Sentence examples for both sufficient and necessary from inspiring English sources

The Assouad dimension of the complement of the open set turns out to play an important role in both sufficient and necessary conditions.

We establish both sufficient and necessary conditions for the validity of the so-called Hardy Sobolev inequalities on open sets of the Euclidean space.

Yet the art itself provides powerful evidence that the term, like the category it signifies, is both sufficient and necessary, at least at this moment in our cultural history.

We show that a linear number (with respect to both n and m) of advice bits is both sufficient and necessary to perform optimally.

Alternatively, for conditional dispersers, it is shown that the strategy known as ideal free dispersal is both sufficient and necessary for evolutionary stability.

Here, we explored a specific interneuron population, OLMα2 cells, in the vHipp and found it to be both sufficient and necessary to maintain a specific type of theta oscillation and to control behavior.

So it seems that any truth-functional conditional sentence states both a sufficient and a necessary condition as well.

Both high evaporation rates and sufficient precipitation are necessary for desert varnish formation.

Altogether, these results show that both IND and SPT are necessary and sufficient for mediating organ radialization.

Selective inhibition of both kinases was necessary and sufficient to re-sensitise cells for staurosporine.

C/EBPα is another adipogenic TF and is both necessary and sufficient for adipogenesis [ 6, 41].