Sentence examples for extend substantially from inspiring English sources

The examples below show that Theorems 2.1 2.4 extend substantially Corollaries 2.5 2.10, respectively.

Example 2.6 below shows that Theorems 2.1-2.4 2.1-2.4substantially Thextend2.1 in [1] and Theorem 2 in [15].

Our results presented in this paper extend substantially the results due to Deng [3], Ishikawa [7], and Senter and Dotson [10].

To efficiently help absorbing thermal stresses during thermal cycling, the second polymer layer, polybenzoxazole (PBO), was constructed to extend substantially over the entire first polymer layer, epoxy contained polysiloxane.

Results presented here extend substantially our previous work in showing that ectopic expression of the mitotic inducer, Spcdc25, results in profound changes to root morphology, meristem architecture and the regulation of the plane of cell division.

For the first time, the Biennial extended substantially beyond the Whitney Museum of American Art's Madison Avenue confines to occupy many of the wood-paneled period rooms and other spaces inside the armory from March 6 through Sunday night (the Biennial exhibits at the Whitney itself remain on display through June 1).

The example below shows that Theorem 3.5 extends substantially the corresponding results in [5, 11].

The following example manifests that Theorem 3.1 extends substantially Theorems 1.1 and 1.4.

The following example proves that Theorem 3.1 both extends substantially Theorem 1.1 and is different from Theorem 1.4.

It was found that there exists an optimal concentration for each polymer additive in a coating solution, at which the maximum coating speed can be extended substantially.

Example 3.2 below shows that Theorem 2.1 extends substantially Theorem 3.1 in [2] and Theorem 2.1 in [5] and differs from Theorems 5 and 6 in [8] and Theorem 2.1 in [4].