Extensive Monte-Carlo simulations were performed to study bond percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered cubic (b.c.c.) lattices, using an epidemic kind of approach. These simulations provide very precise values of the critical thresholds for each of the lattices: pc(s.c.) = 0.248 812 6 ± 0.000 000 5, pc(f.c.c.) = 0.120 163 5 ± 0.000 001 0, and pc(b...

In this paper we give an infinite class of finite simple right Bol loops of exponent 2. The right multiplication group of these loops is an extension of an elementary Abelian 2-group by S5. The construction uses the description of the structure of such loops given by M. Aschbacher (2005). These results answer some questions of M. Aschbacher.

In many applications in engineering and science, it is important to know whether the response of a nonlinear system is chaotic. This characterization is possible by the evaluation of the one-dimensional Lyapunov characteristic exponent (LCE). In this paper, a numerical procedure to calculate the LCE of continuous systems discretized using finite element methods is presented.

We show that finite fields over which there is a curve of a given genus g ≥ 1 with its Jacobian having a small exponent, are very rare. This extends a recent result of W. Duke in the case g = 1. We also show when g = 1 or g = 2 that our bounds are best possible.

We survey properties of the set of possible exponents of subsets of Zn (equivalently, exponents of primitive circulant digraphs on n vertices). Let En denote this exponent set. We point out that En contains the positive integers up to √ n, the ‘large’ exponents ⌊ 3 ⌋+1, ⌊ 2 ⌋, n−1, and for even n ≥ 4, the additional value n 2 −1. It is easy to see that no exponent in [n 2 +1, n−2] is possible, ...