Some extremal functions in Fourier analysis, III

We obtain the best approximation in $L^1(\R)$, by entire functions of exponential type, for a class of even functions that includes $e^{-\lambda|x|}$, where $\lambda >0$, $\log |x|$ and $|x|^{\alpha}$, where $-1 < \alpha < 1$. We also give periodic versions of these results where the approximating functions are trigonometric polynomials of bounded degree.Comment: 26 pages. Submitte

A conceptual basis for surveying fouling communities at exposed and protected sites at sea: Feasible designs with exchangeable test bodies for in-situ biofouling collection

The enhanced inertia load caused by biofouling on device components, such as the foundations of wind turbines or other structures at sea, modifies the hydrodynamic properties, and increases the stress to structures, predominantly in upper water layers with high impact from wave dynamics. This compromises the stability, functioning, operation as well as the durability of these devices especially in exposed environments. A main challenge is the quantification of the impact of hydrodynamic forces on irregular bodies being overgrown by soft- and hard-bodied biofouling organisms. Therefore, test bodies from the upper 1–5 m water depth and thus exposed to the strongest wave actions close to the surface shall be overgrown by biofouling and used in measurement trials in a wave and current flume. These measurements shall shed light on the varying roughness and its influence on the load bearing capacity of foundation piles. Consequently, the main aims of the present work were the development of two independent test stations as holding devices for artificial test bodies for the collection of biofouling organisms during field studies: a carrying unit floating at the surface in an exposed area (System A) and a sampling device with access from a land-based facility (System B). Both systems are relatively easy to access, exhibit straightforward handling, and are reasonable cost-effective. A Test Body Support Unit (TBSU, System A) was designed and mounted on a spare buoy to carry the test bodies (cylinders), which serve as substrate for the fouling. The system was sufficiently robust to withstand several periods of rough sea conditions over the first two years. This system can only be accessed by vessels. System B (MareLift) provided the robustness and functionality needed for areas exhibiting harsh conditions but can be operated from land. The here used test bodies (steel panels) exhibited a sound basis for the monitoring of succession processes in the biofouling development. System B offered the possibility to analyse two habitats (intertidal and subtidal) and revealed clear differences in the composition and development of their fouling communities. Overall, both systems provide advantages in obtaining standardized biofouling samples compared to previous approaches. Such test stations play an important role in the risk management of marine sectors as they could help characterising biofouling communities over different geographical areas. System A and B provide a sound basis for biofouling research but potentially also for other potential research approaches in exposed areas as they provide space for future developments

Purple sulfur bacteria fix N-2 via molybdenum-nitrogenase in a low molybdenum Proterozoic ocean analogue

Biological N-2 fixation was key to the expansion of life on early Earth. The N-2-fixing microorganisms and the nitrogenase type used in the Proterozoic are unknown, although it has been proposed that the canonical molybdenum-nitrogenase was not used due to low molybdenum availability. We investigate N-2 fixation in Lake Cadagno, an analogue system to the sulfidic Proterozoic continental margins, using a combination of biogeochemical, molecular and single cell techniques. In Lake Cadagno, purple sulfur bacteria (PSB) are responsible for high N-2 fixation rates, to our knowledge providing the first direct evidence for PSB in situ N-2 fixation. Surprisingly, no alternative nitrogenases are detectable, and N-2 fixation is exclusively catalyzed by molybdenum-nitrogenase. Our results show that molybdenum-nitrogenase is functional at low molybdenum conditions in situ and that in contrast to previous beliefs, PSB may have driven N-2 fixation in the Proterozoic ocean. N-2 fixation was key to the expansion of life on Earth, but which organisms fixed N-2 and if Mo-nitrogenase was functional in the low Mo early ocean is unknown. Here, the authors show that purple sulfur bacteria fix N-2 using Mo-nitrogenase in a Proterozoic ocean analogue, despite low Mo conditions

The effects of concentration and salinity on polymer adsorption isotherm at sandstone rock surface

Adsorption of hydrolyzed polyacrylamide (HPAM) polymers on sandstone rock surface was studied by static adsorption experiments. Total of 10 Runs of static experiments were conducted in test tubes by mixing the desired solution with crushed rock sample, at temperature of 25 °C, and salinity range from 0-4 wt%. The results are in conformity with Langmuir's isotherm. Ten different isotherms were generated at each Run. The initial polymer concentration was varied from 0.3-2.1 g/l. The effects of salinity have been studied by observation on Langmuir adsorption coefficients (Y and K). The results show that the adsorption coefficient (Y) was found to have linear relationship with salinity. The adsorption coefficient (K) was found to be related to salinity by a quadratic relationship

