Sentence examples for further formulas from inspiring English sources

An axiomatic system of logic can be taken as an example—i.e., a system in which certain unproved formulas, known as axioms, are taken as starting points, and further formulas (theorems) are proved on the strength of these.

In classical logic, the set of conclusions that can be drawn from a set of formulae always increases with the addition of further formulae.

And this result was greatly useful and helpful for the quality control and further formula optimization of the technical study of Zhuyeqing Liquor.

These findings for the first time reveal that oxidative phosphorylation pathway is suppressed in longissimus dorsi muscle of weaned piglets fed low-protein diet supplemented with limiting amino acids, which may provide new insights into further formula design and the choice of limiting amino acids in diets.

Further geometric formulas related object positions to the necessary joint angles needed to allow a robot arm to grasp them, or the steering and drive motions to get a mobile robot around (or to) the object.

Some go further, hiding formulas in a sleeve or in a bathroom stall, Googling facts on an iPhone or snapping a photo of test questions to send to a smart friend for help.

In this phase, right-introduction rules are applied in any order until there are no further asynchronous formulas.

Further specialized formulas of the identity in (3.17), for later use, are obtained as in Lemma 6 below.

For the further investigation, formulas are derived to determine direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions by using the normal form theory and center manifold theorem.

Future studies, with more intensive mathematical analysis of astigmatism itself, are needed to further improve formulas and laser nomograms for cylinder correction.

Further, the formulae obtained are identical with those given in IEC 61508.