The G0V star HD 166435 has been observed by the fiber-fed spectrograph ELODIE as one of the targets in the large extra-solar planet survey that we are conducting at the Observatory of Haute-Provence. We detected coherent, low-amplitude, radial-velocity variations with a period of 3.7987 days, suggesting a possible close-in planetary companion. Subsequently, we initiated a series of high-precisi...

This paper studies local properties of Voronoi diagrams of sets of disjoint compact convex sites in R. It is established that bisectors are C surfaces and trisectors are C curves, and that as a point moves along a trisector its clearance sphere develops monotonically (Lemma 2.4). This monotonicity property is useful in establishing the existence of Voronoi vertices bounding edges in certain sit...

Three independent lines of evidence imply that the young star PV Ceph is moving at roughly 20 km s through the interstellar medium. The first, and strongest, suggestion of motion comes from the geometry of the HH knots in the “giant” Herbig-Haro (HH) flow associated with PV Ceph. Bisectors of lines drawn between pairs of knots at nearly equal distances from PV Ceph imply an E-W motion of the so...

Context. CoRoT-7b, the first transiting “superearth” exoplanet, has a radius of 1.7 R⊕ and a mass of 4.8 M⊕. The HARPS radial velocity (RV) measurements used for deriving this mass also detected an additional companion with a period of 3.7 days and a mass of 8.4 M⊕. The mass of CoRoT-7b is a crucial parameter for planet structure models, but is difficult to determine because CoRoT-7 is a modest...

Voronoi diagrams are a central topic in Computational Geometry. They can be generalized in many ways. Suppose S is a finite set of geometric objects and there is a notion of Voronoi diagram V or(S) that we want to compute. One approach to designing algorithms for V or(S) is to (1) assume some general properties of S, and (2) describe an abstract algorithm based on the Real RAM model that has so...

We introduce the bisector energy of an n-point set P in R2, defined as E(P) = ∣∣{(a, b, c, d) ∈ P | a, b have the same perpendicular bisector as c, d}∣∣ . If no line or circle contains M(n) points of P, then we prove that for any ε > 0 E(P) = O ( M(n) 2 5n 12 5 +ε +M(n)n ) . We also derive the lower bound E(P) = Ω(M(n)n2), which matches our upper bound when M(n) is large. We use our upper bound...

Spectral-line displacements away from the wavelengths naively expected from the Doppler shift caused by stellar radial motion may originate as convective shifts (correlated velocity and brightness patterns in the photosphere), as gravitational redshifts, or perhaps be induced by wave motions. Absolute lineshifts, in the past studied only for the Sun, are now accessible also for other stars than...

We prove that a set of N points on a two dimensional sphere satisfying a discrete energy condition determines at least a constant times N distinct distances. Homogeneous sets in the sense of Solymosi and Vu easily satisfy this condition, as do other sets that in the sense that will be made precise below respect the curvature properties of the sphere. The classical Erdös distance conjecture (EDC...

This paper is an abridged and simplified version of my monograph Reasoning with Arbitrary Objects [4]. It may be read by the diligent as a preparation for the longer work or by the indolent as a substitute for it. But the reader, in either case, may find it helpful to consult the paper, A Defence of Arbitrary Objects [3], for general philosophical orientation. This paper deals with certain prob...