Degenerations of LeBrun twistor spaces

We investigate various limits of the twistor spaces associated to the self-dual metrics on n CP ^2, the connected sum of the complex projective planes, constructed by C. LeBrun. In particular, we explicitly present the following 3 kinds of degenerations whose limits of the metrics are: (a) LeBrun metrics on (n-1) CP ^2$, (b) (Another) LeBrun metrics on the total space of the line bundle O(-n) over CP ^1 (c) The hyper-Kaehler metrics on the small resolution of rational double points of type A_{n-1}, constructed by Gibbons and Hawking.Comment: 21 pages, 7 figures. V2: A new section added at the end of the article. V3: Reference slightly update

Toric anti-self-dual Einstein metrics via complex geometry

Using the twistor correspondence, we give a classification of toric anti-self-dual Einstein metrics: each such metric is essentially determined by an odd holomorphic function. This explains how the Einstein metrics fit into the classification of general toric anti-self-dual metrics given in an earlier paper (math.DG/0602423). The results complement the work of Calderbank-Pedersen (math.DG/0105263), who describe where the Einstein metrics appear amongst the Joyce spaces, leading to a different classification. Taking the twistor transform of our result gives a new proof of their theorem.Comment: v2. Published version. Additional references. 14 page

Open TURNS: An industrial software for uncertainty quantification in simulation

The needs to assess robust performances for complex systems and to answer tighter regulatory processes (security, safety, environmental control, and health impacts, etc.) have led to the emergence of a new industrial simulation challenge: to take uncertainties into account when dealing with complex numerical simulation frameworks. Therefore, a generic methodology has emerged from the joint effort of several industrial companies and academic institutions. EDF R&D, Airbus Group and Phimeca Engineering started a collaboration at the beginning of 2005, joined by IMACS in 2014, for the development of an Open Source software platform dedicated to uncertainty propagation by probabilistic methods, named OpenTURNS for Open source Treatment of Uncertainty, Risk 'N Statistics. OpenTURNS addresses the specific industrial challenges attached to uncertainties, which are transparency, genericity, modularity and multi-accessibility. This paper focuses on OpenTURNS and presents its main features: openTURNS is an open source software under the LGPL license, that presents itself as a C++ library and a Python TUI, and which works under Linux and Windows environment. All the methodological tools are described in the different sections of this paper: uncertainty quantification, uncertainty propagation, sensitivity analysis and metamodeling. A section also explains the generic wrappers way to link openTURNS to any external code. The paper illustrates as much as possible the methodological tools on an educational example that simulates the height of a river and compares it to the height of a dyke that protects industrial facilities. At last, it gives an overview of the main developments planned for the next few years

Deformation of LeBrun's ALE metrics with negative mass

In this article we investigate deformations of a scalar-flat K\"ahler metric on the total space of complex line bundles over CP^1 constructed by C. LeBrun. In particular, we find that the metric is included in a one-dimensional family of such metrics on the four-manifold, where the complex structure in the deformation is not the standard one.Comment: 20 pages, no figure. V2: added two references, filled a gap in the proof of Theorem 1.2. V3: corrected a wrong statement about Kuranishi family of a Hirzebruch surface stated in the last paragraph in the proof of Theorem 1.2, and fixed a relevant error in the proof. Also added a reference [24] about Kuranishi family of Hirzebruch surface

EGRET Observations of the Diffuse Gamma-Ray Emission in Orion: Analysis Through Cycle 6

