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The phrase "and with the initial" is correct and usable in written English.
It can be used when referring to something that is associated with or follows an initial element, such as a letter, number, or event.
Example: "The report should include the findings from the survey and with the initial data collected last month."
Alternatives: "along with the initial" or "together with the initial".
Exact(20)
The average flame height was found to correlate with an overall equivalence ratio and with the initial concentration of droplets at the burner mouth.
For all of the soils, Si linearly increased with the clay content and with the initial exchangeable K content of the soil.
Here is what he said about the need for a public inquiry into what went wrong at The News of the World and with the initial police investigation into the scandal, which had suggested that just one rogue reporter was involved: It is clear that there have been some illegal and utterly unacceptable practices taking place at The News of the World and possibly elsewhere.
Uhrman is a longtime video game exec with more than a decade of experience, and with the initial success of the Kickstarter campaign Ouya quickly attracted interest from independent developers.
Here we compare three cases with the maximum microbial densities of 1, 5, and 10 cell/μm2 and with the initial concentrations of oil degrading microbes and oil droplets of 2.73 × 103 cells/ml and 0.4 mg/L, respectively.
Let u and v be two weak solutions of equation (1.5) with the same boundary value condition (2.5) and with the initial values (u x,0)), (v x,0)), respectively.
Similar(40)
The site is browsed starting with the initial query and storing the requests sent to the site.
Waukesha Lime and Stone Company permitted and assisted with the initial study in their quarry.
In fact, after seeing Ricky's tweet – and dealing with the initial excitement and subsequent dread – I realised that I love it so much that I never want to see it again.
Cells were collected and pooled with the initial media and PBS wash.
The error between prediction and actual values (Eqs. 24 26) is estimated and compared with the initial variabilities (Eqs. 18 20).
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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