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The second method applied when the first condition was violated, that is, ( forall R_{jd},:,(R_{jd}, < - 2omega^{ circ } ) oplus (R_{jd} > 2omega^{ circ } ) ).
If this condition was violated, the Greenhouse-Geisser correction was used.
If this condition was violated the resulting magnitude spectrum was not accurate.
If the condition was violated in any iteration for any line search in a hyper-box, that box was marked as nonconvex.
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We also prove that an extremal function may not exist if the condition is violated.
As previously discussed, the more the SoC diverges from the SoCmax the more the energy neutrality condition is violated.
When this condition is violated we also construct global solutions to the inhomogenous equations having analytic singularities.
First, an event-based data packet processor is introduced to release sampled measurement outputs only if an event condition is violated.
The classical boundary condition of fluid dynamics, i.e. the no-slip condition is violated during the flow of various complex fluids including polymer melts and polymeric suspensions.
As inlet velocity is raised further, the former decreases while the latter increases until the stability condition is violated, leading to blowoff.
If an SLA condition is violated, a proper migration destination is searched over the P2P network for a service picked randomly by a particular container.
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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