14 research outputs found
Modelling and Terrestrial Laser Scanning Methodology (2009–2018) on Debris Cones in Temperate High Mountains
Producción CientíficaDebris cones are a very common landform in temperate high mountains. They are the
most representative examples of the periglacial and nival processes. This work studies the dynamic
behavior of two debris cones (Cone A and Cone B) in the Picos de Europa, in the north of the
Iberian Peninsula. Their evolution was measured uninterruptedly throughout each August for
10 years (2009–2018) using the Terrestrial Laser Scanning (TLS) technique. The observations and
calculations of the two debris cones were treated independently, but both showed the same behavior.
Therefore, if these results are extrapolated to other debris cones in similar environments (temperate
high mountain), they should show behavior similar to that of the two debris cones analyzed. Material
falls onto the cones from the walls, and transfer of sediments follows linear trajectories according to
the maximum slope. In order to understand the linear evolution of the two debris cones, profiles were
created along the maximum slope lines of the Digital Elevation Model (DEM) of 2009, and these profile
lines were extrapolated to the remaining years of measurement. In order to determine volumetric
surface behavior in the DEMs, each year for the period 2009–2018 was compared. In addition,
the statistical predictive value for position (Z) in year 2018 was calculated for the same planimetric
position (X,Y) throughout the profiles of maximum slopes. To do so, the real field data from 2009–2017
were interpolated and used to form a sample of curves. These curves are interpreted as the realization
of a functional random variable that can be predicted using statistical techniques. The predictive
curve obtained was compared with the 2018 field data. The results of both coordinates (Z), the real
field data, and the statistical data are coherent within the margin of error of the data collection.Fondo Europeo de Desarrollo Regional - Agencia Estatal de Investigación (grant TIN2016-76843-C4-2-R)Ministerio de Economía, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (grant CGL2015-68144-R
Exposición “Ríete con las Mates”
This paper presents the exhibition “Laugh with Maths: Mathematical Cartoons” that the
Educational Innovation Group (GIE) “Mathematical Thinking” (“Pensamiento
Matemático”) of the Polytechnic University of Madrid (UPM) has done with the
collaboration of students of the Escuela Técnica Superior de Ingenieros de Caminos,
Canales y Puertos of the UPM. The work wants to show the utility of the exhibitions as a
teaching resource in the teaching of mathematics.Este artículo presenta la exposición “Ríete con las Mates: Viñetas Cómicas Matemáticas”
que el Grupo de Innovación Educativa (GIE) “Pensamiento Matemático” de la Universidad
Politécnica de Madrid (UPM) ha confeccionado con la colaboración de alumnos de la
Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos de la UPM. El
trabajo quiere poner de manifiesto la utilidad de las exposiciones como recurso docente en
la enseñanza de las matemáticas
Ecuaciones diofánticas en enteros gaussianos
In this paper we search for solutions in Gaussian integers to some known Diophantine
equations.En este artículo se resuelven en los enteros gaussianos algunas ecuaciones diofánticas
conocidas
Optimización de recursos y calidad de servicio en las consultas de urgencias de un centro de atención primaria
The hospital emergency services receive a non insignificant proportion of patients who should have been attended in the primary attention services. Planning the emergency services of primary attention for them to improve their quality and to be attractive for the patients can clear the hospital emergencies influencing in an integral way on the whole sanitary emergency service. The reduced wait time is the main factor which the users identify with quality of service. In this article the problem is analysed from a mathematic and computer point of view designing a software which allows obtaining the assignment of doctors to an emergency service of primary attention fulfilling the objective of not surpassing a predetermined wait time as well as optimizing the resources consumption.Los servicios de urgencia hospitalarios reciben una proporción no despreciable de pacientes que deberían haber sido atendidos en los servicios de atención primaria. Planificar los servicios de urgencias de atención primaria para que mejoren su calidad y sean atrayentes para los pacientes puede descongestionar las urgencias hospitalarias incidiendo de manera integral en todo el servicio de urgencias sanitario. El tiempo de espera reducido es el principal factor que los usuarios identifican con la calidad del servicio. En este artículo se analiza el problema desde un punto de vista matemático e informático diseñando un software que permite obtener la asignación de facultativos a un servicio de urgencias de atención primaria cumpliendo el objetivo de no sobrepasar un tiempo de espera prefijado optimizando además el consumo de recursos
