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It is obvious that the aforementioned considerations are valid just in case of contrast enhancement under noise and not in general.
Similar(58)
Obviously, it is sufficient to show the estimate (3.41) is valid just in the case when (3.45) is fulfilled.
Nevertheless, this relationship is valid just in the case of spotlight SAR data, so that applicability of this method is limited.
On Tarski's account, an argument is valid just in case there is no interpretation of its nonlogical constants on which the premises are true and the conclusion false.
On this account, an argument containing no nonlogical constants is valid just in case it is materially truth-preserving (it is not the case that its premises are true and its conclusion false).
An inference is valid just in case the truth of the premises guarantees the truth of the conclusion, or alternatively if the premises are true then the conclusion has to be true as well, or again alternatively, if it can't be that the premises are true but the conclusion is false.
What one gets is a dialogical principle of universalization (U): "A [moral norm] is valid just in case the foreseeable consequences and side-effects of its general observance for the interests and value-orientations of each individual could be jointly accepted by all concerned without coercion" (i.e., in a sufficiently reasonable discourse) (1998a, 42; trans. amended).
Habermas thus proposes a dialogical principle of universalization, (U), stating that a moral norm "is valid just in case the foreseeable consequences and side-effects of its general observance for the interests and value-orientations of each individual could be jointly accepted by all concerned without coercion" (Habermas 1998, 42).
Thus, the presented results are valid just for hydrophilic compounds.
However, they assumed a less justifiable Brownian velocity of nanoparticles as based on the kinetic theory of gas, which is valid just for fine particles suspended in a dilute gas (Boltzmann constant k b = 1.3807 × 10-23J/K, the base fluid temperature T, the nanoparticle densify ρ p, and its diameter d p )--but not quite valid for nanoparticles suspended in liquid.
"As our communities are exposed to more and more pornography - particularly via the internet - we are finding that the standard that used to be valid just isn't good enough any more in terms of judging what is obscene".
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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