Sentence examples for variation operator of from inspiring English sources

Following the approach of Vassilev et al. [1] we propose to estimate landscape properties from random walks using the variation operator of the search heuristic.

We introduce new high level reactive search strategies based on a generic algorithm's controller that is able to schedule the basic variation operators of the evolutionary algorithm, according to the observed state of the search.

As applications, the weighted ((L^{p}, L^{q}))-estimates for the oscillation and variation operators on the iterated commutators of Hilbert transform and Hermitian Riesz transform, the ((L^{p}, dot{wedge}_{(beta -1/p)}))-bounds as well as the endpoint estimates for the oscillation and variation operators of the corresponding first order commutators are established.

We consider oscillation and variation operators for commutators of the Hilbert transform and Hermitian Riesz transform.

In this paper, we will study the behaviors of oscillation and variation operators for the families of commutators defined by (1.7) and (1.8) in Lebesgue spaces.

In this paper, we will study the boundedness of oscillation and variation operators for the family of the multilinear singular integral related to a Lipschitz function defined by (1.5) in weighted Lebesgue space.

Recently, some authors [5 8] researched the weighted estimates of the oscillation and variation operators for the commutators of singular integrals.

As applications, the corresponding boundedness of the oscillation and variation operators for the commutators of Hilbert transform and the Hermitian Riesz transforms will be given.

Recently, Liu and Wu [5] gave a criterion on the weighted norm estimate of the oscillation and variation operators for the commutators of Calderón-Zygmund singular integrals with BMO functions in dimension 1.

Campbell, Jones, Reinhold, and Wierdl in [2] established the (L^{p} -boundedness of variation operator and osciL^{p} -boundednessof the Hilbert transform.

end{aligned} The main purpose of this paper is to establish the weighted (L^{p} -boundedness of the variation operator and the osciL^{p} -boundednessof (theb}).