Niche partitioning by photosynthetic plankton as a driver of CO2-fixation across the oligotrophic South Pacific Subtropical Ocean

Oligotrophic ocean gyre ecosystems may be expanding due to rising global temperatures [1-5]. Models predicting carbon flow through these changing ecosystems require accurate descriptions of phytoplankton communities and their metabolic activities [6]. We therefore measured distributions and activities of cyanobacteria and small photosynthetic eukaryotes throughout the euphotic zone on a zonal transect through the South Pacific Ocean, focusing on the ultraoligotrophic waters of the South Pacific Gyre (SPG). Bulk rates of CO2 fixation were low (0.1 mu mol Cl--(1) d(-1)) but pervasive throughout both the surface mixed-layer (upper 150 m), as well as the deep chlorophyll a maximum of the core SPG. Chloroplast 16S rRNA metabarcoding, and single-cell (CO2)-C-13 uptake experiments demonstrated niche differentiation among the small eukaryotes and picocyanobacteria. Prochlorococcus abundances, activity, and growth were more closely associated with the rims of the gyre. Small, fast-growing, photosynthetic eukaryotes, likely related to the Pelagophyceae, characterized the deep chlorophyll a maximum. In contrast, a slower growing population of photosynthetic eukaryotes, likely comprised of Dictyochophyceae and Chrysophyceae, dominated the mixed layer that contributed 65-88% of the areal CO2 fixation within the core SPG. Small photosynthetic eukaryotes may thus play an underappreciated role in CO2 fixation in the surface mixed-layer waters of ultraoligotrophic ecosystems

Crystalline iron oxides stimulate methanogenic benzoate degradation in marine sediment- derived enrichment cultures

Elevated dissolved iron concentrations in the methanic zone are typical geochemical signatures of rapidly accumulating marine sediments. These sediments are often characterized by co-burial of iron oxides with recalcitrant aromatic organic matter of terrigenous origin. Thus far, iron oxides are predicted to either impede organic matter degradation, aiding its preservation, or identified to enhance organic carbon oxidation via direct electron transfer. Here, we investigated the effect of various iron oxide phases with differing crystallinity (magnetite, hematite, and lepidocrocite) during microbial degradation of the aromatic model compound benzoate in methanic sediments. In slurry incubations with magnetite or hematite, concurrent iron reduction, and methanogenesis were stimulated during accelerated benzoate degradation with methanogenesis as the dominant electron sink. In contrast, with lepidocrocite, benzoate degradation, and methanogenesis were inhibited. These observations were reproducible in sediment-free enrichments, even after five successive transfers. Genes involved in the complete degradation of benzoate were identified in multiple metagenome assembled genomes. Four previously unknown benzoate degraders of the genera Thermincola (Peptococcaceae, Firmicutes), Dethiobacter (Syntrophomonadaceae, Firmicutes), Deltaproteobacteria bacteria SG8_13 (Desulfosarcinaceae, Deltaproteobacteria), and Melioribacter (Melioribacteraceae, Chlorobi) were identified from the marine sediment-derived enrichments. Scanning electron microscopy (SEM) and catalyzed reporter deposition fluorescence in situ hybridization (CARD-FISH) images showed the ability of microorganisms to colonize and concurrently reduce magnetite likely stimulated by the observed methanogenic benzoate degradation. These findings explain the possible contribution of organoclastic reduction of iron oxides to the elevated dissolved Fe2+ pool typically observed in methanic zones of rapidly accumulating coastal and continental margin sediments

First Results from a Broadband Search for Dark Photon Dark Matter in the 4444 to 52 μ52\,\mueV range with a coaxial dish antenna

We present first results from a dark photon dark matter search in the mass range from 44 to 52 $\mu{\rm eV}$ ($10.7 - 12.5\,{\rm GHz}$) using a room-temperature dish antenna setup called GigaBREAD. Dark photon dark matter converts to ordinary photons on a cylindrical metallic emission surface with area $0.5\,{\rm m}^2$ and is focused by a novel parabolic reflector onto a horn antenna. Signals are read out with a low-noise receiver system. A first data taking run with 24 days of data does not show evidence for dark photon dark matter in this mass range, excluding dark photon - photon mixing parameters $\chi \gtrsim 10^{-12}$ in this range at 90% confidence level. This surpasses existing constraints by about two orders of magnitude and is the most stringent bound on dark photons in this range below 49 $\mu$eV.Comment: 7 pages, 4 figure