SL(3,C) elementary instanton configurations

Several SL(3,C) self-dual instanton solutions of the Yang-Mills equations are presented which have very striking properties. While one of them is regular and SU(3) inside (outside) a sphere of arbitrarily large (small) radius, another one has all the characteristics of a meron solution (in particular its topological charge is concentrated at one point) although its Pontryagin number equals one. Their continuation to Minkowski space is also studied.

Los hábitats del proyecto CORINE en el ámbito territorial catalán: delimitación y cartografía.

nd items. Once maps are drawn up they are digitized and put into a GIS and finally subjected to quality control. Table 4 shows the most important habitats (according to polygon number and area covered) and the least represented habitats in the sheets drawn so far. Sheets can be obtained through internet (www.gencat.net/mediamb/pn.htm).

Tendencias demográficas recientes en Cataluña y su repercusión territorial

En los años transcurridos desde 1975, la población de Cataluña ha experimentado cambios drásticos en las tendencias demográficas, a saber: el hundimiento de 10s niveles de nupcialidad y natalidad y la inversión de la relación migratoria con el resto de España. Dichas transformaciones no se han producido de forma homopénea, dándose una notable variedad de shtuaciones a nivel comarcal y local. El presente trabajo se propone, en primer lugar, analizar la evolución de 10s hechos demográficos en Cataluña de 1975 a 1982, intentando poner de manifiesto 10s mecanismos que han provocado el desplome del que fue esplendoroso crecimiento poblacional; en segundo lugar, estudiar la incidencia de dicha evolución en la distribución territorial de la población; y, finalmente, reflexionar sobre las perspectivas de evolución que ofrece la situación actual.

The number of planar central configurations for the 4-body problem is finite when 3 mass positions are fixed

In the n{body problem a central con guration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for n = 3 and for n > 4 that if n ? 1 masses are located at xed points in the plane, then there are only a nite number of ways to position the remaining nth mass in such a way that they de ne a central con guration. Lindstrom leaves open the case n = 4. In this paper we prove the case n = 4 using as variables the mutual distances between the particles.

Double-Antiprism Central Configurations of the 3n-Body Problem

Abstract In this paper we study numerically a new type of central configurations of the 3n-body problem with equal masses which consist of three n-gons contained in three planes z = 0 and z = ±β = 0. The n-gon on z = 0 is scaled by a factor α and it is rotated by an angle of π/n with respect to the ones on z = ±β. In this kind of configurations, the masses on the planes z = 0 and z = β are at the vertices of an antiprism with bases of different size. The same occurs with the masses on z = 0 and z = −β. We call this kind of central configurations double-antiprism central configurations. We will show the existence of central configurations of this type.

On the existence of bi-pyramidal central configurations of the n + 2-body problem with an n-gon base

Abstract. In this paper we prove the existence of central con gurations of the n + 2{body problem where n equal masses are located at the vertices of a regular n{gon and the remaining 2 masses, which are not necessarily equal, are located on the straight line orthogonal to the plane containing the n{gon passing through its center. Here this kind of central con gurations is called bi{pyramidal central con gurations. In particular, we prove that if the masses mn+1 and mn+2 and their positions satisfy convenient relations, then the con guration is central. We give explicitly those relations.

Central configurations of nested rotated regular tetrahedra

In this paper we prove that there are only two different classes of central configura- tions with convenient masses located at the vertices of two nested regular tetrahedra: either when one of the tetrahedra is a homothecy of the other one, or when one of the tetrahedra is a homothecy followed by a rotation of Euler angles = = 0 and = of the other one. We also analyze the central configurations with convenient masses located at the vertices of three nested regular tetrahedra when one them is a homothecy of the other one, and the third one is a homothecy followed by a rotation of Euler angles = = 0 and = of the other two. In all these cases we have assumed that the masses on each tetrahedron are equal but masses on different tetrahedra could be different.

Central configurations of nested regular polyhedra for the spatial 2n–body problem

We consider 2n masses located at the vertices of two nested regular polyhedra with the same number of vertices. Assuming that the masses in each polyhedron are equal, we prove that for each ratio of the masses of the inner and the outer polyhedron there exists a unique ratio of the length of the edges of the inner and the outer polyhedron such that the configuration is central.

Central configurations of three nested regular polyhedra for the spatial 3n–body problem

Three regular polyhedra are called nested if they have the same number of vertices n, the same center and the positions of the vertices of the inner polyhedron ri, the ones of the medium polyhedron Ri and the ones of the outer polyhedron Ri satisfy the relation Ri = ri and Ri = Rri for some scale factors R > > 1 and for all i = 1, . . . , n. We consider 3n masses located at the vertices of three nested regular polyhedra. We assume that the masses of the inner polyhedron are equal to m1, the masses of the medium one are equal to m2, and the masses of the outer one are equal to m3. We prove that if the ratios of the masses m2/m1 and m3/m1 and the scale factors and R satisfy two convenient relations, then this configuration is central for the 3n–body problem. Moreover there is some numerical evidence that, first, fixed two values of the ratios m2/m1 and m3/m1, the 3n–body problem has a unique central configuration of this type; and second that the number of nested regular polyhedra with the same number of vertices forming a central configuration for convenient masses and sizes is arbitrary.

