A STABLE METHOD FOR LINEAR EQUATION IN BANACH SPACES WITH SMOOTH NORMS

A stable method for numerical solution of a linear operator equation in reflexive Banach spaces is proposed. The operator and the right-hand side of the equation are assumed to be known approximately. The corresponding error levels may remain unknown. Approximate operators and their conjugate ones must possess the property of strong pointwise convergence. The exact normal solution is assumed to be sourcewise representable and some upper estimate for the norm of its source element must be known. The norm in the Banach space of solutions is supposed to satisfy the following smoothness-type condition: some function of the norm must be differentiable. Under these conditions a stability of the method with respect to nonuniform perturbations in operator is shown and the strong convergence to the normal solution is proved. A boundary control problem for the one-dimensional wave equation is considered as an example of possible application. The results of the model numerical experiments are presented

Widespread continental mtDNA lineages prevail in the bumblebee fauna of Iceland

Origins of the fauna in Iceland is controversial, although the majority of modern research supports the postglacial colonization of this island by terrestrial invertebrates rather than their long-term survival in glacial refugia. In this study, we use three bumblebee species as a model to test the hypothesis regarding possible cryptic refugia in Iceland and to evaluate a putative origin of recently introduced taxa. Bombus jonellus is thought to be a possible native Icelandic lineage, whereas B. lucorum and B. hortorum were evidently introduced in the second half of the 20th century. These phylogeographic analyses reveal that the Icelandic Bombus jonellus shares two COI lineages, one of which also occurs in populations on the British Isles and in mainland Europe, but a second lineage (BJ-02) has not been recorded anywhere. These results indicate that this species may have colonized Iceland two times and that the lineage BJ-02 may reflect a more ancient Late Pleistocene or Early Holocene founder event (e.g., from the British Isles). The Icelandic populations of both Bombus lucorum and B. hortorum share the COI lineages that were recorded as widespread throughout Eurasia, from the European countries across Russia to China and Japan. The findings presented here highlight that the bumblebee fauna of Iceland comprises mainly widespread ubiquitous lineages that arrived via natural or human-mediated dispersal events from the British Isles or the mainland

Inhibitors of chloride corrosion of reinforcement steel in concrete based on derivatives of salts of carboxylic acids and dimethylaminopropylamine

In our study, we synthesised derivatives of salts of carboxylic acids and dimethylaminopropylamine: 3-(dimethylamino)propyl-1-ammonium acetate, 3-(dimethylamino)propyl-1-ammonium hexanoate, 3-(dimethylamino)propyl-1-ammonium octanoate, and 3-(dimethylamino)propyl-1-ammonium terephthalate. The structures of the molecules of the obtained substances were confirmed using physical methods: Fourier-transform infrared spectroscopy, NMR spectroscopy, and HPLC. Electrochemical methods (voltammetry and electrochemical impedance spectroscopy) and quantum chemical modeling were used to assess the inhibitory effect of the synthesised substances with regard to 35GS reinforcement steel. Experiments were conducted in a water extract from a mortar simulating concrete pore solution in the presence of chlorides inducing pitting corrosion. 3-(dimethylamino)propyl-1-ammonium terephthalate is expected to have the highest degree of protection (up to 71%) at a concentration of 2.0 g·dm–3. The highest degree of protection for the derivatives with alkyl radicals is 41–46% in a range of concentrations from 0.5 to 2.0 g·dm-3. The results of potentiodynamic measurements and quantum chemical modeling were close. Average level of degree of protection can be explained by a high concentration of chlorides in the model solution (1.00 mol·dm–3). The effectiveness of the obtained substances is to be further studied using fine-grained concrete. This will help to assess the impact of the additives on the capillary pore structure (permeability) of concrete and the concentration of chloride

Bioerosion of siliceous rocks driven by rock-boring freshwater insects

Macrobioerosion of mineral substrates in fresh water is a little-known geological process. Two examples of rock-boring bivalve molluscs were recently described from freshwater environments. To the best of our knowledge, rock-boring freshwater insects were previously unknown. Here, we report on the discovery of insect larvae boring into submerged siltstone (aleurolite) rocks in tropical Asia. These larvae belong to a new mayfly species and perform their borings using enlarged mandibles. Their traces represent a horizontally oriented, tunnel-like macroboring with two apertures. To date, only three rock-boring animals are known to occur in fresh water globally: a mayfly, a piddock, and a shipworm. All the three species originated within primarily wood-boring clades, indicating a simplified evolutionary shift from wood to hardground substrate based on a set of morphological and anatomical preadaptations evolved in wood borers (e.g., massive larval mandibular tusks in mayflies and specific body, shell, and muscle structure in bivalves)

Globally invariant metabolism but density-diversity mismatch in springtails.

