Sentence examples for stronger hypothesis from inspiring English sources

This is clearly the stronger hypothesis.

For groups of higher solubility degrees, the picture is substantially different, even under the stronger hypothesis of finite presentability.

Tan and Yuan [4] and Liu [5, 6] extended the theorem to the more general continuous 1-set-contractive maps under some stronger hypothesis.

Wolf [689] then extended the result to general Banach spaces but needed (||P||^2||P-Q|| < 1) and (||1-P||^2||P-Q|| < 1) which is a strictly stronger hypothesis.

Kato didn't assume that (V in L^2({mathbb {R}}^3)+L^infty ({mathbb {R}}^3)) but rather the stronger hypothesis that for some (R < infty ), one has that (int _{|x|< R} |V x)|^2 d^3x < infty ) and (sup _{|x| ge R} |V x)| < infty ), but his proof extends to (L^2({mathbb {R}}^3)+L^infty ({mathbb {R}}^3)).

We make a stronger hypothesis ϒ °that, ϒ holds simultaneously in D A and D B with high probability.

Such estimates go back to Stampacchia [623] and Trudinger [657] who had stronger hypotheses on V.

This property can be found in a wide range of applications where other stronger hypotheses - e.g. tree coefficients' structures - fail to hold.

Proofs of our results, for somewhat stronger hypotheses than ours and in special cases, are scattered in the literature, as briefly reviewed in the 'Introduction' and 'Setting of the problem' sections.

Notice that, by Lemma 3.2, the previous result also holds if we replace condition (A) by one of the following stronger hypotheses: ( A ′ ) T ( X ) ⊆ g ( X ) and ℳ is g-transitive and ( T, g ) -closed.

The results of [15] are established under much stronger hypotheses on the multivalued mappings F and G, made necessary by the fact that some compactness conditions are imposed (Condition ((mathcal{H}2))).