Sentence examples for thus by using from inspiring English sources

Thus, by using Theorem 2.1, the result is achieved.

Thus, by using Lemma 2.4, we conclude that for all.

Thus, by using Theorem 1, we have the following results.

Thus, by using Theorem 3.1, the desired is obtained.

Thus, by using this distribution an inaudible watermark is created.

Thus, by using these semiconductors, red- to ultraviolet (UV -emitting UV -emittingbe fabricatedevices

Thus by using similar arguments to those we used above, statement (b) is proved again.

Thus, by using Lemma 1, we conclude that R { q ( z ) } > 0 ( z ∈ U ).

Thus, by using Theorem 2.3, the boundary value problem (2) has a unique solution.

Thus, by using Theorem 4.2, SICP ( f, g, K ) is strictly feasible.

Thus, by using Theorem 2.2, the problem has a unique solution in P h = P 1.