Sentence examples for improved remainder from inspiring English sources

Then one can prove easily that the standard conditions to the trajectories are fulfilled and we may use the improved remainder estimates.

If we want to improve the remainder estimate (O(N^{frac{5}{3}})), then we need to improve the semiclassical remainder estimates and also deal with (O(N^{frac{5}{3}})) in Lieb's electrostatic inequality (7.7).

To improve this remainder estimate, we should carefully study the propagation of singularities.

We can even improve the remainder estimate to (o(h^{1-d})) under the standard non-periodicity condition.

end{aligned} (2.67 To improve this remainder estimate, one needs to improve (2.65) rather than (2.63) but to get sharper asymptotics, we need to improve both.

This allows us to improve the remainder estimate in the full Weyl asymptotics but we need to include many terms which are difficult to calculate.

It turns out that there are short periodic trajectories with period (asymp mu ^{-frac{1}{2}}), but there are not many of them which allows us to improve the remainder estimate in this zone as well.

The grocer suffered a 2.5 per cent fall in underlying sales over Christmas and trading is not expected to have improved over the remainder of its fourth quarter.

In addition, we estimate that 48% of people using pit latrines use facilities characterized as improved, whereas the remainder uses shared or unimproved facilities (e.g., traditional latrines or pit latrines without slabs).

"As the role of temporary factors set to fade at some point, an improved performance over the remainder of the quarter seems likely, but that industry will make a positive contribution to GDP growth is looking tenuous," Beck said.

With an improved forecast for the remainder of the match, England will be looking to post an imposing total before unleashing their trio of seamers - with Stuart Broad preferred to Tim Bresnan - on India's star-studded batting line-up.