Sentence examples for former equations from inspiring English sources

A comparison of these equations with the simple additive equations which have been previously postulated to account for the viscosity of salt solution mixtures has revealed that the former equations give agreement with observed data to within 1% whereas the latter equations yield errors ranging from 5 to 20%.

Thus, despite the similar structure of (2.4) and (2.5) to (2.1) and (2.2), respectively, the former equations seem to need a specific study.

One equation for the primary commodity now replaces the two former equations.

Since the general momentum equation for any mass m can be written mv = Square root of√2zVm, it is apparent from the former equation that the momentum m2v is appropriate to an ion of mass m 2/2/m1.

The former equation is a prior probability which is calculated before image processing at time t, and the latter is a posterior probability which includes the estimation result.

One of the differences between variational method Eq. (3.5) in this manuscript and BS equation is clear even in the no interaction case ((alpha =0)), that is, the former equation has no negative energy solutions.

In the former equation, Lagrange multipliers corresponding to each sample are expressed as α i *. b* is representative of the classification threshold, which can be calculated through the SVs.

In particular, the former equation does not have any such solutions, while the latter may, but only when or We are then able to pinpoint the exact conditions on, and such that the desired solutions exist.

The absorption coefficient of a compound, in the former equation, is a product of the concentration of the compound and the specific extinction coefficient of the compound.

We now obtain: Gn = Gi1 ∪ Gi2 ∪ {parent}, Ln = Li1 ∪ Li2     (4) The parent is added in the former equation because of the assumed gain event.

v is flux vector that corresponds to the columns of S. Given a set of experimentally-driven constraints, former equation was solved by using linear programming, the approach known as flux balance analysis, or FBA [ 16].