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The solution obtained by a novel approximation method shows perfect agreement with the analytical solution in limiting cases and provides, for the first time in this class of polymerization problems, full multidimensional results.
In this paper we will show that the notion of transitive F-closed (or F-invariant) set is equivalent to the concept of preordered set and, then some recent multidimensional results using F-invariant sets can be reduced to well-known results on partially ordered metric spaces.
Very recently, Karapınar et al. [49] showed that the notion of a transitive F-closed (or F-invariant) set is equivalent to the concept of a preordered set, and then some recent multidimensional results using F-invariant sets can be reduced to well-known results on partially ordered metric spaces.
Imaging biomarkers are usually noninvasive and generate intuitive, multidimensional results on both qualitative and quantitative data.
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In this section, we give a multidimensional result related to Godunova's inequality (1.8).
The 2006 Zorgbalans is comprehensive, robust, and multidimensional, resulting in a set of 125 indicators that are recognizable, relevant and appropriate for their policymakers [ 15, 21, 22].
Multidimensional computational results are presented to demonstrate the order accuracy of these numerical methods.
Multidimensional computational results are presented to demonstrate the second-order accuracy of this numerical method.
The main steps of the procedure are: construct the attribute set; construct the evaluation object set; construct evaluation perspectives with corresponding attributes and weights; select evaluation algorithms for different perspectives; and carry out cluster analysis on the multidimensional evaluation results.
The cumulative score for these multidimensional scales results from summation of sub-scores representing specific activities.
These studies suggest that the interplay between acculturation and mental health is multidimensional and results from the interaction of a network of factors [ 24].
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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