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 $L^\psi$ is equal to the limit of its $n$-widths. We also obtain several inequalities between the measures of noncompactness and the limit of the $n$-widths for modular bounded subsets of $L^\psi$ which do not have $\Delta_2$-condition. Minimum conditions on $\psi$ to have such results are specified and an example of such a function $\psi$ 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 $2 M_{\rm {J}}$. However, even small mass exoplanets ($M_{\rm P} < 20 M_{\oplus}$) 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

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

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

\pi\pi, K\pi and \pi N potential scattering and a prediction of a narrow \sigma meson resonance

Low energy scattering and bound state properties of the \pi N, \pi\pi and K\pi systems are studied as coupled channel problems using inversion potentials of phase shift data. In a first step we apply the potential model to explain recent measurements of pionic hydrogen shift and width. Secondly, predictions of the model for pionium lifetime and shift confirm a well known and widely used effective range expression. Thirdly, as extension of this confirmation, we predict an unexpected medium effect of the pionium lifetime which shortens by several orders of magnitude. The \sigma meson shows a narrow resonance structure as a function of the medium modified mass with the implication of being essentially energy independent. Similarly, we see this medium resonance effect realized for the K\pi system. To support our findings we present also results for the \rho meson and the \Delta(1232) resonance.Comment: 42 pages, 17 PS figures, REFTeX, epsfig.sty needed, submitted to Phys. Re

Microlensing search towards M31

We present the first results of the analysis of data collected during the 1998-99 observational campaign at the 1.3 meter McGraw-Hill Telescope, towards the Andromeda galaxy (M31), aimed to the detection of gravitational microlensing effects as a probe of the presence of dark matter in our and in M31 halo. The analysis is performed using the pixel lensing technique, which consists in the study of flux variations of unresolved sources and has been proposed and implemented by the AGAPE collaboration. We carry out a shape analysis by demanding that the detected flux variations be achromatic and compatible with a Paczynski light curve. We apply the Durbin-Watson hypothesis test to the residuals. Furthermore, we consider the background of variables sources. Finally five candidate microlensing events emerge from our selection. Comparing with the predictions of a Monte Carlo simulation, assuming a standard spherical model for the M31 and Galactic haloes, and typical values for the MACHO mass, we find that our events are only marginally consistent with the distribution of observable parameters predicted by the simulation.Comment: 13 pages, To appear in A&