7,040 research outputs found
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 . The
purpose of this paper is to consider a dual product, denoted , and the
dual residuation of matrices, in order to solve the following inequality . 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
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