1,349 research outputs found
The Hamilton-Waterloo Problem with even cycle lengths
The Hamilton-Waterloo Problem HWP asks for a
2-factorization of the complete graph or , the complete graph with
the edges of a 1-factor removed, into -factors and
-factors, where . In the case that and are both
even, the problem has been solved except possibly when
or when and are both odd, in which case necessarily . In this paper, we develop a new construction that creates
factorizations with larger cycles from existing factorizations under certain
conditions. This construction enables us to show that there is a solution to
HWP for odd and whenever the obvious
necessary conditions hold, except possibly if ; and
; ; or . This result almost completely
settles the existence problem for even cycles, other than the possible
exceptions noted above
IUE observations of oxygen-rich supernova remnants
The IUE observations were used to determine the composition of the ejecta (especially C and Si abundances) and to test models for the ionization and excitation of the ejecta of two oxygen-rich supernova remnants (N132D in the Large Magellanic Cloud and 1E 0102-7219 in the Small Magellanic Cloud). Time-dependent photoionization by the EUV and X-ray radiation from 1E 0102-7219 can qualitatively explain its UV and optical line emission, but the density and ionization structures are complex and prevent a unique model from being specified. Many model parameters are poorly constrained, including the time dependence and shape of the ionizing spectrum. Moreover, the models presented are not self-consistent in that the volumes and densities of the optically emitting gas imply optical depths of order unity in the EUV, but absorption of the ionizing radiation was ignored. It is possible that these shortcomings reflect a more fundamental limitation of the model assumptions. It is assumed that the electron velocity distribution is Maxwellian and that the energy deposited by photoionization heats the electrons directly. The 500 eV electrons produced by the Auger process may excite or ionize other ions before they slow down enough to share their energy with other electrons. Many of the excitations would produce photons that could ionize lower ionization stages
The He II Fowler lines and the O III and N III Bowen fluorescence lines in the symbiotic nova RR Tel
A new measure of reddening (E0.00) has been obtained from the
comparison between the observed and the theoretical intensity decrement for 20
emission lines of the \ion{He}{ii} Fowler (n3) series. This value has
been confirmed by the STIS and IUE continuum distribution, and by the value of
n from the damped profile of the IS H Ly- line. We have obtained
very accurate measurements for about thirty Bowen lines of \ion{O}{iii} and a
precise determination of the efficiency in the O1 and O3 excitation channels
(18 % and 0.7 %, respectively). The relative \ion{O}{iii} intensities are in
good agreement with the predictions by Froese Fischer (1994). A detailed study
of the decays from all levels involved in the Bowen mechanism has lead to the
detection of two new \ion{O}{iii} Bowen lines near 2190. High
resolution IUE data have shown a nearly linear decline with time, from 1978 to
1995, in the efficiency of the O1 and O3 processes, with a steeper slope for
the O3 channel. A detailed study of the \ion{N}{iii} 4640 lines and
of their excitation mechanism has shown that, recombination and continuum
fluorescence being ruled out, line fluorescence remains the only viable
mechanism to pump the 3d and 3d levels of
\ion{N}{iii}. We point out the important role of multiple scattering in the
resonance lines of \ion{O}{iii} and \ion{N}{iii} near 374 and
show that the observed \ion{N}{iii} line ratios and intensities can be
explained in terms of line fluorescence by the three resonance lines of
\ion{O}{iii} at 374.432, 374.162 and 374.073 under
optically thick conditions.Comment: Accepted version for Astronomy and Astrophysic
The Peculiar Type Ic Supernova 1997ef: Another Hypernova
SN 1997ef has been recognized as a peculiar supernova from its light curve
and spectral properties. The object was classified as a Type Ic supernova (SN
Ic) because its spectra are dominated by broad absorption lines of oxygen and
iron, lacking any clear signs of hydrogen or helium line features. The light
curve is very different from that of previously known SNe Ic, showing a very
broad peak and a slow tail. The strikingly broad line features in the spectra
of SN 1997ef, which were also seen in the hypernova SN 1998bw, suggest the
interesting possibility that SN 1997ef may also be a hypernova. The light curve
and spectra of SN 1997ef were modeled first with a standard SN~Ic model
assuming an ordinary kinetic energy of explosion erg. The
explosion of a CO star of mass gives a
reasonably good fit to the light curve but clearly fails to reproduce the broad
spectral features. Then, models with larger masses and energies were explored.
Both the light curve and the spectra of SN 1997ef are much better reproduced by
a C+O star model with 8 \e{51} erg and .
Therefore, we conclude that SN 1997ef is very likely a hypernova on the basis
of its kinetic energy of explosion. Finally, implications for the deviation
from spherical symmetry are discussed in an effort to improve the light curve
and spectral fits.Comment: "To appear in the Astrophysical Journal, Vol.534 (2000)
High Resolution mid-Infrared Imaging of SN 1987A
Using the Thermal-Region Camera and Spectrograph (T-ReCS) attached to the
Gemini South 8m telescope, we have detected and resolved 10 micron emission at
the position of the inner equatorial ring (ER) of supernova SN 1987A at day
6067. ``Hot spots'' similar to those found in the optical and near-IR are
clearly present. The morphology of the 10 micron emission is globally similar
to the morphology at other wavelengths from X-rays to radio. The observed
mid-IR flux in the region of SN1987A is probably dominated by emission from
dust in the ER. We have also detected the ER at 20 micron at a 4 sigma level.
Assuming that thermal dust radiation is the origin of the mid-IR emission, we
derive a dust temperature of 180^{+20}_{-10} K, and a dust mass of 1.- 8.
10^{-5} Mo for the ER. Our observations also show a weak detection of the
central ejecta at 10 micron. We show that previous bolometric flux estimates
(through day 2100) were not significantly contaminated by this newly discovered
emission from the ER. If we assume that the energy input comes from radioactive
decays only, our measurements together with the current theoretical models set
a temperature of 90 leq T leq 100 K and a mass range of 10^{-4} - 2. 10^{-3} Mo
for the dust in the ejecta. With such dust temperatures the estimated thermal
emission is 9(+/-3) 10^{35} erg s^{-1} from the inner ring, and 1.5 (+/-0.5)
10^{36} erg s^{-1} from the ejecta. Finally, using SN 1987A as a template, we
discuss the possible role of supernovae as major sources of dust in the
Universe.Comment: aastex502, 14 pages, 4 figures; Accepted for publication in ApJ
Content changed: new observations, Referee's comments and suggestion
Constructing uniform 2-factorizations via row-sum matrices: solutions to the Hamilton-Waterloo problem
In this paper, we formally introduce the concept of a row-sum matrix over an
arbitrary group . When is cyclic, these types of matrices have been
widely used to build uniform 2-factorizations of small Cayley graphs (or,
Cayley subgraphs of blown-up cycles), which themselves factorize complete
(equipartite) graphs.
Here, we construct row-sum matrices over a class of non-abelian groups, the
generalized dihedral groups, and we use them to construct uniform
-factorizations that solve infinitely many open cases of the
Hamilton-Waterloo problem, thus filling up large parts of the gaps in the
spectrum of orders for which such factorizations are known to exist
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