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In accordance with the preceding reasoning and with the results of Sect.
Repeating the preceding reasoning, we know that there exists (tilde{delta}>0) such that (uin W_{X}^{1,p+tilde{delta}}(Omega)) and the proof is complete.
According to the preceding reasoning, a larger K results in a smaller I1 and the extracted prior information is more precise but less.
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Yet, as Eelco Runia [33] would argue, in historical disjunctions, such as that experienced by Ego, the deed very often, and quite counter-intuitively, precedes the reasoning and not the other way round.
From Theorem 4.2 and the reasoning preceding Theorem 4.2, we obtain the following corollary.
The preceding example highlights precisely the kind of reasoning we would like to formalize in the analysis of encrypted communication.
Reasoning: The line of reasoning is in fact parallel to the preceding argument from causes, although this may not be completely perspicuous due to the fact that the correlates of the two prongs above are here stages of a single on-going experimental situation, the so-called "rotating bucket" experiment, which, Newton intimates, he actually performed.
The majority of Lincoln's public utterances are narrowly, sometimes brilliantly, lawyerly — even, on occasion, crafted to give an appearance of inevitability to oratorical conclusions that are not well supported by the chain of reasoning that precedes them.
In reasoning, P precedes A (R1), and both groups showed high performance.
Their reasoning?- There were 32,000 fewer new Unemployment Insurance Claims in the 4 weeks preceding September 12th than in the 4 weeks preceding August 12th.
Based on the same reasoning, we excluded the use of inhaled or systemic steroids in the six weeks preceding study, since this would likely affect levels of inflammatory cells and mediators in sputum and plasma [ 18].
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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