Sentence examples for modification to the proof from inspiring English sources

By exactly slight modification to the proof above, we can prove (ii) if l = + ∞. □.

A modification to the proof of Theorem 12 allows to get a corollary that is interesting in itself and that will be useful in order to obtain subsequent results.

Then, for all ( f, g ) ∈ F with f ∈ L q ( Ω, ϱ q , the inequality ∥ f ∥ L q ( Ω, ϱ q ≤ C ∥ g ∥ L p ( Ω, ϱ p. is valid with a constant C > 0. Remark 3.6 Note that the condition p ∈ P in the extrapolation theorem of [3] can be released to p ∈ P 0 with nearly no modification to the proof. Proposition 3.7 ([[11], Proposition 2.3]).

Furthermore, minor modifications to the proof show that the problem remains NP-hard for various restrictions of the topology of the graphs.

By making some minor modifications to the proof of Theorem 4.5, we can obtain the existence of at least one positive solution, if one of the following conditions is satisfied: (i), and.

The first approach requires a slight modification to the symmetric proof-key service outlined in Section 2.2.

A second way of using a long-term secret shared by the user and an IdP to provide a second layer of user authentication involves making a small modification to the asymmetric proof-key service, outlined in Section 2.2.

"It's a modification to the modification".

The proof-of-concept model includes evaluation of modifications to the building and its defenses.

Code-Level Modifications to the G2.

we get the result want to be proved by a simple modification of the proof of Lemma 2.2.