Sentence examples for upon substituting from inspiring English sources

Therefore, upon substituting for u in (3.6) we obtain (3.15).

Upon substituting from (2.9) into (2.10), we obtain the desired result.

Upon substituting the above transformations into (2.1)–(2.4) we obtain the following: (2.9).

Upon substituting into (13), the test statistic for the energy detection becomes (16).

This follows easily from Lemma 2.1 upon substituting from (2.3), (2.13) and direct differentiation.

Upon substituting (5) in (4) and following the same procedure as in the Appendix, we get the result in (3).

Perhaps that is inevitable, given that Facebook, like any business, is driven by numbers, and that its success as a business depends upon algorithms substituting for the kind of human judgment that motivates a friend, a family member, or a rabbi to care for another.

Zlatan Ibrahimovic's winner ensured PSG progressed 4-2 on aggregate, while Eden Hazard was booed upon being substituted in the second half and Diego Costa was rendered highly doubtful for Saturday's FA Cup quarter-final at Everton with a recurrence of a tendon problem.

Not surprisingly Beckford was given a standing ovation from the Preston fans upon being substituted on 67 minutes – with two fans later accused of taking the shirt he had given to a young boy upon finding his place on the bench and immediately putting it on eBay.

His style is assumed to have survived to the present day (assumed as no-one knows exactly how the Gakkai practises nowadays), with Ushida being the one who, upon death, substituted the presidency of the association.

These amino-acid substitutions in KRAS alters its GTPase activity to a different extent and/or its ability to interact with its regulators, depending upon the substituted amino-acid residue [ 14].