Euler configurations and quasi-polynomial systems

In the Newtonian 3-body problem, for any choice of the three masses, there are exactly three Euler configurations (also known as the three Euler points). In Helmholtz' problem of 3 point vortices in the plane, there are at most three collinear relative equilibria. The "at most three" part is common to both statements, but the respective arguments for it are usually so different that one could think of a casual coincidence. By proving a statement on a quasi-polynomial system, we show that the "at most three" holds in a general context which includes both cases. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.Comment: 21 pages, 6 figure

GrassPlot - a database of multi-scale plant diversity in Palaearctic grasslands

GrassPlot is a collaborative vegetation-plot database organised by the Eurasian Dry Grassland Group (EDGG) and listed in the Global Index of Vegetation-Plot Databases (GIVD ID EU-00-003). GrassPlot collects plot records (releves) from grasslands and other open habitats of the Palaearctic biogeographic realm. It focuses on precisely delimited plots of eight standard grain sizes (0.0001; 0.001;... 1,000 m(2)) and on nested-plot series with at least four different grain sizes. The usage of GrassPlot is regulated through Bylaws that intend to balance the interests of data contributors and data users. The current version (v. 1.00) contains data for approximately 170,000 plots of different sizes and 2,800 nested-plot series. The key components are richness data and metadata. However, most included datasets also encompass compositional data. About 14,000 plots have near-complete records of terricolous bryophytes and lichens in addition to vascular plants. At present, GrassPlot contains data from 36 countries throughout the Palaearctic, spread across elevational gradients and major grassland types. GrassPlot with its multi-scale and multi-taxon focus complements the larger international vegetationplot databases, such as the European Vegetation Archive (EVA) and the global database " sPlot". Its main aim is to facilitate studies on the scale-and taxon-dependency of biodiversity patterns and drivers along macroecological gradients. GrassPlot is a dynamic database and will expand through new data collection coordinated by the elected Governing Board. We invite researchers with suitable data to join GrassPlot. Researchers with project ideas addressable with GrassPlot data are welcome to submit proposals to the Governing Board

Geochemical and Lu-Hf (LA-ICP-MS) systematic of detrital zircons from lower neoproterozoic Lemeza Sandstones, Southern Urals

5 page(s

Geochemical and Lu/Hf isotopic (LA-ICP-MS) signature of detrital zircons from sandstones of the basal levels of the Riphean stratotype

5 page(s