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When qualitative probability relations are defined on a language with a rich enough vocabulary and satisfy one additional axiom, they can be shown to be representable by probability functions i.e., given any qualitative probability relation ⊆, there is a unique probability function P such that A ⊆ B just in case P[A] ≤ P[B].
The cubic splines are defined on a graded mesh.
Models are defined on a reference site set and are evaluated on a test site set.
The quadratic programs are defined on a polyhedral set, which makes it easier to identify a local optimum.
The particles are defined on a separate Lagrangian mesh that is free to move over an underlying Eulerian grid.
The boundary value problems which are defined on a sequence of multilevel finite element spaces can be solved by some multigrid iteration steps.
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The displacements are defined on an arbitrarily selected co-ordinate system.
As observed in (1), margins are defined on an adjacency basis.
The functions under consideration are defined on an open subset of and take values in the Clifford algebra.
(A lunk is defined, on a poster, as "one who grunts, drops weights, or judges").
Note: In the first catalog release, the source region is defined on a tangent plane projection.
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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