462 research outputs found
Cancelation norm and the geometry of biinvariant word metrics
We study biinvariant word metrics on groups. We provide an efficient
algorithm for computing the biinvariant word norm on a finitely generated free
group and we construct an isometric embedding of a locally compact tree into
the biinvariant Cayley graph of a nonabelian free group. We investigate the
geometry of cyclic subgroups. We observe that in many classes of groups cyclic
subgroups are either bounded or detected by homogeneous quasimorphisms. We call
this property the bq-dichotomy and we prove it for many classes of groups of
geometric origin.Comment: 32 pages, to appear in Glasgow Journal of Mathematic
On the k-Boundedness for Existential Rules
The chase is a fundamental tool for existential rules. Several chase variants
are known, which differ on how they handle redundancies possibly caused by the
introduction of nulls. Given a chase variant, the halting problem takes as
input a set of existential rules and asks if this set of rules ensures the
termination of the chase for any factbase. It is well-known that this problem
is undecidable for all known chase variants. The related problem of boundedness
asks if a given set of existential rules is bounded, i.e., whether there is a
predefined upper bound on the number of (breadth-first) steps of the chase,
independently from any factbase. This problem is already undecidable in the
specific case of datalog rules. However, knowing that a set of rules is bounded
for some chase variant does not help much in practice if the bound is unknown.
Hence, in this paper, we investigate the decidability of the k-boundedness
problem, which asks whether a given set of rules is bounded by an integer k. We
prove that k-boundedness is decidable for three chase variants, namely the
oblivious, semi-oblivious and restricted chase.Comment: 20 pages, revised version of the paper published at RuleML+RR 201
A method to localize gamma-ray bursts using POLAR
The hard X-ray polarimeter POLAR aims to measure the linear polarization of
the 50-500 keV photons arriving from the prompt emission of gamma-ray bursts
(GRBs). The position in the sky of the detected GRBs is needed to determine
their level of polarization. We present here a method by which, despite of the
polarimeter incapability of taking images, GRBs can be roughly localized using
POLAR alone. For this purpose scalers are attached to the output of the 25
multi-anode photomultipliers (MAPMs) that collect the light from the POLAR
scintillator target. Each scaler measures how many GRB photons produce at least
one energy deposition above 50 keV in the corresponding MAPM. Simulations show
that the relative outputs of the 25 scalers depend on the GRB position. A
database of very strong GRBs simulated at 10201 positions has been produced.
When a GRB is detected, its location is calculated searching the minimum of the
chi2 obtained in the comparison between the measured scaler pattern and the
database. This GRB localization technique brings enough accuracy so that the
error transmitted to the 100% modulation factor is kept below 10% for GRBs with
fluence Ftot \geq 10^(-5) erg cm^(-2) . The POLAR localization capability will
be useful for those cases where no other instruments are simultaneously
observing the same field of view.Comment: 13 pages, 10 figure
GRB030406 an extremely hard burst outside of the INTEGRAL field of view
Using the IBIS Compton mode, the INTEGRAL satellite is able to detect and
localize bright and hard GRBs, which happen outside of the nominal INTEGRAL
telescopes field of view. We have developed a method of analyzing such INTEGRAL
data to obtain the burst location and spectra. We present the results for the
case of GRB030406. The burst is localized with the Compton events, and the
location is consistent with the previous Interplanetary Network position. A
spectral analysis is possible with the detailed modeling of the detector
response for such a far off-axis source with the offset of 36.9 . The
average spectrum of the burst is extremely hard: the photon index above 400
\kev is -1.7, with no evidence of a break up to 1.1 \mev at 90% confidence
level.Comment: Astronomy and Astrophysics in pres
Disclination vortices in elastic media
The vortex-like solutions are studied in the framework of the gauge model of
disclinations in elastic continuum. A complete set of model equations with
disclination driven dislocations taken into account is considered. Within the
linear approximation an exact solution for a low-angle wedge disclination is
found to be independent from the coupling constants of the theory. As a result,
no additional dimensional characteristics (like the core radius of the defect)
are involved. The situation changes drastically for 2\pi vortices where two
characteristic lengths, l_\phi and l_W, become of importance. The asymptotical
behaviour of the solutions for both singular and nonsingular 2\pi vortices is
studied. Forces between pairs of vortices are calculated.Comment: 13 pages, published versio
Exceptional flaring activity of the anomalous X-ray pulsar 1E 1547.0-5408
(Abridged) We studied an exceptional period of activity of the anomalous
X-ray pulsar 1E 1547.0-5408 in January 2009, during which about 200 bursts were
detected by INTEGRAL. The major activity episode happened when the source was
outside the field of view of all the INTEGRAL instruments. But we were still
able to study the properties of 84 bursts detected simultaneously by the
anti-coincidence shield of the spectrometer SPI and by the detector of the
imager ISGRI. We find that the luminosity of the 22 January 2009 bursts of 1E
1547.0-5408 was > 1e42 erg/s. This luminosity is comparable to that of the
bursts of soft gamma repeaters (SGR) and is at least two orders of magnitude
larger than the luminosity of the previously reported bursts from AXPs.
Similarly to the SGR bursts, the brightest bursts of 1E 1547.0-5408 consist of
a short spike of ~100 ms duration with a hard spectrum, followed by a softer
extended tail of 1-10 s duration, which occasionally exhibits pulsations with
the source spin period of ~2 s. The observation of AXP bursts with luminosities
comparable to the one of SGR bursts strengthens the conjecture that AXPs and
SGRs are different representatives of one and the same source type.Comment: 9 pages, 10 figures, accepted to Astronomy & Astrophysic
Catchment-Scale Analysis Reveals High Cost-Effectiveness of Wetland Buffer Zones as a Remedy to Non-Point Nutrient Pollution in North-Eastern Poland
Large-scale re-establishment of wetland buffer zones (WBZ) along rivers is regarded as an effective measure in order to reduce non-point source nitrogen (N) and phosphorus (P) pollution in agricultural catchments. We estimated efficiency and costs of a hypothetical establishment of WBZs along all watercourses in an agricultural landscape of the lower Narew River catchment (north-eastern Poland, 16,444 km2, amounting to 5% of Poland) by upscaling results obtained in five sub-catchments (1087 km2). Two scenarios were analysed, with either rewetting selected wetland polygons that collect water from larger areas (polygonal WBZs) or reshaping and rewetting banks of rivers (linear WBZs), both considered in all ecologically suitable locations along rivers. Cost calculation included engineering works necessary in order to establish WBZs, costs of land purchase where relevant, and compensation costs of income forgone to farmers (needed only for polygonal WBZs). Polygonal WBZs were estimated in order to remove 11%–30% N and 14%–42% P load from the catchment, whereas linear WBZs were even higher with 33%–82% N and 41%–87% P. Upscaled costs of WBZ establishment for the study area were found to be 8.9 M EUR plus 26.4 M EUR per year (polygonal WBZ scenario) or 170.8 M EUR (linear WBZ scenario). The latter value compares to costs of building about 20 km of an express road. Implementation of buffer zones on a larger scale is thus a question of setting policy priorities rather than financial impossibility
POLAR, an instrument to measure GRB polarization. Design and laboratory tests.
International audienceReliable polarization measurements of photons from Gamma Ray Bursts (GRB) would make the understanding of the GRB phenomenon progress enormously. POLAR is a concept for an instrument that would enable such a measurement. We report about performances predicted by of Monte-Carlo and on laboratory tests to validate some critical aspects of the desig
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