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In this article we will use some special triangles, to construct polygonal chains that describe the families of logarithmic spirals, among which are the celebrated Golden Spiral, Spira solaris and Pheidia Spiral. [ABSTRACT FROM AUTHOR]

Abstract: A group is called extended residually finite (ERF) if every subgroup is closed in the profinite topology. The ERF-property is studied for nilpotent groups, soluble groups, locally finite groups and FC-groups. A complete characterization is given of FC-groups which are ERF. [Copyright &y& Elsevier]

This study examined the effects of lab-generated acoustic signals on the behaviour and biochemistry of Mediterranean mussels ( Mytilus galloprovincialis ). The experiment was carried out in a tank equipped with a video-recording system using six groups of five mussels exposed to five acoustic treatments (each treatment was replicated three times) for 30 min. The acoustic signals, with a maximum sound pressure level of 150 dB rms re 1 μPa, differed in frequency range as follows: low (0.1–5 kHz), mid-low (5–10 kHz), mid (10–20 kHz), mid-high (20–40 kHz) and high (40–60 kHz). The exposure to sweeps did not produce any significant changes in the mussels' behaviour. Conversely, the specimens exposed to the low frequency band treatment showed significantly higher values of the following biochemical stress parameters measured in their plasma and tissues: glucose, total proteins, total haemocyte number (THC), heat shock protein 70 (Hsp70) expression, and Acetylcholinesterase (AChE) activity. The responses observed in the mussels exposed to low frequency sweeps enable us to suppose a biological and ecological role for this sound, which contains the main frequencies produced by both shipping traffic and the acoustic emissions of fish. [ABSTRACT FROM AUTHOR]

This study examined the effects of recorded boat noises on the behaviour and biochemistry of the common prawn ( Palaemon serratus ) in laboratory settings. The experiment was carried out in a tank equipped with a video-recording system using six groups (three control and three tested) of eight common prawns (48 animals in total). After habituation for 1 h, the behaviour of the prawns was monitored for 1 h. During the last 30 min, the animals in the test groups were exposed to noise resembling a marine area with high anthropogenic acoustic pollution. The exposure to noise produced significant changes in locomotor patterns, presence inside or outside a shelter, total protein concentrations in the haemolymph and brain, DNA integrity, and the expression protein levels of HSP 27 and 70 in brain tissues, revealing a stressful effect of noise on this crustacean species. This study clearly reveals that invertebrates are likely to be susceptible to acoustic stimuli from boat's noise and that they are potential valuable targets for further and detailed investigations into the effects of the anthropogenic noise pollution. [ABSTRACT FROM AUTHOR]