Sentence examples similar to proof is useful for from inspiring English sources

A proof load design is useful for estimation of the dependence between two strength properties of a unit when either property can only be measured by loading to failure.

In addition to preventing these forms of rebirthing/cloning, the proof of identity requirement is useful for raising the risk of detection for an offender, by linking an individual with an attempt to register a vehicle that is subsequently detected as stolen.

Using pre-treatment before the bacterial challenge is arguably a limitation of our studies in the primary pneumonia model; this approach is useful for proof-of-principle but does not mirror likely clinical usage.

The following proposition is useful for the proof of the main result.

The following lemma gives an estimation for the operator Φ, which is useful for the proof of our main results.

In this section, we first give Lemma 4.1 which is useful for the proof of global attractivity.

The following lemma is cited from [17, 18], which is useful for the proof of our main result of this paper.

The following lemma is useful for the proofs of our main results of this paper.

The following famous Lions vanishing lemma is useful for the proofs of Theorems 3.3 3.4.

It should be noted that this wavelength is not ideal for imaging in vivo but is useful for these proof-of-principle studies.

The following lemma is useful for our main proof, which is a generalization of Lemma 1.4 in [3] and Lemma 4 in [9].