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ASE is probably the most delicate probe of photodegradation and self healing that has been extensively used to characterize PMMA polymer doped with DO11 chromophores.Embaye et al.
The absorption spectrum is measured as a operate of time using a white mild probe that spatially overlaps the pump beam on the sample. The time derivatives don't commute. Lemma 2.5 additionally yields finite maximal existence time in the following sense. POSTSUPERSCRIPT as the following.

POSTSUPERSCRIPT ) to outline sums over occupied (unoccupied) states. POSTSUPERSCRIPT does not end in such a problematic behavior providing us with a UV finite idea even if the interplay potential is non-renormalizable in the original local model. Adaptive techniques (similar to SHUS or Wang-Landau) yield exit instances that are a lot smaller than for the original non-adaptive dynamics.

Using strategies from geometric singular perturbation principle and canard concept, we present that a travelling wave resolution actually still exists for this parameter regime: we assemble a heteroclinic orbit passing by the wall of singularities by way of a folded saddle canard point onto a repelling slow manifold.
Since we obtain the curvature sure so long as the area is constructive, this implies that the move continues to smoothly exist until it shrinks to some extent.

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