Thierry, I see some difference here in that VP's questions often are/were at least questions that make sense (the FLT is not in this category), even if they are tersely formulated and too simple. However, perhaps more advertising of math.SE will do; where I think some of the questions would fit in.

By contrast for AB there is often not even a question; one might attribute this to major difficulties with English. But then it did not seem so bad, and then there was a switch to French but the question did not at all become clearer or more detailed. And, also no willingness to communicate somehow with people commenting. So here I am really at a loss regarding the motivation.

I was thinking of bringing this user up, Will. In particular, these answers

http://mathoverflow.net/questions/77634/best-simple-eigen-decomposition-algorithm-for-pca-are-there-multiple-solutions-t/77638#77638

http://mathoverflow.net/questions/76549/modeling-appropriate-set-of-learning-activities/76556#76556

are particularly unhelpful and snide about site polices.

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The user antoine-balan was active again, but is re-suspended (actually re-re I think).

The most recent question however is now 'defended' by JDH and somewhat close to reopening. I do not have the individual competence to judge the merits of that questions, but I certainly trust JDH's judgement on this. Still I see little point in reopening this. The question seems to be alright purely as a mathematical question, but is still not a good MO question (from a more formalistic point of view). And, that user has meanwhile a considerable track-record of asking 'questionable' question and in particular is completely unresponsive to comments in English and French (so that this does not seem to be purely a language problem). Moreover, the question range over several mathematical fields, and so the motivation even seems more unclear. What's the point of all these questions? Just asking some questions on MO, or something else?

So, I think as long as this user does not make some good-faith effort to comply a bit to the basic standards of the site I think there is little reason to be 'friendly'. Just that one of these question happended to be a good one, is to little reason for me. (We already had one other instance where somebody, algori I believe, helped out with the formulation of the question, but this was at least earlier in the process.)

My point here is not so much that I want to enforce standards for MO questions here. My key point is the: happended to be a good one. If one writes enough very terse question, eventually one will be about alright. (If it were not so terse one could infer something more.) I think it is unfortunate to encourage this user in any way, as long as there is no consistent improvement of behavior.

In 10 days when the supension ends, what will happen. We get some new questions. We close five and the sixth one will be sort of alright. This seems a pointless activity to me.

No, I do not suggest a permanent ban. I only suggest to be somewhat stricter than with any other user. In particular, as this was not the first question after the temporary suspension expired. (If this were so, one could say there was some improvement.)

For example, you said, some days ago (my emphasize):

I think MO is for professionals to answer questions of professional interest in ways likely to be useful to the questioner who is honestly in need.

Let's say I doubt the emphaszied part. And, while I would not always be strict regarding this, I think it is justified to be so in this case. To put it differently, I think MO should always be open for things falling into the category you laid out, yet not exclusive for this, in general. Yet, under special circumstance, I think one can fall back to this and require at least implicit/indirect proof for this.

Just to make my point on that last question,

The proof itself is very nontrivial (i.e. it is more than just a simple symmetry argument as with other, simpler, permutation models) and personally I do not have the time to study it in-depth, although I would do so eventually.

Furthermore, when answering a particular user I would always prefer to aim for the user's level. If someone whom I know to be proficient in permutation models asks a question it will be fine just to outline the model and the argument for the proof. On the other hand, if it is someone who is less familiar then I would bring myself to write a short exposition on the topic as well.

Judging from the previous questions, it seems that the latter is the case due to the previous questions. Which makes the job even longer and harder, one more reason for me not to approach this question (even if I'd wanted to do so right now). Maybe in a few weeks I can find the time for it, but I cannot say right now.

Lastly, all been said, I support quid's stand in this case. I believe that somewhat a stricter approach towards this user is in order.

He's back, or at least someone with the same name is:

http://mathoverflow.net/questions/87566/endomorphismes-of-a-fiber.

I have no idea if the question is easy, or hard, or suitable, or interesting.