3,937 research outputs found
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
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