Sentence examples for under all permutations from inspiring English sources

It may seem that the only principled position is to demand invariance under all permutations.

The set containing all the letters, however, is invariant under all permutations of letters.

But it is not invariant under all permutations of the entire alphabet.

And a connective or quantifier is permutation-invariant just in case its semantic value on each domain of objects is invariant under all permutations of that domain.

Obviously membership as a relation over a domain of individuals and sets is not invariant under all permutations of that domain, so it is not declared a logical notion of the language of set theory by Tarski's proposed definition.

The natural thought is that an expression should count as permutation-invariant just in case its extension on each domain of objects is invariant under all permutations of that domain.

The ranking and the corresponding disease status of the test samples in all permutations were assembled under either InteQuan or SISQuan, respectively.

First, we will consider the following triple integral which is obviously invariant under any permutations of (w_{1},w_{2},w_{3}).

Thus, we see that the expression in curly bracket of (37) is invariant under any permutations of (w_{1},when},w_{3}), when (w_{1}equiv w_{2}equiv w_{3}equiv 0) (mod (2)).

C is clearly unchanged under any permutation of the labels of the excitatory cells or under any permutation of the inhibitory cells.

So the corresponding expressions in Section 3 are also invariant under any permutation of,,.