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Hilbert's proof theoretic program can then be seen to be a search for a proof theoretic reduction of all of mathematics to finitary mathematics; in a relativized program one looks for reductions of theories weaker than all of classical mathematics to theories often stronger than finitary mathematics.
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Brian Ashcroft, emeritus professor of economics at the University of Strathclyde, said: "After six years since the start of the great recession we are now witnessing a stronger recovery, although this one is weaker than almost all previous recoveries.
A significant operator effect was identified with weaker concordance than all the other operators in the population without high-risk profile (Figure 1).
In the apo-TRiC map, both a1 and a′1 subunits display a significantly weaker density than all the other subunits.
Especially, the imagined eccentric condition elicited a significant weaker muscular activity than all other conditions.
Revenue fell short of the $3.94 billion expected by analysts and was weaker than expected across all major divisions, including defibrillators, pacemakers and spinal repair products.
Just as international concern over the war in Chechnya at last produced some mild sanctions from the West, Russia's acting president, Vladimir Putin, this week welcomed to Moscow 11 leaders of countries even poorer and weaker than his own, all professing a desire for deeper friendship.
This offers a partial and pessimistic answer to the UK's high-profile productivity puzzle: it may be that productivity growth didn't suddenly fall off a cliff in 2008, it was actually weaker than it appeared all along.
Although associations were weaker than for %DBV, all measures of adiposity and body fat distribution also were significantly inversely associated with ADBV before adjustment for childhood BMI.
Throughout the course the performance of students from a Humanities/law/business/commerce background was significantly weaker than those from all other backgrounds (Overall WAM 69.0 ± 0.8 vs 72.4 ± 0.3, P = 0.001).
Nonetheless, RBR-independent ERs constituted a small proportion of the total SCML2 binding profile, because the N3 SCML2ΔRBR ChIP-seq signal was much weaker than WT when all significant (p <10−5 according to MACS 1.4.0rc2) ERs for SCML2 WT were combined in a single meta-ER plot.
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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