Sentence examples for Based on the proof from inspiring English sources

Based on the proof of Theorem 6.1, we can develop parallel results to Theorems 3.3-3.11 as follows.

Based on the proof, the closed-form expressions of power allocation, relay selection, subcarrier assignment and minimum transmit power consumption were derived.

Based on the proof of Theorem 3.1, for the possible odd antiperiodic solutions of (4.3), there exists a prior bounds in.

Based on the proof, the prototype of the remountable HTS magnet by using the butt joint was fabricated and the performance was evaluated to suggest some issues for the future development.

Based on the proof of Theorem 6.16, we can develop parallel results to Theorems 5.3-5.5 5.3-5.5ows: Theorem 6.17 Let (D2)-(D4) asd (D6) be satisfollowsr each 1 ≤ i ≤ n.

Based on the proof of Theorem 2, we only need to prove that S ( t ) is a completely continuous operator, thus the existence of global attractor can be proved.

It is based on the proof-theoretic concept of a reflection principle; see Zach (2006) for more detail and Dean (forthcoming) for an analysis.

In summary, Δ ≥ 0 is correct based on the proofs in (13 - 20 13 - 20 also proves the proposition in (10).

By conditions (A3) and (A4), we can prove that x i ∗ ( t ) = ∏ 0 < τ k < t ( 1 + γ i k ) y i ∗ ( t ) is an almost periodic function <span class="lh">based on the proofs of Lemma 31 and Theorem 79 in [17].

Ultimately, it is hoped that actual therapeutic agents can be developed based on the proof-of-principle evidence and patterned after BIRD-2.

As a consequence, the transmission and reception polarization vectors cannot be always effectively solved based on A. The proof is concluded.