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A reformulation of (4.2) which presupposes reduced regularity requirements on the solution is as follows.
The reduced regularity negatively affects the approximation property of Lemma 4, and thus the overall convergence behavior of solver.
We also remark the following on the numerical results of high polynomial orders and where the exact solution has reduced regularity.
In the presence of discontinuities in the coefficients, or due to the irregular geometry (e.g., L-shaped domain), the exact solution of elliptic problems has reduced regularity and lies only in H 1 + ∊, where 0 < ∊ < 1 depends on the strength of the singularity.
Further, the ACL group had a reduced ability to control head motion during gait, as indicated by reduced regularity in VT.
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The Celtics are about as blasé as they come in deciding games, the pressure reduced through regularity.
Following Hume, he thought causation could be reduced to regularity: "c causes e" is equivalent to "whenever c then e".
To do this, we stained cells with the membrane-staining dye di-8-ANEPPS (Fig. 5 A ). Unloading did not alter the density of the t-tubule network (Fig. 5 B ), consistent with an unchanged ICa,L, but significantly reduced its regularity (Fig. 5 C, D ), with fewer t tubules lying in their ordinary position.
In addition to altering tremor amplitude, ventrolateral thalamic stimulation may modulate tremor regularity; it has been reported that high frequency stimulation reduces the regularity of postural tremor (Vaillancourt et al., 2003) whereas low frequency stimulation may pace essential tremor, although this observation has never been formally quantified (Bejjani et al., 2000).
Our voltage clamp data show that burst discharges appear to be driven by powerful volleys of glutamate release, whereas tonic spiking is driven by a combination of regular autonomous spiking and irregular glutamate and GABA release, which presumably reduces the regularity of spike discharge.
The upland schemes are designed to reduce the regularity of flooding, not remove risk completely.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com