Although it seems that the user reacts somewhat harshly on questions/suggestions in the comments:
@MatthewLeingang ok , so the truth is I do not know. I am preparing for a competition . i don't have enough time to think about the logics behind the formulas. i am only worried about solving as many question as possible.i hope you understand it.Proof of the result is not given in my book — Kislay TripathiOct 12 at 12:52
Does there exist an example of a polynomial (or, at least, real analytic) differential equation system $\dot x=P(x,y), \dot y=Q(x,y)$ on the plane that has a stable focus and a center simultaneously?
The difficulty is that "center" means "a local conservation law", and "analyticity" normally mea...
Doesn't seem to be a question about math research, which is what we do here on MO. — Gerry MyersonNov 27 at 21:42
@GerryMyerson about math research, which is what we do here on MO Not all of us, not all of us ;-) By the way, how much time will it take you to write a polynomial system like that (assuming that extra stationary points are allowed to keep things at a simple level)? — fedja2 days ago
@fedja, "what we do here on MO" is shorthand for "the kind of question that is on-topic here at MO". It was not meant to imply that only active mathematical researchers are permitted to participate at MO, and I apologize if I gave that impression. — Gerry Myerson2 days ago
@GerryMyerson But is it off-topic really? The only way (IMHO) to prove that it is is to check that you can solve it yourself. The poor guy is trying to create a polynomial example (at least that is how I interpret "trying to arrange the coefficients"). Don't you see at least some non-trivial issue here? ;-) — fedja2 days ago
@fedja, the closing reason says, "This question does not appear to be about research-level mathematics...." Let me put the emphasis on the word, "appear". Appearances can be deceiving, and I accept that maybe we really are talking about research-level mathematics here, and not an undergraduate homework assignment. But the ball is in Daniel's court to convince a few voters of that, by editing the question in the light of these comments and the advice at the help center. — Gerry Myerson2 days ago
@GerryMyerson That is one of the standard formulations I dislike most (if something just "appears" to be something to you, don't take any action until you get convinced one way or another within reasonable limits). As to Daniel, I'm uncertain about whether he has a clear idea of what might "appear" to folks here this way or that, so I'm doing it myself now. :-) — fedja2 days ago
@GerryMyerson Done. So, what does it appear to you now? :-) — fedja2 days ago
@fedja, it looks like a much better question than it did in its original form. — Gerry Myerson2 days ago
@GerryMyerson But it is the same question! Please, pretty please, give at least newcomers some leeway before telling them that something "doesn't appear to you to be research level". They don't really know what exactly to expect and what magic phrases or red flags you are looking for when reading their posts. If the mathematical problem is stated clearly enough, judge the posts by the content, not by the form, when you are able to do it and don't judge at all when you are not. If it is not stated clearly, ask for clarification first and close a couple days later. Is it so hard? — fedja2 days ago
@fedja, it's not even remotely the same question, and I'd be stunned if it would have been closed, had it originally been stated the way it is now. Also, writing "Doesn't seem to be a question about math research" is my way of asking for clarification. I will continue to judge questions and answers as best as I can, secure in the knowledge that if I stuff up there are ways of repairing the damage. — Gerry Myerson2 days ago
@GerryMyerson * Also, writing "Doesn't seem to be a question about math research" is my way of asking for clarification* I know the translation now :-) But are you sure that some commoner knows your way of speaking English well enough to understand that? It certainly requires a higher level of reading between lines than the one I executed when restating the question ;-) OK, let's see what happens with the post now. :-) — fedja2 days ago
Well, if @ChristianRemling (the last reviewer) still finds it trivial, I retreat in shame (though I would appreciate some hint if not about the proof, then at least about the answer) ;-) — fedja5 hours ago
@fedja What I dislike about this situation is that you put effort into improving the question and also you're saying that the question is interesting, but in remains closed. On math.SE it is happens occasionally that if some user is interested in a question which was closed/deleted, then they simply post a better version of the question. Some users dislike it, some users find such approach perfectly acceptable. However, I am not sure what the view of MO community about this approach is. — Martin Sleziak19 secs ago
Maybe waiting a bit to see whether the OP comse back and then reasking the question either here or on math.SE would be a reasonable solution? In any case, if needed we can continue the discussion in chat. (So that we do not leave here too many comments which are completely unrelated to the question.) — Martin Sleziak12 secs ago
If needed, I can even try to find the few situations when I did this on math.SE (reasked question which was closed/deleted) if you are interested in how it was received.
The only think I will add now is that your comment did noc actually ping Christian Remling. (AFAIK reviewers cannot be pinged in this way.)
Feel free to ping me here in chat if there is something more to be said about this.
OK. Took me some time to figure out how the chat room works :-). My attitude is that I made my point as clear as I possibly could and both edited the question so that the format would be to the liking of the people on MO (I still stand by the claim that I haven't changed the mathematical content at all, just spelled out where the difficulty is) and voted to reopen myself.
If other people, who reviewed and voted to keep it closed after my edits still find it trivial, I admire their mathematical strength (I cannot figure it out even in an hour, forget 5 minites, which I consider the cutoff for the closure votes), humbly beg them to condescend and enlighten a hopeless idiot (myself) as to what the answer might be, but not moving a finger any more. :-)
No, your comments were a spoon of honey in the barrel of tar :-). It is all those claims about "not research level" by people who often fail the "solving the problem in under five minutes" test that really annoy me. You meant well and I appreciate your talking to me. I just want to wait and see if some reviewer changes his opinion, really ;-)
> IMO ideally anyone casting a "no effort" -close vote should be able to solve the problem themself. I am aware that the policy I suggested may place too high a burden to the first close-voter. That's where that ideally came from.
I'm quite harsh myself when the posts have really low quality (incomprehensible, no non-trivial content, etc.). But if the problem is posed clearly enough and one cannot solve it, one should not judge one way or another.
I disagree with the answer and using a Calculus textbook James Stewart Essential Calculus on page 46 it states
"If f is defined near a (in other words, f is defined on an open interval containing am except perhaps at a) we say that f is discontinuous at a (or f had a discontinuity at a) if f ...
So my opinion is that asking whether there is maximum/minimum/continuity point at $t=0$ does not make sense if $f(0)$ is undefined.
I guess in this case you were able to get an answer here. But I will still point out that in general you have bigger chance of finding somebody who is able to answer if you try in the main chatroom or in some of the subject-specific chatrooms. (In this case it would be probably calculus.)
I just wanted to let you know that such chatrooms exist - in case they are useful for you in the future.
It is an old thing, really. It is best illustrated by the funny story our real analysis professor told us:
Professor: (to a biology student on a math. test) Can $\sin x$ be greater than $1$? Student: Yes Professor: You failed: even a biology student should know the properties of standard functions on the real line.
Next day (on the exam for math majors)
Professor: (to a biology student on a math. test) Can $\sin x$ be greater than $1$? Student: No Professor: You failed: a mathematics student should know complex numbers and analytic functions.
It is. The same here. For a business calculus student the domain of $\sin x/x$ is the punctured real line. For any mathematician, this formula represents an entire function as written and he would never bother to add "defined as $1$ at $0$" when writing it. So, it is really the question about what level of understanding was expected and the original post lacks that information. That's all :-)
I disagree with the answer and using a Calculus textbook James Stewart Essential Calculus on page 46 it states
"If f is defined near a (in other words, f is defined on an open interval containing am except perhaps at a) we say that f is discontinuous at a (or f had a discontinuity at a) if f ...
