Sentence examples for use in this proof from inspiring English sources

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The construction makes also possible to get a short proof for the dimension formula when k⩾4r+1, and the same method we use in this proof yields the dimension straightaway for many other cases.

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The dispersion is relatively large due to the long catheter used in this proof of concept study.

Then there exists a constant C = C ( u, u h ( 0 ), γ ) such that − ( | D u | 2 D u − | D u h | 2 D u h, D θ ) ≤ C ( ∥ θ ∥ 2 + ∥ η ∥ 2 ) + γ 4 ∥ D 2 θ ∥ 2. Proof First of all, we give some estimates which will be used in this proof.

All the equalities among orbits used in this proof are summarized in Table 2.

This is a useful lemma that we will use in the proof of the main result.

A mutagenicity dataset of 5,439 compounds was used in this proof-of-concept study.

At the dose used in this proof-of-concept phase IB study, aprepitant did not show a significant antiviral activity.

In this section, we give some results which we shall use in the proof of theorems.

There are four paths we will use in the proof.

This notation is deliberately similar to that of the transpose operator we use in the proofs.

The main tool used in the proof of this principle is the Banach fixed-point theorem.

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