Sentence examples for corresponding given from inspiring English sources

Furthermore, our analysis includes nonlocal double-walled carbon nanotubes with different boundary conditions between inner and outer tubes which seem to be scarcely considered in the literature, and the corresponding given results for this case can be considered as a benchmark for further studies.

The three numbers s1, s2 and s3 on the right-hand side, called signs, may equal ±1, and specify whether the desired solution circle should touch the corresponding given circle internally (s = 1) or externally (s = −1).

Let us define g and T as ξ′ matrix and a given validation tumor respectively or a given training matrix and a corresponding given training tumor respectively.

Our results improve and extend the corresponding results given by some authors.

So Proposition 1 extends and improves the corresponding result given in [15], Lemma 2.

Our results extend and improve the corresponding results given by many authors recently in this area.

Our results improve, extend, and generalize the corresponding results given by some authors.

Such systems allow executing basic queries which retrieve values corresponding to given keys.

These conclusions promote and improve the corresponding results given by Ko (J. Inequal. Appl. 2015:2015 2015).

Strong convergence theorems are established, which extend the corresponding works given by some authors.

As special cases, we can deduce the corresponding results given in these works from Theorems 2.1-2.6 2.1-2.6