Sentence examples for according to the proof from inspiring English sources

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 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).

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

According to the proofs of (3.4) and Theorem 2.3 in [17], for any sequence {γ l }l∈N, we have 2 c 1 π ∑ l = 1 n γ l 2 ≤ E ∑ l = 1 n γ l ε l 2 ≤ 2 c 2 π ∑ l = 1 n γ l 2, which implies the desired results by Lemma A.4 and assumption(A2)(i).

According to the undisputed proof, as shown by the record before us, the plaintiff was a working girl, holding a position in which she earned a salary of $10 per week.

According to the above proof.