350 research outputs found
A look at cycles containing specified elements of a graph
AbstractThis article is intended as a brief survey of problems and results dealing with cycles containing specified elements of a graph. It is hoped that this will help researchers in the area to identify problems and areas of concentration
Forbidden triples and traceability: a characterization
AbstractGiven a connected graph G, a family F of connected graphs is called a forbidden family if no induced subgraph of G is isomorphic to any graph in F. If this is the case, G is said to be F-free. In earlier papers the authors identified four distinct families of triples of subgraphs that imply traceability when they are forbidden in sufficiently large graphs. In this paper the authors introduce a fifth family and show these are all such families
Gaps in the Saturation Spectrum of Trees
A graph G is H-saturated if H is not a subgraph of G but the addition of any edge from the complement of G to G results in a copy of H. The minimum number of edges (the size) of an H-saturated graph on n vertices is denoted sat(n, H), while the maximum size is the well studied extremal number, ex(n, H). The saturation spectrum for a graph H is the set of sizes of H-saturated graphs between sat(n, H) and ex(n, H). In this paper we show that paths, trees with a vertex adjacent to many leaves, and brooms have a gap in the saturation spectrum
A Transiting Hot Jupiter Orbiting a Metal-Rich Star
We announce the discovery of Kepler-6b, a transiting hot Jupiter orbiting a
star with unusually high metallicity, [Fe/H] = +0.34 +/- 0.04. The planet's
mass is about 2/3 that of Jupiter, Mp = 0.67 Mj, and the radius is thirty
percent larger than that of Jupiter, Rp = 1.32 Rj, resulting in a density of
0.35 g/cc, a fairly typical value for such a planet. The orbital period is P =
3.235 days. The host star is both more massive than the Sun, Mstar = 1.21 Msun,
and larger than the Sun, Rstar = 1.39 Rsun.Comment: 12 pages, 2 figures, submitted to the Astrophysical Journal Letter
Kepler Mission Stellar and Instrument Noise Properties
Kepler Mission results are rapidly contributing to fundamentally new
discoveries in both the exoplanet and asteroseismology fields. The data
returned from Kepler are unique in terms of the number of stars observed,
precision of photometry for time series observations, and the temporal extent
of high duty cycle observations. As the first mission to provide extensive time
series measurements on thousands of stars over months to years at a level
hitherto possible only for the Sun, the results from Kepler will vastly
increase our knowledge of stellar variability for quiet solar-type stars. Here
we report on the stellar noise inferred on the timescale of a few hours of most
interest for detection of exoplanets via transits. By design the data from
moderately bright Kepler stars are expected to have roughly comparable levels
of noise intrinsic to the stars and arising from a combination of fundamental
limitations such as Poisson statistics and any instrument noise. The noise
levels attained by Kepler on-orbit exceed by some 50% the target levels for
solar-type, quiet stars. We provide a decomposition of observed noise for an
ensemble of 12th magnitude stars arising from fundamental terms (Poisson and
readout noise), added noise due to the instrument and that intrinsic to the
stars. The largest factor in the modestly higher than anticipated noise follows
from intrinsic stellar noise. We show that using stellar parameters from
galactic stellar synthesis models, and projections to stellar rotation,
activity and hence noise levels reproduces the primary intrinsic stellar noise
features.Comment: Accepted by ApJ; 26 pages, 20 figure
Space-based research in fundamental physics and quantum technologies
Space-based experiments today can uniquely address important questions
related to the fundamental laws of Nature. In particular, high-accuracy physics
experiments in space can test relativistic gravity and probe the physics beyond
the Standard Model; they can perform direct detection of gravitational waves
and are naturally suited for precision investigations in cosmology and
astroparticle physics. In addition, atomic physics has recently shown
substantial progress in the development of optical clocks and atom
interferometers. If placed in space, these instruments could turn into powerful
high-resolution quantum sensors greatly benefiting fundamental physics.
