A forgotten little chapter on isoperimetric inequalities. On the fraction of a convex and closed plane area lying outside a circle with which it shares a diameter

[EN]Often some interesting or simply curious points are left out when developing a theory. It seems that one of them is the existence of an upper bound for the fraction of area of a convex and closed plane area lying outside a circle with which it shares a diameter, a problem stemming from the theory of isoperimetric inequalities. In this paper such a bound is constructed and shown to be attained for a particular area. It is also shown that convexity is a necessary condition in order to avoid the whole area lying outside the circle

Eruptive history of the Krakatau volcanic complex, Indonesia

[EN] The 1883 eruption of Krakatau is one of the best known volcanic events in the world, although it was not the largest, nor the deadliest of known eruptions. However, the eruption happened in a critical moment (just after the first global telegraph network was established) and in a strategic place (the Sunda Straits were a naval traffic hot spot at that time). The lecture will explore these events in some detail before presenting an outline on ongoing multidisciplinary efforts to unravel the past and present day plumbing systems of the 1883 eruption and that of the active Anak Krakatau cone. A mid- and a lower-crustal magma storage level exist beneath the volcano, placing significant emphasis on magma-crust interaction in the uppermost, sediment-rich crust. This final aspect shares similarities with the 2011/2012 El Hierro eruption, highlighting the relevance of the interaction between ascending magmas and marine deposits that oceanic magmas have to pass. At Krakatau, shallow-level crustal contamination offers a possible explanation for the explosive nature of the 1883 eruption and also for those of the presently active Anak Krakatau edifice and helps constrain location, style and processes of subvolcanic magma storage.

Taxonomic status and origin of the shrews (soricidae) from the canary islands inferred from a mtdna comparison with the european crocidura species

[EN] European island shrews are either relicts of the endemic Pleistocene fauna, e.g., Crocidura zimmermanni, or were introduced from continental source populations. In order to clarify the taxonomic status and the origin of the two shrew species from the Canary Islands, a 981 bp fragment of cytochrome b gene was investigated in all European Crocidura species and compared with the Canary shrew (Crocidura canariensis) and the Osorio shrew (Crocidura osorio). The first shares its karyotype with the Sicilian shrew Crocidura sicula (2N = 36), the second with the Greater white-toothed shrew Crocidura russula (2N = 42), suggesting possible sister species relationships.