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Is there any difference between these examples?

Example 1
(a) An example of function that satisfies the required condition is given by...
(b) A wave equation is an equation that describes the behaviour...

Example 2
(a) An example of function satisfying the required condition is given by...
(b) A wave equation is an equation describing the the behaviour...

I need to write sentences like these in a scientific paper, but I don't know if one of them is wrong or is more appropriate than the other.

Here is a similar question, but I'd like an explanation about my specific examples.

  • Side note: This is "that [present perfect]", not "present [infinitive]". That + Infinitive would be something like "give an example that satisfy" or "give an example that to satisfy" which isn't valid. – Mark Jun 10 '15 at 17:22
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    @Mark That satisfies/describes is not present perfect (which would be that has satisfied/described but (simple) present. – StoneyB on hiatus Jun 10 '15 at 17:25
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    As a side note, in both of your a) examples, I want to add 'a' or 'the' to the word 'function'. This becomes: An example of a function... – Michael Dorgan Jun 10 '15 at 17:42
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Grammatically, they're both identical to each other when telling someone what to do. In different contexts however, they can mean different things:

This is a dog that chases chickens

The dog might not be chasing chickens right now, but he likes chasing chickens and does it often. Sometimes he chases one chicken, and other times he chases several.

This is a dog chasing chickens

This dog is chasing chickens (more than one) right now. This might be the first time he's ever chased chickens, but maybe he's chased them before.

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