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

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

Mass distribution and structural parameters of Small Magellanic Cloud star clusters

In this work we estimate, for the first time, the total masses and mass function slopes of a sample of 29 young and intermediate-age SMC clusters from CCD Washington photometry. We also derive age, interstellar reddening and structural parameters for most of the studied clusters by employing a statistical method to remove the unavoidable field star contamination. Only these 29 clusters out of 68 originally analysed cluster candidates present stellar overdensities and coherent distribution in their colour-magnitude diagrams compatible with the existence of a genuine star cluster. We employed simple stellar population models to derive general equations for estimating the cluster mass based only on its age and integrated light in the B, V, I, C and T1 filter. These equations were tested against mass values computed from luminosity functions, showing an excellent agreement. The sample contains clusters with ages between 60 Myr and 3 Gyr and masses between 300 and 3000 Mo distributed between ~0.5 deg. and ~2 deg. from the SMC optical centre. We determined mass function slopes for 24 clusters, of which 19 have slopes compatible with that of Kroupa IMF (2.3 +/- 0.7), considering the uncertainties. The remaining clusters - H86-188, H86-190, K47, K63 and NGC242 - showed flatter MFs. Additionally, only clusters with masses lower than ~1000 Mo and flatter MF were found within ~0.6 deg. from the SMC rotational centre.Comment: 12 pages, 19 figures. Includes another 29 full-page figures of supplementary material. Accepted for publication in the MNRA