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3:44 AM
Q: regarding decomposition of singular matrix pencil

Urgent$A,E$ are $m\times n$ matrices, $m\ne n$ and $A-\lambda E$ can be thought of as a linear polynomial with matrix coefficient. Could anyone help me to understand: how to show there exists orthogonal matrices of appropriate dimesions, $U_0$ and $V_0$ such that $U_0(A-\lambda E)V_0=\begin{bmatrix}A_...

2 hours later…
5:23 AM
$p$-harmonic functions, infinite-harmonic functions and the corresponding stochastic games also have mean value properties. — Tommi Brander 16 hours ago
Just in case some users would consider a separate tag for useful (in case the current discussion is reconsidered in the future), should we in some way save the list of posts which are in the tag currently?
@quid @JohnMa AFAICT the remaining questions in the (mean-value-theorem) are either about -s or about .
It least this is my impression when I look at questions tagged mean-value-theorem but not harmonic-functions.
I will leave retagging of PDE questions to somebody with more knowledge in the area. (I guess the tagging of those questions might be improved also in other way.)
I am not sure whether this might be useful for some reason, but I have save currently tagged questions in the Wayback Machine.
I have also downloaded csv I get from this SEDE query - most likely it should be all questions with this tag.
As mentioned, I have only checked the questions from here: math.stackexchange.com/questions/tagged/… (there are 4 at the moment). Maybe it is worth having a look at other questions too before the merge. (If in some of them retags or some improvements are needed, they might be made manually - after all those posts were bumped not too long ago, anyway.)
6:14 AM
Somebody who knows enough about PDEs would probably able to say whether some question where the new tag will be removed after the merge should be tagged with (harmonic-functions): mean-value-theorem+pde+-harmonic-functions,
2 hours later…
8:38 AM
@MartinSleziak three of the four contained the word harmonic, and the sole remaining one seemed close enough. I merged. Thanks for having done the main part of the retagging!
This is not to say I know enough about PDEs, though.
2 hours later…
10:48 AM
Q: What is the scope of the [utility] tag?

Asaf KaragilaIt was pointed out to me that the description of the utility is ambiguous. It currently reads: A tag for all questions involving a type of utility function. With a wiki which is even worse: STUB!!! See utility function. Since I figured that I don't have enough knowledge about this top...

