Sentence examples for substantial generalization from inspiring English sources

We provide an example to show that our results are a substantial generalization of comparable results in the existing literature.

This objective requires a substantial generalization of methods utilized for ex post analysis of input-output databases for past years.

We next prove that even a substantial generalization of this transformation cannot be a compiler for even a very restricted class of 3-process programs.

Example 2.1 below shows that Theorem 2.6 is a substantial generalization of Theorem 2.1 in [2] and Theorems 2.1 and 2.2 in [4].

The core element of the proposed algorithm, making it competitive and even superior to the algorithms with higher communication requirements proposed in [7, 8], is the distributed adaptation scheme, developed as a substantial generalization of the adaptation strategy originally described in [2, 3] (see also [16]).

A substantial generalization of the Pythagorean theorem to three dimensions is de Gua's theorem, named for Jean Paul de Gua de Malves: If a tetrahedron has a right angle corner (like a corner of a cube), then the square of the area of the face opposite the right angle corner is the sum of the squares of the areas of the other three faces.

The left (right) (mathcal{G} -families (mathcal{K}_{C;mathcal{A}}) and (mathcal{W})-families (mathcal{K}_{C;mathcal{A}}) G} -families (mathcal{M}_{C;mathcal{A}}) are substantial generalizations of (mathcal{M}_{C;mathcal{A}}).

The left (right) (mathcal{G} -families (mathcal{J}_{C;mathcal{A}}) and left (riG} -familiesl{W})-famathcal{mathcal{J}_{C mathcal{A}}) generandd by (mathcaleft_{C;mathcal{A}}) arightbstantial generalizations of (mathcal{D}_{C;mathcal{A}}).

Our results are substantial generalizations and improvements of the corresponding results of Jachymski [8] and Sehgal [12] and others (see, e.g., [1, 2, 4]).

Neither is it a substantiated historical generalization.

However, we are cautious in the generalization of our findings, as substantial socioeconomic and geographic differences exist in many African-based treatment programs, which may make the application of a similar KC difficult.