Sentence examples for estimate proposition from inspiring English sources

The oscillation estimate Proposition 3.3 can be used to obtain the following interior Hölder estimate by the method of iteration.

Using the center (L_{0} -average Lipschitz condition, we also estimate in Proposition 3.7 the quasi-regular bound function.

Then, from the estimate of Proposition 2.1, we see that (widehat{X}^{varepsilon}(0)rightarrowwidehat{X}(0)) as (varepsilonrightarrow0).

In view of the a priori stability estimate in Proposition 5.1 and the following result of local existence of a small solution to the transformed MHD problem, we immediately obtain Theorem 2.1.

The main ingredient of our proofs will be the estimate in Proposition 2.4 (see below) which relates the K-functional of the couple ((A_{0}+A_{1}, A_{0}cap A_{1})) with that of the original couple ((A_{0}, A_{1})), whereas this estimate has not been used in [7].

end{aligned}Applying Schauder estimates in Proposition we immediately deduce the proof of Theorem 8.1.

By taking into account the energy estimates of Proposition 3.1, we establish the following existence result.

Finally, all estimates in Proposition 27 hold under these weaker regularity assumptions.

The DOVCs of the gravitational gradients can be estimated using Proposition 1 based on stochastic model 1.

Thus we can derive the L2 estimates in Proposition 3.4 from (73) by using a standard method under assumption of the smallness of initial data.

After legislation analysts estimated that Proposition 209 would result in savings up to "$75 million in state spending on public schools and community colleges,"6 it passed by a 55% to 45% margin on the November 1996 ballot.