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This is achieved by developing a probabilistically equivalent structure scale model using two approaches – one based on probabilistic equivalence of a nodal response and the other seeking equivalence on the probabilistic characteristics of the constitutive matrix.
He said: "I do consider dogs to be intelligent, with the average dog having a mental capacity equivalent to a two-and-a-half-year-old child, and the super dogs (those in the top 20 per cent of canine intelligence) perhaps reaching the equivalence of a human three-year-old.
Now we shall prove the equivalence of (A) and (B).
(a) ALE; (b) equivalence of (a); (c) approximation of (b).
The equivalence of a number of estimation procedures is demonstrated.
The equivalence of (a), (b), (e) and (f) was given in Theorem 1.
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Another purpose of this paper is to establish the follow equivalence of Theorem A and its inclusion version Theorem A'.
The equivalence of statements (a -(c) follows from Theorem 3.6.
Both are biconditionals asserting the equivalence of an identity among singular terms (the left-side condition) with an equivalence relation on concepts (the right-side condition).
We also establish the equivalence of an affine isoperimetric inequality and its inclusion version for -John ellipsoids.
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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