18 research outputs found
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
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
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
Global fine-resolution data on springtail abundance and community structure
CODE AVAILABILITY : Programming R code is openly available together with the database from Figshare.SUPPLEMENTARY MATERIAL 1 : Template for data collectionSUPPLEMENTARY MATERIAL 2 : Data Descriptor WorksheetSpringtails (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.Open Access funding enabled and organized by Projekt DEAL.http://www.nature.com/sdatahj2024Plant Production and Soil ScienceSDG-15:Life on lan