On approximations by trigonometric polynomials of classes of functions defined by moduli of smoothness

In this paper, we give a characterization of Nikol'ski\u{\i}-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to a such a class are given. In order to prove our results, we make use of certain recent reverse Copson- and Leindler-type inequalities.Comment: 18 pages. arXiv admin note: substantial text overlap with arXiv:1208.612

New species of Entomobryini from Russia and Armenia (Collembola, Entomobryomorpha)

This paper is part of the results of a systematic study of the specimens of Entomobrya and related genera from various European museums and other material obtained from private collections. Various new species from Russia and Armenia were identified: Entomobrya karasukensis n. sp., Entomobrya tuvinica n. sp., Entomobrya pseudolanuginosa n. sp., Entomobrya stebaevae n. sp., Entomobrya kuznetsovae n. sp., Entomobrya brinevi n. sp., Entomobrya primorica n. sp., Entomobrya kabardinica n. sp., Entomobrya taigicola n. sp., Entomobryoides sotoadamesi n. sp. and Prodrepanura altaica n. sp. from Russia, and Entomobrya armeniensis n. sp. from Armenia. For the identification and description of these species we used the set of characters proposed by Jordana and Baquero (2005)

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

On Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of Smoothness

In this paper, we give a characterization of Nikol'skiȋ-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to such a class are given. In order to prove our results, we make use of certain recent reverse Copson-type and Leindler-type inequalities

A nearly complete database on the records and ecology of the rarest boreal tiger moth from 1840s to 2020

Global environmental changes may cause dramatic insect declines but over century-long time series of certain species’ records are rarely available for scientific research. The Menetries’ Tiger Moth (Arctia menetriesii) appears to be the most enigmatic example among boreal insects. Although it occurs throughout the entire Eurasian taiga biome, it is so rare that less than 100 specimens were recorded since its original description in 1846. Here, we present the database, which contains nearly all available information on the species’ records collected from 1840s to 2020. The data on A. menetriesii records (N = 78) through geographic regions, environments, and different timeframes are compiled and unified. The database may serve as the basis for a wide array of future research such as the distribution modeling and predictions of range shifts under climate changes. It represents a unique example of a more than century-long dataset of distributional, ecological, and phenological data designed for an exceptionally rare but widespread boreal insect, which primarily occurs in hard-to-reach, uninhabited areas of Eurasia.Peer reviewe

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)