How to use of "the" with some equations? [duplicate]

Question

I am thinking which one you should use

A

Lorem ipsun which is the Wigner-Ville transform.

B

Lorem ipsun which is Wigner-Ville transform.

Some says that the first but I like the last one because it is shorter and because the first letter of the transform is capital.

Should use the article the in the above example?

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I have had an idea that if the first letter is uppercase, then you do not need the, because of the following other example

AA - right according to my teacher

Here in Equation (11) and Figure (2).

BB - wrong according to my teacher

Here in the Equation (11) and the Figure (7).

Answer 1

I don't think the examples and your actual case are analoguous.

In your examples AA and BB, you are merely identifying two nouns, while in your actual prose, you are specifying a noun (apparently from some previous phrase not included in your post).

Your first case:

Lorem ipsun which is the Wigner-Ville transform.

Is using "the Wigner-Ville transform" as a noun, and saying that something is something else..its a noun-noun relation.

Your second case:

Lorem ipsun which is Wigner-Ville transform

Is using "Wigner-Ville transform" as an adjective, so it is modifying something to make it more specific, it is a noun-modifier relation. To clarify, look at the following two sentences:

1. The dog is a poodle
2. The dog is poodle

I think you can see that (1) makes sense as it is going from a general category to a more specific category, noun to noun, while the second only makes sesnse if "poodle" were some type of adjective, which is it not.

Therefore, since a mathematical transform is a noun, the first is correct, at least by my reading.