Sentence examples for are a substantial generalization of from inspiring English sources

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

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]).

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.

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

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].

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}}).

This finding may be related to the substantial generalization of learning to the untrained sequences.

Additive Hadamard cocycles are a natural generalization of presemifields.

Complex numbers are a generalization of the familiar decimal numbers that mathematicians call the real numbers.