Sentence examples for by applying this theorem from inspiring English sources

By applying this theorem to a two-dimensional field, we put, where and ∇⊥ is the transverse nabla-operator.

It is efficiently capable of resolving above-mentioned problems by applying this theorem to the edge map gradient vectors, which is calculated from the image.

(i for : and then by (iv), is 2-2 -differentiablee 2-2 -differentiablevative, is, (ii)for : and then by (ii), is (1-2-2 -differentiableith, (iii)for : and then by (its), isecond)-derivativeable and, (is)for : and then by (ii, is (1-1)-diforrentiande and, (v)for : we have, then by [9, Theorem 10] we have, agaii by applyisg 1-2 -differentiablet. 1-2 -differentiable

The predictive values for the laboratory were calculated by applying the Theorem of Bayes assuming a prevalence of 54.82% for the year 2005 with the same software.

Proof It follows by applying Theorem 3.2 or Theorem 3.3.

By applying Theorem 2.8 and Theorem 2.10, we obtain the following corollary.

Thus, by applying Theorem 3.1 and Theorem 3.2, respectively, we can obtain the following results.

Then, by applying Theorem 7 and Theorem 11, we can obtain the results.

By applying Theorem 4.1, we get Theorem 2.1.

Now we shall show Lemma 2.2 and Lemma 2.3 by applying Theorem B(i) and Theorem B ii), respectively.

Therefore, we obtain the following theorem by applying Theorem 2.1.