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which may be rewritten as (3.39).
Consider the second-order difference equation (1.1), which may be rewritten as (2.1).
After some calculations, we showed that the method is a linear and implicit technique which may be rewritten in vector form through the multiplication by a real square matrix that, under suitable conditions on the parameters of the analytical and computational models, turns out to be an M-matrix.
More precisely, when no danger of confusion is present, we will denote the function (F _{m, n} ^{k}) by F. It is obvious that F is a cubic polynomial on u which may be rewritten as F (u) = Delta t _{k} u ^{3} - (1 + gamma) Delta t _{k} u ^{2} + bigl[ gammaDelta t _{k} + D_{m,n}^{k} bigr] u - C _{m,n} ^{k}.
Taking the dot product of A with itself yields an equation involving the energy, A^2= m^2 k^2 + 2 m E L^2 \,, which may be rewritten in terms of the eccentricity, : e^{2} - 1= \frac{2L^{2}}{mk^{2}}E ~.
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He rewrites so much that the first chapter of a book may be rewritten 40 or 50 times.
Then (3.1) may be rewritten as (3.3).
Therefore, (A.3) may be rewritten as (A4).
This may be rewritten as (3.9).
Thus, Problem I may be rewritten as follows.
The last expression now may be rewritten as (2.22).
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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