We propose a M(atrix) model for N = 4 SU(k) Super-Yang-Mills theory compactified on T 4. In this model it is possible to make T 4 noncommutative and it is easy to turn on all 6 components of the noncommutativity on T 4. The action of S-duality on the noncommutativity parameters is also manifest. The M(atrix)-model is given by the large N limit of a σ-model on T 2 whose target space is the modul...

Introduction. If £ is a group with a normal subgroup K one may form the quotient group E/K^M. Conversely, for preassigned groups K, M, there is the extension problem: to determine (in some sense) all groups E with K as normal subgroup such that E/K^M. Much progress has been made on this problem, particularly through the work of Baer [l, 2, 3] and the cohomology theory of Eilenberg and MacLane [...

Let fb k (n)g 1 n=0 be the Bell numbers of order k. It is proved that the sequence fb k (n)=n!g 1 n=0 is log-concave and the sequence fb k (n)g 1 n=0 is log-convex, or equivalently, the following inequalities hold for all n 0, 1 b k (n + 2)b k (n) b k (n + 1) 2 n + 2 n + 1 : Let f(n)g 1 n=0 be a sequence of positive numbers with (0) = 1. We show that if f(n)g 1 n=0 is log-convex, then (n)(m) (n...