Una propuesta de fórmula electoral matemáticamente justa
This paper proposes a system of distribution of the seats that is more balanced than the one applied in the Spanish elections. To do this, a distribution based in a largest remainder system (the Hare quotient) is performed. This yields a system that is more proportional than the D’Hont law. But the main contribution of the paper is the change in the order of the distribution of the seats: first an assignation of the seats in a general level is done and then the seats earned by each party are distributed along the circumscriptions. This avoids the loss of votes that the small parties suffer in each circumscription with the current system.En este artículo se propone un sistema de reparto de escaños que no penalice tanto a los partidos pequeños como lo hace el sistema de reparto que se utiliza en las elecciones en España. Para ello se realiza un reparto basado en un sistema de resto mayor (el cociente Hare), más proporcional que el sistema D’Hont vigente en España y, como novedad principal, se cambia el orden en que se hace la distribución de escaños: primero se realiza el reparto a nivel general y luego se distribuyen los escaños de los partidos por las distintas circunscripciones, para evitar la pérdida de votos por circunscripciones (votos que no dan escaños) que tienen los partidos pequeños en el sistema de reparto actual
Danza, Ciencia e Ingeniería
En este trabajo se muestra cómo la danza puede ayudar al acercamiento del público
general a materias relacionadas con la ciencia y la tecnología, concretamente a la ingeniería
industrial y la arquitectura.
Se muestran relaciones, a veces nada evidentes, entre ciencia y danza, y se enseñan
ejemplos de vídeos de coreografías con elementos matemáticos, arquitectónicos e
ingenieriles que ayudan a la comprensión y aplicación de ciertos conceptos matemáticos.
Además, se presenta el conjunto de audiovisuales que miembros del Grupo de
Innovación Educativa “Pensamiento Matemático” que pertenecen al Aula Taller Museo de
las Matemáticas “π-ensa”, están elaborando en esta línea.The members of the Innovative Education Group “Pensamiento Matemático”,
participants of the Museum of the Mathematics “π-ensa” are preparing a collection of
videos to include in the web page of the Museum. The aim of the videos is to show the
relation of sciences such as the engineering and the architecture with the dance. The videos
express how to “dance architecture, engineering or mathematics” and give a way to
approach the science to the people by means of the dance
Equitable Seat Allocation in Spanish General Elections: A Weight Redistribution Approach
This research paper aims to reduce and minimize the disproportions (overrepresentation or underrepresentation) involved in some Proportional Representation (PR) rules such as D’Hondt Law, applied in the Spanish elections. To do this, we create a system of weighted seats that corrects these deviations. These weighted seats give a proportional allocation of seats in the global realm. Next, we distribute the weights of the parties among the constituencies in a way that minimizes a predetermined measure of disproportionality
Estudio del equilibrio mínimo en un modelo circular de competición política
This paper develops a political competition game between two parties. The aim of the game is for each party to attract the greatest possible weight of a weighted set of voters located on the unit circumference.
The Nash equilibrium is studied in the proposed game. Firstly, restricted equilibria are employed, and an analysis of which of them will give rise to Nash equilibria carried out. The study of Nash equilibrium raises the definition of a new type of equilibrium: minimum equilibrium. To conclude, necesary and sufficient conditions for the existence of minimum equilibrium positions are given.En este artículo se plantea un juego un juego de competición política entre dos partidos, definido en un espacio de políticas unidimensional, como es la circunferencia unidad.
