Descending Dungeons and Iterated Base-Changing

For real numbers a, b> 1, let as a_b denote the result of interpreting a in base b instead of base 10. We define ``dungeons'' (as opposed to ``towers'') to be numbers of the form a_b_c_d_..._e, parenthesized either from the bottom upwards (preferred) or from the top downwards. Among other things, we show that the sequences of dungeons with n-th terms 10_11_12_..._(n-1)_n or n_(n-1)_..._12_11_10 grow roughly like 10^{10^{n log log n}}, where the logarithms are to the base 10. We also investigate the behavior as n increases of the sequence a_a_a_..._a, with n a's, parenthesized from the bottom upwards. This converges either to a single number (e.g. to the golden ratio if a = 1.1), to a two-term limit cycle (e.g. if a = 1.05) or else diverges (e.g. if a = frac{100{99).Comment: 11 pages; new version takes into account comments from referees; version of Sep 25 2007 inculdes a new theorem and several small improvement

Modeling of the saturation current of a fission chamber taking into account the distorsion of electric field due to space charge effects

Fission chambers were first made fifty years ago for neutron detection. At the moment, the French Atomic Energy Commission \textsf{(CEA-Cadarache)} is developing a sub-miniature fission chamber technology with a diameter of 1.5 mm working in the current mode (Bign). To be able to measure intense fluxes, it is necessary to adjust the chamber geometry and the gas pressure before testing it under real neutron flux. In the present paper, we describe a theoretical method to foresee the current-voltage characteristics (sensitivity and saturation plateau) of a fission chamber whose geometrical features are given, taking into account the neutron flux to be measured (spectrum and intensity). The proposed theoretical model describes electric field distortion resulting from charge collection effect. A computer code has been developed on this model basis. Its application to 3 kinds of fission chambers indicates excellent agreement between theoretical model and measured characteristics

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

The IBIS view of the galactic centre: INTEGRAL's imager observations simulations

The Imager on Board Integral Satellite (IBIS) is the imaging instrument of the INTEGRAL satellite, the hard-X/soft-gamma ray ESA mission to be launched in 2001. It provides diagnostic capabilities of fine imaging (12' FWHM), source identification and spectral sensitivity to both continuum and broad lines over a broad (15 keV--10 MeV) energy range. It has a continuum sensitivity of 2~10^{-7} ph cm^{-2} s^{-1} at 1 MeV for a 10^6 seconds observation and a spectral resolution better than 7 % at 100 keV and of 6 % at 1 MeV. The imaging capabilities of the IBIS are characterized by the coupling of the above quoted source discrimination capability with a very wide field of view (FOV), namely 9 x 9 degrees fully coded, 29 x 29 degrees partially coded FOV. We present simulations of IBIS observations of the Galactic Center based on the results of the SIGMA Galactic Center survey. They show the capabilities of this instrument in discriminating between different sources while at the same time monitoring a huge FOV. It will be possible to simultaneously take spectra of all of these sources over the FOV even if the sensitivity decreases out of the fully coded area. It is envisaged that a proper exploitation of both the FOV dimension and the source localization capability of the IBIS will be a key factor in maximizing its scientific output.Comment: 5 pages, LaTeX, to be published in the 4th Compton Symposium Conference Proceedings, uses aipproc.cls, aipproc.sty (included

Carryless Arithmetic Mod 10

We investigate what arithmetic would look like if carry digits into other digit position were ignored, so that 9 + 4 = 3, 5 + 5 = 0, 9 X 4 = 6, 5 X 4 = 0, and so on. For example, the primes are now 21, 23, 25, 27, 29, 41, 43, 45, 47, ... .Comment: 7 pages. To the memory of Martin Gardner (October 21, 1914 -- May 22, 2010). Revised version (with a number of small improvements), July 7 201

Contact Moishezon threefolds with second Betti number one

We prove that the only contact Moishezon threefold having second Betti number equal to one is the projective space.Comment: 5 pages. v2: exposition improved as suggested by the referee. To appear in Archiv der Mat

An Estimate of the Spectral Intensity Expected from the Molecular Bremsstrahlung Radiation in Extensive Air Showers

A detection technique of ultra-high energy cosmic rays, complementary to the fluorescence technique, would be the use of the molecular Bremsstrahlung radiation emitted by low-energy electrons left after the passage of the showers in the atmosphere. The emission mechanism is expected from quasi-elastic collisions of electrons produced in the shower by the ionisation of the molecules in the atmosphere. In this article, a detailed calculation of the spectral intensity of photons at ground level originating from the transitions between unquantised energy states of free ionisation electrons is presented. In the absence of absorption of the emitted photons in the plasma, the obtained spectral intensity is shown to be 5 10^{-26} W m^{-2}Hz^{-1} at 10 km from the shower core for a vertical shower induced by a proton of 10^{17.5} eV.Comment: 16 pages, 6 figures, accepted in Astroparticle Physics. Compared to v1 version: 1. Inclusion of ro-vibrational processes. 2. Use of more accurate ionization potential values and energy distribution of the secondary electron

Imaging extended sources with coded mask telescopes: Application to the INTEGRAL IBIS/ISGRI instrument

Context. In coded mask techniques, reconstructed sky images are pseudo-images: they are maps of the correlation between the image recorded on a detector and an array derived from the coded mask pattern. Aims. The INTEGRAL/IBIS telescope provides images where the flux of each detected source is given by the height of the local peak in the correlation map. As such, it cannot provide an estimate of the flux of an extended source. What is needed is intensity sky images giving the flux per solide angle as typically done at other wavelengths. Methods. In this paper, we present the response of the INTEGRAL IBIS/ISGRI coded mask instrument to extended sources. We develop a general method based on analytical calculations in order to measure the intensity and the associated error of any celestial source and validated with Monte-Carlo simulations. Results. We find that the sensitivity degrades almost linearly with the source extent. Analytical formulae are given as well as an easy-to-use recipe for the INTEGRAL user. We check this method on IBIS/ISGRI data but these results are general and applicable to any coded mask telescope.Comment: 9 pages, 6 figures, Accepted for publication in A&