The phrase "as we replace with" is not correct in English as it is incomplete and lacks clarity.
It can be used in contexts where you are discussing a substitution or change, but it needs to be followed by a clear object or explanation.
Example: "As we replace the old software with the new version, we expect to see improved performance."
Alternatives: "as we substitute with" or "as we change to".
For one thing, not every case of replacement counts as substitution: the expression we replace with its synonym within a larger expression must be a constituent of the larger expression.
As we replace our vending machines with healthier foods, I think we can move our fundraisers to healthier alternatives also.
And Race to the Top should be the approach we follow this year as we replace No Child Left Behind with a law that is more flexible and focused on what's best for our kids.
"We are positioning it as we are replacing with motion and all the contacts in your house.
(2) and (3) can be written as: (8) (9) Now we replace and with the vectors and and replace and with and, respectively.
Since ICVD0 is used as the benchmark, we replace ICVD with ICVD1 and set it equal to 1 if the firm is in the category of ICVD1, and zero otherwise.
Notice that we could replace with, as real isotropy (to first order) does not depend on the fixed orientation on.
For example, in example (21), 'genre', as an element in the input test takers receive, is evaluated as 'essential', and if we replace 'essential' with 'useless', a negative evaluation, this will undermine the writer's effort to justify the importance of examining genre.
In terms of estimation, conceptually, one can estimate β js in a way analogous to linear reduction, i.e. through the eigen decomposition:, where Σ ϕ= Cov{ ϕ(X)} and Ωϕ is defined similarly as Ω x except we replace X with ϕ(X).
As such, we replace the expectation from (4) with an approximation defined as ({{tilde{V}}_t}(x_t)).
