Sentence examples for order regularity from inspiring English sources
Now we turn to the higher order regularity of the velocity field.
This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region.
Applying the Schauder estimates from Theorem 1.4 one obtains higher order regularity, uniformly in (epsilon rightarrow 0 ) and so in particular we obtain smoothness of solutions in the case (epsilon =0).
In this section, we derive the higher-order regularity estimates of the solutions.
Similar to Theorem 2 in [8], we can obtain a higher-order regularity of the local solution to (1.2) as follows.
In order to get the higher-order regularity estimates of the solution, we need to bound (P_{mm}), (P_{mn}), (P_{nn}), (P_{mmm}), (P_{mmn}), (P_{mnn}), and (P_{nnn}).
Finally, we give the proof of the high-order regularity estimates of ((m,n,u)), which is due to [22 24, 30] for the single-fluid Navier-Stokes equations.
However, an ordering regularity of the PMAA core-PS shell-type microspheres was not observed.
If humans generally prefer images with the higher-order regularities typical of natural scenes and/or shiny objects, we would expect this to be the case.
Our clickstream data lends itself well to tracing higher-order regularities in usage behavior.
This suggests that higher visual areas are recruited if high-order regularities can be extracted from stimuli (i.e., objects vs. scrambled objects; meaningless objects vs. meaningful objects).
