Sentence examples for holds providing from inspiring English sources

The result of the match is a relation and a degree confidence that the relation holds providing an estimate of the correctness of the matches.

If the seismic coupling is below 100%%, it is not necessary that the scaling of d ∝ M 0 1/3 or T r ∝ M 0 1/3 holds, providing possibly d ∝ M 0 1/6 as proposed by Nadeau and Johnson (1998).

holds, provided (resp., ).

Hence (iii) holds provided (ii) holds.

We mention that the above discussion holds provided that (p>1).

holds provided that is sufficiently small, where is in Lemma 1.3.

This equation holds provided that r N 0 − i ≠ r N 0 − j ∀ i, j.

However, the inequality (7.1) holds provided that ∫ 0 ∞ m ( y ) f ( y ) d y = 0.

Finally, it is straightforward that (2.7) holds provided that satisfies (2.6).

In the following theorem, we shall prove that the converse of (9.6) holds provided that Y is normal and solid.

Further, by (4.20) and the coderivative criterion (2.17) for the Lipschitz-like property, the coderivative criterion holds provided the (4.22).