44,267 research outputs found
Solutions to polynomial congruences in well shaped sets
We use a generalization of Vinogradov's mean value theorem of S. Parsell, S.
Prendiville and T. Wooley and ideas of W. Schmidt to give nontrivial bounds for
the number of solutions to polynomial congruences, for arbitrary polynomials,
when the solutions lie in a very general class of sets, including all convex
sets
The Stagger-grid: A grid of 3D stellar atmosphere models - IV. Limb darkening coefficients
We compute the emergent stellar spectra from the UV to far infrared for
different viewing angles using realistic 3D model atmospheres for a large range
in stellar parameters to predict the stellar limb darkening. We have computed
full 3D LTE synthetic spectra based on 3D radiative hydrodynamic atmosphere
models from the Stagger-grid. From the resulting intensities at different
wavelength, we derived coefficients for the standard limb darkening laws
considering a number of often-used photometric filters. Furthermore, we
calculated theoretical transit light curves, in order to quantify the
differences between predictions by the widely used 1D model atmosphere and our
3D models. The 3D models are often found to predict steeper limb darkening
compared to the 1D models, mainly due to the temperature stratifications and
temperature gradients being different in the 3D models compared to those
predicted with 1D models based on the mixing length theory description of
convective energy transport. The resulting differences in the transit light
curves are rather small; however, these can be significant for high-precision
observations of extrasolar transits, and are able to lower the residuals from
the fits with 1D limb darkening profiles. We advocate the use of the new limb
darkening coefficients provided for the standard four-parameter non-linear
power law, which can fit the limb darkening more accurately than other choices.Comment: Accepted for publication in A&A, 10 pages, 9 figures, 1 tabl
Convex Combinatorial Optimization
We introduce the convex combinatorial optimization problem, a far reaching
generalization of the standard linear combinatorial optimization problem. We
show that it is strongly polynomial time solvable over any edge-guaranteed
family, and discuss several applications
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