Convective line asymmetries in the optical spectrum of two metal-poor stars, Gmb1830 and HD140283, are compared to those observed for solar metallicity stars. The line bisectors of the most metal-poor star, the subgiant HD140283, show a significantly larger velocity span that the expectations for a solar-metallicity star of the same spectral type and luminosity class. The enhanced line asymmetr...

If the points in S are uniformly distributed, a reasonable approach would be to use a grid-based structure. Thus, with a √ n× √ n grid, we have, on an average, 1 point per square, hence, a constant query time complexity on expectation. This is similar to the grid-based method used for the closest pair problem. For a general distribution of points, in 1 dimension, an effective approach would be ...

Voronoi diagrams are a well-studied data structure of proximity information, and although most cases require Ω(n log n) construction time, it is interesting and useful to develop linear-time algorithms for certain Voronoi diagrams. We develop a linear-time algorithm for abstract Voronoi diagrams in a domain where each site has a unique face and no pair of bisectors intersect outside the domain....

We consider the minimization of an energy functional given by sum a crystalline perimeter and nonlocal interaction Riesz type, under volume constraint. show that, in small mass regime, if Wulff shape anisotropic has certain symmetry properties, then it is unique global minimizer total energy. In dimension two this applies to convex polygons which are reflection symmetric with respect bisectors ...

The (distance) k-sector is a generalization of the concept of bisectors proposed by Asano, Matoušek and Tokuyama. We prove the uniqueness of the 4-sector of two points in the Euclidean plane. Despite the simplicity of the unique 4-sector (which consists of a line and two parabolas), our proof is quite non-trivial. We begin by establishing uniqueness in a small region of the plane, which we show...

We present an algorithm to nd a at folding of a piece of paper, so that one complete straight cut on the folding creates any desired plane graph of cuts. The folds are based on the straight skeleton, which lines up the desired edges by folding along various bisectors; and a collection of perpendiculars that make the crease pattern foldable. We prove that the crease pattern is at foldable by dem...