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A graphical representation of relation between P f and P f f and the index classes (i.e. index values) is depicted in Fig. 3. To accommodate uncertainty in floating point computations and to allow the user to loosen the requirements for the interior cells, we introduce the interior limit i l and optionally use the following condition: lvert P_{f} - 1 rvert < i_{l}.
The interior limit value of ({mathbf{C}^_{gamma}}f) is then given by bigl({mathbf{C}^_{gamma}}^fbigr) (t)=f(t)- T_{Omega }bigl[partial_{bar{z}}^{J}mathcal{E}_{0}f bigr](t), quad tingamma, whence (H^_{gamma}f) is well defined.
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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