Soil life supports the functioning and biodiversity of terrestrial ecosystems. Springtails (Collembola) are among the most abundant soil arthropods regulating soil fertility and flow of energy through above- and belowground food webs. However, the global distribution of springtail diversity and density, and how these relate to energy fluxes remains unknown. Here, using a global dataset representing 2470 sites, we estimate the total soil springtail biomass at 27.5 megatons carbon, which is threefold higher than wild terrestrial vertebrates, and record peak densities up to 2 million individuals per square meter in the tundra. Despite a 20-fold biomass difference between the tundra and the tropics, springtail energy use (community metabolism) remains similar across the latitudinal gradient, owing to the changes in temperature with latitude. Neither springtail density nor community metabolism is predicted by local species richness, which is high in the tropics, but comparably high in some temperate forests and even tundra. Changes in springtail activity may emerge from latitudinal gradients in temperature, predation and resource limitation in soil communities. Contrasting relationships of biomass, diversity and activity of springtail communities with temperature suggest that climate warming will alter fundamental soil biodiversity metrics in different directions, potentially restructuring terrestrial food webs and affecting soil functioning

Global fine-resolution data on springtail abundance and community structure

Springtails (Collembola) inhabit soils from the Arctic to the Antarctic and comprise an estimated ~32% of all terrestrial arthropods on Earth. Here, we present a global, spatially-explicit database on springtail communities that includes 249,912 occurrences from 44,999 samples and 2,990 sites. These data are mainly raw sample-level records at the species level collected predominantly from private archives of the authors that were quality-controlled and taxonomically-standardised. Despite covering all continents, most of the sample-level data come from the European continent (82.5% of all samples) and represent four habitats: woodlands (57.4%), grasslands (14.0%), agrosystems (13.7%) and scrublands (9.0%). We included sampling by soil layers, and across seasons and years, representing temporal and spatial within-site variation in springtail communities. We also provided data use and sharing guidelines and R code to facilitate the use of the database by other researchers. This data paper describes a static version of the database at the publication date, but the database will be further expanded to include underrepresented regions and linked with trait data.</p

Effects of miniaturization in the anatomy of the minute springtail Mesaphorura sylvatica (Hexapoda: Collembola: Tullbergiidae)

Smaller animals display pecular characteristics related to their small body size, and miniaturization has recently been intensely studied in insects, but not in other arthropods. Collembola, or springtails, are abundant soil microarthropods and form one of the four basal groups of hexapods. Many of them are notably smaller than 1 mm long, which makes them a good model for studying miniaturization effects in arthropods. In this study we analyze for the first time the anatomy of the minute springtail Mesaphorura sylvatica (body length 400 µm). It is described using light and scanning electron microscopy and 3D computer reconstruction. Possible effects of miniaturization are revealed based on a comparative analysis of data from this study and from studies on the anatomy of larger collembolans. Despite the extremely small size of M. sylvatica, some organ systems, e.g., muscular and digestive, remain complex. On the other hand, the nervous system displays considerable changes. The brain has two pairs of apertures with three pairs of muscles running through them, and all ganglia are shifted posteriad by one segment. The relative volumes of the skeleton, brain, and musculature are smaller than those of most microinsects, while the relative volumes of other systems are greater than or the same as in most microinsects. Comparison of the effects of miniaturization in collembolans with those of insects has shown that most of the miniaturization-related features of M. sylvatica have also been found in microinsects (shift of the brain into the prothorax, absent heart, absence of midgut musculature, etc.), but also has revealed unique features (brain with two apertures and three pairs of muscles going through them), which have not been described before

A New Family of Vinyl Selenocyanates with the Amide Function Based on the Reaction of Potassium Selenocyanate with 3-Trimethylsilyl-2-Propynamides

An efficient approach to a novel family of (Z)-3-amino-3-oxo-1-propenyl selenocyanates was developed based on the reaction of KSeCN with 3-trimethylsilyl-2-propynamides in the presence of ammonium chloride in methanol. The reaction was accompanied by a desilylation process. The products were not formed under the same reaction conditions in the absence of ammonium chloride, which was used for the first time in the reactions of selenocyanates with acetylenes. The use of this new methodology allowed the reaction to carry out in a regio- and stereoselective fashion as anti-addition affording vinyl selenocyanates with a (Z)-configuration in high yields