No abstract

Two or more bilateral Laplace transforms with a complex argument “s” may be equal in a finite vertical interval when, in fact, the transforms correspond to different functions. In this article, we prove that the existence of a bilateral Laplace transform in any finite horizontal interval uniquely determines the corresponding function. The result appears to be new as we could not find it in the literature. The novelty of the result is that the interval need not contain zero, the function need not be nonnegative and need not be integrable. The result has a potential to be useful in the context of fitting probability distributions to data using Laplace transforms or moment generating functions.

Previous observations in the St Lawrence Estuary (eastern Canada) suggested that larvae of intertidal barnacles (Semibalanus balanoides) would settle almost exclusively inside crevices on shores that are scoured by sea ice every winter. It was suggested that the strong ice scour in winter on that coast (which removes organisms outside of crevices) would select for such a larval behaviour. We tested the generality of this pattern by sampling other ice-scoured shores within the Gulf of St Lawrence system. In particular, we surveyed a shore in Nova Scotia where exposed habitats (subjected to strong ice scour in winter) are interspersed with sheltered habitats (which suffer milder ice scour). Such a topographical complexity might allow for the coastal larval pool to contain a proportion of larvae that have no particular settlement preference for crevices, as selective pressures for such a behaviour would be minimal in ice-sheltered habitats. Consistently with this notion, barnacle recruits (which appear after the winter ice melts) occurred abundantly both inside and outside of crevices across the shore in the spring seasons of 2005 and 2006. Average recruit density on rocky surfaces ranged between 337 and 588 recruits dm−2, depending on the habitat. It is therefore possible that barnacle recruitment patterns on ice-scoured shores may be affected indirectly by the structural complexity of the coast.

No abstract

It is established that if a time series satisfies the Berman condition, and another related (summability) condition, the result of filtering that series through a certain type of filter also satisfies the two conditions. In particular it follows that if Xt satisfies the two conditions and if Xt and at are related by an invertible ARMA model, then the at satisfy the two conditions.