Sentence examples for the obtained assertion from inspiring English sources

We now illustrate the obtained assertion.

We can assume that u λ is a strictly local minimizer of J ˜ λ in the W 1, p ( x ) topology, otherwise we have obtained assertion (3).

Substituting this inequality into the right-hand side of the above equality, we obtain assertion (25) immediately.

As a result, we obtain assertion (a) and (b) of the theorem.

Finally, by using Lemma 1.1, we obtain assertion (2.4) of Theorem 2.1.

From the above estimate, we obtain assertions (a) and (b).

This allows us to formulate our question also in the form: how can we make the conclusions about nonoscillation of the equation or about positivity of the Cauchy function of (1.1) without assumption about nonoscillation of the equation In this paper we obtain assertions allowing to make such conclusions.

This assertion that the obtained numerical results are very accurate and compare favorably with the exact solution.

It is observed that the obtained dispersion equation is in assertion with the classical Love wave equation for both the cases when a single and double layer lies over a half space.

We can assume that uλ is a strictly local minimizer of J ̃ λ in the X-topology, otherwise we have obtained the assertion of Theorem 1.2.

Then, by applying the trace theorem [27, Section 1.8.2] to the space, we obtain the assertion.