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The phrase "and we insert the" is correct and usable in written English.
It can be used when describing a process or action where something is being added or included in a particular context.
Example: "In the final step of the procedure, and we insert the necessary data into the system to complete the update."
Alternatives: "and we add the" or "and we include the".
Exact(1)
We consider θ0 as the number of vertices of the maximal clique that contains v1, minus one; and we insert the vertices of this clique in (P^{theta_{0}}).
Similar(59)
During operation, we tried to retrieve incarcerated small bowel from intersigmoid fossa by tender operation, and we inserted the tissue pad of power device to the edge of hernia orifice to prevent small bowel injury, because incarcerated small bowel was fixed to the hernia orifice of sigmoid mesocolon.
In this new computation we used the de-phosphorylation rate we just estimated and we inserted the translocation rates α and β measured in the FRAP experiments with the ERK1-GFP protein.
"Put another way, every other day we leave a foreign object in someone's body, every week we operate on the wrong part of someone's body, and every fortnight we insert the wrong implant.
In order to measure the background noise generated by the amplifier and the glass micropipette, we insert the micropipette directly into the dead brain tissue submerged in a saline solution to maintain tissue freshness.
And we insert into text the word sic, the three-lettered bitchy Latin put-down which, between parentheses, signposts: "Don't for one second assume that was my sloppy error, I'm merely replicating verbatim the poorly spelled musings of the great unwashed".
Given the distribution of population, the growth function of populated locations and the largest population size, we insert the above expressions of P s,t), l(t), and n(t) as shown in Eq. 4, Eq. 5 and Eq. 6 into Eq. 3. Then we have GP ( t ) = ∫ 1 a ∗ t b + c ( ( φ ∗ s - λ ) ∗ ( η ∗ t ε ) ∗ s ) ds = ηφ t ε 2 - λ [ ( a ∗ t b + c ) 2 - λ - 1 ].
"We take a cell derived from humans that we can insert our genetic circuits into… we insert the DNA and encoding and deliver those cells via an IV infusion.
We insert the heat and mass transfer through temperature and Gibbs free energy relaxation effects.
Specifically, we insert the template and watermark at level 1 and levels 2 to 3, respectively, of the DPT pyramid in the embedding process.
To balance stress tolerance and fermentation performance, we inserted the promoter of a gluconeogenic gene, PCK1, into the 5′-untranslated 5′-untranslated of the regiongene in a laboratory strain to achieve repression of RIM15 gene expression in the glucose-rich early stage with its induction in the stressful late stage of alcoholic fermentation.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com