On a large class of post-critically finite (finitely ramified) self-similar fractals with possibly little symmetry, we consider the question of existence and uniqueness of a Laplace operator. By considering positive refinement weights (local scaling factors) which are not necessarily equal, we show that for each such fractal, under a certain condition, there are corresponding refinement weights which support a unique self-similar Dirichlet form. As compared with previous results, our technique allows us to replace symmetry by connectivity arguments.
Since its inauguration in 2005, the INE-Beamline for actinide research at the synchrotron source ANKA (KIT North Campus) provides dedicated instrumentation for x-ray spectroscopic characterization of actinide samples and other radioactive materials. R&D work at the beamline focuses on various aspects of nuclear waste disposal within INE's mission to provide the scientific basis for assessing long-term safety of a final nuclear waste repository. The INE-Beamline is accessible for the actinide and radiochemistry community through the ANKA proposal system and the European Union Integrated Infrastructure Initiative ACTINET-I3. Experiments with activities up to 1 × 10(+6) times the European exemption limit are feasible within a safe but flexible containment concept. Measurements with monochromatic radiation are performed at photon energies varying between ~2.1 keV (P K-edge) and ~25 keV (Pd K-edge), including the lanthanide L-edges and the actinide M- and L3-edges up to Cf. The close proximity of the INE-Beamline to INE controlled area labs offers infrastructure unique in Europe for the spectroscopic and microscopic characterization of actinide samples. The modular beamline design enables sufficient flexibility to adapt sample environments and detection systems to many scientific questions. The well-established bulk techniques x-ray absorption fine structure (XAFS) spectroscopy in transmission and fluorescence mode have been augmented by advanced methods using a microfocused beam, including (confocal) XAFS/x-ray fluorescence detection and a combination of (micro-)XAFS and (micro-)x-ray diffraction. Additional instrumentation for high energy-resolution x-ray emission spectroscopy has been successfully developed and tested.
The short-cut test detects existence and uniqueness of "Laplacians" on finitely ramified, graph-directed fractals. Previous results by Sabot, Nussbaum and the author are improved and extended. It opens up the way for further studies because it combines well established spectral, dynamical and analytic techniques. Its algorithmic and recursive structure is designed to provide computable and flexible criteria.
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