Gaussian Subordination for the Beurling-Selberg Extremal Problem

We determine extremal entire functions for the problem of majorizing, minorizing, and approximating the Gaussian function $e^{-\pi\lambda x^2}$ by entire functions of exponential type. This leads to the solution of analogous extremal problems for a wide class of even functions that includes most of the previously known examples (for instance \cite{CV2}, \cite{CV3}, \cite{GV} and \cite{Lit}), plus a variety of new interesting functions such as $|x|^{\alpha}$ for $-1 < \alpha$; \,$\log \,\bigl((x^2 + \alpha^2)/(x^2 + \beta^2)\bigr)$, for $0 \leq \alpha < \beta$;\, $\log\bigl(x^2 + \alpha^2\bigr)$; and $x^{2n} \log x^2$\,, for $n \in \N$. Further applications to number theory include optimal approximations of theta functions by trigonometric polynomials and optimal bounds for certain Hilbert-type inequalities related to the discrete Hardy-Littlewood-Sobolev inequality in dimension one

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

Conspicuous Smooth and White Egg-Shaped Sulfur Structures on a Deep-Sea Hydrothermal Vent Formed by Sulfide-Oxidizing Bacteria

Conspicuous egg-shaped, white, and smooth structures were observed at a hydrothermal vent site in the Guaymas Basin, Gulf of California. The gelatinous structures decomposed within hours after sampling. Scanning electron microscopy (SEM) and light microscopy showed that the structure consisted of filaments of less than 0.1 mm thickness, similar to those observed for "Candidatus Arcobacter sulfidicus." SEM-energy-dispersive X-ray spectroscopy (EDS) showed that the filaments were sulfur rich. According to 16S rRNA gene amplicon and fluorescence in situ hybridization (FISH) analyses, Arcobacter, a sulfide oxidizer that is known to produce filamentous elemental sulfur, was among the dominant species in the structure and was likely responsible for its formation. Arcobacter normally produces woolly snowflake like structures in opposed gradients of sulfide and oxygen. In the laboratory, we observed sulfide consumption in the anoxic zone of the structure, suggesting an anaerobic conversion. The sulfide oxidation and decomposition of the structure in the laboratory may be explained by dissolution of the sulfur filaments by reaction with sulfide under formation of polysulfides. IMPORTANCE At the deep-sea Guaymas Basin hydrothermal vent system, sulfide-rich hydrothermal fluids mix with oxygenated seawater, thereby providing a habitat for microbial sulfur oxidation. Microbial sulfur oxidation in the deep sea involves a variety of organisms and processes and can result in the excretion of elemental sulfur. Here, we report on conspicuous white and smooth gelatinous structures found on hot vents. These strange egg-shaped structures were often observed on previous occasions in the Guaymas Basin, but their composition and formation process were unknown. Our data suggest that the notable and highly ephemeral structure was likely formed by the well-known sulfide-oxidizing Arcobacter. While normally Arcobacter produces loose flocs or woolly layers, here smooth gel-like structures were found

The rate and fate of N-2 and C fixation by marine diatom-diazotroph symbioses

N-2 fixation constitutes an important new nitrogen source in the open sea. One group of filamentous N-2 fixing cyanobacteria (Richelia intracellularis, hereafter Richelia) form symbiosis with a few genera of diatoms. High rates of N-2 fixation and carbon (C) fixation have been measured in the presence of diatom-Richelia symbioses. However, it is unknown how partners coordinate C fixation and how the symbiont sustains high rates of N-2 fixation. Here, both the N-2 and C fixation in wild diatom-Richelia populations are reported. Inhibitor experiments designed to inhibit host photosynthesis, resulted in lower estimated growth and depressed C and N-2 fixation, suggesting that despite the symbionts ability to fix their own C, they must still rely on their respective hosts for C. Single cell analysis indicated that up to 22% of assimilated C in the symbiont is derived from the host, whereas 78-91% of the host N is supplied from their symbionts. A size-dependent relationship is identified where larger cells have higher N-2 and C fixation, and only N-2 fixation was light dependent. Using the single cell measures, the N-rich phycosphere surrounding these symbioses was estimated and contributes directly and rapidly to the surface ocean rather than the mesopelagic, even at high estimated sinking velocities (<10 m d(-1)). Several eco-physiological parameters necessary for incorporating symbiotic N-2 fixing populations into larger basin scale biogeochemical models (i.e., N and C cycles) are provided

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

Nitrate respiration and diel migration patterns of diatoms are linked in sediments underneath a microbial mat

Diatoms are among the few eukaryotes known to store nitrate (NO3−) and to use it as an electron acceptor for respiration in the absence of light and O2. Using microscopy and 15N stable isotope incubations, we studied the relationship between dissimilatory nitrate/nitrite reduction to ammonium (DNRA) and diel vertical migration of diatoms in phototrophic microbial mats and the underlying sediment of a sinkhole in Lake Huron (USA). We found that the diatoms rapidly accumulated NO3− at the mat-water interface in the afternoon and 40% of the population migrated deep into the sediment, where they were exposed to dark and anoxic conditions for ~75% of the day. The vertical distribution of DNRA rates and diatom abundance maxima coincided, suggesting that DNRA was the main energy generating metabolism of the diatom population. We conclude that the illuminated redox-dynamic ecosystem selects for migratory diatoms that can store nitrate for respiration in the absence of light. A major implication of this study is that the dominance of DNRA over denitrification is not explained by kinetics or thermodynamics. Rather, the dynamic conditions select for migratory diatoms that perform DNRA and can outcompete sessile denitrifiers

The NY-Ålesund TurbulencE Fiber Optic eXperiment (NYTEFOX): investigating the Arctic boundary layer, Svalbard

The NY-Ålesund TurbulencE Fiber Optic eXperiment (NYTEFOX) was a field experiment at the Ny-Ålesund Arctic site (78.9◦ N, 11.9◦ E) and yielded a unique meteorological data set. These data describe the distribution of heat, airflows, and exchange in the Arctic boundary layer for a period of 14 d from 26 February to 10 March 2020. NYTEFOX is the first field experiment to investigate the heterogeneity of airflow and its transport of temperature, wind, and kinetic energy in the Arctic environment using the fiber-optic distributed sensing (FODS) technique for horizontal and vertical observations. FODS air temperature and wind speed were observed at a spatial resolution of 0.127 m and a temporal resolution of 9 s along a 700 m horizontal array at 1 m above ground level (a.g.l.) and along three 7 m vertical profiles. Ancillary data were collected from three sonic anemometers and an acoustic profiler (minisodar; sodar is an acronym for “sound detection and ranging”) yielding turbulent flow statistics and vertical profiles in the lowest 300 m a.g.l., respectively. The observations from this field campaign are publicly available on Zenodo (https://doi.org/10.5281/zenodo.4756836, Huss et al., 2021) and supplement the meteorological data set operationally collected by the Baseline Surface Radiation Network (BSRN) at Ny-Ålesund, Svalbard

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