12,533 research outputs found
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
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
Using the UM dynamical cores to reproduce idealised 3D flows
We demonstrate that both the current (New Dynamics), and next generation
(ENDGame) dynamical cores of the UK Met Office global circulation model, the
UM, reproduce consistently, the long-term, large-scale flows found in several
published idealised tests. The cases presented are the Held-Suarez test, a
simplified model of Earth (including a stratosphere), and a hypothetical
tidally locked Earth. Furthermore, we show that using simplifications to the
dynamical equations, which are expected to be justified for the physical
domains and flow regimes we have studied, and which are supported by the
ENDGame dynamical core, also produces matching long-term, large-scale flows.
Finally, we present evidence for differences in the detail of the planetary
flows and circulations resulting from improvements in the ENDGame formulation
over New Dynamics.Comment: 34 Pages, 23 Figures. Accepted for publication in Geoscientific Model
Development (pre-proof version
The Mira-based distance to the Galactic centre
Mira variables are useful distance indicators, due to their high luminosities
and well-defined period-luminosity relation. We select 1863 Miras from SAAO and
MACHO observations to examine their use as distance estimators in the Milky
Way. We measure a distance to the Galactic centre of kpc,
which is in good agreement with other literature values. The uncertainty has
two components of 0.2 kpc each: the first is from our analysis and
predominantly due to interstellar extinction, the second is due to zero-point
uncertainties extrinsic to our investigation, such as the distance to the Large
Magellanic Cloud (LMC). In an attempt to improve existing period-luminosity
calibrations, we use theoretical models of Miras to determine the dependence of
the period-luminosity relation on age, metallicity, and helium abundance, under
the assumption that Miras trace the bulk stellar population. We find that at a
fixed period of , changes in the predicted magnitudes can
be approximated by , and these coefficients are
nearly independent of period. The expected overestimate in the Galactic centre
distance from using an LMC-calibrated relation is 0.3 kpc. This
prediction is not validated by our analysis; a few possible reasons are
discussed. We separately show that while the predicted color-color diagrams of
solar-neighbourhood Miras work well in the near-infrared, though there are
offsets from the model predictions in the optical and mid-infrared.Comment: Accepted for publication in The Astrophysical Journal. 16 pages, 8
figures, 6 table
Closed-Cycle, Frequency-Stable CO2 Laser Technology
These proceedings contain a collection of papers and comments presented at a workshop on technology associated with long-duration closed-cycle operation of frequency-stable, pulsed carbon dioxide lasers. This workshop was held at the NASA Langley Research Center June 10 to 12, 1986. The workshop, jointly sponsored by the National Aeronautics and Space Administration (NASA) and the Royal Signals and Radar Establishment (RSRE), was attended by 63 engineers and scientists from the United States and the United Kingdom. During the 2 1/2 days of the workshop, a number of issues relating to obtaining frequency-stable operation and to the catalytic control of laser gas chemistry were discussed, and specific recommendations concerning future activities were drafted
New Zealand Guidelines for cyanobacteria in recreational fresh waters: Interim Guidelines
This document is divided into four main sections, plus 14 appendices.
Section 1. Introduction provides an overview of the purpose and status of the document as well as advice on who should use it.
Section 2. Framework provides a background to the overall guidelines approach, recommendations on agency roles and responsibilities, and information on the condition of use of this document.
Section 3. Guidelines describes the recommended three-tier monitoring and action sequence for planktonic and benthic cyanobacteria.
Section 4. Sampling provides advice on sampling planktonic and benthic cyanobacteria.
The appendices give further background information and include templates for data collection and reporting, including:
• background information on known cyanotoxins and their distribution in New Zealand
• information on the derivation of guideline values
• photographs of typical bloom events
• a list of biovolumes for common New Zealand cyanobacteria
• templates for field assessments
• suggested media releases and warning sign templates.
A glossary provides definitions for abbreviations and terms used in these guidelines
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