Duality and interval analysis over idempotent semirings

In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities $A \otimes X \preceq B$. The purpose of this paper is to consider a dual product, denoted $\odot$, and the dual residuation of matrices, in order to solve the following inequality $A \otimes X \preceq X \preceq B \odot X$. Sufficient conditions ensuring the existence of a non-linear projector in the solution set are proposed. The results are extended to semirings of intervals

An alternative theoretical approach to describe planetary systems through a Schrodinger-type diffusion equation

In the present work we show that planetary mean distances can be calculated with the help of a Schrodinger-type diffusion equation. The obtained results are shown to agree with the observed orbits of all the planets and of the asteroid belt in the solar system, with only three empty states. Furthermore, the equation solutions predict a fundamental orbit at 0.05 AU from solar-type stars, a result confirmed by recent discoveries. In contrast to other similar approaches previously presented in the literature, we take into account the flatness of the solar system, by considering the flat solutions of the Schrodinger-type equation. The model has just one input parameter, given by the mean distance of Mercury.Comment: 6 pages. Version accepted for publication in Chaos, Solitons & Fractal

Particle Creation by a Moving Boundary with Robin Boundary Condition

We consider a massless scalar field in 1+1 dimensions satisfying a Robin boundary condition (BC) at a non-relativistic moving boundary. We derive a Bogoliubov transformation between input and output bosonic field operators, which allows us to calculate the spectral distribution of created particles. The cases of Dirichlet and Neumann BC may be obtained from our result as limiting cases. These two limits yield the same spectrum, which turns out to be an upper bound for the spectra derived for Robin BC. We show that the particle emission effect can be considerably reduced (with respect to the Dirichlet/Neumann case) by selecting a particular value for the oscillation frequency of the boundary position

Inertial forces in the Casimir effect with two moving plates

We combine linear response theory and dimensional regularization in order to derive the dynamical Casimir force in the low frequency regime. We consider two parallel plates moving along the normal direction in $D-$dimensional space. We assume the free-space values for the mass of each plate to be known, and obtain finite, separation-dependent mass corrections resulting from the combined effect of the two plates. The global mass correction is proportional to the static Casimir energy, in agreement with Einstein's law of equivalence between mass and energy for stressed rigid bodies.Comment: 9 pages, 1 figure; title and abstract changed; to appear in Physical Review

¿Conflictos en la integración regional? Consideraciones acerca de la superposición de los acuerdos internacionales de inversión, los acuerdos comerciales regionales y la OMC

La creciente interdependencia económica internacional resultó en el desarrollo de diversas organizaciones y acuerdos regionales como los acuerdos comerciales regionales, los acuerdos internacionales de inversión y la Organización Mundial de Comercio (omc). En el panorama actual, diversos países son miembros de estos acuerdos y organizaciones concomitantemente. El gran incremento de los resultados de soluciones de diferencias debido al éxito del Entendimiento sobre Solución de Diferencias (esd) de la omc y el crecimiento paralelo del uso de las provisiones de los aii sobre solución de diferencias entre Estados e inversores llevaron a afirmaciones sobre el distanciamiento del derecho internacional de las inversiones y el derecho internacional comercial, lo que podría generar problemas con relación a la coherencia y estabilidad del derecho económico

Quantum radiation in a plane cavity with moving mirrors

We consider the electromagnetic vacuum field inside a perfect plane cavity with moving mirrors, in the nonrelativistic approximation. We show that low frequency photons are generated in pairs that satisfy simple properties associated to the plane geometry. We calculate the photon generation rates for each polarization as functions of the mechanical frequency by two independent methods: on one hand from the analysis of the boundary conditions for moving mirrors and with the aid of Green functions; and on the other hand by an effective Hamiltonian approach. The angular and frequency spectra are discrete, and emission rates for each allowed angular direction are obtained. We discuss the dependence of the generation rates on the cavity length and show that the effect is enhanced for short cavity lengths. We also compute the dissipative force on the moving mirrors and show that it is related to the total radiated energy as predicted by energy conservation.Comment: 17 pages, 1 figure, published in Physical Review

Study od a Slice at +9 to +15 degrees of Declination: I. The Neutral Hydrogen Content of Galaxies in Loose Groups

We examine the H1 content of spiral galaxies in groups by using a catalog of loose groups of galaxies identified in a magnitude limited sample m < 15.7 spanning the range 8 h to 18 h in right ascension and +9 to +15 in declination. The redshift completeness of the galaxy sample is ~95%. No significant effect of H1 depletion is found, although there may be a hint that the earliest type spirals are slightly deficient.Comment: 10 pages, Latex, 3 tables, 5 figures, to appear in the Astronomical Journa