On the existence of exponential polynomials with prefixed gaps

This paper shows that the conjecture of Lapidus and Van Frankenhuysen on the set of dimensions of fractality associated with a nonlattice fractal string is true in the important special case of a generic nonlattice self-similar string, but in general is false. The proof and the counterexample of this have been given by virtue of a result on exponential polynomials P(z), with real frequencies linearly independent over the rationals, that establishes a bound for the number of gaps of RP, the closure of the set of the real projections of its zeros, and the reason for which these gaps are produced.

Aggregation dynamics and foraging behaviour of striped red mullet Mullus surmuletus in the western Mediterranean Sea

Habitat-related heterogeneity of striped red mullet Mullus surmuletus heterospecific foraging assemblages was examined off the coast of Spain. Video-based focal-follows conducted on 122 M. surmuletus assemblages (446 total individuals) revealed an array of attendant species (n = 7) with composition linked to benthic habitat complexity; bare sandy substrata were characterized by homospecific groups of M. surmuletus, while habitats with rock and vegetation attracted a variety of scrounging labrids and sparids. Although the nature of the relationship between M. surmuletus and attendants requires further exploration, the present study indicates that substratum composition can be a driving factor explaining the dynamics of this heterospecific assemblage.