6,576 research outputs found
Measures of non-compactness in Orlicz modular spaces
In this paper we show that the ball measure of non-compactness of a norm bounded subset of an Orlicz modular space is equal to the limit of its -widths. We also obtain several inequalities between the measures of noncompactness and the limit of the -widths for modular bounded subsets of which do not have -condition. Minimum conditions on to have such results are specified and an example of such a function is provided
AGAPE, an experiment to detect MACHO's in the direction of the Andromeda galaxy
The status of the Agape experiment to detect Machos in the direction of the
andromeda galaxy is presented.Comment: 4 pages, 1 figure in a separate compressed, tarred, uuencoded uufile.
In case ofproblem contact [email protected]
AgapeZ1: a Large Amplification Microlensing Event or an Odd Variable Star Towards the Inner Bulge of M31
AgapeZ1 is the brightest and the shortest duration microlensing candidate
event found in the Agape data. It occured only 42" from the center of M31. Our
photometry shows that the half intensity duration of the event6 is 4.8 days and
at maximum brightness we measure a stellar magnitude of R=18.0 with B-R=0.80
mag color. A search on HST archives produced a single resolved star within the
projected event position error box. Its magnitude is R=22.Comment: 4 pages with 5 figure
Microlensing towards M31 with MDM data
We report the final analysis of a search for microlensing events in the
direction of the Andromeda galaxy, which aimed to probe the MACHO composition
of the M31 halo using data collected during the 1998-99 observational campaign
at the MDM observatory. In a previous paper, we discussed the results from a
first set of observations. Here, we deal with the complete data set, and we
take advantage of some INT observations in the 1999-2000 seasons. This merging
of data sets taken by different instruments turns out to be very useful, the
study of the longer baseline available allowing us to test the uniqueness
characteristic of microlensing events. As a result, all the candidate
microlensing events previously reported turn out to be variable stars. We
further discuss a selection based on different criteria, aimed at the detection
of short--duration events. We find three candidates whose positions are
consistent with self--lensing events, although the available data do not allow
us to conclude unambiguously that they are due to microlensing.Comment: Accepted for publication in Astronomy and Astrophysic
Search for exoplanets in M31 with pixel-lensing and the PA-99-N2 event revisited
Several exoplanets have been detected towards the Galactic bulge with the
microlensing technique. We show that exoplanets in M31 may also be detected
with the pixel-lensing method, if telescopes making high cadence observations
of an ongoing microlensing event are used. Using a Monte Carlo approach we find
that the mean mass for detectable planetary systems is about .
However, even small mass exoplanets () can cause
significant deviations, which are observable with large telescopes. We
reanalysed the POINT-AGAPE microlensing event PA-99-N2. First, we test the
robustness of the binary lens conclusion for this light curve. Second, we show
that for such long duration and bright microlensing events, the efficiency for
finding planetary-like deviations is strongly enhanced with respect to that
evaluated for all planetary detectable events.Comment: 14 pages, 8 figures. Paper presented at the "II Italian-Pakistani
Workshop on Relativistic Astrophysics, Pescara, July 8-10, 2009. To be
published in a special issue of General Relativity and Gravitation (eds. F.
De Paolis, G.F.R. Ellis, A. Qadir and R. Ruffini
AGAPE: a microlensing search in the direction of M31
A status report of the microlensing search by the pixel method in the direction of M31, on the 2 meter telescope at Pic du Midi is given. Pixels are stable to a level better than 0.5%. Pixel variations as small as 0.02 magnitude can clearly be detected
From error bounds to the complexity of first-order descent methods for convex functions
This paper shows that error bounds can be used as effective tools for
deriving complexity results for first-order descent methods in convex
minimization. In a first stage, this objective led us to revisit the interplay
between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can
show the equivalence between the two concepts for convex functions having a
moderately flat profile near the set of minimizers (as those of functions with
H\"olderian growth). A counterexample shows that the equivalence is no longer
true for extremely flat functions. This fact reveals the relevance of an
approach based on KL inequality. In a second stage, we show how KL inequalities
can in turn be employed to compute new complexity bounds for a wealth of
descent methods for convex problems. Our approach is completely original and
makes use of a one-dimensional worst-case proximal sequence in the spirit of
the famous majorant method of Kantorovich. Our result applies to a very simple
abstract scheme that covers a wide class of descent methods. As a byproduct of
our study, we also provide new results for the globalization of KL inequalities
in the convex framework.
Our main results inaugurate a simple methodology: derive an error bound,
compute the desingularizing function whenever possible, identify essential
constants in the descent method and finally compute the complexity using the
one-dimensional worst case proximal sequence. Our method is illustrated through
projection methods for feasibility problems, and through the famous iterative
shrinkage thresholding algorithm (ISTA), for which we show that the complexity
bound is of the form where the constituents of the bound only depend
on error bound constants obtained for an arbitrary least squares objective with
regularization
The CAT Imaging Telescope for Very-High-Energy Gamma-Ray Astronomy
The CAT (Cherenkov Array at Themis) imaging telescope, equipped with a
very-high-definition camera (546 fast phototubes with 0.12 degrees spacing
surrounded by 54 larger tubes in two guard rings) started operation in Autumn
1996 on the site of the former solar plant Themis (France). Using the
atmospheric Cherenkov technique, it detects and identifies very high energy
gamma-rays in the range 250 GeV to a few tens of TeV. The instrument, which has
detected three sources (Crab nebula, Mrk 421 and Mrk 501), is described in
detail.Comment: 24 pages, 15 figures. submitted to Elsevier Preprin
Variable stars towards the bulge of M31: the AGAPE catalogue
We present the AGAPE astrometric and photometric catalogue of 1579 variable
stars in a 14'x10' field centred on M31. This work is the first survey devoted
to variable stars in the bulge of M31. The R magnitudes of the objects and the
B-R colours suggest that our sample is dominated by red long-period variable
stars (LPV), with a possible overlap with Cepheid-like type II stars. Twelve
nova candidates are identified. Correlations with other catalogues suggest that
2 novae could be recurrent novae and provide possible optical counterparts for
2 supersoft X-ray sources candidates observed with Chandra.Comment: 11 pages, Latex, accepted for publication in A&
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