Sentence examples for extension of known from inspiring English sources

This approach suggest that any extension of known fixed point result to cone metric spaces is redundant.

We also showed on examples in previous section that this idea produces nonempty extension of known results.

As a consequence, many of the new results for differential equations with the neutral operator A will not be a direct extension of known theorems for neutral differential equations.

Here we present Metabolic In silico Network Expansions (MINEs), an extension of known metabolite databases to include molecules that have not been observed, but are likely to occur based on known metabolites and common biochemical reactions.

To lowest order, agreement is found with Eulerian mean theories, and the present approximation provides an explicit extension of known wave-averaged equations to short-scale variations of the wave field, and vertically varying currents only limited to weak or localized profile curvatures.

We apply the method to the TCGA collection of 145 glioblastoma samples, resulting in extension of known pathways and discovery of new functional modules.

Those inequalities obtained are extensions of known Bonnesen-style inequalities and reverse Bonnesen-style inequalities.

The results obtained in this paper are extensions of known results in [1, 5, 9 11], and [4].

An example shows that the new concepts are distinct from the existing ones, so our results are extensions of known ones.

Finally, two examples show that the comparability is a sufficient condition for the uniqueness of common fixed point in the case of ordered g-contractions, so our results are extensions of known ones.

Finally, two examples show that the comparability is a sufficient condition for the uniqueness of a common fixed point in the case of an ordered g-quasicontraction, so our results are extensions of known ones.