Sentence examples for under the same suppositions from inspiring English sources

Under the same suppositions as in Proposition  2.1, there exists a strictly increasing convex continuous function γ : [ 0, ∞ ) → [ 0, ∞ ) with γ ( 0 ) = 0 depending only on the diameter of C such that γ ( ∥ ∑ i = 1 n λ i x i − T ( ∑ i = 1 n λ i x i ) ∥ ) ≤ max 1 ≤ i ≤ n ( ∥ x i − T x i ∥ ).

We consider the same supposition given by (4.16), where the received signal involves only the noise samples.

Does 'himself' have the same supposition as 'man' (or 'every man') and if so, why can the antecedent not replace it?

"You differ from a donkey, therefore you differ from a man or from a donkey" follows, and Heytesbury proposes the rule that if 'or' occurs after a term that produces distributed or confused supposition, then an argument from an inferior (narrower) term to its superior (wider) term with the same supposition is valid.

The similarity appears even more striking when we note that Newton formulates the same supposition in Query 31 of the Opticks as "Nature will be very conformable to her self and very simple" (Opticks, 397).

At the outset of our experiments, we had the same supposition as the reviewers: that PP2A-B55 would be the main such enzyme because CDK phosphorylations activate Gwl and PP2A-B55 can remove certain such phosphorylations.

It mimics the very same supposition of which women my age are accused: the idea that feminism's work is done.

Language naturally comes under the same microscope.

"Everybody's playing under the same conditions.

under the same conditions.

All under the same hashtag.