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

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

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

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

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

Double solid twistor spaces: the case of arbitrary signature

In a recent paper (math.DG/0701278) we constructed a series of new Moishezon twistor spaces which is a kind of variant of the famous LeBrun twistor spaces. In this paper we explicitly give projective models of another series of Moishezon twistor spaces on nCP^2 for arbitrary n>2, which can be regarded as a generalization of the twistor spaces of a 'double solid type' on 3CP^2 studied by Kreussler, Kurke, Poon and the author. Similarly to the twistor spaces of 'double solid type' on 3CP^2, projective models of present twistor spaces have a natural structure of double covering of a CP^2-bundle over CP^1. We explicitly give a defining polynomial of the branch divisor of the double covering whose restriction to fibers are degree four. If n>3 these are new twistor spaces, to the best of the author's knowledge. We also compute the dimension of the moduli space of these twistor spaces. Differently from math.DG/0701278, the present investigation is based on analysis of pluri-(half-)anticanonical systems of the twistor spaces.Comment: 30 pages, 3 figures; v2: title changed (the original title was "Explicit construction of new Moishezon twistor spaces, II".

The CLIC Programme: Towards a Staged e+e- Linear Collider Exploring the Terascale : CLIC Conceptual Design Report

This report describes the exploration of fundamental questions in particle physics at the energy frontier with a future TeV-scale e+e- linear collider based on the Compact Linear Collider (CLIC) two-beam acceleration technology. A high-luminosity high-energy e+e- collider allows for the exploration of Standard Model physics, such as precise measurements of the Higgs, top and gauge sectors, as well as for a multitude of searches for New Physics, either through direct discovery or indirectly, via high-precision observables. Given the current state of knowledge, following the observation of a 125 GeV Higgs-like particle at the LHC, and pending further LHC results at 8 TeV and 14 TeV, a linear e+e- collider built and operated in centre-of-mass energy stages from a few-hundred GeV up to a few TeV will be an ideal physics exploration tool, complementing the LHC. In this document, an overview of the physics potential of CLIC is given. Two example scenarios are presented for a CLIC accelerator built in three main stages of 500 GeV, 1.4 (1.5) TeV, and 3 TeV, together with operating schemes that will make full use of the machine capacity to explore the physics. The accelerator design, construction, and performance are presented, as well as the layout and performance of the experiments. The proposed staging example is accompanied by cost estimates of the accelerator and detectors and by estimates of operating parameters, such as power consumption. The resulting physics potential and measurement precisions are illustrated through detector simulations under realistic beam conditions.Comment: 84 pages, published as CERN Yellow Report https://cdsweb.cern.ch/record/147522

INTEGRAL discovery of a bright highly obscured galactic X-ray binary source IGR J16318-4848

INTEGRAL regularly scans the Galactic plane to search for new objects and in particular for absorbed sources with the bulk of their emission above 10-20 keV. The first new INTEGRAL source was discovered on 2003 January 29, 0.5 degree from the Galactic plane and was further observed in the X-rays with XMM-Newton. This source, IGR J16318-4848, is intrinsically strongly absorbed by cold matter and displays exceptionally strong fluorescence emission lines. The likely infrared/optical counterpart indicates that IGR J16318-4848 is probably a High Mass X-Ray Binary neutron star or black hole enshrouded in a Compton thick environment. Strongly absorbed sources, not detected in previous surveys, could contribute significantly to the Galactic hard X-ray background between 10 and 200 keV.Comment: 6 pages, 4 figures (fig 1 quality lowered), accepted for publication in A&A letters (INTEGRAL special issue

Optimizing magneto-dipolar interactions for synchronizing vortex based spin-torque nano-oscillators

We report on a theoretical study about the magneto-dipolar coupling and synchronization between two vortex-based spin-torque nano-oscillators. In this work we study the dependence of the coupling efficiency on the relative magnetization parameters of the vortices in the system. For that purpose, we combine micromagnetic simulations, Thiele equation approach, and analytical macro-dipole approximation model to identify the optimized configuration for achieving phase-locking between neighboring oscillators. Notably, we compare vortices configurations with parallel (P) polarities and with opposite (AP) polarities. We demonstrate that the AP core configuration exhibits a coupling strength about three times larger than in the P core configuration.Comment: 8 pages, 11 figure