Sentence examples for with this substitution from inspiring English sources

This will be the ansatz of our mean-field approach where we ignore quantum fluctuations in the two outer resonators and substitute a ˆ 1, 3 → α 1, 3. With this substitution, the Hamiltonian for resonator 2 takes the form H ˆ M F = Δ ω a ˆ 2 † a ˆ 2 − U 2 a ˆ 2 † a ˆ 2 † a ˆ 2 a ˆ 2 − J ( α 1 + α 3 ) a ˆ 2 † − J ( α 1 ∗ + α 3 ∗ ) a ˆ 2 (20).

With this substitution, the message becomes: Democracy Redeems Worldly Desires.

It could save 43% cost of SCC with this substitution.

With this substitution and after some rearrangement, (A.8) becomes (A.10 Finally, reduces to (19).

With this substitution, and using the fact that is an even function of and, (23) becomes.

In addition, the workability has been also improved with this substitution.

To begin with, we note that this substitution is one-to-one.

A screen for evolutionary conservation with SIFT v.2.0 predicted this substitution to be tolerated [ 32].

Consistent with this epidemiological observation, this substitution weakened the anti-HIV-1 and anti-HIV-2 activity in vitro[ 84].

If a nonsense mutation coincided with the predicted PTC, this substitution was regarded as the causative event.

There was only partial segregation of this substitution with breast cancer in the single family but such observations have also been made for other susceptibility alleles with low to moderate penetrance and do not exclude a possible contribution to breast cancer risk.