The author of the above mentioned paper found that pointwise ergodic theorem for bounded additive processes, cf. Theorem 7.11 needs an additional assumption.
Kalman filters make an additional assumption about the variables that they are tracking.
Under an additional assumption, explicit nested predictor feedback controllers involving only 1-fold integrals are established.
Then, a stabilizing controller is constructed for the reduced-order model under an additional assumption.
Also, we obtain Gaussian bound for Robin Green's function under an additional assumption that weak solutions of Robin problem are locally bounded up to the boundary.
It starts with the formulation of the Lagrangian variational principle with an additional assumption that the volume of domain (in 2D the area) describing the structure in the undeformed state remains constant during the deformation process.
This technique has the advantage, under an additional assumption, to ensure a global asymptotic stability property and to allow the user to directly tune the minimum inter-transmission interval.
Under an additional assumption of log-concavity for the measures we prove the existence of a gap at the lower end of spectrum of the Dirichlet operator and the ergodicity of the corresponding semi-group.
Note that there was an additional assumption made that ({upomega }_{mathrm{responding}} > 0).
However, to achieve such improvement, an additional assumption (3.35) is required.
Note that under an additional assumption that is strictly increasing, we have.
