101,010 research outputs found
Redshift estimate of a gravitational lens from the observed reddening of a multiply imaged quasar
Light rays from a multiply imaged quasar usually sample different path
lengths across the deflector. Extinction in the lensing galaxy may thus lead to
a differential obscuration and reddening between the observed macro-lensed QSO
images. These effects naturally depend on the precise shape of the extinction
law and on the redshift of the lens. By means of numerical Monte-Carlo
simulations, using a least-squares fitting method and assuming an extinction
law similar to that observed in the Galaxy, we show how accurate photometric
observations of multiply imaged quasars obtained in several spectral bands
could lead to the estimate of the lens redshift, irrespective of the visibility
of the deflector. Observational requirements necessary to apply this method to
real cases are thoroughly discussed. If extinction laws turn out to be too
different from galaxy to galaxy, we find out that more promising observations
should consist in getting high signal-to-noise low resolution spectra of at
least three distinct images of a lensed quasar, over a spectral range as wide
as possible, from which it should be straightforward to extract the precise
shape of the redshifted extinction law. Very high signal-to-noise, low spectral
resolution, VLT observations of H1413+117 and MG 0414+0534 should enable one to
derive such a redshifted extinction law.Comment: 7 pages, 11 figures, to appear in Astronomy and Astrophysics (also
available at http://vela.astro.ulg.ac.be/preprint/
Extremal functions for Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities
We consider a family of Caffarelli-Kohn-Nirenberg interpolation inequalities
and weighted logarithmic Hardy inequalities which have been obtained recently
as a limit case of the first ones. We discuss the ranges of the parameters for
which the optimal constants are achieved by extremal functions. The comparison
of these optimal constants with the optimal constants of Gagliardo-Nirenberg
interpolation inequalities and Gross' logarithmic Sobolev inequality, both
without weights, gives a general criterion for such an existence result in some
particular cases.Comment: Proc. Edinburgh A (2012) To appea
Extremal functions in some interpolation inequalities: Symmetry, symmetry breaking and estimates of the best constants
This contribution is devoted to a review of some recent results on existence,
symmetry and symmetry breaking of optimal functions for
Caffarelli-Kohn-Nirenberg and weighted logarithmic Hardy inequalities. These
results have been obtained in a series of papers in collaboration with M. del
Pino, S. Filippas, M. Loss, G. Tarantello and A. Tertikas and are presented
from a new viewpoint
Pure emitter dephasing : a resource for advanced solid-state single photon sources
We have computed the spectrum emitted spontaneously by a quantum dot coupled
to an arbitrarily detuned single mode cavity, taking into account pure
dephasing processes. We show that if the emitter is incoherent, the cavity can
efficiently emit photons with its own spectral characteristics. This effect
opens unique opportunities for the development of devices exploiting both
cavity quantum electrodynamics effects and pure dephasing, such as wavelength
stabilized single photon sources robust against spectral diffusion.Comment: 5 pages, 3 figure
Insights on the physics of SNIa obtained from their gamma-ray emission
Type Ia supernovae are thought to be the outcome of the thermonuclear
explosion of a carbon/oxygen white dwarf in a close binary system. Their
optical light curve is powered by thermalized gamma-rays produced by the
radioactive decay of Ni, the most abundant isotope present in the
debris. Gamma-rays escaping the ejecta can be used as a diagnostic tool for
studying the structure of the exploding star and the characteristics of the
explosion. The fluxes of the Ni lines and the continuum obtained by
INTEGRAL from SN2014J in M82, the first ever gamma-detected SNIa, around the
time of the maximum of the optical light curve strongly suggest the presence of
a plume of Ni in the outermost layers moving at high velocities. If this
interpretation was correct, it could have important consequences on our current
understanding of the physics of the explosion and on the nature of the systems
that explode.Comment: Proceedings of the 11th INTEGRAL Conference Gamma-Ray AStrophysics in
Multi-Wavelength Perspectiv
Infinite products involving binary digit sums
Let denote the Thue-Morse sequence with values . The
Woods-Robbins identity below and several of its generalisations are well-known
in the literature
\begin{equation*}\label{WR}\prod_{n=0}^\infty\left(\frac{2n+1}{2n+2}\right)^{u_n}=\frac{1}{\sqrt
2}.\end{equation*} No other such product involving a rational function in
and the sequence seems to be known in closed form. To understand these
products in detail we study the function
\begin{equation*}f(b,c)=\prod_{n=1}^\infty\left(\frac{n+b}{n+c}\right)^{u_n}.\end{equation*}
We prove some analytical properties of . We also obtain some new identities
similar to the Woods-Robbins product.Comment: Accepted in Proc. AMMCS 2017, updated according to the referees'
comment
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