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The first theorem states conditions under which the allocation associated with any competitive market equilibrium is Pareto-optimal, whereas the second theorem states conditions under which any Pareto-optimal allocation can be achieved as a competitive market equilibrium following the use of lump-sum transfers of wealth.
Barnes (1982) states conditions under which any argument of this form is soritical.
This improvement is reached when the transportation system is under steady as well as transient states conditions.
And second, the test set is composed of target (ship) and clutter (sea states) conditions different from the ones used in the training and validation sets.
end{aligned} (2.12) Before stipulating a criterion of self-adjointness, we give a proposition which states conditions under which (Zin D(A^)), quoted from [15], Proposition 10.3.3.
Reference [32] studies the degrees of freedom of the multi-way relay channel with three users in each cluster and then states conditions under which the results can be generalized.
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As an attempt to avoid computational complexity in real-time operation, a simple look-up table is produced for various sea-states conditions.
All measurements start from steady-state conditions.
These are plainly mean to state conditions on individual persistence.
Under steady-state conditions, pDCs are absent from the skin.
Samples were drawn under near-steady state conditions.
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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