Sentence examples for regularity required from inspiring English sources

For harmonic symbols we find the regularity required of the symbol for the formula to hold.

As has been pointed out before, the functionals Φ, Ψ satisfy the assumptions of regularity required in Lemma 2.4.

Depending on the precise situation and on the regularity required of the solution, boundary conditions at just one or both endpoints of the free surface need to be imposed.

Regularities require explanations, and to be natural these explanations must come from the natures of the creatures.

(2.54) We note that the regularity properties of (c x,t)) in (2.45) ensure that (varphi x,t)) has the regularity properties required in (2.6).

Obviously, all the regularity assumptions required in Lemma 2.8 are satisfied.

Now, as has been pointed out before, the functionals Φ and Ψ satisfy the regularity assumptions required in Theorem 2.1.

This paper develops a technique of robust approximate tracking and regulation for nonlinear systems that do not satisfy the restrictive regularity assumptions required by exact feedback linearization approach.

To verify our result, the following basic property of asymptotical regularity is required; also cf. [6], Proposition 2.1] in a topological vector space.

Put Φ and Ψ as in (2.1) and (2.2), it is easily checked that Φ and Ψ satisfy all regularity assumptions required in Theorem 2.1.

We also show that, in this set-up, the regularity conditions required for the identification of the mean counterfactual outcome for participants marginally eligible for the programme are essentially the same as in a sharp RDD.