The phrase "and high regularity of" is correct and usable in written English.
It can be used when discussing the consistency or frequency of a particular phenomenon or behavior.
Example: "The experiment demonstrated a high regularity of results, indicating the reliability of the method used."
Alternatives: "and strong consistency of" or "and significant frequency of".
In order to obtain existence and higher regularity of global solutions, there are many complicated estimates on external force and higher derivations of solution to be involved, this is our difficulty.
Matrix queries in NVIVO found FUn Group interviewees, with lower and higher regularity of attendance, often talked about the value and benefit of mixing across cultures further supporting the findings around other-group orientation.
Stated simply, the high nonlinearity of the k-ε equations leads to the necessity of high regularity of some unknown functions and thus leads to much difficulties for the a priori estimates.
The matrix query revealed a gradient in proactivity in peer relationships associated with regularity of attendance – those with low attendance in Football United speak of positive peer relationships, but do not report being as proactive in seeking and engaging in peer relationships as those with high regularity of attendance.
Moreover, due to the strong-coupling property of the k-ε equations, we need a corresponding high regularity of the unknown functions k and ε.
The continuity and curvature terms need to be weighted with values just high enough to maintain a high regularity of the mesh.
The justification for the above assumption is the following: The continuity and curvature terms need to be weighted with values just high enough to maintain a high regularity of the mesh.
More precisely, Holschneider (1995) has shown that a high regularity of the signal is translated via the CWT from a power-law variation: (9)This result confirms that if the stochastic process s(t) is self-affine or, if it has some long-range dependence properties characterised by the local exponent h(t), then the wavelet coefficients, at a fixed scale, form a stationary process.
In fact, the better inclusion between Morrey and Hölder spaces permits to obtain higher regularity of the solutions to different elliptic and parabolic boundary problems.
For truncated approximation the reconsideration partly arises from the difference between fractional derivative in R L sense and Caputo sense: Caputo fractional derivative requires higher regularity of the unknown than R L version.
