9,872 research outputs found
GPI spectra of HR 8799 c, d, and e from 1.5 to 2.4m with KLIP Forward Modeling
We explore KLIP forward modeling spectral extraction on Gemini Planet Imager
coronagraphic data of HR 8799, using PyKLIP and show algorithm stability with
varying KLIP parameters. We report new and re-reduced spectrophotometry of HR
8799 c, d, and e in H & K bands. We discuss a strategy for choosing optimal
KLIP PSF subtraction parameters by injecting simulated sources and recovering
them over a range of parameters. The K1/K2 spectra for HR 8799 c and d are
similar to previously published results from the same dataset. We also present
a K band spectrum of HR 8799 e for the first time and show that our H-band
spectra agree well with previously published spectra from the VLT/SPHERE
instrument. We show that HR 8799 c and d show significant differences in their
H & K spectra, but do not find any conclusive differences between d and e or c
and e, likely due to large error bars in the recovered spectrum of e. Compared
to M, L, and T-type field brown dwarfs, all three planets are most consistent
with mid and late L spectral types. All objects are consistent with low gravity
but a lack of standard spectra for low gravity limit the ability to fit the
best spectral type. We discuss how dedicated modeling efforts can better fit HR
8799 planets' near-IR flux and discuss how differences between the properties
of these planets can be further explored.Comment: Accepted to AJ, 25 pages, 16 Figure
Uniform hypergraphs containing no grids
A hypergraph is called an rĂr grid if it is isomorphic to a pattern of r horizontal and r vertical lines, i.e.,a family of sets {A1, ..., Ar, B1, ..., Br} such that AiâŠAj=BiâŠBj=Ď for 1â¤i<jâ¤r and {pipe}AiâŠBj{pipe}=1 for 1â¤i, jâ¤r. Three sets C1, C2, C3 form a triangle if they pairwise intersect in three distinct singletons, {pipe}C1âŠC2{pipe}={pipe}C2âŠC3{pipe}={pipe}C3âŠC1{pipe}=1, C1âŠC2â C1âŠC3. A hypergraph is linear, if {pipe}EâŠF{pipe}â¤1 holds for every pair of edges Eâ F.In this paper we construct large linear r-hypergraphs which contain no grids. Moreover, a similar construction gives large linear r-hypergraphs which contain neither grids nor triangles. For râĽ. 4 our constructions are almost optimal. These investigations are motivated by coding theory: we get new bounds for optimal superimposed codes and designs. Š 2013 Elsevier Ltd
-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray-Lions problems
In this work we prove optimal -approximation estimates (with
) for elliptic projectors on local polynomial spaces. The
proof hinges on the classical Dupont--Scott approximation theory together with
two novel abstract lemmas: An approximation result for bounded projectors, and
an -boundedness result for -orthogonal projectors on polynomial
subspaces. The -approximation results have general applicability to
(standard or polytopal) numerical methods based on local polynomial spaces. As
an illustration, we use these -estimates to derive novel error
estimates for a Hybrid High-Order discretization of Leray--Lions elliptic
problems whose weak formulation is classically set in for
some . This kind of problems appears, e.g., in the modelling
of glacier motion, of incompressible turbulent flows, and in airfoil design.
Denoting by the meshsize, we prove that the approximation error measured in
a -like discrete norm scales as when
and as when .Comment: keywords: -approximation properties of elliptic projector on
polynomials, Hybrid High-Order methods, nonlinear elliptic equations,
-Laplacian, error estimate
- âŚ