Sentence examples for standard regularity from inspiring English sources

By standard regularity (see [17]), it follows that A − 1 is bounded and compact.

The following standard regularity conditions are made as in [15] and [19] throughout the paper.

So, (A5) is a standard regularity condition used commonly in the literature.

The equivalence between this condition and an H∞ optimal control problem which satisfies the standard regularity assumptions in H∞ optimization theory is shown.

By the standard regularity arguments as in the proof of Theorem 1.4 of [11] we see that ũ is a positive ground state solution for problem (5.1).

By the standard regularity arguments as in the proof of Theorem 1.4 of [11] we see that u is a positive ground state solution for problem (1.4).

The existence of local solutions can be obtained by utilizing the method of the standard regularization, and the regularities of the solutions can be derived by the argument similar to that in [18].

In a last experiment we conducted a qualitative comparison of the criterion Δ3 with two standard mesh regularity criteria, namely, the radii ratio regularity criterion and the area regularity criterion.

Standard parabolic regularity [[30], Sect.

Assuming a finite number of mass points, see Frühwirt-Schnatter (2006), standard likelihood regularity conditions holds.

It follows from standard elliptic regularity theory that F τ is a completely continuous operator.