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Using a spherical coordinate system, the Green's function can be shown as the composition of two independent functions, one depends only on the radial distance of the field point to the origin and the other is in spherical angles.
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The quickest way to learn all this stuff is to study successful mass movements which ones depends only on your interests and passion.
It was shown that the ICI ensuing from these impairments has three components: one solely caused by Doppler spread, one that depends only on the synchronization offsets, and one that is nonzero only when imperfect synchronization and channel variation happen together.
So the probability of picking one element depends only on its weight, and not on the other elements, which means that the elements are pairwise independent.
Conservation of angular velocity, in particular, reflects rotational symmetry; it results from themotion being determined by a central force field (Arnold 1989), i.e., one which depends only on the size ("norm") of the dynamical variable, and not on its direction.
In order to make the optimization problem independent of the channel realizations, we replace the constraint in (28) by a deterministic one, which depends only on the statistics of the channel.
Our strategy for reconciling improved growth with a high level of l-lysine production was to use GapA together with GapN only in the early growth phase, and subsequently shift this combination-type glycolysis to one that depends only on GapN in the rest of the growth phase.
According to such theories, whether one is justified depends only on whether one's perceptual belief was produced by a reliable mechanism or process.
The theory is based on the fact that both the elastic and the plastic part of the stress field two-scale converge to a limit, which can be factorized by parts, one of which depends only on the macroscopic, and the other one – only on the microscopic characteristics.
"This decision depends not on us, it depends only on one person – Yanukovych," she said.
The system from one state to another depends only on the current departure state and has nothing to do with the previous history.
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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