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The population balance equation (PBE) is solved using the quadrature method of moments (QMOM) technique along with a correction procedure implemented to check and correct invalid moment sets.
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The proposed procedure achieves three objectives in one-step: (i) the valid and relevant moments are distinguished from the invalid or irrelevant ones; (ii) all desired moments are selected in one step instead of in a stepwise manner; (iii) the parameters of interest are automatically estimated with all selected moments as opposed to a post-selection estimation.
He is inescapable: Bruyas as a dandy in a snazzy burnoose; Bruyas in his salon, pontificating, or in a studio telling an artist what to do; Bruyas as Hamlet; Bruyas as an invalid; and Bruyas, in his golden moment, as the ambitious patron greeting Courbet, the most interesting artist he would ever know.
Sort out valid reasons, which will remain throughout your academic career, from invalid ones, which could change at any moment.
It is thus more parsimonious to conclude at the moment, that A. leucokranos is an invalid species.
Cases of initial failure are where, rather than an established charitable trust failing, a gift has failed at the moment of its creation by having an invalid purpose.
But Ondaatje Rolls illuminates corners others have not thought to visit – the dark shelves of the pantry, the final blurry moments of a dinner party, the tray brought quietly to an invalid – and as a result, they start to seem vastly more likeable.
Peering into a grandson's crib, reading a bedtime story to an invalid wife, glimpsing the erotic curve of a daughter-in-law's hip -- all become encores of earlier moments, manifestations of the "cycles of devotion, tragedy, idiosyncrasy and outrage" that make up his (or any) life.
were invalid.
Gorbachev ruled this invalid.
A: Invalid question.
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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