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5:34 AM
A new tag was created by Rodrigo de Azevedo. He also created a tag-excerpt and added the tag to twelve questions.
Q: Is a basin of attraction necessarily an open set?

Mathematicing Definition: The basin of attraction is the defined as the set of all initial conditions $x_{0}$ such that $x(t$) tends to an attracting fixed point $x^{\ast}$ as time $t$ tends to $\infty$. Is this basin of attraction necessarily an open set? My text mentioned nothing about the basin of attrac...

Q: Ensuring that the basin of attraction is convex

DCaoThe question can be stated in a short way, although I provide motivation after. Given a non-linear vector field (for a first attempt, we can assume polynomial vector field) and an asymptotically stable equilibrium point, is there any result that ensures that the basin of attraction of this equili...

Q: Bounding the basins of attraction of Newton's method

Jay LemmonIn general, Newton's method for root finding has a "bubbly" boundary between basins of convergence for different roots. This is where fractals are usually created from. But outside these "bubbly" boundaries there are very clear areas where there's no ambiguity about which root Newton's method w...

Q: Newton's method — for which initial guesses does it converge?

AnneWe've got a function: $ f : \Bbb R \to \Bbb R$ defined by $f(x) = x^3 - 9$. Let $x^* $ be its root, which means $ f(x^*) = 0$. We want to find approximation for $x^*$ using a Newton's method. There are two questions I don't know how to answer: We choose an initial guess: $x_0 = 2,5$. Does it lin...

Q: simple connectedness of basin of attraction

Cor GaajetaanI want to prove that the immediate basin of attraction of a finite attracting fixed or periodic point is simply connected. We are talking about complex numbers ! According to Remark 2 p. 281 and Exercise 4.2 p. 283 of the text of Devaney [1], If $z_0$ is a finite attracting orbit (i.e., $z_0...

Q: Basin of attraction of a fixed point

user271990I want to find the basin of attraction of a fixed point. For example, I have $f(x)=\frac 1{x+1}$, whose fixed points are $\frac{-1\pm \sqrt{5}}{2}$. Now, I must create a neighborhood around the $x$ point that would consist of all points around it that would attract to it. How can I figure out the...

A new tag was created by tthnew. The same user created a tag-excerpt:
> This tag could be used to find a new inequality or the stronger version of an inequality by hand or computer also. So it's not necessary to post the solution of it. But if you have the solution$,$ you can post it!
Q: Find the stronger inequality of $\frac{1}{ab+2c^{2}+2c}+\frac{1}{bc+2a^{2}+2a}+\frac{1}{ca+2b^{2}+2b}\geq \frac{1}{\sum ab}$

tthnewFor $a,b,c>0$ and $a+b+c=1.$ Prove$:$ $$\frac{1}{ab+2c^{2}+2c}+\frac{1}{bc+2a^{2}+2a}+\frac{1}{ca+2b^{2}+2b}\geqq \frac{1}{ab+bc+ca}$$ This inequality is easy and there are two nice proof by AM-GM or by C-S also. SOS also help here$:$ $$\text{LHS}-\text{RHS}=\frac{3\Big[\sum\limits_{cyc} (ab+b...

Q: Find the stronger version of $9 ( a+b+c ) ^{2} ( ab+ac+bc ) ^{2}+108a^2b^2c^2-31abc ( a+b+c ) ^{3} \geqslant 0$

tthnewFor $a,b,c \geqslant 0.$ Then $$9 ( a+b+c ) ^{2} ( ab+ac+bc ) ^{2}+108a^2b^2c^2-31abc ( a+b+c ) ^{3} \geqslant 0.$$ I use computer and found that the following stronger inequality holds for all reals of $a,b,c.$ $$\sum (a^2 -bc) \Big[9\, \left( a+b+c \right) ^{2} \left( ab+ac+bc \right) ^{2}+108\...

The same user created a tag-excerpt and a tag-wiki for .
2 hours later…
8:06 AM
I will include also the SEDE queries - although they will give more information only after the next updated of the database.
Posts where the tag was added removed (including the editors): data.stackexchange.com/math/query/1105163/… data.stackexchange.com/math/query/1038474/…
@MartinSleziak pqr has something like $uvw.$ It's a method to prove symmetric inequality!
More important question is whether it is really suitable as a tag.
I am not sure to which extent you're familiar with the tag system on this site. It is important to keep in mind that a question can only have five tags. (Which is one of the reasons why having too many too specialized tags can be a problem.)
A: Tag management 2020

tthnewProposal pqr tag created. The pqr method is a very useful method for the proof of polynomial inequalities with three variables. This tag should be used for questions that could be tackled with this method, or questions about the method itself. So I think it should be created. I'm sorry, my Englis...

18 hours ago, by Arnaud D.
In my opinion, one of the problems with these inequalities tags is that very often, the same question can be solved using several different known inequalities/methods; since the number of tags on a question is limited, it is often not possible to tag a question with all the relevant solution methods.
19 hours ago, by Arnaud D.
@MartinSleziak Apparently these methods apply to symmetric inequalities. Maybe we should create a tag to replace both and (and maybe others)? Personnally I would find such a tag more descriptive.
18 hours ago, by Martin Sleziak
In any case, if there are some people who are familiar with the type of questions which are often asked in tag and who understand the tag-system a bit, their input might be useful.
So far: The tag (pqr) was created on August 13, then removed and created again, there were several edits on other posts where it was eventually removed by a moderator and today the tag-info was created. (Having said that, I appreciate that you brought this to meta - rather than continuing editing/retagging wars). — Martin Sleziak 10 mins ago
@MartinSleziak I agree to your idea, "Apparently these methods apply to symmetric inequalities. Maybe we should create a tag symmetric-inequalities to replace both uvw and pqr (and maybe others)? Personnally I would find such a tag more descriptive."
8:16 AM
@tthnew Actually, that is Arnaud D.'s suggestion, not mine.
@MartinSleziak Ok.
In any case, now the suggestion have been posted on meta, we'll see whether some other users are going to respond there and what they think about the tag.
@MartinSleziak Okay, I will waiting. How about [inequality-finding] tag?
In any case, since the tag has been repeatedly created and removed (in one case by a moderator), it is definitely better to discuss on meta that to continue with creating/removing the tag again and again.
@tthnew I do not really follow tag. In any case, for me the tag name seems rather non-descript.
I see that @AlexanderGruber did not leave any comments in the edit summary when he removed the tag, but perhaps he might be willing to leave some comments about the tag and why he decided to remove it.
inequality-finding is by a friend suggestion with me, he say it would be great to having a tag to create new, nice inequality.
8:21 AM
I do not really know what you mean by "friend suggestion with me"?
Did you mean that somebody else has proposed the tag? They have insufficient reputation to create tags?
Yes I mean that.
If that's the case, maybe your friend can post on meta and explain why they consider this as a useful tag.
will suffice for that purpose.
@AlexanderGruber but the inequality tag need the solution?
if you have a question that is about inequality discovery, use the inequalities tag, we do not need a new tag for this
I like Arnaud's suggestion about uvw and pqr but this should be discussed on meta
8:28 AM
@AlexanderGruber So you mean for inequality discovery, we don't need the solution for it. Because some inequality I can only check it by Maple but can't not prove?
I agree with Arnaud's suggestion.
1 hour later…
9:29 AM
@MartinSleziak The tag was removed. Probably by the automated script - it is not shown in the revision history.
@MartinSleziak The tag was removed a few days after its creation: math.stackexchange.com/posts/3461464/revisions
@MartinSleziak The tag has grown to 20 questions since then.

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