6,639 research outputs found
Effects of moderate abundance changes on the atmospheric structure and colours of Mira variables (Research Note)
Aims. We study the effects of moderate deviations from solar abundances upon
the atmospheric structure and colours of typical Mira variables. Methods. We
present two model series of dynamical opacity-sampling models of Mira variables
which have (1) 1 solar metallicity 3 and (2) "mild" S-type C/O abundance ratio
([C/O]=0.9) with typical Zr enhancement (solar +1.0). These series are compared
to a previously studied solar-abundance series which has similar fundamental
parameters (mass, luminosity, period, radius) that are close to those of o Cet.
Results. Both series show noticeable effects of abundance upon stratifications
and infrared colours but cycle-to-cycle differences mask these effects at most
pulsation phases, with the exception of a narrow-water-filter colour near
minimum phase.Comment: 4 pages, 3 figures, accepted for A&
On the general position subset selection problem
Let be the maximum integer such that every set of points in
the plane with at most collinear contains a subset of points
with no three collinear. First we prove that if then
. Second we prove that if
then , which implies all previously known lower bounds on and
improves them when is not fixed. A more general problem is to consider
subsets with at most collinear points in a point set with at most
collinear. We also prove analogous results in this setting
Which point sets admit a k-angulation?
For k >= 3, a k-angulation is a 2-connected plane graph in which every
internal face is a k-gon. We say that a point set P admits a plane graph G if
there is a straight-line drawing of G that maps V(G) onto P and has the same
facial cycles and outer face as G. We investigate the conditions under which a
point set P admits a k-angulation and find that, for sets containing at least
2k^2 points, the only obstructions are those that follow from Euler's formula.Comment: 13 pages, 7 figure
On the connectivity of visibility graphs
The visibility graph of a finite set of points in the plane has the points as
vertices and an edge between two vertices if the line segment between them
contains no other points. This paper establishes bounds on the edge- and
vertex-connectivity of visibility graphs.
Unless all its vertices are collinear, a visibility graph has diameter at
most 2, and so it follows by a result of Plesn\'ik (1975) that its
edge-connectivity equals its minimum degree. We strengthen the result of
Plesn\'ik by showing that for any two vertices v and w in a graph of diameter
2, if deg(v) <= deg(w) then there exist deg(v) edge-disjoint vw-paths of length
at most 4. Furthermore, we find that in visibility graphs every minimum edge
cut is the set of edges incident to a vertex of minimum degree.
For vertex-connectivity, we prove that every visibility graph with n vertices
and at most l collinear vertices has connectivity at least (n-1)/(l-1), which
is tight. We also prove the qualitatively stronger result that the
vertex-connectivity is at least half the minimum degree. Finally, in the case
that l=4 we improve this bound to two thirds of the minimum degree.Comment: 16 pages, 8 figure
Thoughts on Barnette's Conjecture
We prove a new sufficient condition for a cubic 3-connected planar graph to
be Hamiltonian. This condition is most easily described as a property of the
dual graph. Let be a planar triangulation. Then the dual is a cubic
3-connected planar graph, and is bipartite if and only if is
Eulerian. We prove that if the vertices of are (improperly) coloured blue
and red, such that the blue vertices cover the faces of , there is no blue
cycle, and every red cycle contains a vertex of degree at most 4, then is
Hamiltonian.
This result implies the following special case of Barnette's Conjecture: if
is an Eulerian planar triangulation, whose vertices are properly coloured
blue, red and green, such that every red-green cycle contains a vertex of
degree 4, then is Hamiltonian. Our final result highlights the
limitations of using a proper colouring of as a starting point for proving
Barnette's Conjecture. We also explain related results on Barnette's Conjecture
that were obtained by Kelmans and for which detailed self-contained proofs have
not been published.Comment: 12 pages, 7 figure
Laser anemometer measurements in a transonic axial-flow fan rotor
Laser anemometer surveys were made of the 3-D flow field in NASA rotor 67, a low aspect ratio transonic axial-flow fan rotor. The test rotor has a tip relative Mach number of 1.38. The flowfield was surveyed at design speed at near peak efficiency and near stall operating conditions. Data is presented in the form of relative Mach number and relative flow angle distributions on surfaces of revolution at nine spanwise locations evenly spaced from hub to tip. At each spanwise location, data was acquired upstream, within, and downstream of the rotor. Aerodynamic performance measurements and detailed rotor blade and annulus geometry are also presented so that the experimental results can be used as a test case for 3-D turbomachinery flow analysis codes
Pittosporum halophilum Rock (Pittosporaceae: Apiales): Rediscovery,Taxonomic Assessment, and Conservation Status of a Critically Endangered Endemic Species from Moloka‘i, Hawaiian Islands
v. ill. 23 cm.Also available through BioOne: http://www.bioone.org/doi/abs/10.2984/65.4.465QuarterlyPittosporum halophilum Rock originally was known only from the type collections made in 1910 and 1911 along the windward sea cliffs of Moloka‘i. In the most recent revision of Hawaiian Pittosporum it was treated as synonymous with the more common species P. confertiflorum A. Gray. Since 1994, several plants fitting the circumscription of P. halophilum have been discovered near the type locality. Careful studies of these individuals and of plants cultivated from their seeds clearly revealed that they are not only characterized by salt tolerance, but differ from P. confertiflorum also in several other characters (i.e., a small, shrubby habit; smaller leaves with cuneate bases and unique tan to golden yellow wooly dense tomentum on abaxial leaf surfaces; shorter petioles; subcuboid to ovoid capsules; and, in most individuals, functionally unisexual flowers). Based on these substantial differences we conclude that P. halophilum merits recognition on species level. In this paper we give a detailed description of P. halophilum including remarks on its conservation status
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