In this paper we deal with two problems on star-shaped polygons. At rst, we present a Las-Vegas algorithm that uniformly at random creates a star-shaped polygon whose vertices are given by a point set S of n points in the plane that does not admit degenerated star-shaped polygons. The expected running time of the algorithm is O(n logn) and it uses O(n) memory. We call a starshaped polygon degen...

An S-space is a normal topological space in which each covering by open sets has a refinement which is star-finite, that is, each set of the refinement meets only a finite number of sets of the refinement. Thus a compact ( = bicompact) space is an S-space, and an S-space is paracompact [ l ] . 1 In this note we discuss cartesian products in which one of the factors is an S-space. We show that i...

After more than a decade of actively accreting at about a tenth of the Eddington critical mass accretion rate, the neutron-star X-ray transient KS 1731–260 returned to quiescence in early 2001. We present a Chandra/ACIS-S observation taken several months after this transition. We detected the source at an unabsorbed flux of ∼ 2 × 10 erg cm s (0.5–10 keV). For a distance of 7 kpc, this results i...

We study when the product of separable metric spaces has the selective screenability property, the Menger property, or the Rothberger property. Our results imply The product of a Lusin set and (1) a Sierpinski set always has the Menger property (Corollary 12); (2) a γ-set always has the Rothberger property (Corollary 13). All topological spaces considered in this paper are assumed to be separab...

We present a five-band Herschel study (100–500 μm) of three galaxy clusters at z 1.2 ~ from the Spitzer Adaptation of the Red-Sequence Cluster Survey. With a sample of 120 spectroscopically confirmed cluster members, we investigate the role of environment on galaxy properties utilizing the projected cluster phase space (line-of-sight velocity versus clustercentric radius), which probes the time...

We report the discovery of PM J13420-3415, a faint (V=17) white dwarf with a very high proper motion μ = 2.55 yr−1. The star was found in the southern sky extension of the SUPERBLINK proper motion survey. A red spectrum shows the classical signature of a DA white dwarf, with a weak Hα line in absorption as the only prominent feature. The star is also found to have a large radial velocity Vrad =...

We consider the problem of recognizing star-polygons under staircase visibility (s-visibility). We show that the s-visibility polygon from a point inside a simple orthogonal polygon of n sides can be computed in O(n) time. When the polygon contains holes the algorithm runs in O(n log n) time, which we prove to be optimal by linear time reduction from sorting. We present an algorithm for computi...

The Aharonov-Casher (AC) effect in non-commutative(NC) quantum mechanics is studied. Instead of using the star product method, we use a generalization of Bopp’s shift method. After solving the Dirac equations both on noncommutative space and noncommutative phase space by the new method, we obtain the corrections to AC phase on NC space and NC phase space respectively. PACS number(s): 02.40.Gh, ...