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Open image in new window Fig. 10 An example showing the necessity of condition (6.16) to deduce that f is a translated of (f^star ).
end{aligned}Then, the anisotropic isoperimetric inequality states that begin{aligned} P_varphi (E ge P_varphi (W_varphi ) end{aligned}for all sets of finite perimeter such that (|E|=|W_varphi |), with equality holding if and only if E is a translated of the Wulff shape set (W_varphi ) (see [69, 70] and also [50] for a proof in two dimensions).
Note that in dealing with general sets one has to replace the Hausdorff distance with the weaker one given by the measure of the symmetric difference between a translated of the set E and B. This is unavoidable if one thinks that by adding to B some long thin spikes the volume and the perimeter of the resulting set change very little while its Hausdorff distance from B goes to infinity.
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Bibliographic databases were searched for articles concerning the translation or evaluation of the measurement properties of a translated version of a neck-specific questionnaire.
The main limitation of our study was the use of a translated version of the GDS-15.
To evaluate the validity of a translated version of the Voice Handicap Index-10 (VHI-10).
Name of Ethics Committee (translated): Research Ethics Committee of the Antiguo Hospital Civil de Guadalajara "Fray Antonio Alcalde", A translated letter of the Committee's approval has been submitted together with this manuscript.
Facebook added a translated version of the site today in honor of Talk Like A Pirate Day.
The questionnaire includes a translated version of the British COMRADE instrument [ 33- 39] consisting of two subscales.
The other way I brought a song into Soul Coughing was as a translated version of an acoustic-guitar song.
The New York Times posted a translated version of the accompanying article on its Russian-language blog on livejournal.com on Tuesday.
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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