We present a study of the high-energy diffuse emission observed toward Orion by the Energetic Gamma-Ray Experiment Telescope (EGRET) on the Compton Gamma-Ray Observatory. The total exposure by EGRET in this region has increased by more than a factor of two since a previous study. A simple model for the diffuse emission adequately fits the data; no significant point sources are detected in the region studied ($l = 195^\circ$ to $220^\circ$ and $b = -25^\circ to -10^\circ$) in either the composite dataset or in two separate groups of EGRET viewing periods considered. The gamma-ray emissivity in Orion is found to be $(1.65 \pm 0.11) \times 10^{-26} {s sr}^{-1}$ for E > 100 MeV, and the differential emissivity is well-described as a combination of contributions from cosmic-ray electrons and protons with approximately the local density. The molecular mass calibrating ratio is $N(H_2)/W_{CO} = (1.35 \pm 0.15) \times 10^{20} cm^{-2} (K km/s)^{-1}$.Comment: 16 pages, including 5 figures. 3 Tables as three separate files. Latex document, needs AASTEX style files. Accepted for publication in Ap

Registration of the First Thermonuclear X-ray Burst from AX J1754.2-2754

During the analysis of the INTEGRAL observatory archival data we found a powerful X-ray burst, registered by JEM-X and IBIS/ISGRI telescopes on April 16, 2005 from a weak and poorly known source AX J1754.2-2754. Analysis of the burst profiles and spectrum shows, that it was a type I burst, which result from thermonuclear explosion on the surface of nutron star. It means that we can consider AX J1754.2-2754 as an X-ray burster. Certain features of burst profile at its initial stage witness of a radiation presure driven strong expansion and a corresponding cooling of the nutron star photosphere. Assuming, that the luminosity of the source at this phase was close to the Eddington limit, we estimated the distance to the burst source d=6.6+/-0.3 kpc (for hidrogen atmosphere of the neutron star) and d=9.2+/-0.4 kpc (for helium atmosphere).Comment: 12 pages, 6 figure

The signature of 44Ti in Cassiopeia A revealed by IBIS/ISGRI on INTEGRAL

We report the detection of both the 67.9 and 78.4 keV 44Sc gamma-ray lines in Cassiopeia A with the INTEGRAL IBIS/ISGRI instrument. Besides the robustness provided by spectro-imaging observations, the main improvements compared to previous measurements are a clear separation of the two 44Sc lines together with an improved significance of the detection of the hard X-ray continuum up to 100 keV. These allow us to refine the determination of the 44Ti yield and to constrain the nature of the nonthermal continuum emission. By combining COMPTEL, BeppoSAX/PDS and ISGRI measurements, we find a line flux of (2.5 +/- 0.3)*10(-5) cm(-2) s(-1) leading to a synthesized 44Ti mass of 1.6 (+0.6-0.3)*10(-4) solar mass. This high value suggests that Cas A is peculiar in comparison to other young supernova remnants, from which so far no line emission from 44Ti decay has been unambiguously detected.Comment: 5 pages, 4 figures, Accepted for publication in ApJ

Properties of equations of the continuous Toda type

We study a modified version of an equation of the continuous Toda type in 1+1 dimensions. This equation contains a friction-like term which can be switched off by annihilating a free parameter \ep. We apply the prolongation method, the symmetry and the approximate symmetry approach. This strategy allows us to get insight into both the equations for \ep =0 and \ep \ne 0, whose properties arising in the above frameworks are mutually compared. For \ep =0, the related prolongation equations are solved by means of certain series expansions which lead to an infinite- dimensional Lie algebra. Furthermore, using a realization of the Lie algebra of the Euclidean group $E_{2}$, a connection is shown between the continuous Toda equation and a linear wave equation which resembles a special case of a three-dimensional wave equation that occurs in a generalized Gibbons-Hawking ansatz \cite{lebrun}. Nontrivial solutions to the wave equation expressed in terms of Bessel functions are determined. For \ep\,\ne\,0, we obtain a finite-dimensional Lie algebra with four elements. A matrix representation of this algebra yields solutions of the modified continuous Toda equation associated with a reduced form of a perturbative Liouville equation. This result coincides with that achieved in the context of the approximate symmetry approach. Example of exact solutions are also provided. In particular, the inverse of the exponential-integral function turns out to be defined by the reduced differential equation coming from a linear combination of the time and space translations. Finally, a Lie algebra characterizing the approximate symmetries is discussed.Comment: LaTex file, 27 page