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This is a trivial case, though.
Should politicians decide what is a "trivial case"?
This seemingly trivial case could affect the balance of power between the legislature and the executive.
We conclude that thermal stresses necessarily occur in the FGM cylinder, except in the trivial case of zero temperature.
Note that we always have the trivial case where all these conditions are satisfied and that is when there is only one such projector.
In the trivial case, there are no transmission peaks inside the bandgap, consequently no edge modes are measured on the interface between free space and the trivial sample.
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Finally, two realistic non-trivial case studies are considered for validation of the proposed methodology.
In this work, we give fast state-optimal deterministic algorithms for the first non-trivial case f="1.
However, it turns out that such a non-trivial case is indeed possible for our and and we can see the effect in Fig. 2. Whilst the result is general and applicable to any Markovian system, we identified the first non-trivial case only for phase observable measurements in an optical lattice.
In this paper, we provide an overview of MAZE and illustrate its use on a non-trivial case study: a swarm robotic algorithm for self-assembly.
So the non-trivial case is (k=2n), (nin{mathbf{N}}).
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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