Benthic Foraminiferal Assemblages in a Restricted Environment - An Example from the Mljet Lakes (Adriatic Sea, Croatia)

Benthic foraminiferal assemblages from a peculiar restricted marine environment, the Mljet Lakes (Mljet Island, Adriatic Sea, Croatia) have been studied. These lakes are drowned karst dolines, which are connected with the Adriatic Sea through a narrow, shallow channel. Occasional stagnant conditions in the marine lakes cause hypoxic and anoxic conditions in the bottom waters. Such stressed conditions are reflected in oligospecific benthic foraminiferal assemblages with a Shannon-Wiener species diversity index (H) ranging from 0.8 to 1.0 and equitability index (E) ranging from 0.18 to 0.26, identified in samples from each marine lake. In the more dysoxic Malo Jezero, Haynesina depressula dominates an assemblage of 12 benthic foraminiferal species. In the less (and less frequently) hypoxic Veliko Jezero, we found an Asterigerinata mamilla assemblage with 18 foraminiferal species. A more diverse assemblage containing 55 different benthic foraminiferal species occupies an adjacent open-sea station. Long-term salinity measurements indicate that H. depressula tolerates higher salinity than formerly presumed (up to 38‰), and is well adapted to stressed hypoxic conditions

Reducible means and reducible inequalities

It is well-known that if a real valued function acting on a convex set satisfies the $n$-variable Jensen inequality, for some natural number $n\geq 2$, then, for all $k\in\{1,\dots, n\}$, it fulfills the $k$-variable Jensen inequality as well. In other words, the arithmetic mean and the Jensen inequality (as a convexity property) are both reducible. Motivated by this phenomenon, we investigate this property concerning more general means and convexity notions. We introduce a wide class of means which generalize the well-known means for arbitrary linear spaces and enjoy a so-called reducibility property. Finally, we give a sufficient condition for the reducibility of the $(M,N)$-convexity property of functions and also for H\"older--Minkowski type inequalities