Sentence examples for thus applying from inspiring English sources

Thus, applying Theorem 2.1 with (alpha=0), we obtain (1.1).

Thus, applying Theorem 2.2, we obtain the result.

Thus applying this to (4.8), we can finish the proof.

Thus, applying Lemma 2.5 to (3.49), it follows that as.

Thus applying Part of the lemma, we get (60).

Thus, applying Lemma 2.2 gets the assertion (3.6), as desired.

Thus, applying the mathematical induction, we complete the proof of the theorem.

Thus, applying the proposed image alignment system to real image cases is feasible.

Thus, applying Corollary 1, we get z ∈ F ( S ) Open image in new window.

Thus, applying the proceeding constructed function to the -reverse Carleson condition gives (4.9).

Thus, applying security services to the underlying layer (i.e. hypervisor, cloud platform) is a preferred solution.