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'closes a cycle' is a correct and usable phrase in written English.
You could use it when you want to talk about the completion of a cycle, as in "This experience closes a cycle in my life."
Exact(4)
It simply closes a cycle.
The achievement closes a cycle in scientific history that began in 1910, when Thomas Morgan of Columbia University chose Drosophila as the experimental animal with which he and his students would work out many of the basic principles of genetics.
R closes a cycle because of a symmetrical argument to that made for F. Case 2 F and R reach the same vertex v simultaneously.
R closes a cycle because of a symmetrical argument to that made for F. F and R reach the same vertex v simultaneously.
Similar(56)
Last year, Rankin waved farewell to Inspector Rebus as Exit Music closed a cycle of 17 novels that not only sold in stupendous quantities but, in their richness of context and character, helped to re-draw the cultural map of Scotland.
"These elections close a cycle and now a new phase starts in our country.
The Fourth High Level Forum on Aid Effectiveness in Busan, South Korea (29 Nov - 1 Dec 2011) will close a cycle that has largely focused on aid and mark a transition to addressing the challenge of how we apply what we know in order to make development -- not just development assistance -- work better.
Both paths close a cycle in this case.
We conclude that F has an edge outgoing from v and thus it closed a cycle.
We prove that in that case, F must close a cycle.
"This year of the Oxlajuj B'aktun [5,125-year [5,125-yearses on a cycle of time, but operiod new one when we hope peace and mutual respect will prevail," says Calvo.
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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