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The phrase "a first search" is correct and usable in written English
It can be used when referring to an initial attempt to find information or data on a particular topic. Example: "After conducting a first search on the topic, I found several relevant articles that could help with my research."
Exact(13)
This paper presents a contribution to handle this kind of problems by implementation of a hybrid optimization technique based on the successive use of a Genetic Algorithm (GA) and of a classical Sequential Quadratic Programming (SQP) method: the GA is used to perform a first search in the solution space and to locate the neighborhood of the solution.
Unfortunately, a first search in the literature indicated that none of the retrieved in vivo studies provided quantitative values to identify this combination.
A first search of PubMed to identify relevant papers for our meta-analysis was conducted on September 6th 2007 using search string 'rotavirus' AND 'infection' NOT 'review' NOT 'letter' NOT 'clinical trial'.
A first search was performed with the FASTA algorithm of the Wisconsin GCG program package [ 44].
A first search addressed the key terms shock wave, shock waves, shockwave, shockwaves, lithotrypsy and lithotrypter.
A first search revealed a series of conserved predicted promoter elements (Additional file 15: Figure S4a).
Similar(47)
A second search also was unsuccessful.
A second search yielded a suggestion for two out of three ingredients necessary to make gunpowder.
Saturday 4 August: Police launch a second search of Murat's house.
Before hiring Dr. Schnur, the Montgomery school board turned down eight candidates and started a second search.
Tia's body was found there a week later during a fourth search of the property.
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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