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OK, so now if I compute the inner integral, well, what do I get if I get partial M partial y with respect to y? I'll get M back, OK?
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Therefore, if I computed the KL for all pair-wise pdf's within each pool, the averaged or mean-Kullback-Leibler (MKL) measure approximately quantifies the degrees of universality or scale invariance of that pool.
Also, again if it's a sphere, I compute its maximum and minimum z-value using its aperture and curvature (and some basic math!).
And if you're less mathematically inclined perhaps, you can ask, can I compute a good value in practice.
If both are equal, C i computes M9 = h(M1|| R c || M8) and sends the reply message { M9} for its authentication to S i.
If both are equal, C i computes M 12 = h (M 2|| R c || M 11) (which is indeed h [ h (ID i || x s )|| R c || R s ]).
If both are equal, C i computes M 9 = h (M 1|| R c || M 8) and sends the reply message { M 9} for its authentication to S i. (4) On receiving { M 9} from C i, the server checks if M 9 = h (M 4|| M 5|| R s ) or not.
If ID i is valid, S i computes M 8 = h (ID i || x s ).
If ID i is valid, S i computes M 4 = h (ID i || x s ) and M 5 = M 2 ⊕ M 4. (2) S i checks if M 3 = h (M 4|| M 5) or not.
SC i computes h (B i ⊕ K i ) and verifies if f i = h (B i ⊕ K i ) or not.
For example, if the polar form i = 1e is used to compute i i, the power is found to be e−; the principal value of i i, computed above, is e−.
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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