We show that under some mild continuity restrictions this set has a non-zero volume, hence such bounded yet potentially globally unstable motions are realizable with a non-zero probability.
We quantify the possible deteriorating effects of the Gibbs phenomenon present in the Fourier based schemes due to continuity restrictions of the penalized Navier Stokes equations on the wall.
By the continuity of the restriction of z ˜ to the compact set S 2, there exists δ > 0 such that if p, p ′ ∈ S 2 and | p − p ′ | < δ, then | z ˜ ( p ) − z ˜ ( p ′ ) | < ε ′.
In their study of the bioenergy industry in the Netherlands, they found out that uncertainty about future restrictions and continuity of existing financial subsidies hindered the development and implementation of biomass gasification significantly.
Implementation of more stringent regulations on duty hours and supervision by the Accreditation Council for Graduate Medical Education in July 2011 makes it challenging to design inpatient Medicine teaching service that complies with the duty hour restrictions while optimizing continuity of patient care.
Finally, condition (13) is implied by conditions (11)–(12), Restriction i and the continuity of both MR and C′ q).
Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying mapping.
In fact, some data indicate that it is sleep continuity disturbance, rather than simple sleep restriction, that impairs endogenous pain-inhibitory function and increases spontaneous pain [4].
Last, we prove the global Hölder continuity of solutions provided that their restrictions on boundary are Hölder continuous.
In fact, Cambanis's approach is valid for any type of second-order signals and observation intervals, and it is not necessary to impose conditions such as stationarity, Gaussianity or continuity on the involved processes, nor restrictions of finite intervals.
