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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]

It is well-known that the side length of a regular hexagon is half the length of its longest diagonals. From this property, one can easily see that for every positive integer m > 1 , any regular 6m-gon contains two non-congruent diagonals that are commensurable. In this paper, we show that if n is not a multiple of 6, then all pairs of diagonals of different lengths of a regular n-gon are incommensurable. This yields a characterization of regular n-gons whose pairs of diagonals are either congruent or incommensurable. The main result gives positive answers to some questions on this topic. [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]

In this article we will give a positive answer to a recent conjecture on orthic quadrilaterals: If a convex quadrilateral Q is cyclic and orthodiagonal, among all orthic quadrilaterals associated to Q the one of maximum area is Qpo, the principal orthic quadrilateral of Q. [ABSTRACT FROM AUTHOR]

This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which of course are ascendant [Stonehewer S.E., Permutable subgroups of infinite groups, Math. Z., 1972, 125(1), 1-16]. [ABSTRACT FROM AUTHOR]

A subgroup X of a group G is called pronormal-by-finite if there exists a pronormal subgroup Y of G such that Y ≤ X and | X : Y| is finite. The structure of (generalized) soluble groups in which all subgroups are pronormal-by-finite is investigated. Among other results, it is proved in particular that a finitely generated soluble group with such property is central-by-finite, provided that it has no infinite dihedral sections. [ABSTRACT FROM AUTHOR]

A group is called metahamiltonian if all its non-normal subgroups are abelian. The structure of metahamiltonian groups has been investigated by Romalis and Sesekin. In this paper groups are studied in which every non-normal subgroup has a transitive normality relation. [ABSTRACT FROM AUTHOR]

In semi-terrestrial crabs, the production of sounds has been recognized to be related to courtship communication dynamics. The present study aimed to assess if the crab Neohelice granulata (Varunidae) was able to emit acoustic signals and if they played a role in the crab's behaviour. We also assessed the locomotor behaviours to examine these parameters in different mating contexts of crabs. The study was divided into two different experimental conditions: 'solitary experiment' (consisting of three combination layouts with male, unreceptive and receptive females alone) and 'group experiment' (consisting of mixed combinations layouts of males, unreceptive, and receptive females). Synchronized acoustic and video monitoring systems were used to record the acoustic signals and locomotor behaviours of alone and grouped specimens. The greatest values of locomotor behavioural parameters were observed in layouts with receptive females alone and with 2 males plus 1 receptive female, probably related to courtship behaviour. N. granulata produced two distinct signals, a multi-pulse rasp signal (highest numbers were recorded in layouts with male alone and with 2 males plus 1 receptive female) and a single rasp signal. These results may suggest that males use the multi-rasp signal to advertise their presence to other males or to attract receptive females. [ABSTRACT FROM AUTHOR]