Sentence examples for is sharp that from inspiring English sources

The result is sharp, that is, | b | cannot be increased.

(2.9) The result is sharp, that is, the order α is best possible.

(2.13) The result is sharp, that is, the bound (alpha_{n}(sigma,lambda)) cannot be increased.

Proposition 4.3 The inequality in Theorem  4.4 is sharp; that is, there exists a convex function such that (9) is satisfied with equality.

For edit operations that affect positions q letters apart, it is easy to show that the inequality is sharp, that is L1 gives the edit distance with affine gap costs.

If the note on the 12th fret is sharp, that would mean that the saddle for that string needs to be moved back away from the headstock.

You still have to be sharp; that's why you prepare well.

That is to say, the result of Lemma 2.2 is sharper than that of Theorem 2.1 in [8].

we see that our new lower bound in (3) is sharper than that in (2).

The strict inequality (3.11) shows that the error estimate in Theorem 3.5 is sharper than that of Theorem 1.1.

The stability result in Corollary 3.3 is sharper than that of Corollary 2.5.