Subsets of finite groups exhibiting additive regularity

In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In particular, we show that any sum set must exhibit higher-order regularity and that an abelian sum set is necessarily a reversible difference set. We next develop several general construction techniques under the hypothesis that the over-riding group contains a normal subgroup of order 2. Finally, by exploiting properties of dihedral groups and Frobenius groups, several infinite classes of sum sets and partial sum sets are introduced

Unmarried fertility, crime, and cocial stigma

Children born to unmarried parents may receive lower human capital investments in youth, leading to higher levels of criminal activity as adults. Therefore, unmarried fertility may be positively associated with future crime. On the other hand, in an environment in which social stigma attached to non-marital fertility is high, many low match quality parents will choose (or be forced) to marry, and children reared in these families may actually be worse off than had their parents not married. We explore these effects empirically, finding that over the long run, unmarried fertility is positively associated with murder and property crime, but that the degree of social stigma has affected this relationship. For instance, our results suggest that some marriages in the 1940s and 1950s were of such low quality that the children involved would have been better off in single-parent households; however, this finding is reversed for marriages in the 1960s and thereafter – many marriages that would have benefited children have since been foregone. We also discuss implications for the debate over the “abortion-crime” link of Donohue and Levitt (2001).unmarried fertility; abortion; future crime; social stigma

Lunar fiberglass: Properties and process design

A Clemson University ceramic engineering design for a lunar fiberglass plant is presented. The properties of glass fibers and metal-matrix composites are examined. Lunar geology is also discussed. A raw material and site are selected based on this information. A detailed plant design is presented, and summer experiments to be carried out at Johnson Space Center are reviewed