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The phrase "on the relationship between" is correct and usable in written English.
It is used to introduce two things that have a relationship. For example, "This article will explore the relationship between mental health and self-image."
Exact(43)
In order to promote public acceptance on nuclear energy, an experimental study named "Local Civic Forum" has been performed as one of the research activities on relationship between nuclear energy and society promoted by the 21st Century Center of Excellence Program: "Innovative Nuclear Energy Systems for Sustainable Development of the World" conducted in Tokyo Institute of Technology (Tokyo Tech).
The use of these functions depends on relationship between the inputs and outputs.
Our approach is focused on relationship between SNR and Hartley entropy.
This paper focus on relationship between sentiment words and name entities.
The standard calibration curves of methane and hydrogen were made based on relationship between peak area and the respective concentrations (R2 = 0.994, n = 6).
Fundamental studies on relationship between surface structure of semiconductor nanocrystals and their excited-state properties had been studied and attract full interest recently [15 18].
Similar(17)
Another explanation, the distal cause, turns on relationships between male and female elks.
The only person who could get through to him was Lana Tisdel, who had known him since they were children, and with whom he maintained an off-and-on relationship between incarcerations.
"Whereas religious systems premise themselves on relationships between man and deity".
He continued: "But on secular matters, on legal matters on relationships between two people, it is not infallible".
The deep story here focuses on relationships between social groups within the national borders of the United States.
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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