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Todd set the timer and went off somewhere, perhaps to write note to self: "Never do another makeover".
For an arbitrary decomposition x=x1+x2, we write (note that the notation introduced in Eq. 28 is extended here, since x≠x i, in general) begin{array}rcl@ &widetilde{V}(x_{1},p,varphi,A,mathcal{X}) := (mathcal{B} (x))^{-1} widetilde{V}(x_{1},p,varphi,A,mathcal{X}), &widetilde{V}(x_{2},p,bar varphi,-A,mathcal{Y}) := (mathcal{B} (x))^{-1} widetilde{V}(x_{2},p,bar varphi,-A,mathcal{Y}).
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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