Se estudian las posiciones de equilibrio de Nash en el juego planteado, para lo que se dan unas condiciones necesarias o suficientes de existencia de dichas posiciones de equilibrio. Primeramente, se trabaja con unos equilibrios restringidos analizándose cuáles de ellos dan lugar a equilibrios de Nash. El hecho de que puedan existir posiciones de equilibrio de Nash desventajosas para uno de los partidos, suscita la definición de un nuevo tipo de equilibrio, llamado equilibrio mínimo, caracterizándose las posiciones de equilibrio mínimo en el juego planteado
Modelling and Terrestrial Laser Scanning Methodology (2009–2018) on Debris Cones in Temperate High Mountains
Debris cones are a very common landform in temperate high mountains. They are the most representative examples of the periglacial and nival processes. This work studies the dynamic behavior of two debris cones (Cone A and Cone B) in the Picos de Europa, in the north of the Iberian Peninsula. Their evolution was measured uninterruptedly throughout each August for 10 years (2009–2018) using the Terrestrial Laser Scanning (TLS) technique. The observations and calculations of the two debris cones were treated independently, but both showed the same behavior. Therefore, if these results are extrapolated to other debris cones in similar environments (temperate high mountain), they should show behavior similar to that of the two debris cones analyzed. Material falls onto the cones from the walls, and transfer of sediments follows linear trajectories according to the maximum slope. In order to understand the linear evolution of the two debris cones, profiles were created along the maximum slope lines of the Digital Elevation Model (DEM) of 2009, and these profile lines were extrapolated to the remaining years of measurement. In order to determine volumetric surface behavior in the DEMs, each year for the period 2009–2018 was compared. In addition, the statistical predictive value for position (Z) in year 2018 was calculated for the same planimetric position (X,Y) throughout the profiles of maximum slopes. To do so, the real field data from 2009–2017 were interpolated and used to form a sample of curves. These curves are interpreted as the realization of a functional random variable that can be predicted using statistical techniques. The predictive curve obtained was compared with the 2018 field data. The results of both coordinates (Z), the real field data, and the statistical data are coherent within the margin of error of the data collection
Aplicación del Láser Escáner Terrestre (TLS) y de modelos matemáticos para la modelización de conos de derrubios en la alta montaña templada
Debris cones are a very common landform in temperate high mountains, being one of the most representative examples of the periglacial and nival processes. This article analyzes two debris cones (Cone A and Cone B) located in “La Vueltona” in Picos de Europa. Their evolution was measured uninterruptedly throughout each August for 10 years (2009–2018) using the Terrestrial Laser Scanning (TLS) technique. The observations and calculations of the two debris cones were treated independently, but both showed the same behavior. Material falls onto the cones from the walls, and transfer of sediments follows linear trajectories according to the maximum slope. In order to understand the linear evolution of the two debris cones, profiles were created along the maximum slope lines of the Digital Elevation Model (DEM) of 2009, and these profile lines were extrapolated to the remaining years of measurement. In addition, the statistical predictive value for position (Z) in year 2018 was calculated for the same planimetric position (X,Y) throughout the profiles of maximum slopes. To do so, the real field data from 2009-2017 were interpolated and used to form a sample of curves. These curves are interpreted as the realization of a functional random variable that can be predicted using statistical techniques. The predictive curve obtained was compared with the 2018 field data. The results of both coordinates (Z), the real field data and the statistical data are coherent, within the margin of error of the data collection. As an interpretation of this study, it can be indicated that the behavior of the two debris cones of
La Vueltona has an undulating dynamic along the maximum slope line, which allows to calculate statistically its evolution in a short period of time.Los conos de derrubios son una forma de relieve muy común en la alta montaña templada, siendo uno de los procesos periglaciales y nivales más representativos. En este artículo se analizan dos conos de derrubios (Cono A y Cono B) situados en la zona de “La Vueltona” en Picos de Europa. Los conos de derrubios tienen un comportamiento dinámico y su evolución se ha medido de forma ininterrumpida en los meses de agosto durante un periodo de 10 años (2009-2018) aplicando la técnica del Láser Escáner Terrestre (TLS). Para comprender la evolución lineal de los dos conos de derrubios se han realizado perfiles siguiendo las líneas de máxima pendiente del Modelo Digital de Elevaciones (MDE) del año 2009, y se han extrapolado estas líneas de perfiles para el resto de años de medición. Para la
misma posición planimétrica (X, Y) a lo largo de los perfiles, y su evolución altimétrica durante los años (2009-2017), se ha calculado por métodos estadísticos la posición (Z) de esos puntos para el año 2018. Este valor estadístico se ha comparado con la información de la toma de datos en campo del año 2018. Los resultados de ambas coordenadas (Z), esto es la real de campo y la estadística son coherentes, dentro del margen de error propio de la toma de datos. Como interpretación a este estudio se puede indicar que el comportamiento de los dos conos de derrubios de La Vueltona tiene una dinámica ondulatoria siguiendo la línea de máxima pendiente, lo cual permite calcular mediante estadística su evolución en un plazo corto de tiempo