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The independence of formula B from formula A is established by a matrix that (i) preserves the validity of the rules of the system and that (ii) under an interpretation σ assigns to A but not to B a designated value.
The Turkey Constitution, Article 174, preserves the validity of Turkey's reform laws on marriage.
The energy required to obtain and use the information preserves the validity of the second law (Schneider, 2010).
The robustness of the results also preserves the validity of the NPA approach against the possibility of HYPs and network models evolving slightly due to the constantly improving understanding of the biological processes they describe.
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The announcements are significant in part because they indicate that the chip industry may find a way to preserve the validity of Moore's Law.
Since then, an online petition has been circulated urging Mr. Love to reconsider "in order to preserve the validity of 'The Beach Boys' as a whole, and not as a 'money-saving, stripped-down version".
Calling Russian opposition to the proposal "unjustifiable and negative," Sir Jeremy said that "preserving the validity of that resolution means, in the view of the United Kingdom and most members of the Council -- perhaps all members of the Council -- avoiding a crash over the next couple of days because that does damage to the draft resolution".
In order to preserve the validity of this approximation even for larger input signals, the amplitude α of the pump field needs to be increased.
Now, it is certainly true that insisting on the need to preserve the validity of the above inferences in any account of external metafictional sentences is a good antidote to the antirealist 'paraphrase' strategy.
According to Burley, all of this is necessary to preserve the validity of our knowledge of the external world, which he believed can be made evident without falling prey to Ockham's criticisms.
For example, if we drop axiom K5 (preserving the validity of K1 – K4) the agent's possibility sets need not partition the space set (follow the link for an example. For more details and applications, cf. Samet 1990).
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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