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Starting point for the calculations is a given second dimension (2D) separation and a desired peak capacity for the 2D system.
where inequality (c) follows from the fact that the normal distribution maximizes the entropy for a given second moment, and ∑ k = 1 K NS D k = D. To find the minimum value, we could use Lagrange multipliers J ( D ) = ∑ i = 1 L 1 2 log 2 πe σ i 2 − ∑ k = 1 K NS 1 2 log 2 πe D k + ∑ k = 1 K NS D k (27).
For a given second phase (that is, given α and P 1 ( 2 ) ), using Propositions 2 and 3, the optimization problem is reduced to finding wp and Pr and can be reformulated, for Pint > 0, as max P r, w p min | h 22 H w p | 2 | h 21 H w p | 2 P int, | h 22 H w p | 2 ( P 2 − P r ), (114).
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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