Sentence examples for provided that the initial from inspiring English sources
provided that the initial conditions satisfy (3.5).
where ( small enough), provided that the initial conditions satisfies.
Based on BLF-based backstepping, we show that asymptotic output tracking is achieved without violation of any constraint, provided that the initial states and control parameters are feasible.
Provided that the initial vectors ((tilde{u},tilde{w})) are close enough to ((u,w)) the sequence of approximations ((tilde{u},tilde{w})) converges quadratically to ((u,w)).
Provided that the initial distribution of a population and the vital rates are known, we estimate the population density in the worst and in the best case scenarios.
The existence and uniqueness of global weak solutions for Eq. (3) have been established provided that the initial data satisfy appropriate conditions in [6].
Seeding can lead to a low toughening improvement, providing that the initial powder is free from large pre-existing β nuclei.
It was found that the transient stress dip of Fotheringham and Cherry could successfully predict the recovery providing that the initial deformation which produces the molecular orientation is undertaken at a sufficiently fast strain rate.
Provided that initial therapy was appropriate, the clinical course appears favourable, and microbiologic data do not point to a very difficult-to-treat microorganism, the physician could switch to mono-therapy on days 3 5.
We first show how to generate guaranteed upper and lower bounds on the state, provided that known intervals for the initial condition and the uncertainties are available.
In [7, 29 33], the spacial decay rates for the strong solutions to the Camassa-Holm equation, the b-equation, and the Novikov equation were established provided that the corresponding initial data decay at infinity.
