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Providing that/Provide that

I'd like to find out what we should use after them
I've been studying different examples and found out that we can use
indicative mood
subjunctive mood

1) indicative mood
Tony will attend provided that Sarah is not chairing the meeting.
Provided (that) she studies hard, she'll pass her exams.

2) subjunctive mood
The newspaper did not publish the photographs because they were given by a confidential source who did so provided that we not release them before the elections.

THE QUESTIONS

1) How do we define which tense to use? Why do we us PRESNET SIMPLE here

Provided (that) she studies hard, she'll pass her exams.
Why not?
Provided (that) she is studying hard, she'll pass her exams.

Or this one

Tony will attend provided that Sarah is not chairing the meeting.
Why not?
Tony will attend provided that Sarah does not chair the meeting

2) When do we use subjunctive mood? Can we always use subjuntive mood here or only upon certain conditions?

Can we say like

Provided (that) she study hard, she'll pass her exams.
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I like this question - because it's difficult!

'Provided that' means 'if the following condition is met'. 1) She will pass if she studies hard - over a long time period (between now and the exam), or habitually. 'She is studying' implies just an action happening right now. So most accurately, the condition to be met is habitual or repeated or long-term, so 'she studies hard'.

In the second example I think either is ok - but I suppose the condition to be met is that Sarah is not chairing the meeting at the time the meeting happens - so an immediate state, needing 'chairing'. But I'd happily use either.

2) yes technically I think you can say that but the subjunctive here sounds old-fashioned. It sounds less strange to me if the subjunctive clause comes second, but the indicative is more usual now. Even the subjunctive example you use about the newspaper sounds unusual to me

Hope that helps
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First of all I would like to thank you for this fair answer. I think that ability to explain language phenomena is an art. Sometimes I get saddened because of poor answers received from contributers and make them sad in return, too. )))) However, this is defenitely not the case. I am quite content and grateful to you for the answer.

There are some minor details I would like elaborated.

1)
deborah_d'She is studying' implies just an action happening right now. So most accurately, the condition to be met is habitual or repeated or long-term, so 'she studies hard'.
Present Continuous, as you fairly said, conveys an ongoing action at a certain moment. However, this moment can be quite long. For example

We are not growing potato this year. He is not playing football this season.
I think that it should be enough to get ready for an exam (I mean 1 year, or a season)

Again, she doesn't take exams everyday what makes it also a temporary action. She is to study hard only within a certain period of time. How would it sound to you if I said

Provided that she is stadying hard (this month) she will pass the exam.

I think this is all what I would like to tackle on this issue.
Interesting, and good examples. Yes, you could say that - I wouldn't include 'this month' as it implies continuous study for the whole of the month. I've had to say it to myself a few times to check it sounds right, and it does! The 'she studies' form is more common, though, in my experience.