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Simple test cases show that our method exhibits 4th-order accuracy for reinitializing the regional level-set functions and strictly satisfies the interface-preserving property.
Note that the ideal D ¯ is supposed to be close to zero if the allocated power strictly satisfies the constraints.
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This restriction cannot be strictly satisfied in every application.
It is proved by several numerical examples that the manufacturability constraints are always strictly satisfied.
It is consistent with the rigorous electromagnetic field analysis when the approximation conditions are strictly satisfied.
The analysis operators and the synthesis operator of MUDW strictly satisfy the pyramid condition.
Herein, we successfully rendered this desirable material compatible as lithium metal interface, which strictly satisfied the critical requirements.
All of the pseudo-time advancement terms converge monotonically and the conservation laws are strictly satisfied in the steady state.
Other expressions such as statistical and quasi-equilibrium which do not strictly satisfy the Exner conditions are also acknowledged for their practical use.
Theoretical solutions are obtained in a closed form, in which both the dynamic governing equations and the boundary conditions are strictly satisfied.
We demonstrate how this formulation enables the estimation of fiber orientation distributions which strictly satisfy the physical constraints of realness, symmetry, and non-negativity.
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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