The phrase "a substantial generalization of" is a correct and usable phrase in written English.
You can use it when you want to describe a large-scale, sweeping statement or idea that covers general principles. For example: "The study provided a substantial generalization of how sleep deprivation affects academic success in college."
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.
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].
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.
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.
This finding may be related to the substantial generalization of learning to the untrained sequences.
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}}).
It is worth noticing that the fuzzy quasi-triangular spaces ((X,mathcal {M}_{C mathcal{A}},ast)), introduced in this section, are not necessarily topological or Hausdorff or sequentially complete and are, in particular, substantial generalizations of fuzzy metric spaces [3, 4] and fuzzy quasi-metric spaces [5].
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]).
