with A being something OR with A to be something, which one is correct?

Question

The wavenumber ky = ω/cR with cR being the shear-wave velocity of the bedrock.
OR
The wavenumber ky = ω/cR with cR to be the shear-wave velocity of the bedrock.
I am wondering which expression is correct or more preferred by natives.

Joce · Accepted Answer

Using 'to be' implies something expected rather than a current fact, implying 'due to be`:

We expect to have a lot of people come up this weekend with the weather to be quite nice

In mathematics and other sciences, you would either use the present tense as @Jim suggests, 'where cR is...' or write 'The wavenumber ky = = ω/(cR), cR being...'

with A being something OR with A to be something, which one is correct?

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