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where ws, (i) denotes the i th row vector of W s.
where v r (i,i) denotes the (i,i) element of V r and ws;i the i th column vector of Ws, aug≡W s Udim.
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w i d t h.
w i : Sample weights.
We show that w i < w j.
Assume that w i = w j.
The iteration ends when W i (t+1)=W i (t) or W i (t)>D i.
Then w = sup i w i and k w = ⋃ i k v i and G w = ⋃ i G v i. .
Let w i = u it.
Mean amplitude: w i = 1/n 5.
where the Wronskian w i is given by (2.5) and m ∗ ( w i, w ˜ i ) is defined by (2.11) with w i + 1 : = w ˜ i.
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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