The three-loop vacuum polarization function Π(q 2) induced by a massive quark is calculated. A comprehensive description of the method is presented. From the imaginary part the O(α 2 s) result for the production of heavy quarks R(s) = σ(e + e − → hadrons)/σ(e + e − → µ + µ −) can be extracted. Explicit formulae separated into the different colour factors are given.

1. Introduction. Let 6 be a class of real valued functions defined on an interval [a, b]. A set E is called stationary for Q provided any member of C which is constant on E must be constant on all of [a, b]. Several recent articles have been concerned with the problem of determining the stationary sets for various classes of functions [l], [2],

The two most commonly used topologies on R are the ordinary topology and the density topology. The ordinary topology is, of course, more widely known, and has the open intervals as its basic sets. The density topology, on the other hand, appears naturally in deeper studies of the structure of measurable sets. Its open sets are all measurable sets S ⊂ R which have the property that if x ∈ S, the...

We give a necessary condition for a meromorphic function in several variables to give rise to a Milnor fibration of the local link (respectively of the link at infinity). In the case of two variables we give some necessary and sufficient conditions for the local link (respectively the link at infinity) to be fibred.

Eigenspace models are a convenient way to represent sets of observations with widespread applications, including classification. In this paper we describe a new constructive method for incrementally adding observations to an eigenspace model. Our contribution is to explicitly account for a change in origin as well as a change in the number of eigenvectors needed in the basis set. No other metho...

This talk concerns when the complete graph on n vertices can be decomposed into d-dimensional cubes, where d is odd and n is even. (All other cases have been settled.) Necessary conditions are that n ≡ 1 (mod d) and n ≡ 0 (mod 2). These are known to be sufficient for d equal to 3 or 5, but for larger values of d a decomposition has been proven to exist for only sparce sets of n. We prove that f...