Equilibrium points and central configurations for the Lennard-Jones 2-and 3-body problems

Abstract. In this paper we study the relative equilibria and their stability for a system of three point particles moving under the action of a Lennard{Jones potential. A central con guration is a special position of the particles where the position and acceleration vectors of each particle are proportional, and the constant of proportionality is the same for all particles. Since the Lennard{Jones potential depends only on the mutual distances among the particles, it is invariant under rotations. In a rotating frame the orbits coming from central con gurations become equilibrium points, the relative equilibria. Due to the form of the potential, the relative equilibria depend on the size of the system, that is, depend strongly of the momentum of inertia I. In this work we characterize the relative equilibria, we nd the bifurcation values of I for which the number of relative equilibria is changing, we also analyze the stability of the relative equilibria.

Asentamientos rurales y estructuración de la Layetania interior (Barcelona): romanización e impacto de los programas de organización territorial

This paper presents the results of the first phase of archaeological and historical study developed in the Vallès Oriental. It has done a complete study of the archaeological information available from the several documentary sources (bibliography, IPAC, etc.). This has lead to an interpretative update on the forms of occupation and settlement dynamics developed in the study area during the 5th BC to 1st century AD. Preliminary results of the archaeomorphological analysis focused primarily on the road network are also presented. The first results highlight the importance of territorial organization programs of the late 2nd BC and 1st century BC. In this sense, it has been documented a close relationship between the road network and the distribution of rural settlements in late-Republican and Augustan periods. The use of databases in the management of archaeological information, and especially the application of GIS in the analysis and interpretation of data, suggest new interpretive approaches.

Llibre Blanc de l’Eurodistricte Català Transfronterer: creació de projecte i reestructuració territorial

En aquest article, s’hi presenta el procés d’elaboració, la metodologia, les reflexions i les conclusions del Llibre Blanc de l’Eurodistricte Català Transfronterer elaborat per la Mission Opérationnelle Transfrontalière (MOT) i la Universitat de Girona (UdG). L’estudi té per objectiu acompanyar la definició i l’emergència d’un projecte de territori transfronterer basat en la realitat d’un àmbit territorial compartit entre el departament dels Pirineus Orientals i les comarques de la província de Girona. El contingut del Llibre Blanc es divideix en tres parts: un diagnòstic transfronterer complet, l’anàlisi dels reptes d’aquest territori i les opcions de governança del territori transfronterer. Després de descriure el context territorial, la metodologia i les conclusions de l’estudi, s’hi fa un breu repàs de quin és l’estat del procés en l’actualitat

L'estructura territorial al Bisbat de Girona

Estudi sobre l'estructura socioeconòmica del Bisbat de Girona amb la finalitat de dibuixar les àrees funcionals que estructures aquest espai, i poder endegar, a la llarga una reforma dels actuals límits de l'arxiprestat

Análisis arqueomorfológico y dinámica territorial en el Vallés Oriental (Barcelona) de la Protohistoria s. VI-V a.C.) a la alta Edad Media (s. IX-X)

La investigación sobre el paisaje en zonas urbanas o periurbanas implica importantes limitaciones metodológicas. En el presente estudio, el trabajo se centra en un llano pre-litoral próximo a la ciudad de Barcelona, el Vallès Oriental, profundamente urbanizado en las últimas dos décadas, hecho que condiciona la recuperación de nuevos datos arqueológicos y la implementación de programas de prospección arqueológica. Asimismo, la particular topografía que presenta el llano, caracterizado por unos relieves suaves, ha obligado a adaptar la metodología del análisis arqueomorfológico a este contexto geográfico. El artículo presenta los resultados del análisis arqueomorfológico realizado, que han sido cruzados con la documentación histórica y arqueológica para caracterizar —desde una perspectiva diacrónica— la red viaria, la estructuración territorial y la evolución del poblamiento de esta área y, finalmente, determinar las dinámicas del paisaje en época romana. La investigación sobre la morfología del territorio se ha llevado a cabo a partir de un intenso trabajo de fotointerpretación y análisis de la cartografía histórica en entorno SIG, especialmente útil en un paisaje marcado por las importantes trasformaciones del medio rural. Igualmente, los datos generados en los últimos años por la investigación arqueológica han sido revisados de forma detallada, a fin de contribuir a la planificación de las prospecciones arqueológicas y arqueomorfológicas desarrolladas.

Análisis territorial de la accesibilidad a la vivienda en España

El trabajo es una análisis territorial del problema de la accesibilidad a la vivienda en España. El ámbito de estudio son las Comunidades Autónomas (CCAA) y el objetivo es evaluar qué CCAA gozan de mejores condiciones de accesibilidad a la vivienda en propiedad. Para alcanzar tal objetivo se trabaja con cuatro grupos de variables: variables relacionadas con la oferta de viviendas, variables relacionadas con los precios de la vivienda, variables relacionadas con la política de la vivienda y variables relacionadas con las características y equipamiento de la vivienda. La metodología aplicada cae dentro de la programación multicriterio. Esta técnica ha sido elegida porque permite incluir en la función objetivo todas las variables consideradas relevantes e ir desgranando qué CCAA optimizan los criterios marcados de accesibilidad.