Sentence examples for use the same proof from inspiring English sources

Property 1 can be derived from the definition of the Z-parameter and we can use the same proof process of (24) that exploits the inequality relation between the arithmetic mean and the geometric mean.

It turns out that the revised theorem is more general than the original one given an evolutionary algorithm with mutation probability pm=1/(2n), using the same proof method as given by J.

By using the same proof as Theorem 3.2, we can easily obtain the following conclusions.

Using the same proof as above, we have the following result.

By using the same proof, we obtain that and are nonexpansive.

Using the same proof method as in Step 3, we know that y ∗ ∈ Γ.

By using the same proof of Theorem 1, we show the existence of optimal controls.

Using the same proof method as in Theorem 1, we get assertion of Theorem 2.

Then, using the same proof above, it can be shown that (2.17).

Using the same proof as in Lemma 3.2, we get a contradiction.

Then, using the same proof as that of Lemma 2.3, it can be shown that (2.20).