Distribution functions for a family of axially symmetric galaxy models

We present the derivation of distribution functions for the first four members of a family of disks, previously obtained in (MNRAS, 371, 1873, 2006), which represent a family of axially symmetric galaxy models with finite radius and well behaved surface mass density. In order to do this we employ several approaches that have been developed starting from the potential-density pair and, essentially using the method introduced by Kalnajs (Ap. J., 205, 751, 1976) we obtain some distribution functions that depend on the Jacobi integral. Now, as this method demands that the mass density can be properly expressed as a function of the gravitational potential, we can do this only for the first four discs of the family. We also find another kind of distribution functions by starting with the even part of the previous distribution functions and using the maximum entropy principle in order to find the odd part and so a new distribution function, as it was pointed out by Dejonghe (Phys. Rep., 133, 217, 1986). The result is a wide variety of equilibrium states corresponding to several self-consistent finite flat galaxy models.Comment: 12 pages, 7 figures, updated version, accepted for publication in Rev. Acad. Colomb. Cienc. Ex. Fis. Na

Motion around a Monopole + Ring system: I. Stability of Equatorial Circular Orbits vs Regularity of Three-dimensional Motion

We study the motion of test particles around a center of attraction represented by a monopole (with and without spheroidal deformation) surrounded by a ring, given as a superposition of Morgan & Morgan discs. We deal with two kinds of bounded orbits: (i) Equatorial circular orbits and (ii) general three-dimensional orbits. The first case provides a method to perform a linear stability analysis of these structures by studying the behavior of vertical and epicyclic frequencies as functions of the mass ratio, the size of the ring and/or the quadrupolar deformation. In the second case, we study the influence of these parameters in the regularity or chaoticity of motion. We find that there is a close connection between linear stability (or unstability) of equatorial circular orbits and regularity (or chaoticity) of the three-dimensional motion.Comment: 13 pages, 17 figures, to appear in MNRA

On the computation of invariant sets for constrained nonlinear systems: An interval arithmetic approach

This paper deals with the computation of control invariant sets for constrained nonlinear systems. The proposed approach is based on the computation of an inner approximation of the one step set, that is, the set of states that can be steered to a given target set by an admissible control action. Based on this procedure, control invariant sets can be computed by recursion. We present a method for the computation of the one-step set using interval arithmetic. The proposed specialized branch and bound algorithm provides an inner approximation with a given bound of the error; this makes it possible to achieve a trade off between accuracy of the computed set and computational burden. Furthermore an algorithm to approximate the one step set by an inner bounded polyhedron is also presented; this allows us to relax the complexity of the obtained set, and to make easier the recursion and storage of the sets.Ministerio de Ciencia y Tecnología DPI2004-07444-c04-01Ministerio de Ciencia y Tecnología DPI2003-04375-c03-01Ministerio de Ciencia y Tecnología DPI2003-07146-c02-0

The Chadwicks and Lord Raglan: A Retrospective Analysis

Article

A set-membership state estimation algorithm based on DC programming

This paper presents a new approach to guaranteed state estimation for nonlinear discrete-time systems with a bounded description of noise and parameters. The sets of states that are consistent with the evolution of the system, the measured outputs and bounded noise and parameters are represented by zonotopes. DC programming and intersection operations are used to obtain a tight bound. An example is given to illustrate the proposed algorithm.Ministerio de Ciencia y Tecnología DPI2006-15476-C02-01Ministerio de Ciencia y Tecnología DPI2007-66718-C04-01

Organic Matter in Space - an Overview

Organic compounds are ubiquitous in space: they are found in diffuse clouds, in the envelopes of evolved stars, in dense star-forming regions, in protoplanetary disks, in comets, on the surfaces of minor planets, and in meteorites and interplanetary dust particles. This brief overview summarizes the observational evidence for the types of organics found in these regions, with emphasis on recent developments. The Stardust sample-return mission provides the first opportunity to study primitive cometary material with sophisticated equipment on Earth. Similarities and differences between the types of compounds in different regions are discussed in the context of the processes that can modify them. The importance of laboratory astrophysics is emphasized.Comment: Introductory overview lecture presented at IAU Symposium 251, "Organic matter in space", held at Hong Kong, February 2008; to appear in IAU Symposium 251 proceedings, Cambridge University Press, ed. S. Kwok et a

Eternal Independent Sets in Graphs

The use of mobile guards to protect a graph has received much attention in the literature of late in the form of eternal dominating sets, eternal vertex covers and other models of graph protection. In this paper, eternal independent sets are introduced. These are independent sets such that the following can be iterated forever: a vertex in the independent set can be replaced with a neighboring vertex and the resulting set is independent