On eulerian equilibria in K-order approximation of the gyrostat in the three-body

We consider the noncanonical Hamiltonian dynamics of a gyrostat in the three-body problem. By means of geometric-mechanics methods we study the approximate Poisson dynamics that arises when we develop the potential in series of Legendre and truncate this in an arbitrary order k. Working in the reduced problem, the existence and number of equilibria, that we denominate of Euler type in analogy with classic results on the topic,are considered. Necessary and sufficient conditions for their existence in an approximate dynamics of order k are obtained and we give explicit expressions of these equilibria, useful for the later study of the stability of the same ones. A complete study of the number of Eulerian equilibria is made in approximate dynamics of orders zero and one. We obtain the main result of this work, the number of Eulerian equilibria in an approximate dynamics of order k for k ≥ 1 is independent of the order of truncation of the potential if the gyrostat S0 is close to the sphere. The instability of Eulerian equilibria is proven for any approximate dynamics if the gyrostat is close to the sphere. In this way, we generalize the classical results on equilibria of the three-body problem and many of those obtained by other authors using more classic techniques for the case of rigid bodies.The authors are grateful to the referee for his useful suggestions and comments which improved the paper. This research was partially supported by the Spanish Ministerio de Ciencia y Tecnologìa (Project BFM2003-02137) and by the Consejerìa de Educaciòn y Cultura de la Comunidad Autónoma de la Región de Murcia (Project S´eneca 2002: PCMC/ 3/00074/FS/02)

Polynomial Properties in Unitriangular Matrices

AbstractLet Gn=Gn(q) be the group of the upper unitriangular matrices of size n over Fq, the finite field of q=pt elements. G. Higman has conjectured that, for each n, the number of conjugacy classes of elements of Gn is a polynomial expression in q. In this paper we prove that the number of conjugacy classes of Gn of cardinality qs, with s≤n−3, is a polynomial in q−1, with non-negative integral coefficients, fs(q−1), of degree less than or equal to the integer part of 2s+1. In addition, fs(q−1) depends only on s and not on n. We determine these polynomials arguing with the methods we gave previously (1995, J. Algebra177, 899–925). In fact, the coefficients of these polynomials are obtained by certain generating functions

Planar rotations for a gyrostat in the three-body problem

We consider the non-canonical Hamiltonian dynamics of a gyrostat in the three body problem. By means of geometric-mechanics methods we study the approximate Poisson dynamics that arises when we develop the potential in series of Legendre and truncate this in an arbitrary order k. Working in the reduced problem,the existence and number of equilibria, that we denominate planar rotation type in analogy with classic results on the topic, is considered. Necessary and sufficient conditions for their existence in a approximate dynamics of order k is obtained and we give explicit expressions of this equilibria, useful for the later study of the stability of the same ones. A complete study of the planar rotation type equilibria is made in approximate dynamics or order zero and one.This research was partially supported by the Spanish Ministerio de Ciencia y Tecnología (Project BFM2003-02137) and by the Consejería de Educación y Cultura de la Comunidad Autónoma de la Región de Murcia (Project Séneca 2002: PC-MC/3/00074/FS/02)

Handheld mobile mapping applied to historical urban areas

Mapping historical urban areas is an assignment that can be tackled by using different systems and devices. In the last decade many surveying systems have emerged in this this ever-evolving market. So, despite having a wide spectrum ofoptions to choose, the decision-making is not an easy task. It depends on the budget, the training, the experience, the available delivery term, the specific features of the streets and buildings, etc. In this article a complete high-speed recording procedure, by using a handheld mobile mapping instrument to record a typical old town street, is going to be described. The aim is to enlighten the decision-making when choosing the appropriate methodology. The characteristics of this kind of streets, such as an extreme narrowness and accessibility difficulties make this type of areas more difficult to surveying. Additionally, a comparison between this procedure and stop-and-go systems will be carried out. The research shows that the graphical documentation obtained fulfils perfectly the initial requirements and the fieldwork has turned out much less time-consuming by using mobile mapping devices than standard stop-and-go laser scanning systems and photogrammetry procedure

Communication and guidance of teachers preservice through virtual campus

La investigación que presentamos en este artículo es parte de un estudio sobre las posibilidades que ofrece el campus virtual de la Universidad Complutense en el desarrollo del practicum de futuros Licenciados en Pedagogía. Se encuadra dentro del análisis de las posibilidades que ofrecen al campo de la educación las redes de comunicación soportadas por herramientas informáticas (TIC).In this article we pretend to illustrate this opportunities of educative innovation with part of a research on the possibility the virtual campus of UCM to development the practicum of school pedagogy by means to analyse of the use in education of communication networks and ICT

