Module approximate amenability of Banach algebras

Abstract. In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same properties. It is also shown that module uniform approximate (contractibility) amenability and module (contractibility, respectively) amenability for commutative Banach modules are equivalent. Applying these results to 1 (S) as an 1 (E)-module, for an inverse semigroup S with the set of idempotents E, it is shown that 1 (S) is module approximately amenable (contractible) if and only if it is module uniformly approximately amenable if and only if S is amenable. Moreover, 1 (S) * * is module (uniformly) approximately amenable if and only if a maximal group homomorphic image of S is finite

Microplastics in agricultural soils from a semi-arid region and their transport by wind erosion.

Despite the importance of agricultural soils, little is known about the fate of microplastics (MPs) in this environment. In the present study, MPs have been determined in soils and wind-eroded sediments from two vegetable-growing fields in the Fars province of Iran, one using plastic mulch for water retention (Field 1) and the other using wastewater for irrigation (Field 2). MPs were heterogeneously distributed in the surface (0-5 cm) and subsurface (5-15 cm) soils of both fields, with a maximum concentration overall of about 1.1 MP g-1 and no significant differences in concentrations between either fields or depths. Fibres represented the principal shape of MPs, but spherules, presumably from wastewater, also made a significant (∼25%) contribution to MPs in Field 2. Analysis of selected samples by Raman spectroscopy and scanning electron microscopy revealed that polyethylene terephthalate (PET) and nylon were the most abundant polymers and that MPs exhibited varying degrees of weathering. Concentrations of MPs in this study are within the range reported previously for agricultural soils, although the absence of PET observed in earlier studies is attributed to the use of insufficiently dense solutions to isolate plastics. Deployment of a portable wind tunnel revealed threshold wind velocities for soil erosion of up to 7 and 12 m s-1 and MP erosion rates up to about 0.4 and 1.1 MP m-2 s-1 for Fields 1 and 2, respectively. Erosion rates are considerably greater than published depositional rates for MPs and suggest that agricultural soils act as both a temporary sink and dynamic secondary source of MPs that should be considered in risk assessments and global transport budgets

Microplastics captured by snowfall: A study in Northern Iran.

Samples of fresh snow (n = 34) have been collected from 29 locations in various urban and remote regions of northern Iran following a period of sustained snowfall and the thawed contents examined for microplastics (MPs) according to established techniques. MP concentrations ranged from undetected to 86 MP L-1 (mean and median concentrations ~20 MP and 12 MP L-1, respectively) and there was no significant difference in MP concentration between sample location type or between different depths of snow (or time of deposition) sampled at selected sites. Fibres were the dominant shape of MP and μ-Raman spectroscopy of selected samples revealed a variety of polymer types, with nylon most abundant. Scanning electron microscopy coupled with energy-dispersive X-ray analysis showed that some MPs were smooth and unweathered while others were more irregular and exhibited significant photo-oxidative and mechanical weathering as well as contamination by extraneous geogenic particles. These characteristics reflect the importance of both local and distal sources to the heterogeneous pool of MPs in precipitated snow. The mean and median concentrations of MPs in the snow samples were not dissimilar to the published mean and median concentrations for MPs in rainfall collected from an elevated location in southwest Iran. However, compared with rainfall, MPs in snow appear to be larger and more diverse in their shape and composition (and include rubber particulates), possibly because of the greater size but lower terminal velocities of snowflakes relative to raindrops. Snowfall represents a significant means by which MPs are scavenged from the atmosphere and transferred to soil and surface waters that warrants further attention