Mass of the milky way

We present a new estimate of the mass of the Milky Way based on the escape velocity of a sample of distant stars, about 12 kpc from the Galactic centre and about 5 kpc from the plane of the Galaxy. Our sample is very different from previous escape-velocity studies, being compiled from an all-object spectroscopic survey of a region of sky. The derived mass within 12 kpc of the Galactic centre is (1.3 +/- 0.3) x 10(11) M-circle dot.

The mu-way intersection problem for m-cycle systems

An m-cycle system of order upsilon is a partition of the edge-set of a complete graph of order upsilon into m-cycles. The mu -way intersection problem for m-cycle systems involves taking mu systems, based on the same vertex set, and determining the possible number of cycles which can be common to all mu systems. General results for arbitrary m are obtained, and detailed intersection values for (mu, m) = (3, 4), (4, 5),(4, 6), (4, 7), (8, 8), (8, 9). (For the case (mu, m)= (2, m), see Billington (J. Combin. Des. 1 (1993) 435); for the case (Cc,m)=(3,3), see Milici and Quattrochi (Ars Combin. A 24 (1987) 175. (C) 2001 Elsevier Science B.V. All rights reserved.