Sentence examples for proof can be modified from inspiring English sources

The proof can be modified from Proposition 4.1 in [9].

The methods used in the above proofs can be modified to obtain the following results for unsaturated solutions.

Next, the proof of Theorem 5.2 can be modified to exclude real hypersurface orbits and yield a classification in the case (dim G(X)=N^2-1) for (Nge 3), with (X) being non-homogeneous (see [37], [41], Theorem 4.1]): Let (Nge 3), (dim G(X)=N^2-1) and (X) be non-homogeneous.

However, for the moment, what has been demonstrated is the proof of concept that any plant gene can be modified in a predictable way, thereby opening the door to redesigning native gene sequences to modify their function or to reverse mutations in a directed way.

This proof-of-concept study shows that short peptides can be modified chemoselectively by synthetic HS mimetics for improving their ability to interact with HS-binding proteins.

Proof of concept experiments have been successful illustrating that minichromosome platforms can be modified in vivo.

With this in mind, we embarked on a study to test proof-of-principle if genetically engineered mesenchymal stem cells (MSCs) transfected with HCN2 genes can be modified to be cardiac pacemaker cells.

Production lines can be modified accordingly.

As more facts arise, models can be modified or expanded.

Both can be modified to deliver forms of proportional representation.

This activity can be modified for small groups or pairs.