Superintegrable Lissajous systems on the sphere

A kind of systems on the sphere, whose trajectories are similar to the Lissajous curves, are studied by means of one example. The symmetries are constructed following a unified and straightforward procedure for both the quantum and the classical versions of the model. In the quantum case it is stressed how the symmetries give the degeneracy of each energy level. In the classical case it is shown how the constants of motion supply the orbits, the motion and the frequencies in a natural way.Comment: 16 pages, 3 figures. Submitte

Intertwining Symmetry Algebras of Quantum Superintegrable Systems

We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or $(su(p,q),so(2p,2q))$. The eigenstates of the associated Hamiltonian hierarchies belong to unitary representations of these algebras. It is shown that these intertwining operators, related with separable coordinates for the system, are very useful to determine eigenvalues and eigenfunctions of the Hamiltonians in the hierarchy. An study of the corresponding superintegrable classical systems is also included for the sake of completness

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Realismo selectivo: ¿un programa de investigación regresivo?

El realismo selectivo (RS) es la versión del realismo científico preponderante en nuestros días, y de hecho la única versión del realismo defendible después de las críticas de Laudan basadas en la llamada inducción pesimista. RS sostiene que (i) las predicciones observacionales novedosas (e.g. que la teoría no se ha diseñado con la intención de realizarlas) y exitosas de una teoría se deben a que aquella parte del contenido inobservable de la teoría que es responsable de la predicción exitosa es (aproximadamente) verdadero, y (ii) las teorías posteriores que la suceden retienen (aproximadamente) dicha parte del contenido teórico. RS es una tesis empírica, y por tanto debe ser verificada o falsada por la historia de la ciencia. En este trabajo repasaremos los principales versiones de RS y sus principales anomalías históricas.Universidad de Málaga. Campus de Excelencia Internacional Andalucia Tech

How to achieve full electrification: Lessons from Latin America

Electricity coverage in Latin America has increased substantially in recent decades, rising from 50% of the population in 1970 to more than 95% in 2015. Growth, however, slowed in the 1990s as many countries experienced difficulties in extending their networks further, in particular to serve those living in isolated and rural areas. In spite of this, the process of electrification was not interrupted and at the beginning of the 2010s decade most countries in the region were able to provide access to electricity to almost all of their populations. In this paper, we examine the main strategies used in Latin America to increase coverage and argue that only a combination of policy efforts has made it possible to achieve the current situation. We also examine the remaining obstacles, at policy and institutional levels, to achieving full coverage

Structure of a bacterial type IV secretion core complex at subnanometre resolution

Type IV secretion (T4S) systems are able to transport DNAs and/or proteins through the membranes of bacteria. They form large multiprotein complexes consisting of 12 proteins termed VirB1-11 and VirD4. VirB7, 9 and 10 assemble into a 1.07 MegaDalton membrane-spanning core complex (CC), around which all other components assemble. This complex is made of two parts, the O-layer inserted in the outer membrane and the I-layer inserted in the inner membrane. While the structure of the O-layer has been solved by X-ray crystallography, there is no detailed structural information on the I-layer. Using high-resolution cryo-electron microscopy and molecular modelling combined with biochemical approaches, we determined the I-layer structure and located its various components in the electron density. Our results provide new structural insights on the CC, from which the essential features of T4S system mechanisms can be derived

Superintegrability and higher order polynomial algebras II

In an earlier article, we presented a method to obtain integrals of motion and polynomial algebras for a class of two-dimensional superintegrable systems from creation and annihilation operators. We discuss the general case and present its polynomial algebra. We will show how this polynomial algebra can be directly realized as a deformed oscillator algebra. This particular algebraic structure allows to find the unitary representations and the corresponding energy spectrum. We apply this construction to a family of caged anisotropic oscillators. The method can be used to generate new superintegrable systems with higher order integrals. We obtain new superintegrable systems involving the fourth Painleve transcendent and present their integrals of motion and polynomial algebras.Comment: 11 page