Os resultados mostram que todas as categorias de resposta estavam representadas em todos os itens. Validade do construto- a análise fatorial identificou uma solução de seis componentes que explicam 71% da variância total. Fiabilidade - os valores da correlação item-total variam entre 0,387 e 0,722, existindo uma correlação positiva moderada a forte. O valor de alfa de Cronbach (α=0,928) indica que a consistência interna é excelente. O instrumento construído apresenta boas propriedades psicométricas. Fica assim disponível uma nova ferramenta para auxiliar na gestão e no processo de planeamento necessários ao incremento da qualidade nos serviços e instituições de saúde.