Random l-colourable structures with a pregeometry

We study finite $l$-colourable structures with an underlying pregeometry. The probability measure that is used corresponds to a process of generating such structures (with a given underlying pregeometry) by which colours are first randomly assigned to all 1-dimensional subspaces and then relationships are assigned in such a way that the colouring conditions are satisfied but apart from this in a random way. We can then ask what the probability is that the resulting structure, where we now forget the specific colouring of the generating process, has a given property. With this measure we get the following results: 1. A zero-one law. 2. The set of sentences with asymptotic probability 1 has an explicit axiomatisation which is presented. 3. There is a formula $\xi(x,y)$ (not directly speaking about colours) such that, with asymptotic probability 1, the relation "there is an $l$-colouring which assigns the same colour to $x$ and $y$" is defined by $\xi(x,y)$. 4. With asymptotic probability 1, an $l$-colourable structure has a unique $l$-colouring (up to permutation of the colours).Comment: 35 page

Liquid polymorphism and density anomaly in a three-dimensional associating lattice gas

We investigate the phase diagram of a three-dimensional associating gas $(ALG)$ model. This model combines orientational ice-like interactions and ``van der Waals'' that might be repulsive, representing, in this case, a penalty for distortion of hydrogen bonds. These interactions can be interpreted as two competing distances making the connection between this model and continuous isotropic soft-core potentials. We present Monte Carlo studies of the $ALG$ model showing the presence of two liquid phase, two critical points and A density anomaly

Optical Sky Brightness at Cerro Tololo Inter-American Observatory from 1992 to 2006

We present optical UBVRI sky brightness measures from 1992 through 2006. The data are based on CCD imagery obtained with the CTIO 0.9-m, 1.3-m, and 1.5-m telescopes. The B- and V-band data are in reasonable agreement with measurements previously made at Mauna Kea, though on the basis of a small number of images per year there are discrepancies for the years 1992 through 1994. Our CCD-based data are not significantly different than values obtained at Cerro Paranal. We find that the yearly averages of V-band sky brightness are best correlated with the 10.7-cm solar flux taken 5 days prior to the sky brightness measures. This implies an average speed of 350 km/sec for the solar wind. While we can measure an enhancement of the night sky levels over La Serena 10 degrees above the horizon, at elevation angles above 45 degrees we find no evidence that the night sky brightness at Cerro Tololo is affected by artificial light of nearby towns and cities.Comment: 24 pages, 5 figures, to be published in the June, 2007, issue of the Publications of the Astron. Society of the Pacifi

On global models for isolated rotating axisymmetric charged bodies; uniqueness of the exterior field

A relatively recent study by Mars and Senovilla provided us with a uniqueness result for the exterior vacuum gravitational field generated by an isolated distribution of matter in axial rotation in equilibrium in General Relativity. The generalisation to exterior electrovacuum gravitational fields, to include charged rotating objects, is presented here.Comment: LaTeX, 21 pages, uses iopart styl

Lattice calculations on the spectrum of Dirac and Dirac-K\"ahler operators

We present a matrix technique to obtain the spectrum and the analytical index of some elliptic operators defined on compact Riemannian manifolds. The method uses matrix representations of the derivative which yield exact values for the derivative of a trigonometric polynomial. These matrices can be used to find the exact spectrum of an elliptic operator in particular cases and in general, to give insight into the properties of the solution of the spectral problem. As examples, the analytical index and the eigenvalues of the Dirac operator on the torus and on the sphere are obtained and as an application of this technique, the spectrum of the Dirac-Kahler operator on the sphere is explored.Comment: 11 page

Tourist spaces and tourism policy in Spain and Portugal

Advances in Cultura, Tourism and Hospitality Research;10, 235-249This study analyses the relationship between the development of the tourism policy of Spain and Portugal and their effects on regional imbalances. Despite the proximity of the two countries and their specialisation in tourism, there are few comparative studies on tourism of the two Iberian countries. The study focuses on the two major phases of tourism policy: the period of mass tourism and post-Fordist stage. In the conclusions we refer the debate on the existence of a model of development based on tourism to the Latin countries of Southern Europe and we note the export process of the Spanish low-cost tourism model to other countries.Financiado por el Gobierno de España, Programa Fundamental de Investigación, Proyecto de I+D (CSO2012-30840) "Geografías de la crisis: análisis de los territorios urbanos y turísticos de las Islas Baleares, Costa del Sol y principales destinos del Caribe y América Central"

A note on the intersection properties of subsets of integers

From the introduction: "According to the de Bruijn-Erdős theorem, if A1,⋯,AN are subsets of an n-element set S and |Ai∩Aj|=1 for i≠j (where |X| denotes the cardinality of X), then N≤n. This result is sharp, e.g., if S={1,⋯,n}=[1,n] and A1={1,n}, A2={2,n},⋯,An−1={n−1,n}, and An={1,2,⋯,n−1}, then Ai∩Aj=1 for 1≤i<j≤n. Many similar theorems have been proved for sets. One could also ask what analogous results can be proved if the Ai have some extra structure and the condition on the intersection also refers to this structure. For example, it has been proved [Simonovits and Sós, Problèmes combinatoires et théorie des graphes (Orsay, 1976), pp. 389–391, CNRS, Paris, 1980: MR0540021 (80i:05062a)], that if A1,⋯,AN are graphs on the same n vertices and the intersection of two graphs Ai and Aj is defined as the graph without isolated vertices whose edges are the common edges of Ai and Aj, then the condition `Ai∩Aj is a (nonempty) cycle for 1≤i<j≤N' implies that N≤(n2)−2, which is again sharp. Here we investigate the case in which A1,⋯,AN is a system of subsets of {1,⋯,n} and the intersection condition is of a number-theoretic type.'