Sentence examples for minimal nonnegative integer from inspiring English sources

end{aligned}in the space ({{mathscr {S}}}^prime ({mathbb R}^d)), where r is the minimal nonnegative integer such that (r>s-d/p) ((rge s-d/p) if (q=1)).

In particular, the elements f ∈ X (i ) for ℓ = 11 satisfy the valuation conditions v ℓ (U (i ) (f ) ) = v ℓ (f ) + 1, where v ℓ (f ) is defined to be the minimal nonnegative integer such that all the coefficients in the q -expansion of f are divisible by ℓ v ℓ (f ).

Photons belong to one of the two great classes of elementary or submicroscopic particles defined by whether their quantum spin is a nonnegative integer (0, 1, 2, …) or an odd half integer (1/2, 3/2, …).

Let for nonnegative integer.

where is some nonnegative integer.

with a fixed nonnegative integer.

Let n be nonnegative integer.

Let be a nonnegative integer.

where d is a nonnegative integer.

(40) Here, n is a nonnegative integer.

Let be a nonnegative integer and.