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The phrase "a relation based on" is correct and usable in written English.
It can be used to describe the foundation or underlying principles of a relationship, whether personal, professional, or theoretical.
Example: "Their friendship is a relation based on mutual respect and trust."
Alternatives: "a relationship founded on" or "a connection rooted in".
Exact(6)
As with most children, theirs was a relation based on verbs, not nouns.
This method consists in staggering the wavelength distribution following a relation based on the Padé approximant.
A relation based on a finite element model was then developed and used to calculate stresses.
Thus the non-transitivity of the counterpart relation (a relation based on resemblance) appears neatly to allow the counterpart theorist to respect both the tolerance principle and the restriction principle, without falling into contradiction.
Fowkes [12] proposed a relation based on the surface energy of the material in its pure phase (γa), which is a sum of the contribution from the dispersion (γad) and the polar (γap) components and may be represented as; (1).
3. Active Participation: "a relation based on partnership with government, in which citizens actively engage in the policy-making process.
Similar(54)
We note that defining physically an effective temperature for non-thermal-equilibrium electrons is non-trivial [34], which is not always a scaling relation based on a linear response theory for perturbative thermal-equilibrium states.
We introduce a dependency relation based on a set of minimal T-invariants.
We performed the same comparisons as illustrated in this report using a neighbor relation based on a Delaunay triangulation.
This paper proposes a synchronized horizontal fragmentation, replication and allocation model that adopts a new approach to horizontally fragment a database relation based on attribute retrieval and update frequency to find an optimal solution for the allocation problem.
Previously, it has been reported that the Agenet/Tudor domains from Arabidopsis proteins contain an average of 60 amino acids within a few conserved positions and a distant relation based on sequence alignment with Royal family domains [ 3].
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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