Sentence examples for formula will be useful from inspiring English sources

The following discrete backward fractional Taylor formula will be useful.

Nevertheless, as we show in Section The MulRF Problem, the formula will be useful for computing the RF distance between input gene tree and a species tree.

The proposed formulae will be useful for strength and fatigue designs of engineering structures with notches and holes.

The following formula will be used extensively.

The formulas derived can be used to determine whether cooperation will be useful based on the characteristics of the considered scenario.

The shortcut formulae and methods presented here will be useful in the design and troubleshooting of industrial beef chillers.

For this, the formula presented in Eq. (16) will be useful.

Their backshift operator formulas reveal factorizations like others that will be useful: begin{aligned} hat{N}_{t}= & left( 1+Phi right) ^{-2}left{ -Phi B^{q}+left( 1+Phi ^{2}right) -Phi B^{-q}right} Z_{t}nonumber = & left( 1+Phi right) ^{-2}left{ left( 1-Phi B^{q}right) left( 1-Phi B^{-q}right) right} Z_{t}.

The simple formula obtained in this paper (Eq. (10)) will be useful for systematically analyzing the relationship between these complex effects of the magma properties and the conduit flow dynamics.

Before you start this problem set, you might want to read over our Guide to Negating Formulas and Guide to Logic Translations, both of which will be useful in the course of completing the assignment.

It can be difficult to create beautiful spaces when there is a formula but this is a year of good architecture that will be useful".