We discuss the current status of space-based research in fundamental physics,
its discovery potential, and its importance for modern science. We offer a set
of recommendations to be considered by the upcoming National Academy of
Sciences' Decadal Survey in Astronomy and Astrophysics. In our opinion, the
Decadal Survey should include space-based research in fundamental physics as
one of its focus areas. We recommend establishing an Astronomy and Astrophysics
Advisory Committee's interagency ``Fundamental Physics Task Force'' to assess
the status of both ground- and space-based efforts in the field, to identify
the most important objectives, and to suggest the best ways to organize the
work of several federal agencies involved. We also recommend establishing a new
NASA-led interagency program in fundamental physics that will consolidate new
technologies, prepare key instruments for future space missions, and build a
strong scientific and engineering community. Our goal is to expand NASA's
science objectives in space by including ``laboratory research in fundamental
physics'' as an element in agency's ongoing space research efforts.Comment: a white paper, revtex, 27 pages, updated bibliograph
Taking the Measure of the Universe: Precision Astrometry with SIM PlanetQuest
Precision astrometry at microarcsecond accuracy has application to a wide
range of astrophysical problems. This paper is a study of the science questions
that can be addressed using an instrument that delivers parallaxes at about 4
microarcsec on targets as faint as V = 20, differential accuracy of 0.6
microarcsec on bright targets, and with flexible scheduling. The science topics
are drawn primarily from the Team Key Projects, selected in 2000, for the Space
Interferometry Mission PlanetQuest (SIM PlanetQuest). We use the capabilities
of this mission to illustrate the importance of the next level of astrometric
precision in modern astrophysics. SIM PlanetQuest is currently in the detailed
design phase, having completed all of the enabling technologies needed for the
flight instrument in 2005. It will be the first space-based long baseline
Michelson interferometer designed for precision astrometry. SIM will contribute
strongly to many astronomical fields including stellar and galactic
astrophysics, planetary systems around nearby stars, and the study of quasar
and AGN nuclei. SIM will search for planets with masses as small as an Earth
orbiting in the `habitable zone' around the nearest stars using differential
astrometry, and could discover many dozen if Earth-like planets are common. It
will be the most capable instrument for detecting planets around young stars,
thereby providing insights into how planetary systems are born and how they
evolve with time. SIM will observe significant numbers of very high- and
low-mass stars, providing stellar masses to 1%, the accuracy needed to
challenge physical models. Using precision proper motion measurements, SIM will
probe the galactic mass distribution and the formation and evolution of the
Galactic halo. (abridged)Comment: 54 pages, 28 figures, uses emulateapj. Submitted to PAS
Planet Occurrence within 0.25 AU of Solar-type Stars from Kepler
We report the distribution of planets as a function of planet radius (R_p),
orbital period (P), and stellar effective temperature (Teff) for P < 50 day
orbits around GK stars. These results are based on the 1,235 planets (formally
"planet candidates") from the Kepler mission that include a nearly complete set
of detected planets as small as 2 Earth radii (Re). For each of the 156,000
target stars we assess the detectability of planets as a function of R_p and P.
We also correct for the geometric probability of transit, R*/a. We consider
first stars within the "solar subset" having Teff = 4100-6100 K, logg =
4.0-4.9, and Kepler magnitude Kp < 15 mag. We include only those stars having
noise low enough to permit detection of planets down to 2 Re. We count planets
in small domains of R_p and P and divide by the included target stars to
calculate planet occurrence in each domain. Occurrence of planets varies by
more than three orders of magnitude and increases substantially down to the
smallest radius (2 Re) and out to the longest orbital period (50 days, ~0.25
AU) in our study. For P < 50 days, the radius distribution is given by a power
law, df/dlogR= k R^\alpha. This rapid increase in planet occurrence with
decreasing planet size agrees with core-accretion, but disagrees with
population synthesis models. We fit occurrence as a function of P to a power
law model with an exponential cutoff below a critical period P_0. For smaller
planets, P_0 has larger values, suggesting that the "parking distance" for
migrating planets moves outward with decreasing planet size. We also measured
planet occurrence over Teff = 3600-7100 K, spanning M0 to F2 dwarfs. The
occurrence of 2-4 Re planets in the Kepler field increases with decreasing
Teff, making these small planets seven times more abundant around cool stars
than the hottest stars in our sample. [abridged]Comment: Submitted to ApJ, 22 pages, 10 figure
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