Sentence examples for require regularity from inspiring English sources

Moreover, our theoretical analysis and convergence results do not require regularity assumptions of the model problems.

Note that KKT necessary conditions usually require regularity of a local optimum, which amounts to (in the context of Problem (25)) linear independence of the gradients of the active inequality constraints evaluated at the local optimum (see Proposition 3.3.1, p. 310 in[25]).

Rhythm required "regularity," and so the Pill had to produce regularity as well...It has often been said of the Pill that no other drug has ever been so instantly recognizable by its packaging: that small, round plastic dial pack.

An optimal order error estimate in the L2 norm was proved via the well known Nitsche lifting technique under the assumption that the true solution to the corresponding boundary-value problem of the fractional diffusion equation has the required regularity for each right-hand side.

The proof of this theorem is quite interesting since, unlike the regular case (i.e., when (L_gamma =L_0=-Delta )) or in the situation when the singularity 0 is in the interior of the domain (Omega ), the application of the standard Nash-Moser iterative scheme is not sufficient to obtain the required regularity.

A few patients felt that they would become used to long-term treatment but required regularity and organization.

Third, the solutions of the novel method to the optimal control problems require low regularities.

Our results yield the existence of unstable solutions, localized by means of α and β, requiring weak regularity of the coefficients of the equation.

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.

So there is a tradeoff between (Ren et al. 2016b) and the present paper: (Ren et al. 2016b) requires stronger regularity while this paper requires certain piecewise Markovian structure.

Taking the lim sup on both sides of the above estimate and using (3.6 - 3.7 3.6 - 3.7the required asymptotic regularity of the k th-mapping S k, that is, lim n → ∞ d ( x n, S k x n ) = 0. Let { u n } be any subsequence of { x n } weth A K ( { u n } ) = { u }, then lim n → ∞ d ( u n, S k u n ) = 0. (3.8).