7,161 research outputs found
A nullstellensatz for sequences over F_p
Let p be a prime and let A=(a_1,...,a_l) be a sequence of nonzero elements in
F_p. In this paper, we study the set of all 0-1 solutions to the equation a_1
x_1 + ... + a_l x_l = 0. We prove that whenever l >= p, this set actually
characterizes A up to a nonzero multiplicative constant, which is no longer
true for l < p. The critical case l=p is of particular interest. In this
context, we prove that whenever l=p and A is nonconstant, the above equation
has at least p-1 minimal 0-1 solutions, thus refining a theorem of Olson. The
subcritical case l=p-1 is studied in detail also. Our approach is algebraic in
nature and relies on the Combinatorial Nullstellensatz as well as on a Vosper
type theorem.Comment: 23 page
Flares in Open Clusters with K2. I. M45 (Pleiades), M44 (Praesepe) and M67
The presence and strength of a stellar magnetic field and activity is rooted
in a star's fundamental parameters such as mass and age. Can flares serve as an
accurate stellar "clock"?
To explore if we can quantify an activity-age relation in the form of a
flaring-age relation, we measured trends in the flaring rates and energies for
stars with different masses and ages.
We investigated the time-domain photometry provided by Kepler's follow-up
mission K2 and searched for flares in three solar metallicity open clusters
with well-known ages, M45 (0.125 Gyr), M44 (0.63 Gyr), and M67 (4.3 Gyr). We
updated and employed the automated flare finding and analysis pipeline
Appaloosa, originally designed for Kepler. We introduced a synthetic flare
injection and recovery subroutine to ascribe detection and energy recovery
rates for flares in a broad energy range for each light curve. We collected a
sample of 1 761 stars, mostly late-K to mid-M dwarfs and found 751 flare
candidates with energies ranging from erg to
erg, of which 596 belong to M45, 155 to M44, and none to M67.
We find that flaring activity depends both on , and age. But
all flare frequency distributions have similar slopes with , supporting a universal flare generation process. We discuss
implications for the physical conditions under which flares occur, and how the
sample's metallicity and multiplicity affect our results.Comment: 17 pages, 11 figures, appendix. Accepted to A&
The Pros and Cons of Compressive Sensing for Wideband Signal Acquisition: Noise Folding vs. Dynamic Range
Compressive sensing (CS) exploits the sparsity present in many signals to
reduce the number of measurements needed for digital acquisition. With this
reduction would come, in theory, commensurate reductions in the size, weight,
power consumption, and/or monetary cost of both signal sensors and any
associated communication links. This paper examines the use of CS in the design
of a wideband radio receiver in a noisy environment. We formulate the problem
statement for such a receiver and establish a reasonable set of requirements
that a receiver should meet to be practically useful. We then evaluate the
performance of a CS-based receiver in two ways: via a theoretical analysis of
its expected performance, with a particular emphasis on noise and dynamic
range, and via simulations that compare the CS receiver against the performance
expected from a conventional implementation. On the one hand, we show that
CS-based systems that aim to reduce the number of acquired measurements are
somewhat sensitive to signal noise, exhibiting a 3dB SNR loss per octave of
subsampling, which parallels the classic noise-folding phenomenon. On the other
hand, we demonstrate that since they sample at a lower rate, CS-based systems
can potentially attain a significantly larger dynamic range. Hence, we conclude
that while a CS-based system has inherent limitations that do impose some
restrictions on its potential applications, it also has attributes that make it
highly desirable in a number of important practical settings
Cooling with heat recovery for electrical cable tunnels in cities
Within cities, electrical power is often distributed by means of underground cable tunnels, frequently extending for many kilometres. Cables can generate significant heat, with the quantity of heat being directly related to the electrical load carried. Tunnel air temperatures are generally controlled by ventilation using outside air; preventing the cables from overheating. If active cooling was provided, tunnel air temperatures could be further reduced, permitting higher electrical loadings to be used. Using an air/water heat exchanger to cool the outside air entering the
ventilation shaft has been investigated. The temperature of the heat extracted (to water) was increased using a heat pump before transfer to a heat network. Benefits identified included reduction in cable temperatures, and carbon and cost savings compared to conventional heat delivery
Phase separation and electron pairing in repulsive Hubbard clusters
Exact thermal studies of small (4-site, 5-site and 8-site)
Hubbard clusters with local electron repulsion yield intriguing insight into
phase separation, charge-spin separation, pseudogaps, condensation, in
particular, pairing fluctuations away from half filling (near optimal doping).
These exact calculations, carried out in canonical (i.e. for fixed electron
number N) and grand canonical (i.e. fixed chemical potential ) ensembles,
monitoring variations in temperature T and magnetic field h, show rich phase
diagrams in a T- space consisting of pairing fluctuations and signatures
of condensation. These electron pairing instabilities are seen when the onsite
Coulomb interaction U is smaller than a critical value U(T) and they point
to a possible electron pairing mechanism. The specific heat, magnetization,
charge pairing and spin pairing provide strong support for the existence of
competing (paired and unpaired) phases near optimal doping in these clusters as
observed in recent experiments in doped LaSrCuO high T
superconductors.Comment: 5 pages, 5 figure
The current progress of the ALICE Ring Imaging Cherenkov Detector
Recently, the last two modules (out of seven) of the ALICE High Momentum
Particle Identification detector (HMPID) were assembled and tested. The full
detector, after a pre-commissioning phase, has been installed in the
experimental area, inside the ALICE solenoid, at the end of September 2006. In
this paper we review the status of the ALICE/HMPID project and we present a
summary of the series production of the CsI photo-cathodes. We describe the key
features of the production procedure which ensures high quality photo-cathodes
as well as the results of the quality assessment performed by means of a
specially developed 2D scanner system able to produce a detailed map of the CsI
photo-current over the entire photo-cathode surface.
Finally we present our recent R&D efforts toward the development of a novel
generation of imaging Cherenkov detectors with the aim to identify, in heavy
ions collisions, hadrons up to 30 GeV/c.Comment: Presented at the Imaging-2006 Conference, Stockholm, Sweden, June
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