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 $f(n,\ell)$ be the maximum integer such that every set of $n$ points in the plane with at most $\ell$ collinear contains a subset of $f(n,\ell)$ points with no three collinear. First we prove that if $\ell \leq O(\sqrt{n})$ then $f(n,\ell)\geq \Omega(\sqrt{\frac{n}{\ln \ell}})$. Second we prove that if $\ell \leq O(n^{(1-\epsilon)/2})$ then $f(n,\ell) \geq \Omega(\sqrt{n\log_\ell n})$, which implies all previously known lower bounds on $f(n,\ell)$ and improves them when $\ell$ is not fixed. A more general problem is to consider subsets with at most $k$ collinear points in a point set with at most $\ell$ 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 $G$ be a planar triangulation. Then the dual $G^*$ is a cubic 3-connected planar graph, and $G^*$ is bipartite if and only if $G$ is Eulerian. We prove that if the vertices of $G$ are (improperly) coloured blue and red, such that the blue vertices cover the faces of $G$, there is no blue cycle, and every red cycle contains a vertex of degree at most 4, then $G^*$ is Hamiltonian. This result implies the following special case of Barnette's Conjecture: if $G$ 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 $G^*$ is Hamiltonian. Our final result highlights the limitations of using a proper colouring of $G$ 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