Optimización de las redes de distribución del Servicio Postal Universal

La necesidad cotidiana de los ciudadanos de comunicarse, con el fin de realizar diferentes actividades de cualquier naturaleza, se ha visto afectada en gran medida por los cambios recientemente producidos. Las ventajas generadas por la inclusión de las nuevas tecnologías como modo de comunicación, y la proliferación de su uso entre la ciudadanía, son innumerables y se extienden tanto en el ámbito personal como en el privado. En la actualidad los servicios postales están sufriendo una transformación sin precedentes debido al cambio de las cartas en papel por los correos electrónicos, ya que éstos presentan mayor rapidez que los tradicionales al ser el tiempo de entrega inmediato. También se está produciendo un cambio en el tipo de envío, debido a que en la red postal se incrementa progresivamente el uso de la paqueteria, provocado por la implantación de los comercios electrónicos, donde desde casa se puede comprar de todo. En definitiva, todos y cada uno de estos servicios tienen la misma finalidad, comunicarnos. Y para permitir una comunicación permanente en todo el territorio, con unos criterios de calidad y a precios asequibles para los usuarios, nace el Servicio Postal Universal. El Servicio Postal Universal pretende que todos los usuarios de los servicios postales puedan acceder a la red postal. Este acceso debe realizarse sin discriminación alguna, en especial geográfica, al existir en España muchas zonas rurales. Estas zonas rurales no atraen a los operadores postales, por su bajo beneficio, obligando a la designación por parte del Estado de un operador que garantice este servicio en todo el territorio español, en régimen de servicio público. Este Servicio requiere por parte del operador de una planificación logística de sus rutas de transporte y entrega. Las rutas de transporte entre sus diversos centros han sido objeto de estudio detallado por parte del propio operador designado, a diferencia de las rutas de entrega, donde cada repartidor la hace en función de su experiencia o preferencias, sin seguir un criterio unificado. Este último paso representa el mayor coste en el servicio postal, entre el 40% y el 50% del total, debido fundamentalmente a la cantidad de medios personales y motorizados que se requieren. En este trabajo se presenta un modelo matemático, basado en los problemas de rutas de vehículos a través de la programación lineal entera, para el diseño óptimo de una red destinada a la entrega del Servicio Postal Universal. En concreto, el sistema determina las características de dicha red basándose en criterios de teoría de grafos. Se obtiene, por tanto, un modelo destinado a la mejora de la planificación, diseño y gestión de los diferentes recursos del proceso de entrega, provocando a la vez un importante ahorro en los costes producidos en este proceso o, lo que es lo mismo, un gran beneficio final para el operador postal.The daily need of citizens to communicate, in order to carry out different activities of any nature, has been affected to a large extent by the changes recently produced. The advantages generated by the inclusion of new technologies as a mode of communication, and the proliferation of their use among citizens, are innumerable and extend both in the personal as in the private. Currently postal services are undergoing an unprecedented transformation due to the change of paper letters by e-mails, as these are faster than traditional ones because of the immediate delivery time. Also is a change in the type of delivery, because in the postal network is progressively increased use of paqueteria, caused by the introduction of electronic commerce, where from home can buy everything. In short, each and every one of these services have the same purpose, to communicate. And to allow permanent communication throughout the territory, with quality criteria and at affordable prices for users, the Universal Postal Service is born. The Universal Postal Service is intended that all users of postal services can access the postal network. This access must be made without any discrimination, especially geographical, as there are many rural areas in Spain. These rural areas do not attract postal operators, its low profit, forcing the appointment by the State of an operator to guarantee this service throughout the Spanish territory under public service. This service requires the operator of a logistics planning their transport routes and delivery. Transportation routes between its various centers have been studied detailed by the designated operator itself, unlike delivery routes, where each dealer makes a function of their experience or preferences, without following a unified approach. This last step represents the highest cost in the postal service, between 40% and 50% of the total, mainly due to the amount of personal and motorized means that are required. This paper presents a mathematical model, based on the problems of vehicle routes through the entire linear programming, for the optimal design of a network destined to the delivery of the Universal Postal Service. Specifically, the system determines the characteristics of the network based on criteria of graph theory. It is obtained therefore a model for improving the planning, design and management of the various resources of the delivery process, causing both a significant savings in the costs incurred in this process or what is the same, a great end benefit to the postal operator

Métodos de asignación dinámica de intervalos de tiempo para redes de comunicaciones tácticas militares

