12,150 research outputs found
TAX REFORM AND REVENUE SHARING CHANGES: FISCAL IMPACTS ON SMALL, RURAL MASSACHUSETTS TOWNS
Public Economics,
Accurate fundamental parameters for Lower Main Sequence Stars
We derive an empirical effective temperature and bolometric luminosity
calibration for G and K dwarfs, by applying our own implementation of the
InfraRed Flux Method to multi-band photometry. Our study is based on 104 stars
for which we have excellent BVRIJHK photometry, excellent parallaxes and good
metallicities. Colours computed from the most recent synthetic libraries
(ATLAS9 and MARCS) are found to be in good agreement with the empirical colours
in the optical bands, but some discrepancies still remain in the infrared.
Synthetic and empirical bolometric corrections also show fair agreement. A
careful comparison to temperatures, luminosities and angular diameters obtained
with other methods in literature shows that systematic effects still exist in
the calibrations at the level of a few percent. Our InfraRed Flux Method
temperature scale is 100K hotter than recent analogous determinations in the
literature, but is in agreement with spectroscopically calibrated temperature
scales and fits well the colours of the Sun. Our angular diameters are
typically 3% smaller when compared to other (indirect) determinations of
angular diameter for such stars, but are consistent with the limb-darkening
corrected predictions of the latest 3D model atmospheres and also with the
results of asteroseismology. Very tight empirical relations are derived for
bolometric luminosity, effective temperature and angular diameter from
photometric indices. We find that much of the discrepancy with other
temperature scales and the uncertainties in the infrared synthetic colours
arise from the uncertainties in the use of Vega as the flux calibrator. Angular
diameter measurements for a well chosen set of G and K dwarfs would go a long
way to addressing this problem.Comment: 34 pages, 20 figures. Accepted by MNRAS. Landscape table available
online at http://users.utu.fi/luccas/IRFM
Covering collections and a challenge problem of Serre
We answer a challenge of Serre by showing that every rational point on the projective curve X + Y = 17 Z is of the form (1, 2, 1) or (2, 1, 1). Our approach builds on recent ideas from both Nils Bruin and the authors on the application of covering collections and Chabauty arguments to curves of high rank. This is the only value of c81 for which the Fermat quartic X + Y = c Z cannot be solved trivially, either by local considerations or maps to elliptic curves of rank 0, and it seems likely that our approach should give a method of attack for other nontrivial values of c
Finding rational points on bielliptic genus 2 curves
We discuss a technique for trying to find all rational points on curves of the form , where the sextic has nonzero discriminant. This is a bielliptic curve of genus 2. When the rank of the Jacobian is 0 or 1, Chabauty's Theorem may be applied. However, we shall concentrate on the situation when the rank is at least 2. In this case, we shall derive an associated family of elliptic curves, defined over a number field Q(a). If each of these elliptic curves has rank less than the degree of Q(a) : Q, then we shall describe a Chabauty-like technique which may be applied to try to find all the points (x,y) defined over Q(a) on the elliptic curves, for which x is in Q. This in turn allows us to find all Q-rational points on the original genus 2 curve. We apply this to give a solution to a problem of Diophantus (where the sextic in X is irreducible over Q), which simplifies the recent solution of Wetherell. We also present two examples where the sextic in X is reducible over Q
Lattice-Constrained Parametrizations of Form Factors for Semileptonic and Rare Radiative B Decays
We describe the form factors for semileptonic B to rho l nu and radiative B
to K* gamma decays with just two parameters and the two form factors for
semileptonic B to pi l nu decays with three parameters. The parametrizations
are constrained by lattice results and are consistent with heavy quark
symmetry, kinematic constraints and light cone sum rule scaling relations.Comment: 3 pages, latex, 2 eps files, uses epsf.sty and espcrc2.sty, poster
presented at Lattice 97, Edinburgh, 22-26 July 199
The arithmetic of hyperelliptic curves
We summarise recent advances in techniques for solving Diophantine problems on hyperelliptic curves; in particular, those for finding the rank of the Jacobian, and the set of rational points on the curve
Galactic Archaeology and Minimum Spanning Trees
Chemical tagging of stellar debris from disrupted open clusters and
associations underpins the science cases for next-generation multi-object
spectroscopic surveys. As part of the Galactic Archaeology project TraCD
(Tracking Cluster Debris), a preliminary attempt at reconstructing the birth
clouds of now phase-mixed thin disk debris is undertaken using a parametric
minimum spanning tree (MST) approach. Empirically-motivated chemical abundance
pattern uncertainties (for a 10-dimensional chemistry-space) are applied to
NBODY6-realised stellar associations dissolved into a background sea of field
stars, all evolving in a Milky Way potential. We demonstrate that significant
population reconstruction degeneracies appear when the abundance uncertainties
approach 0.1 dex and the parameterised MST approach is employed; more
sophisticated methodologies will be required to ameliorate these degeneracies.Comment: To appear in "Multi-Object Spectroscopy in the Next Decade: Big
Questions, Large Surveys and Wide Fields"; Held: Santa Cruz de La Palma,
Canary Islands, Spain, 2-6 Mar 2015; ed. I Skillen & S. Trager; ASP
Conference Series (Figures now optimised for B&W printing
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