TY - JOUR A1 - Nitze, Ingmar A1 - Grosse, Guido A1 - Jones, Benjamin M. A1 - Romanovsky, Vladimir E. A1 - Boike, Julia T1 - Remote sensing quantifies widespread abundance of permafrost region disturbances across the Arctic and Subarctic JF - Nature Communications N2 - Local observations indicate that climate change and shifting disturbance regimes are causing permafrost degradation. However, the occurrence and distribution of permafrost region disturbances (PRDs) remain poorly resolved across the Arctic and Subarctic. Here we quantify the abundance and distribution of three primary PRDs using time-series analysis of 30-m resolution Landsat imagery from 1999 to 2014. Our dataset spans four continental-scale transects in North America and Eurasia, covering similar to 10% of the permafrost region. Lake area loss (-1.45%) dominated the study domain with enhanced losses occurring at the boundary between discontinuous and continuous permafrost regions. Fires were the most extensive PRD across boreal regions (6.59%), but in tundra regions (0.63%) limited to Alaska. Retrogressive thaw slumps were abundant but highly localized (< 10(-5)%). Our analysis synergizes the global-scale importance of PRDs. The findings highlight the need to include PRDs in next-generation land surface models to project the permafrost carbon feedback. Y1 - 2018 U6 - https://doi.org/10.1038/s41467-018-07663-3 SN - 2041-1723 VL - 9 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Roos, Saskia T1 - The Dirac operator under collapse to a smooth limit space JF - Annals of global analysis and geometry N2 - Let (M-i, g(i))(i is an element of N) be a sequence of spin manifolds with uniform bounded curvature and diameter that converges to a lower-dimensional Riemannian manifold (B, h) in the Gromov-Hausdorff topology. Then, it happens that the spectrum of the Dirac operator converges to the spectrum of a certain first-order elliptic differential operator D-B on B. We give an explicit description of D-B and characterize the special case where D-B equals the Dirac operator on B. KW - Collapse KW - Dirac operator KW - Spin geometry Y1 - 2019 U6 - https://doi.org/10.1007/s10455-019-09691-8 SN - 0232-704X SN - 1572-9060 VL - 57 IS - 1 SP - 121 EP - 151 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Güneysu, Batu A1 - Keller, Matthias T1 - Scattering the Geometry of Weighted Graphs JF - Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics N2 - Given two weighted graphs (X, b(k), m(k)), k = 1, 2 with b(1) similar to b(2) and m(1) similar to m(2), we prove a weighted L-1-criterion for the existence and completeness of the wave operators W-+/- (H-2, H-1, I-1,I-2), where H-k denotes the natural Laplacian in l(2)(X, m(k)) w.r.t. (X, b(k), m(k)) and I-1,I-2 the trivial identification of l(2)(X, m(1)) with l(2) (X, m(2)). In particular, this entails a general criterion for the absolutely continuous spectra of H-1 and H-2 to be equal. KW - Graphs KW - Laplacian KW - Scattering theory Y1 - 2018 U6 - https://doi.org/10.1007/s11040-018-9285-1 SN - 1385-0172 SN - 1572-9656 VL - 21 IS - 3 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Fedchenko, Dmitry A1 - Tarkhanov, Nikolai Nikolaevich T1 - A Rado theorem for the porous medium equation JF - Boletin de la Sociedad Matemática Mexicana N2 - We prove that if u is a locally Lipschitz continuous function on an open set chi subset of Rn + 1 satisfying the nonlinear heat equation partial derivative(t)u = Delta(vertical bar u vertical bar(p-1) u), p > 1, weakly away from the zero set u(-1) (0) in chi, then u is a weak solution to this equation in all of chi. KW - Quasilinear equations KW - Removable sets KW - Porous medium equation Y1 - 2017 U6 - https://doi.org/10.1007/s40590-017-0169-3 SN - 1405-213X SN - 2296-4495 VL - 24 IS - 2 SP - 427 EP - 437 PB - Springer CY - Cham ER - TY - JOUR A1 - Dimitrova, Ilinka A1 - Koppitz, Jörg T1 - On the semigroup of all partial fence-preserving injections on a finite set JF - Journal of Algebra and Its Applications N2 - For n∈N , let Xn={a1,a2,…,an} be an n-element set and let F=(Xn;