The definability criterions for convex projective polyhedral reflection groups

Following Vinberg, we find the criterions for a subgroup generated by reflections \Gamma \subset \SL^{\pm}(n+1,\mathbb{R}) and its finite-index subgroups to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally closed Noetherian ring in the field $\mathbb{R}$. We apply the criterions for groups generated by reflections that act cocompactly on irreducible properly convex open subdomains of the $n$-dimensional projective sphere. This gives a method for constructing injective group homomorphisms from such Coxeter groups to \SL^{\pm}(n+1,\mathbb{Z}). Finally we provide some examples of \SL^{\pm}(n+1,\mathbb{Z})-representations of such Coxeter groups. In particular, we consider simplicial reflection groups that are isomorphic to hyperbolic simplicial groups and classify all the conjugacy classes of the reflection subgroups in \SL^{\pm}(n+1,\mathbb{R}) that are definable over $\mathbb{Z}$. These were known by Goldman, Benoist, and so on previously.Comment: 31 pages, 8 figure

An Inverse Method for Cracks Characterization from Ultrasonic Bscan Images

Concern has been expressed about the capabilities of performing non destructive evaluation (NDE) of flaws located near to the outer surface in nuclear pressurized water reactor (PWR) vessels. The ultrasonic examination of PWR is accomplished from the inside with ultrasonic focused transducers working in the pulse echo mode. By recording the echoes as a function of time, the Ascan representation may be obtained. Many ultrasonic flaw detectors used for NDE are based on the simple Ascan concept involving measuring a time interval called “time of flight”. By combining the Ascan concept with synchronized transducer scanning, one can produce Bscan images that are two dimensional descriptions of the flaw interaction with the ultrasonic field

A2163: Merger events in the hottest Abell galaxy cluster II. Subcluster accretion with galaxy-gas separation

Located at z = 0.203, A2163 is a rich galaxy cluster with an intra-cluster medium (ICM) that exhibits extraordinary properties, including an exceptionally high X-ray luminosity, average temperature, and a powerful and extended radio halo. The irregular and complex morphology of its gas and galaxy structure suggests that this cluster has recently undergone major merger events that involve two or more cluster components. In this paper, we study the gas structure and dynamics by means of spectral-imaging analysis of X-ray data obtained from XMM-Newton and Chandra observations. From the evidence of a cold front, we infer the westward motion of a cool core across the E-W elongated atmosphere of the main cluster A2163-A. Located close to a galaxy over-density, this gas 'bullet' appears to have been spatially separated from its galaxy (and presumably dark matter component) as a result of high-velocity accretion. From gas brightness and temperature profile analysis performed in two opposite regions of the main cluster, we show that the ICM has been adiabatically compressed behind the crossing 'bullet' possibly because of shock heating, leading to a strong departure of the ICM from hydrostatic equilibrium in this region. Assuming that the mass estimated from the Yx proxy best indicates the overall mass of the system and that the western cluster sector is in approximate hydrostatic equilibrium before subcluster accretion, we infer a merger scenario between two subunits of mass ratio 1:4, leading to a present total system mass of M500 $\propto 1.9 \times 1015 M_{\odot}$. The exceptional properties of A2163 present various similarities with those of 1E0657-56, the so-called 'bullet-cluster'. These similarities are likely to be related to a comparable merger scenario.Comment: A&A, in pres

ESO Imaging survey: Optical Deep Public Survey

This paper presents new five passbands (UBVRI) optical wide-field imaging data accumulated as part of the DEEP Public Survey (DPS) carried out as a public survey by the ESO Imaging Survey (EIS) project. Out of the 3 square degrees originally proposed, the survey covers 2.75 square degrees, in at least one band (normally R), and 1.00 square degrees in five passbands. The median seeing, as measured in the final stacked images, is 0.97", ranging from 0.75" to 2.0". The median limiting magnitudes (AB system, 2" aperture, 5 sigma detection limit) are U_(AB)=25.65, B_(AB)=25.54, V_(AB)=25.18, R_(AB) = 24.8 and I_(AB)=24.12 mag, consistent with those proposed in the original survey design. The paper describes the observations and data reduction using the EIS Data Reduction System and its associated EIS/MVM library. The quality of the individual images were inspected, bad images discarded and the remaining used to produce final image stacks in each passband, from which sources have been extracted. Finally, the scientific quality of these final images and associated catalogs was assessed qualitatively by visual inspection and quantitatively by comparison of statistical measures derived from these data with those of other authors as well as model predictions, and from direct comparison with the results obtained from the reduction of the same dataset using an independent (hands-on) software system. Finally to illustrate one application of this survey, the results of a preliminary effort to identify sub-mJy radio sources are reported. To the limiting magnitude reached in the R and I passbands the success rate ranges from 66 to 81% (depending on the fields). These data are publicly available at CDS.Comment: 24 pages, 26 figures. Accepted for pubblication in A&

