We studied the fields of nine nearby open star clusters based on the Tycho–2 catalogue. We determined membership probabilities for the stars in the cluster fields from the stellar proper motions and used the Tycho–2 photometry to compute the initial mass function (IMF) of the clusters from the main sequence turn-off point down to approx. 1M⊙. We found IMF slopes ranging from Γ = −0.69 down to Γ...

Let (Er ; dr) be the LHS spectral sequence associated to a split extension 1! H ! G! G=H ! 1 of nite groups with coe cients in a eld k. We prove a version of a theorem of Charlap and Vasquez which gives an explicit formula for d2. We then apply this to the case where p is an odd prime, k has characteristic p, G is extraspecial of order p and exponent p, and H is elementary abelian of order p. W...

We present astrometric and spectroscopic observations confirming that two nearby G dwarf systems (Gliese 417 = BD+362162 and Gliese 584AB = η CrB AB) have a widely separated, L dwarf, substellar companion. Using age estimates of the G dwarf primaries, we estimate masses for these L dwarfs from theoretical evolutionary tracks. For the L4.5 dwarf Gl 417B we estimate an age of 0.08-0.3 Gyr and a mass

Preliminary positions and magnitudes derived from the analysis of 12 weeks of observations from the Hipparcos star mappers are systematically compared with the various sources of ground-based data used in the Hipparcos Input Catalogue. These comparisons allow to cross-check the accuracies claimed by the various sources of ground-based data and by the analysis method of star mapper data. The par...

We present astrometric and spectroscopic observations confirming that two nearby G dwarf systems (Gliese 417 = BD+362162 and Gliese 584AB = η CrB AB) have a widely separated, L dwarf, substellar companion. Using age estimates of the G dwarf primaries, we estimate masses for these L dwarfs from theoretical evolutionary tracks. For the L4.5 dwarf Gl 417B we estimate an age of 0.08-0.3 Gyr and a m...

Remark. This is also known as the Lubell-Yamamoto-Meshalkin inequality. Solution: Generate a random permutation σ = (x1, . . . , xM ) of [M ]. Let each Ei be the event that the set Ai appears as the initial segment of σ, i.e., that {x1, . . . , xai} = Ai. Since none of the Ai contain each other, the Ei are mutually exclusive. But each P [Ei] = ( M ai )−1 , so the LHS is P [∪Ei], and probabiliti...

Proof. Suppose z is in the RHS. Then, for some f ∈ Y X , z ∈ Sxfx for all x ∈ X. Hence for each x ∈ X there is y = fx so that z ∈ Sxy, so z is in the LHS. Suppose z is in the LHS. Then for each x ∈ X there is some y ∈ Y so that z ∈ Sxy. Hence for each x ∈ X the set Tx = { y : z ∈ Sxy } is not empty. By AC there is a function f ∈ Y x so that, for all x ∈ X, fx ∈ Tx. Hence, for all x ∈ X, z ∈ Sxf...

Sketch based image retrieval is a particular case of the image retrieval problem, in which a query is not a regular example image. Instead, the query is a hand-drawn sketch representing what the user is looking for. This kind of problem has a lot of applications, in particular when an example image is not available. For instance, in searching for design pieces in digital catalogs. The natural a...