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In this article, we will show that for every choice of real numbers a 1 and a 2 , the set (loci) of solutions of all polynomials of the type x 3 + a 2 x 2 + a 1 x + d , where d ∈ R , can be characterized in terms of hyperbolas. Furthermore, relations between such hyperbolas and Steiner ellipses (inellipses and circumellipses) associated with cubics will be pointed out. [ABSTRACT FROM AUTHOR]

In this study, we used long-term passive acoustic monitoring (PAM) to improve knowledge about the use and spatiotemporal distribution of Erignathus barbatus vocalisations. Two autonomous passive acoustic recorders were deployed between August 2014 and July 2015 in the inner and outer parts of the Kongsfjorden (Svalbard Islands, Norway) resulting in 1728 h of data recorded and 17,220 vocalisations detected. We investigated the vocalisation occurrence with respect to the presence of ice in the fjord (sea ice and glacier iceberg) and to the light cycle. The vocalisation rate varied significantly daily and monthly, and a correlation to the light and darkness turnover was shown during the period between the end of February and the first part of April. Bearded seal vocalisations, which started on 12 February and ceased on 22 June, intensified with the ice coverage peak but also continued during ice retreat, coinciding with the mating season. Additionally, a spatial displacement was highlighted from the inner to the external part of Kongsfjorden in the second part of May corresponding to the disappearance of sea ice within the fjord. This study highlights the ability of PAM to be a useful tool for both understanding abiotic and biotic processes in the marine environment, and ultimately the potential interactions between them. [ABSTRACT FROM AUTHOR]