Sentence examples for based on the proofs of from inspiring English sources

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 based on the proofs of Lemma 31 and Theorem 79 in [17].

Based on the proofs of Lemmas 4.1-4.5 4.1-4.5orem 4.1 we candsee Theoreme signs of (A_{h_{1}}) and (A_{h}) play the key roles in determining the domains of the impulsive set and phase set, and in defining the Poincaré map ({mathcal{P}}(y_{i}^)).

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

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

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.

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.

Future studies, based on the proof of concept provided here, can explore that question productively for the entire first post-transplant year.

Based on the proof of Theorem 1, the base of the log must be greater then C in order to achieve the speed up.

Beliefs and theories are possibly true depending on how rational they are whereas knowledge and facts are definitely true based on the proof of observation and experience.

Because the proposed algorithm has a similar strategy of backtracking which is used in ASP, the proofs are mainly based on the proof framework of ASP/ACoSaMP.