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"research have shown" is correct and usable in written English.
You can use it when you want to refer to research that has been conducted in the past and yielded certain results. For example, "Research have shown that people who are exposed to too much blue light from screens can have trouble sleeping at night."
Exact(60)
Many avenues of research have shown that ABA is a key player in such stress resistance.
Decades of research have shown that the criminal courts sentence black defendants more harshly than whites.
Three decades of research have shown that nonverbal signals, so prized by the Reid trainers, bear no relation to deception.
As several pieces of research have shown recently fiction helps us to understand other people and empathise with them.
Recent findings in psoriasis research have shown that psoriasis is frequently associated with systemic comorbidities.
Studies from social cognitive research have shown that processing fluency influences decision-making and evaluation processes.
Decades of research have shown that consumers often say they want sustainable products but rarely purchase them.
His 20 years of research have shown that the brain matures by becoming more connected and specialized.
But younger Silicon Valley executives, particularly those in A.I. research, have shown little interest in seeing their new technology used by the military.
Decades of research have shown that experiences at home and in neighborhoods have far more influence on children's academic achievement than classroom instruction.
Traffic crash statistics and previous research have shown an increased risk of traffic crashes at signalized intersections.
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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