11,835 research outputs found
An analogue of Ryser's Theorem for partial Sudoku squares
In 1956 Ryser gave a necessary and sufficient condition for a partial latin
rectangle to be completable to a latin square. In 1990 Hilton and Johnson
showed that Ryser's condition could be reformulated in terms of Hall's
Condition for partial latin squares. Thus Ryser's Theorem can be interpreted as
saying that any partial latin rectangle can be completed if and only if
satisfies Hall's Condition for partial latin squares.
We define Hall's Condition for partial Sudoku squares and show that Hall's
Condition for partial Sudoku squares gives a criterion for the completion of
partial Sudoku rectangles that is both necessary and sufficient. In the
particular case where , , , the result is especially simple, as
we show that any partial -Sudoku rectangle can be completed
(no further condition being necessary).Comment: 19 pages, 10 figure
A softer look at MCG--6-30-15 with XMM-Newton
We present analysis and results from the Reflection Grating Spectrometer
during the 320 ks XMM observation of the Seyfert 1 galaxy MCG-6-30-15. The
spectrum is marked by a sharp drop in flux at 0.7 keV which has been
interpreted by Branduardi-Raymont et al. as the blue wing of a relativistic
OVIII emission line and by Lee at al. as a dusty warm absorber. We find that
the drop is well explained by the FeI L2,3 absorption edges and obtain
reasonable fits over the 0.32-1.7 keV band using a multizone, dusty warm
absorber model. Some residuals remain which could be due to emission from a
relativistic disc, but at a much weaker level than from any model relying on
relativistic emission lines alone. A model based on such emission lines can be
made to fit if sufficient (warm) absorption is added, although the line
strengths exceed those expected. The EPIC pn difference spectrum between the
highest and lowest flux states of the source indicates that this is a power-law
in the 3-10 keV band which, if extrapolated to lower energies, reveals the
absorption function acting on the intrinsic spectrum, provided that any
emission lines do not scale exactly with the continuum. We find that this
function matches our dusty warm absorber model well. The soft X-ray spectrum is
therefore dominated by absorption structures, with the equivalent width of any
individual emission lines in the residuals being below about 30 eV. (abridged)Comment: 8 pages, 10 figures, submitted to MNRA
The Impact of Lidar Detection Sensitivity on Assessing Aerosol Direct Radiative Effects
Spaceborne lidar observations have great potential to provide accurate global estimates of the aerosol direct radiative effect (DRE) in both clear and cloudy conditions. However, comparisons between observations from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite (CALIPSO) and multiple years of Atmospheric Radiation Measurement (ARM) programs ground-based Raman lidars (RL) show that CALIPSO does not detect all radiatively significant aerosol, i.e. aerosol that directly modifies the Earths radiation budget. We estimated that using CALIPSO observations results in an underestimate of the magnitude of the global mean aerosol DRE by up to 54%. The ARM RL datasets along with NASA Langley airborne high spectral resolution lidar (HSRL) data from multiple field campaigns are used to compute the detection sensitivity required to accurately resolve the aerosol DRE. This shows that a lidar with a backscatter coefficient detection sensitivity of about 12x10(exp -4)km(exp -1)sr(exp -1) at 532nm would resolve all the aerosol needed to derive the DRE to within 1%
Rapid X-ray Variability of Seyfert 1 Galaxies
The rapid and seemingly random fluctuations in X-ray luminosity of Seyfert
galaxies provided early support for the standard model in which Seyferts are
powered by a supermassive black hole fed from an accretion disc. However, since
EXOSAT there has been little opportunity to advance our understanding of the
most rapid X-ray variability. Observations with XMM-Newton have changed this.
We discuss some recent results obtained from XMM-Newton observations of Seyfert
1 galaxies. Particular attention will be given to the remarkable similarity
found between the timing properties of Seyferts and black hole X-ray binaries,
including the power spectrum and the cross spectrum (time delays and
coherence), and their implications for the physical processes at work in
Seyferts.Comment: To appear in From X-ray Binaries to Quasars: Black Hole Accretion on
All Mass Scales, ed. T. J. Maccarone, R. P. Fender, and L. C. Ho (Dordrecht:
Kluwer
Thermally stable laminating resins Final report
Polyimide resin and resin reinforced composite
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