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 section, we give a multidimensional result related to Godunova's inequality (1.8).
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.
In other words, the term disability is used to "to denote a multidimensional phenomenon resulting from the interaction between people and their physical and social environment" [ 1].
Patients with HF describe their engagement in healthcare as a process-like and multidimensional experience resulting from the combined cognitive, emotional and conative enactment of individuals towards their health management.
Most depression rating scales are multidimensional and the resulting heterogeneity may impede identification of coherent biomarkers.
Thus, the resulting multidimensional schema would satisfy the end-user requirements and would be conciliated with the data sources.
On the other hand, starting from the data sources [8, 14, 16, 31], the bottom-up approach ensures that the resulting multidimensional schema is loadable and respects the conformity constraints; however, it does not guarantee the structural well-formedness of the schema nor the satisfaction of decision makers' needs.
