Z-Pencils

The matrix pencil (A,B) = {tB-A | t \in C} is considered under the assumptions that A is entrywise nonnegative and B-A is a nonsingular M-matrix. As t varies in [0,1], the Z-matrices tB-A are partitioned into the sets L_s introduced by Fiedler and Markham. As no combinatorial structure of B is assumed here, this partition generalizes some of their work where B=I. Based on the union of the directed graphs of A and B, the combinatorial structure of nonnegative eigenvectors associated with the largest eigenvalue of (A,B) in [0,1) is considered.Comment: 8 pages, LaTe

Z' Physics

The limits on extra neutral gauge bosons, which could be reached at LEP2, are reviewed. Exclusion and discovery limits are discussed for f\bar f and WW production.Comment: 20 pages Latex, 7 figures included by epsfig, Contribution to the Proceedings the workshop "Physics at LEP2", Geneva, 199

Elliptic curves with torsion group Z/6Z\Z /6\Z

We exhibit several families of elliptic curves with torsion group isomorphic to $\Z/6\Z$ and generic rank at least $3$. Families of this kind have been constructed previously by several authors: Lecacheux, Kihara, Eroshkin and Woo. We mention the details of some of them and we add other examples developed more recently by Dujella and Peral, and MacLeod. Then we apply an algorithm of Gusi\'c and Tadi\'c and we find the exact rank over \Q(t) to be 3 and we also determine free generators of the Mordell-Weil group for each family. By suitable specializations, we obtain the known and new examples of curves over \Q with torsion $\Z/6\Z$ and rank $8$, which is the current record