On some properties of solutions of transonic potential flow problems

summary:The paper deals with solutions of transonic potential flow problems handled in the weak form or as variational inequalities. Using suitable generalized methods, which are well known for elliptic partial differential equations of the second order, some properties of these solutions are derived. A maximum principle, a comparison principle and some conclusions from both ones can be established

Rigid spheres in Riemannian spaces

Choice of an appropriate (3+1)-foliation of spacetime or a (2+1)-foliation of the Cauchy space, leads often to a substantial simplification of various mathematical problems in General Relativity Theory. We propose a new method to construct such foliations. For this purpose we define a special family of topological two-spheres, which we call "rigid spheres". We prove that there is a four-parameter family of rigid spheres in a generic Riemannian three-manifold (in case of the flat Euclidean three-space these four parameters are: 3 coordinates of the center and the radius of the sphere). The rigid spheres can be used as building blocks for various ("spherical", "bispherical" etc.) foliations of the Cauchy space. This way a supertranslation ambiguity may be avoided. Generalization to the full 4D case is discussed. Our results generalize both the Huang foliations (cf. \cite{LHH}) and the foliations used by us (cf. \cite{JKL}) in the analysis of the two-body problem.Comment: 23 page

Ubiquitous Presence and Novel Diversity of Anaerobic Alkane Degraders in Cold Marine Sediments

Alkanes are major constituents of crude oil and are released to the marine environment by natural seepage and from anthropogenic sources. Due to their chemical inertness, their removal from anoxic marine sediments is primarily controlled by the activity of anaerobic alkane-degrading microorganisms. To facilitate comprehensive cultivation-independent surveys of the diversity and distribution of anaerobic alkane degraders, we designed novel PCR primers that cover all known diversity of the 1-methylalkyl succinate synthase gene (masD/assA), which catalyzes the initial activation of alkanes. We studied masD/assA gene diversity in pristine and seepage-impacted Danish coastal sediments, as well as in sediments and alkane-degrading enrichment cultures from the Middle Valley (MV) hydrothermal vent system in the Pacific Northwest. MasD/assA genes were ubiquitously present, and the primers captured the diversity of both known and previously undiscovered masD/assA gene diversity. Seepage sediments were dominated by a single masD/assA gene cluster, which is presumably indicative of a substrate-adapted community, while pristine sediments harbored a diverse range of masD/assA phylotypes including those present in seepage sediments. This rare biosphere of anaerobic alkane degraders will likely increase in abundance in the event of seepage or accidental oil spillage. Nanomolar concentrations of short-chain alkanes (SCA) were detected in pristine and seepage sediments. Interestingly, anaerobic alkane degraders closely related to strain BuS5, the only SCA degrader in pure culture, were found in mesophilic MV enrichments, but not in cold sediments from Danish waters. We propose that the new masD/assA gene lineages in these sediments represent novel phylotypes that are either fueled by naturally occurring low levels of SCA or that metabolize medium- to long-chain alkanes. Our study highlights that masD/assA genes are a relevant diagnostic marker to identify seepage and microseepage, e.g., during prospecting for oil and gas, and may act as an indicator of anthropogenic oil spills in marine sediments

A communal catalogue reveals Earth's multiscale microbial diversity

Our growing awareness of the microbial world's importance and diversity contrasts starkly with our limited understanding of its fundamental structure. Despite recent advances in DNA sequencing, a lack of standardized protocols and common analytical frameworks impedes comparisons among studies, hindering the development of global inferences about microbial life on Earth. Here we present a meta-analysis of microbial community samples collected by hundreds of researchers for the Earth Microbiome Project. Coordinated protocols and new analytical methods, particularly the use of exact sequences instead of clustered operational taxonomic units, enable bacterial and archaeal ribosomal RNA gene sequences to be followed across multiple studies and allow us to explore patterns of diversity at an unprecedented scale. The result is both a reference database giving global context to DNA sequence data and a framework for incorporating data from future studies, fostering increasingly complete characterization of Earth's microbial diversity.Peer reviewe

A communal catalogue reveals Earth’s multiscale microbial diversity

Our growing awareness of the microbial world’s importance and diversity contrasts starkly with our limited understanding of its fundamental structure. Despite recent advances in DNA sequencing, a lack of standardized protocols and common analytical frameworks impedes comparisons among studies, hindering the development of global inferences about microbial life on Earth. Here we present a meta-analysis of microbial community samples collected by hundreds of researchers for the Earth Microbiome Project. Coordinated protocols and new analytical methods, particularly the use of exact sequences instead of clustered operational taxonomic units, enable bacterial and archaeal ribosomal RNA gene sequences to be followed across multiple studies and allow us to explore patterns of diversity at an unprecedented scale. The result is both a reference database giving global context to DNA sequence data and a framework for incorporating data from future studies, fostering increasingly complete characterization of Earth’s microbial diversity