Sentence examples for rendering the two from inspiring English sources

Consequently, we have to modify our joint probability distribution from P b,w) to P ( b ̂, w ) = δ ( b ) P ( w ), that is, where P(b|w), viewed as a generative mechanism, has been replaced by δ(b), thereby rendering the two random variables independent.

and substitute it into Equation (3) hence rendering the two Equations (1) and (3), each of which depends on both Ts and Tf, into separate equations for Ts and Tf, respectively, in the form: τ q ∂ 2 T i ∂ t * 2 + ∂ T i ∂ t * = α e [ 1 r * ∂ ∂ r * ( r * ∂ T i ∂ r * ) + τ T r * ∂ ∂ r * ( r * ∂ 2 T i ∂ r * ∂ t * ) ]  for  i = s, f (7).

The cluster has a noncrystallographic C2 axis passing through the μ2-oxygen O3 and Ti5, thus rendering the two Ti3O units chemically equivalent.

This proposal says the Maglev could put London's airports within 20 minutes of another rendering the five airports one giant hub.

Two topics dominated conversation: the day ahead and the weather that had rendered the two previous days a waste.

The size and configuration of their primitive feathers, as well as the size of their forelimbs and other characteristics, probably rendered the two creatures flightless.

However, given that FVM09 is a non-neutralizing and non-protective antibody, viral escape from ADI-15946 neutralization would render the two antibody combination non-protective.

Banking mandates, however, could render the two microfinance-license aspirants incapable of lending to the poor and credit-less as they do now, Trivedy told me.

Firefighters did manage to keep the flames away from a nearby company warehouse that was stocked with the imports that had rendered the two factories — and the seven hundred workers who'd once worked in them — obsolete.

Calculating the temperature profile within the two hypothetical nuclear explosive device models showed that this plutonium vector would render the two models useless by causing the high explosives to undergo self-explosion.

Then, the movement of the platform, after accurate data georeferencing and calibration, can render the two series of 2D scanning profiles in parallel into a full 3D representation of each row of plants of interest.