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(Dual version of Zorn's lemma).
For all the results presented here, there is a dual version which has the same importance.
Inequality (1.14) can be viewed as a dual version of inequality (1.10).
We finally consider the dual version of the problem, precisely, we show how to achieve simultaneous optimality by filter blending.
(3) Use the dual version of the basic method so that inputs–outputs and left right eigenvectors are switched.
In the last section, we prove a dual version of Olsen's inequality on predual of Morrey spaces (Theorem 3.1).
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If not, the dual versions will make one more trip.
There follows a bizarre relationship, retold from both sides in interlocking dual versions of events.
The teaser images of Tim Burton's 3D Alice in Wonderland were really something, and pure Burton: dual versions, seemingly moulded from dough, of Matt Lucas as Tweedledee and Tweedledum, and Helena Bonham Carter as the Red Queen with scarlet hair, cupid's-bow lips and a huge bulbous head.
One can apply CoreducThen to the celluser mestraightforward -cells are arbitrarily removedual a similar but dual manner as in the Reduce-Omit algorithm.
We list the dual versions of Theorem 3.1 as theorems below.
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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