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- Boundary value problems (1)
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- ellipticity in the edge calculus (1)
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The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy sigma = (sigma(psi), sigma(boolean AND)), where the second component takes values in operators on the infinite model cone of the local wedges. In the general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the ellipticity of the principal edge symbol sigma(boolean AND) which includes the (in general not explicity known) number of additional conditions of trace and potential type on the edge. We focus here on these questions and give explicit answers for a wide class of elliptic operators that are connected with the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation and ellipticity for Dirichlet-Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues of the Agranovich-Dynin formula for edge boundary value problems.
Paleomagnetic dating of the India-Asia collision hinges on determining the Paleogene latitude of the Lhasa terrane (southern Tibet). Reported latitudes range from 5 degrees N to 30 degrees N, however, leading to contrasting paleogeographic interpretations. Here we report new data from the Eocene Linzizong volcanic rocks in the Nanmulin Basin, which previously yielded data suggesting a low paleolatitude (similar to 10 degrees N). New zircon U-Pb dates indicate an age of similar to 52Ma. Negative fold tests, however, demonstrate that the isolated characteristic remanent magnetizations, with notably varying inclinations, are not primary. Rock magnetic analyses, end-member modeling of isothermal remanent magnetization acquisition curves, and petrographic observations are consistent with variable degrees of posttilting remagnetization due to low-temperature alteration of primary magmatic titanomagnetite and the formation of secondary pigmentary hematite that unblock simultaneously. Previously reported paleomagnetic data from the Nanmulin Basin implying low paleolatitude should thus not be used to estimate the time and latitude of the India-Asia collision. We show that the paleomagnetic inclinations vary linearly with the contribution of secondary hematite to saturation isothermal remanent magnetization. We tentatively propose a new method to recover a primary remanence with inclination of 38.1 degrees (35.7 degrees, 40.5 degrees) (95% significance) and a secondary remanence with inclination of 42.9 degrees (41.5 degrees,44.4 degrees) (95% significance). The paleolatitude defined by the modeled primary remanence21 degrees N (19.8 degrees N, 23.1 degrees N)is consistent with the regional compilation of published results from pristine volcanic rocks and sedimentary rocks of the upper Linzizong Group corrected for inclination shallowing. The start of the Tibetan Himalaya-Asia collision was situated at similar to 20 degrees N and took place by similar to 50Ma.