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The recent M9 Tohoku Japan earthquake of March 11, 2011 was the largest recorded earthquake ever to hit this nation. We retrospectively analyzed the temporal and spatial variations of four different physical parameters -outgoing long wave radiation (OLR), GPS/TEC, Low-Earth orbit tomography and critical frequency foF2. These changes characterize the state of the atmosphere and ionosphere several days before the onset of this earthquake. Our first results show that on March 8 th a rapid increase of emitted infrared radiation was observed from the satellite data and an anomaly developed near the epicenter. The GPS/TEC data indicate an increase and variation in electron density reaching a maximum value on March 8. Starting on this day in the lower ionospheric there was also confirmed an abnormal TEC variation over the epicenter. From March 3-11 a large increase in electron concentration was recorded at all four Japanese ground based ionosondes, which return to normal after the main earthquake. We found a positive correlation between the atmospheric and ionospheric anomalies and the Tohoku earthquake. This study may lead to a better understanding of the response of the atmosphere /ionosphere to the Great Tohoku earthquake.

Under study is the absolute continuity of the functions satisfying the Poincaré inequality on s-regular metric spaces.

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Alpine ecosystems represent varied climates and vegetation structures globally, with the potential to support rich and functionally diverse avian communities. High mountain habitats and species are under significant threat from climate change and other anthropogenic factors. Yet, no global database of alpine birds exists, with most mountain systems lacking basic information on species breeding in alpine habitats, their status and trends, or potential cryptic diversity (i.e., sub-species distributions). To address these critical knowledge gaps, we combined published literature, regional monitoring schemes, and expert knowledge from often inaccessible, data-deficient mountain ranges to develop a global list of alpine breeding bird species with their associated distributions and select ecological traits. This dataset compiles alpine breeding records for 1,310 birds, representing 12.0% of extant species and covering all major mountain regions across each continent, excluding Antarctica. The Global Alpine Breeding Bird dataset (GABB) is an essential resource for research on the ecological and evolutionary factors shaping alpine communities, as well as documenting the value of these high elevation, climate-sensitive habitats for conserving biodiversity.

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We consider the relationship between the p-capacity of the pairs of opposite sides of a flat quadrilateral and the resultant class of extremal mappings.In this article we establish a natural connection between the conjugate capacities of the two capacitors formed by the pairs of opposite sides of a flat curvilinear quadrilateral. Modifying the proofs of [1] in the general case of domains G ⊂ R n , we can obtain a similar result that relates the p-capacity of a pair of compact sets F 0 , F 1 ⊂ G and the conjugate modulus of a family of surfaces separating F 0 and F 1 . We do not pursue a comprehensive and scrupulous investigation of this question; our goal is to find a rather simple proof that visualizes the internal relationships between the objects under study and the available corollaries to the results obtained, possibly not in the most general situation. I. Nonlinear Capacity and the Modulus of a Family of CurvesConsider some simply-connected domain G on the plane R 2 bounded by a closed Jordan curve Γ as well as four distinct successive boundary points a 1 , a 2 , a 3 , a 4 ∈ Γ. Assume for definiteness that the numbering of the points agrees with the positive orientation of the boundary. We call a domain G with four marked boundary points a quadrilateral and denote it by G . The closed boundary arcs F 0 = Γ a 1 a 4 , F 1 = Γ a 2 a 3 , E 0 = Γ a 1 a 2 , and E 1 = Γ a 3 a 4 are referred to as the sides of G .

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