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I noticed both of them are used in academic papers.

If both of them are correct, is there any difference between the two?

  • Usually 'some constant' introduces "some constant where ..." or "some constant defined by.." That's a certain fixed number, not just any fixed number. If you are defining a as a constant, then 'a is constant' is all you need to set a as any constant. – Yosef Baskin Jul 12 '17 at 21:28
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    Both versions are fine. – GEdgar Jul 12 '17 at 22:01
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There's a slight nuance, in that the word "some" implies that some choice is possible. Compare:

  1. The ratio of the input voltage to the output frequency is a constant, whose exact value depends on the purity of the material, vs

  2. The ratio of the input voltage to the output frequency is some constant, whose exact value depends on how finely the machinist followed the specifications.

Another way of looking at this is to form a sentence referring to a well-known constant where no "choice" is possible. For example:

  1. The number of pennies in a dollar is a constant, vs

  2. The number of pennies in a dollar is some constant.

The second form seems strange to the ears. Either that, or it serves to introduce some speculative work in theoretical economics...

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