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The problem is finally reduced to a group of singular integral equations which are solved by numerical method.
The model is finally reduced to a single nonlinear objective and for a hypothetical numerical example it is solved by Particle Swarm Optimization method.
Then (22), and hence the characteristic equation (det{mathbf{Q}} = 0) for (kappa> 0), is finally reduced to the following equivalent form: p kappa) = varphi_{pm} kappa quad text{for } kappa> 0, (25) which means (p kappa) = varphi_ kappa) ) or (p kappa) = varphi_ kappa) ) for (kappa> 0).
Not only details, but the whole scaffolding of narrative, must be dismissed, ending in such drivel in her late work, as: "...it is a place / holding a place: it is an eclipse of: of holding / on: of on: or in: or what a here can be / if what one is / is finally reduced to here: it is not 'now,'" and on and on, from "High Tide," in Never.
The respiratory flux is due to the donation of electrons from NAD- or FAD-dependent substrates, via respiratory chain, to molecular oxygen which is finally reduced to water.
Cholesterol oxidase (EC 1.1.3.6, ChoA) is a FAD-dependent bifunctional enzyme that catalyzes the oxidation and isomerization of cholesterol to cholest-4-en-3-one (3) while dioxygen is finally reduced to H2O2 as by-product.
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Spark Streaming, a popular tool for processing live data streams, offers a good divide-and-conquer solution, where data stream is split into batches that are then processed in parallel by mappers, and the intermediate data from the mappers are finally reduced by reducers.
It was finally reduced to a heap of rubble in May to create a landing pad for Hadid's spaceship.
"Why in the world," Dana asked testily, "are we getting up at dawn to spend 12 hours on a train?" I tried mumbling something about the glories of the rails but was finally reduced to saying, "Because it's there".
David Thewlis plays her British husband, the Oxford academic Dr Michael Aris, who had to leave his beloved wife behind in Burma and was finally reduced, poignantly, to waiting by the phone for news.
She spent months arguing down her bills, which were finally reduced: About $1,400 for the Mohs surgeon, $765 for the anesthesiologist, $1,375 for the ophthalmological plastic surgeon, plus $1,050 in operating-room charges from the hospital.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com