Sentence examples for based on the proofs from inspiring English sources

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 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}^)).

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

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

In Lemma 2.3, based on the proof line from [53], we make a generalization of this inequality.

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.

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