Differences in meaning between phrases with and without indefinite article

Could you please help me by clarifying the meaning of the two phrases below:

• a profound analysis of the problem



• profound analysis of the problem

Here's the context: I want to convey information that some mathematical tool is applied to analyse extra-mathematical phenomena. Which should I use while saying: The tool is applied in (a) profound analysis of such-and-such phenomena?

Or maybe both versions are correct, but their meaning is different?

Answer

The use of the indefinite article implies to me that the thing only happened once.

'A profound analysis' suggests this was one discrete event.

'Profound analysis', suggests the analysis has been going on for some time, including perhaps a number of different people and experiments etc.

This is a very simple explanation and clearly cannot be used as a hard and fast rule.

'An experiment' suggests something slightly different to 'Experimentation', as does 'I have been for a swim' sounds different to saying 'I have been swimming'. 'A swim' sort of implies you just did six lengths of the pool and then got dressed. 'Swimming' suggests you stayed in the pool for some time, and did various types of swimming, and perhaps socialised.