In post-Classical Greek, declarative infinitive clauses (DInf) frequently contain a Perfect Infinitive (Pf. Inf.). According to Mandilaras (1973: p. 329), this is the most common form of DInf in Greek non-literary papyri. On the other hand, Rijksbaron (2006: p. 98) claims that such clauses were uncommon in earlier periods. It has been suggested that the spread of this construction is a result of intensified contacts between speakers of Latin and Greek, which is a hypothesis going back to Harry (1906: p. 69). Focusing on DInf containing the Pf. Inf. ἐσχηκέναι, this paper examines the Latin-contact hypothesis, as well as the hypothesis that the spread of this construction is an independent development of Ancient Greek (AG). It is claimed that the phenomenon can be accounted for in terms of independent development of AG. However, there is also evidence suggesting that some uses of the construction investigated were more acceptable for bilingual authors such as Polybius than for authors that had no significant contact with Latin.
An abelian $*$-semigroup $S$ is perfect (resp. Stieltjes perfect) if every positive definite (resp. completely so) function on $S$ admits a unique disintegration as an integral of hermitian multiplicative functions (resp. nonnegative such). We prove that every Stieltjes perfect semigroup is perfect. The converse has been known for semigroups with neutral element, but is here shown to be not true in general. We prove that an abelian $*$-semigroup $S$ is perfect if for each $s \in S$ there exist $t\in S$ and $m,n\in \mathbb{N}_0$ such that $m+n\ge 2$ and $s+s^ *=s^*+mt+nt^*$. This was known only with $s=mt+nt^*$ instead. The equality cannot be replaced by $s+s^*+s=s+s^*+mt+nt^*$ in general, but for semigroups with neutral element it can be replaced by $s+p(s+s^*)=p(s+s^*)+ mt+nt^*$ for arbitrary $p\in \mathbb{N}$ (allowed to depend on $s$).