Sentence examples for upon noting from inspiring English sources

In 1676 the Danish astronomer Ole Rømer, upon noting discrepancies between the observed and calculated times of such eclipses, correctly explained them as being due to the difference in the travel time of light when Earth is nearest to Jupiter or farther away from it.

Inequality (2.1) follows from above upon noting that.

where the last inequality follows upon noting the positive semi-definite ordering.

end{aligned} (31) Expression (31) can be simply shown by induction upon noting that, due to remark 1), we have φ(ℓ+j)=φ and hence r(ℓ+j)=r and γ(ℓ+j)=γ, for j∈[0,L−ℓ].  .

Note also that from (2.20) it follows upon noting (F'>0) that the solution (mathscr{G}) is monotone in r, that is, increasing when (2pi m + z>0) and decreasing when (2pi m + z<0).

Proof The 'if' part follows from Theorem 2.2, Corollary 2.3 and Corollary 2.4 upon noting that S H ¯ μ q ( n, p, λ, α ) ⊂ S H μ q ( n, p, λ, α ).

Flash spotting relied upon observers noting the azimuth of gun flashes and plotting these so as to obtain intersections.

Strategy Informer felt the game had updated and improved upon the original, noting better controls, more forgiving health bars and save points, and more engaging mission goals.

In this paper, we describe a method and an implementation of web-based notes sharing system that can immediately update upon students' notes drawing.

Here performance and composition merge when players often stumble upon notes, chords, and rhythms that defy expected patterns and beget entirely new structures.

Each team member's response was built not only upon memory in hindsight, but also upon notes taken throughout the research process.