No Silver Grievance Exists

Nursing a Grievance

Bhopal: No Silver Linings

In the November 2003 issue of EHP, Liu et al. (2003) concluded that " relatively low concentrations of gaseous air pollutants are associated with adverse effects on birth outcomes. " Although this may be true from a purely statistical sense, there appear to be limitations of this research that suggest cautious interpretation of the findings. Liu et al. (2003) evaluated individual-level birth ce...

There exists no Steiner system S(4, 5, 17)

If a Steiner system S(4, 5, 17) exists, it would contain derived S(3, 4, 16) designs. By relying on a recent classification of the S(3, 4, 16), an exhaustive computer search for S(4, 5, 17) is carried out. The search shows that no S(4, 5, 17) exists, thereby ruling out the existence of Steiner systems S(t, t+ 1, t+ 13) for t ≥ 4.

There Exists No Ultimate Solution to Skorokhod ’ S Problem

Let (X,Y) be a mean zero martingale pair, i.e., X and Y possess mean zero and E(YIX) = X a.s.. It has been proved in various ways that (1) there exist stopping times T on Brownian motion {B(t); such that B(T) is distributed like X and is uniformly integrable; and (2) for any such t there exist stopping times i’ such that T I’ a.s., (B(T), B(I’)) is distributed like (X,Y) and {B(tAT’); is unifor...

There exists no self-dual [24,12,10] code over F5

Self-dual codes over F5 exist for all even lengths. The smallest length for which the largest minimum weight among self-dual codes has not been determined is 24, and the largest minimum weight is either 9 or 10. In this note, we show that there exists no self-dual [24, 12, 10] code over F5, using the classification of 24-dimensional odd unimodular lattices due to Borcherds.