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We compute explicitly, and without any extra regularity assumptions, the large time limit of the fibrewise heat operator for Bismut-Lott type superconnections in the L-2-setting. This is motivated by index theory on certain non-compact spaces (families of manifolds with cocompact group action) where the convergence of the heat operator at large time implies refined L-2-index formulas.
As applications, we prove a local L-2-index theorem for families of signature operators and an L-2-Bismut-Lott theorem, expressing the Becker-Gottlieb transfer of flat bundles in terms of Kamber-Tondeur classes. With slightly stronger regularity we obtain the respective refined versions: we construct L-2-eta forms and L-2-torsion forms as transgression forms.
We examined face memory deficits in patients with Idiopathic Parkinson's disease (IPD) with specific regard to the moderating role of sex and the different memory processes involved. We tested short- and long-term face recognition memory in 18 nonclinical participants and 18 IPD-patients matched for sex, education and age. We varied the duration of item presentation (1, 5, 10s), the time of testing (immediately, 1hr, 24hrs) and the possibility to re-encode items. In accordance with earlier studies, we report face memory deficits in IPD. Moreover, our findings indicate that sex and encoding conditions may be important moderator variables. In contrast to healthy individuals, IPD-patients cannot gain from increasing duration of presentation. Furthermore, our results suggest that I PD leads to face memory deficits in women, only.
We present a new integral field spectroscopic dataset of the central part of the Orion Nebula (M 42), observed with the MUSE instrument at the ESO VLT. We reduced the data with the public MUSE pipeline. The output products are two FITS cubes with a spatial size of similar to 5'9 x 4'9 (corresponding to similar to 0.76 x 0.63 pc(2)) and a contiguous wavelength coverage of 4595 ... 9366 angstrom, spatially sampled at 0 ''.2. We provide two versions with a sampling of 1.25 angstrom and 0.85 angstrom in dispersion direction. Together with variance cubes these files have a size of 75 and 110 GiB on disk. They are the largest integral field mosaics to date in terms of information content. We make them available for use in the community. To validate this dataset, we compare world coordinates, reconstructed magnitudes, velocities, and absolute and relative emission line fluxes to the literature values and find excellent agreement. We derive a 2D map of extinction and present de-reddened flux maps of several individual emission lines and of diagnostic line ratios. We estimate physical properties of the Orion Nebula, using the emission line ratios [N II] and [S III] (for the electron temperature T-e) and [S II] and [Cl III] (for the electron density N-e), and show 2D images of the velocity measured from several bright emission lines.
Earthquakes occurring close to hydrocarbon fields under production are often under critical view of being induced or triggered. However, clear and testable rules to discriminate the different events have rarely been developed and tested. The unresolved scientific problem may lead to lengthy public disputes with unpredictable impact on the local acceptance of the exploitation and field operations. We propose a quantitative approach to discriminate induced, triggered, and natural earthquakes, which is based on testable input parameters. Maxima of occurrence probabilities are compared for the cases under question, and a single probability of being triggered or induced is reported. The uncertainties of earthquake location and other input parameters are considered in terms of the integration over probability density functions. The probability that events have been human triggered/induced is derived from the modeling of Coulomb stress changes and a rate and state-dependent seismicity model. In our case a 3-D boundary element method has been adapted for the nuclei of strain approach to estimate the stress changes outside the reservoir, which are related to pore pressure changes in the field formation. The predicted rate of natural earthquakes is either derived from the background seismicity or, in case of rare events, from an estimate of the tectonic stress rate. Instrumentally derived seismological information on the event location, source mechanism, and the size of the rupture plane is of advantage for the method. If the rupture plane has been estimated, the discrimination between induced or only triggered events is theoretically possible if probability functions are convolved with a rupture fault filter. We apply the approach to three recent main shock events: (1) the M-w 4.3 Ekofisk 2001, North Sea, earthquake close to the Ekofisk oil field; (2) the M-w 4.4 Rotenburg 2004, Northern Germany, earthquake in the vicinity of the Sohlingen gas field; and (3) the M-w 6.1 Emilia 2012, Northern Italy, earthquake in the vicinity of a hydrocarbon reservoir. The three test cases cover the complete range of possible causes: clearly human induced, not even human triggered, and a third case in between both extremes.
Das Hochwasser im Juni 2013
(2015)