Sentence examples for used for this proof from inspiring English sources

A Sprague-Dawley male rat was used for this proof of concept and underwent MRI and PET/CT imaging sessions on the same systems as the bone sample.

We limit this conclusion to the dye-labels and combination of biological system (adult mouse testes) and platform (custom spotted mouse array) used for this proof of concept, although in theory the same approach is usable in other experiments.

However, in describing the BSS methods here, only two FSHD1 subjects, four FSHD2 subjects, and four unaffected control subjects were used for this proof-of-principle analysis.

In this subsection, we provide useful definition and lemmas used for the proof of Theorem 1.1.

The latter fact is used for the proof of the ergodicity of this process.

Begin with the model used for the proof of (12).

We now present the primary estimates which have been used for the proof of the main theorem.

In Section 3, we give some preliminaries that will be used for the proof of the main result.

By an argument analogous to that used for the proof of the first part of Theorem 2.1, we have (21).

Now, we give the following lemma which will be used for the proof of theorems: Lemma 1.

We have to prove that A has a unique fixed point in P. Theorem 2.6 will be used for the proof.