Sentence examples for corollary based from inspiring English sources

We formulate the divergence theorem in the 4D time-space and related corollary based on the appropriate 6 sets of increments in this article.

We formulate the divergence theorem in the 3D space and related corollary based on the appropriate two sets of increments in this article.

In order to compare with the main result of [3], we may as well educe the following corollary based on Theorem 3.1.

This article also includes revisions of the divergence theorems and the related corollaries based on the appropriate increments of the double and the triple sequences in the calculation processes of the triangular triple and quadruple integrals for 3- and 4-variable functions.

Corollary 1: Based on Lemma 1, if T is a random variable with PDF f T (x), then (i) The random variable X = θ cot(πe − T ) follows a distribution in the T-Cauchy{exponential} family.

The result in [[26], Corollary 4.6] is based on the Rayleigh principle for system ( S λ ) with (1.5), compare also with [[15], Theorem 3.2], and on the fact that the space of admissible functions is independent of λ (as a consequence of the structure in (1.2)).

Theorem 3.2 may also be extended straightforwardly by replacing controllable by stabilizable, and Corollaries 3.3-3.4 3.3-3.4o directly extendaree balso on Corollary 4.1.

Based on Corollaries 3.2 and 3.12, Corollary 3.13 is obvious.

Based on Corollaries 3.6 and 3.19, we get Corollary 3.20.

Based on Corollary 1, the following results can be obtained when r = 1 2.

However, we can derive an estimate of exponential convergence rate of the trivial solution of system (5) based on Corollary 1.