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The comparison principle in (Ren et al. 2016b), however, is also in a smaller solution class by requiring a somewhat stronger regularity on the solutions, and consequently, the coefficients of the PPDE should also have the same stronger regularity.
The lower y is in value, the harder the problem is to solve because there is a smaller solution space.
A large λ will lead to a smaller solution space and vice versa.
Then one can obtain a smaller solution by removing one of the edges (v1, v2), (v n, v1) (depending on their orientations), a contradiction.
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These design shifts — the authors and others propose more of them on the behavioral economics site www.ideas42.org — are a small solution to a very big problem.
The presence of a small solution concentration of Mg2+ ions leads to the accumulation of a Mg(OH 2 deposit when the surface pH is maintained sufficiently alkaline.
It is accurate because matched with real values and robustness shows a small solution time of 12 s on average.
Hence, for every positive integer sufficiently large, there exists a smallest solution of problem (1.1) in the order interval.
This is one of the big advantages of a distribute system: it's also scalable, so you can start with a small solution, make modifications and keep adding more functions to make it a bigger system.
In view of the a priori stability estimate in Proposition 5.1 and the following result of local existence of a small solution to the transformed MHD problem, we immediately obtain Theorem 2.1.
It's a small solution to a growing crisis.
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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