Las redes de comunicaciones tácticas militares tienen como objetivo el intercambio de información entre un gran número de unidades tácticas dispersas en un área, cada una de las cuales tiene un terminal para la transmisión de datos, optimizando las funciones militares operativas conjuntas. Link-16 es actualmente el estándar más avanzado de este tipo de redes de la OTAN. En esta red, a cada participante se le asigna un grupo de intervalos de tiempo (time slots) para transmitir sus mensajes. Existen tres modos de acceso a esos time slots: dedicado, por contienda y por reasignación de time slots (Time Slot Reallocation). En el modo Time Slot Reallocation (TSR) se asigna un mismo conjunto de time slots a varios participantes en la red para la transmisión de sus mensajes, pero se van distribuyendo dinámicamente de forma automática a cada unidad de acuerdo a sus requisitos de transmisión en cada periodo de reasignación. El algoritmo de asignación de time slots reside en cada terminal, que puede calcular qué time slots debe usar en el siguiente periodo de reasignación de slots. Cuando la suma de las demandas de bloques de slots de todos los terminales participantes en la red es menor que el número de bloques de slots disponible en el conjunto TSR, a cada terminal se le asigna un número de bloques de slots igual al demandado, y no existe ningún conflicto. Pero si es mayor, a cada terminal se le asigna un número de bloques de slots proporcional al número demandado, con lo que se va creando una cola de mensajes sin poder transmitirse en cada terminal, ya que no todos los mensajes podrán transmitirse en el siguiente periodo de reasignación y tendrán que esperar a los siguientes periodos. El problema del algoritmo de reasignación actual es que permite conflictos en la asignación de bloques de slots. Además, intenta asignar el máximo número de bloques de slots a las unidades con una mayor prioridad según un orden, con lo que, a las unidades de menor prioridad les asigna un número bastante menor de bloques de slots. Esto quiere decir que la cola máxima de mensajes que no pueden ser transmitidos para algunos terminales es mucho mayor que para otros terminales. En esta Tesis se estudia la mejora del algoritmo TSR (Time Slot Reallocation) de reasignación dinámica de time slots para una red Link-16, en las dos situaciones posibles: que la suma de las demandas de bloques de slots de todos los terminales participantes en la red sea mayor que el número de bloques de slots disponible, o que sea menor. En el primer caso, se propone la utilización de diversas técnicas de Optimización Combinatoria. Con ello, se pretende eliminar los casos de conflicto en la asignación y minimizar el valor medio de la cola máxima de mensajes no transmitidos en cada terminal participante, es decir, que las colas de mensajes no transmitidos en todos los participantes en una red se mantengan lo más pequeñas posibles en todos los periodos de reasignación. En el segundo caso, se propone la utilización de Técnicas Predictivas y Teoría de Juegos para asignar los bloques de slots que quedan sin asignar. Con ello se pretende minimizar el tiempo de transmisión de los mensajes para cada terminal participante en la red, desde que se demandan los slots hasta que se transmiten, ya que, al asignarle más bloques de slots, puede transmitir antes en el siguiente periodo de reasignación. _____________________________________________The tactical military data communications networks have the purpose of the exchanging of tactical information among different military units, each one of these has a terminal for data communication, optimizing the joint operational military functions. Link-16 is at the moment the most advanced standard of these NATO networks. In this network, each terminal is assigned a pool of time slots to transmit their messages. There are three access modes to these time slots: dedicated access, contention access and Time Slot Reallocation access. In Time Slot Reallocation (TSR) access mode, participants in the networks are assigned the same pool of time slots for the transmission of the messages, and these time slots are dynamically distributed to each transmitter according to its transmission requirements for each reallocation period. An algorithm within the terminals redistributes the pool of time slots in real time to meet these needs for the next reallocation period. If the sum of all time slots blocks requested by all terminals in the network is less than the total number of time slots blocks available for TSR, each terminal is assigned the number of requested time slots blocks, and there is no conflict. But, if it exceeds the total number of time slots blocks available for TSR, each terminal is assigned a number of time slots blocks in proportion to the terminal´s request. So, a queue of messages that has not been transmitted is created in each terminal, because not all messages can be transmitted in the next reallocation period and will have to be transmitted in other periods. The problem in the current assignment algorithm is that there are conflicts in the time slots blocks assignments. Moreover, it tries to assign as many of the time slots blocks as required to satisfy their requests to the terminals with a greater priority according to a priority order, so the terminals with a less priority are assigned a few time slots blocks. That is, the maximum queue of messages that can not be transmitted increase for some terminals. In this Thesis, improved Time Slot Reallocation (TSR) algorithms of dynamic time slots assignment in Link-16 networks are studied for the two possible situations: the sum of all time slots blocks requested by all terminals in the network exceeds the total number of time slots blocks available for TSR, or it is less than the total number of time slots blocks available for TSR. In the first case, the use of different Combinatorial Optimization Techniques is proposed. These new algorithms are focused on avoiding the conflicts in the time slots assignments and minimizing the maximum queue average of messages that can not be transmitted in each participant terminal, that is, the queues of messages that can not be transmitted in all participant terminals in the network keep the smallest as possible for all reallocation periods. In the second case, the use of Predictive Techniques and Game Theory is proposed for the assignment of the slots blocks that not have been assigned. With these methods, the objective is to minimize the time for messages transmission, from the time slots blocks are requested to the messages are transmitted, since when terminals are assigned more time slots blocks, they can transmit before in the next reallocation period

Soluciones de equilibrio en un problema generalizado del de Lagrange-Poisson: condiciones necesarias y suficientes de estabilidad

In this paper, we consider the problem of motion of a symmetrical gyrostat with a fixed point in a Newtonian force field, where the potential function adopts the form U = U(K3), the gyrostatic momentum and the position vector of the center of mass are on the axis of symmetry. First, we obtain the equilibrium positions of this problem; then, by means of the Energy-Casimir method, we give sufficient conditions of stability for some of these equilibria and, by spectral methods, we obtain necessary conditions of stability. The obtained results generalize the previous papers [7], [8],[9], [1] and [2].MECD (Proyecto no PB98-1576)