18,015 research outputs found
Relation-based Galois connections: towards the residual of a relation
Inma P. Cabrera, Pablo Cordero, Manuel Ojeda-Aciego, Relation-based Galois connections: towards the residual of a relation, CMMSE 2017: Proceedings of the 17th International Conference on Mathematical Methods in Science and Engineering ( ISBN: 978-84-617-8694-7) , pp. 469--475We explore a suitable generalization of the notion of Galois connection in which their components are binary relations. Many different approaches are possible depending both on the (pre-)order relation between subsets in the underlying powerdomain and the chosen type of relational composition.Universidad de Málaga. Campus de Excelencia Internacional AndalucĂa Tech
Boltzmann entropy of a Newtonian Universe
A dynamical estimate is given for the Boltzmann entropy of the Universe,
under the simplifying assumptions provided by Newtonian cosmology. We first
model the cosmological fluid as the probability fluid of a quantum-mechanical
system. Next, following current ideas about the emergence of spacetime, we
regard gravitational equipotentials as isoentropic surfaces. Therefore
gravitational entropy is proportional to the vacuum expectation value of the
gravitational potential in a certain quantum state describing the matter
contents of the Universe. The entropy of the matter sector can also be
computed. While providing values of the entropy that turn out to be somewhat
higher than existing estimates, our results are in perfect compliance with the
upper bound set by the holographic principle.Comment: 15 page
The role of excitons and trions on electron spin polarization in quantum wells
We have studied the time evolution of the electron spin polarization under
continuous photoexcitation in remotely n-doped semiconductor quantum wells. The
doped region allows us to get the necessary excess of free electrons to form
trions. We have considered electron resonant photoexcitation at free, exciton
and trion electron energy levels. Also, we have studied the relative effect of
photoexcitation energy density and doping concentration. In order to obtain the
two-dimensional density evolution of the different species, we have performed
dynamic calculations through the matrix density formalism. Our results indicate
that photoexcitation of free electron level leads to a higher spin
polarization. Also, we have found that increasing the photoexcitation energy or
diminishing the doping enhances spin polarization.Comment: 30 pages, 11 figures, 1 tabl
Talbot effect for dispersion in linear optical fibers and a wavelet approach
We shortly recall the mathematical and physical aspects of Talbot's
self-imaging effect occurring in near-field diffraction. In the rational
paraxial approximation, the Talbot images are formed at distances z=p/q, where
p and q are coprimes, and are superpositions of q equally spaced images of the
original binary transmission (Ronchi) grating. This interpretation offers the
possibility to express the Talbot effect through Gauss sums. Here, we pay
attention to the Talbot effect in the case of dispersion in optical fibers
presenting our considerations based on the close relationships of the
mathematical representations of diffraction and dispersion. Although dispersion
deals with continuous functions, such as gaussian and supergaussian pulses,
whereas in diffraction one frequently deals with discontinuous functions, the
mathematical correspondence enables one to characterize the Talbot effect in
the two cases with minor differences. In addition, we apply, for the first time
to our knowledge, the wavelet transform to the fractal Talbot effect in both
diffraction and fiber dispersion. In the first case, the self similar character
of the transverse paraxial field at irrational multiples of the Talbot distance
is confirmed, whereas in the second case it is shown that the field is not self
similar for supergaussian pulses. Finally, a high-precision measurement of
irrational distances employing the fractal index determined with the wavelet
transform is pointed outComment: 15 text pages + 7 gif figs, accepted at Int. J. Mod. Phys. B, final
version of a contribution at ICSSUR-Besancon (May/05). Color figs available
from the first autho
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