Sentence examples for according to their proof from inspiring English sources

Finally, he tried to reconcile these "two conclusions so contradictory according to their utterance, so necessary according to their proof", by distinguishing two senses of "being wholly in a place".

Proof According to the proof of Lemma 2.1, we can easily obtain local asymptotical stability of w ∗ for ODE system (1.2).

According to security proof in [22], the design of the decryption key is secure.

According to the proof of Step 1, we know that (3.39).

According to the proof of Theorem 3.1, there exists, such that implies and implies.

According to the proof given by Chipot et al. [25], we have the following theorem.

According to the proof of Theorem 3.1 we can get that (3.19).

According to the proof of Theorem 6.7, we see that (75) is satisfied.

According to the proof of the second part of Theorem 2.1, this inequality is false.

According to the proof of Theorem 5, φ ( y ) is Schur harmonically concave on R + k.

According to the proof of Theorem 3.1 and Lemma 2.7, we have (5.5).