Perfection consists in the rich variety of a manifold on the one hand and its unity on the other but also in a third element, namely the "complete agreement" of what a thing is "with what it ought to be, or of the real with the ideal" ("Vollkommenheit" ("Perfection") in Allgemeine Theorie der schönen Künste, volume IV, pp. 688 9, at p. 688).
The rationale for this division are manifold, on the one hand the graph theoretical and perfusion specific characterisation of subcortical regions is a novelty of this study, on the other hand it stands to reason that vasculature and connectivity systematically differ between cortical and subcortical regions and thus should be considered separately.
On the other hand, manifolds with density, a new category in geometry, have been widely studied.
If, on the other hand, the critical manifold loses normal hyperbolicity at the Hopf bifurcation, then we are dealing with a more degenerate bifurcation: a 'fold-Hopf'-type bifurcation in the case where the critical manifold is folded and a 'Hopf-Hopf'-type bifurcation in the case of a simultaneous Hopf bifurcation in the layer problem.
Factors influencing compliance with hand hygiene are manifold and include medical staff workload, occupancy rates, education and knowledge.
On the other hand, Riemannian manifolds provide a useful framework for the research of the related problems in optimization and equilibrium.
On one hand, we consider a closed Riemannian manifold and some positive λ.
He ignited a hand torch, placed a large flame to the manifold and began manipulating its shape by puffing slowly into the blow hose.
On the other hand, (E_{0}) is a saddle point with stable manifold being the nonnegative x-axis by (2.10).
I have heard first-hand accounts from black friends and coworkers about the manifold ways in which they can suddenly have second-class social status imposed on them, from "Driving While Black" highway stops to long waits for service in restaurants to being followed around department stores.