The XMM-LSS survey: the Class 1 cluster sample over the extended 11 deg2^2 and its spatial distribution

This paper presents 52 X-ray bright galaxy clusters selected within the 11 deg$^2$ XMM-LSS survey. 51 of them have spectroscopic redshifts ($0.05<z<1.06$), one is identified at $z_{\rm phot}=1.9$, and all together make the high-purity "Class 1" (C1) cluster sample of the XMM-LSS, the highest density sample of X-ray selected clusters with a monitored selection function. Their X-ray fluxes, averaged gas temperatures (median $T_X=2$ keV), luminosities (median $L_{X,500}=5\times10^{43}$ ergs/s) and total mass estimates (median $5\times10^{13} h^{-1} M_{\odot}$) are measured, adapting to the specific signal-to-noise regime of XMM-LSS observations. The redshift distribution of clusters shows a deficit of sources when compared to the cosmological expectations, regardless of whether WMAP-9 or Planck-2013 CMB parameters are assumed. This lack of sources is particularly noticeable at $0.4 \lesssim z \lesssim 0.9$. However, after quantifying uncertainties due to small number statistics and sample variance we are not able to put firm (i.e. $>3 \sigma$) constraints on the presence of a large void in the cluster distribution. We work out alternative hypotheses and demonstrate that a negative redshift evolution in the normalization of the $L_{X}-T_X$ relation (with respect to a self-similar evolution) is a plausible explanation for the observed deficit. We confirm this evolutionary trend by directly studying how C1 clusters populate the $L_{X}-T_X-z$ space, properly accounting for selection biases. We point out that a systematically evolving, unresolved, central component in clusters and groups (AGN contamination or cool core) can impact the classification as extended sources and be partly responsible for the observed redshift distribution.[abridged]Comment: 33 pages, 21 figures, 3 tables ; accepted for publication in MNRA

Cystathionine beta synthase deficiency and brain edema associated with methionine excess under betaine supplementation: Four new cases and a review of the evidence.

CBS deficient individuals undergoing betaine supplementation without sufficient dietary methionine restriction can develop severe hypermethioninemia and brain edema. Brain edema has also been observed in individuals with severe hypermethioninemia without concomitant betaine supplementation. We systematically evaluated reports from 11 published and 4 unpublished patients with CBS deficiency and from additional four cases of encephalopathy in association with elevated methionine. We conclude that, while betaine supplementation does greatly exacerbate methionine accumulation, the primary agent causing brain edema is methionine rather than betaine. Clinical signs of increased intracranial pressure have not been seen in patients with plasma methionine levels below 559 μmol/L but occurred in one patient whose levels did not knowingly exceed 972 μmol/L at the time of manifestation. While levels below 500 μmol/L can be deemed safe it appears that brain edema can develop with plasma methionine levels close to 1000 μmol/L. Patients with CBS deficiency on betaine supplementation need to be regularly monitored for concordance with their dietary plan and for plasma methionine concentrations. Recurrent methionine levels above 500 μmol/L should alert clinicians to check for clinical signs and symptoms of brain edema and review dietary methionine intake. Levels approaching 1000 μmol/L do increase the risk of complications and levels exceeding 1000 μmol/L, despite best dietetic efforts, should be acutely addressed by reducing the prescribed betaine dose

Vortex matter in superconducting mesoscopic disks: Structure, magnetization, and phase transitions

The dense vortex matter structure and associated magnetization are calculated for type-II superconducting mesoscopic disks. The magnetization exhibits generically first-order phase transitions as the number of vortices changes by one and presents two well-defined regimes: A non-monotonous evolution of the magnitude of the magnetization jumps signals the presence of a vortex glass structure which is separated by a second-order phase transition at $H_{c2}$ from a condensed state of vortices (giant vortex) where the magnitude of the jumps changes monotonously. We compare our results with Hall magnetometry measurements by Geim et al. (Nature 390, 259 (1997)) and claim that the magnetization exhibits clear traces of the presence of these vortex glass states.Comment: 4 pages, 3 figure

Anosov representations: Domains of discontinuity and applications

The notion of Anosov representations has been introduced by Labourie in his study of the Hitchin component for SL(n,R). Subsequently, Anosov representations have been studied mainly for surface groups, in particular in the context of higher Teichmueller spaces, and for lattices in SO(1,n). In this article we extend the notion of Anosov representations to representations of arbitrary word hyperbolic groups and start the systematic study of their geometric properties. In particular, given an Anosov representation of $\Gamma$ into G we explicitly construct open subsets of compact G-spaces, on which $\Gamma$ acts properly discontinuously and with compact quotient. As a consequence we show that higher Teichmueller spaces parametrize locally homogeneous geometric structures on compact manifolds. We also obtain applications regarding (non-standard) compact Clifford-Klein forms and compactifications of locally symmetric spaces of infinite volume.Comment: 63 pages, accepted for publication in Inventiones Mathematica