2 hours later…
12:58 PM
@quid Re: Thanks for having done the main part of the retagging! Certainly, a lot of retagging was done by some other users. (I am pretty sure I've seen your retags and some done by Johna Ma. I am not sure whether somebody else joined the fun.)
Indeed @JohnMa did a significant share too. Thanks to him as well.
1:14 PM
I will just add that the tag has been recently removed - based on this discussion (and partially also some discussions in chat - see, for example, here, here and here). — Martin Sleziak 26 secs ago
I am not sure it's really necessary, but I don't think it can cause any harm that this is saved somewhere (for archival purposes).
I see that Michael Greinecker joined the discussion of tag. It is good that an economists gets involved into this.
@AsafKaragila Results related to utility theory might occur in functional analysis, measure theory, and even -gasp- set theory. — Michael Greinecker ♦ 48 mins ago
BTW since Riesz representation theorem was discussed not too long ago, I will add that other two tags related to functional analysis have been created quite recently - namely and .
I can imagine that both tags (or at least the latter) might be useful.
The question Tag for semicontinuity? has been around for some time, I am not sure that we get much more feedback on that.
@MichaelGreinecker Your answer is currently at +6 and comments were general positive. So perhaps created tag - with the scope suggested in your answer - would be reasonable. Or should we wait a bit longer?
IIRC a question which is more than 14 days old is no longer displayed in . So after one or two more days, the question will not gain any additional views in this way.
1:40 PM
@MartinSleziak Since you are the expert: How does the retagging process usually work?
Sorry, you have to be a bit more specific.
1. Do you mean something like we did not - removal of ?
2. Do you mean something like the ongoing process with partition tag which is being divided in smaller tags?
3. Do you mean how new tags (for example ) then gets to the older question?
@MartinSleziak Yes, how would tagging with the new tag best be handled?
I am not sure to which extent I can answer. I'd guess I am probably just going to say a few self-evident things.
First of all, we should not retag too many questions at once - but this comes under "not too much bumping" and every experienced user knows this.
Some question will come organically - people will notice a new tag, somebody might retag an old question here and there, somebody might add new question with this tag.
I do think it would be over-ambitious to find and retag all old question related to this tag. But perhaps the most important ones should get this tag.
So what would I do is that if I can think of a result in this topic which is quite important and I can find questions about this, I'll add tag there. (Or maybe just mark the question to add the tag later if I have already bump too muched question.)
And I would also search for the relevant keywords and then sort the results by score - this might also help to find some relevant question.
I guess the thing I would most like to know is how much bumping how fast is normal and acceptable.
And from there questions will be added just by "random browsing". At least the users who were involved in the creation of the new tag are aware of it. So it's safe to assume that they might occasionally notice a questions from that topic. (For example, if you or me are just randomly browsing the site and we stumble upon question related to semicontinuity, we might add the tag.)
@MichaelGreinecker This was discussed some time ago, but the site has probably grown too much since then to be still considered relevant.
I have to admit I am not always too careful about this. But some stuff I try to follow:
- I do not bump too many questions at once (certainly not more than 10, I try to stay under 5 at the same time; probably it's better to do more smaller batches).
- I have a few lists on my computer of questions where I should get back and edit something - if I have already bumped some questions I simply add a question to that list instead of editing.
1:55 PM
@MichaelGreinecker I'd guess that the answer is "as long as it is not noticeable on the main browsing pages".
@MartinSleziak Okay, I think we can go on and at least create the semicontinuous-functions tag. The case of multifunctions needs probably more effort in identifying the relevant questions.
So if you do something like three-four at a time, with intervals of a few hours, depending on the current time and traffic, this should be fine.
- At least sometimes I also check whether there were many old posts bumped recently by checking something like this: math.stackexchange.com/… (If I see only a few bumped questions in the last 30 minutes, I usually consider this as the green light.)
I guess a good rule of thumb is that no more than 5 retagged questions should occupy the front page.
I have mentioned 30 minutes exactly for the reason that it's about the size of the first page at the present rate (if you are displaying 50 questions per page).
- Another thing to do is to look whether some other improvements can be done to the question you bumped (or answers posted there). If you bump questions in this way, sometimes one question will keep you occupied for a few minutes.
- And I should add that I do not count questions which has already been bumped for some reason. (If a question was bumped anyway during the last day or two and I see some further improvements to the tagging, title, formatting, ... then this is certainly a good time to edit - this is certainly better than two separate bumps long time apart.)
2:00 PM
@MartinSleziak Thank you for all the info! Shall I go on and start retagging (and hopefully improving) some relevant questions?
Feel free to do so. Are you talking about tag?
Yes, that one.
I also have a few questions saved somewhere which could be added to that tag. But I have some stuff to do now anyway - so I'll probably do them later.
Okay, I think there are a handful that are standard to be good seed (closure under infs(resp sups, measurability, existence of maximizers/minimizers on compact sets, approximation by continuous functions.)
That sound like a good plan.
BTW I am glad that this room is much more active now than it used to be and that also some other users talk here. If you look a few pages back in the transcript, this room seemed like rather lonely place.
2:07 PM
@MartinSleziak Yes, I'm very grateful for the effort you've put into making tagging work smoothly!
Well, to say that the tagging works smoothly would be an exaggeration (there are several unresolved issues from the past, some of them quite important). But at least if something is occasionally posted here and/or on meta, it might remind other users that one should also occasionally look at how questions are tagged, whether there are new tags, tag synonyms, etc.
And probably there are many users who care a lot about tags and put quite a lot of work into retagging, but they are less noticeable simply because they do not post that much on meta or in chat.
@MartinSleziak Maybe, but at least the kind of questions I look at are often retagged by you. There might be some selection bias at work.
For example, of you look at recently active questions in and , you can see that quite a lot of work in this current retagging effort is being done by Peter Taylor. (He also posted the meta question about partitions tag which basically started this.)
I see. Speaking of partitions, do you know of a readable introduction to the partition calculus? I read a bit in Mary Ellen Rudin's notes, but found her writing a bit too casual for my taste (and beginner status).
I wrote very short tag-excerpt and tag-wiki for semiconontinuous-functions. There is certainly a lot of space for improvement - so go ahead if you feel like editing. Do you think that the fact that this is not for multifunctions should also be explicitly mentioned in the excerpt (i have mentioned it in the body).
@MichaelGreinecker You are asking a wrong person. I do not know about this much more than that it is something denoted by arrows. (I have reposted your question to the set theory room on the off-chance that somebody notices it there.)
Maybe @AsafKaragila might have some suggestions for you about partition calculus.
2:23 PM
@MartinSleziak Thank you! The information for the tag seems to be clear and concrete, I see no immedate scope for improvement.
@MichaelGreinecker What do you mean exactly? Infinite Ramsey theory stuff, like coloring and homogeneous sets (which can be recast as partitions, of course)?
2:41 PM
Based on the voting and comments posted here I have accepted Michael Greinecker's answer. The tag (semicontinuous-functions) was created recently, the tag-info was created also based on the discussion here. (In particular, it includes that the tag is for semicontinuity of functions, but not for multifunctions.) @AlexRavsky Since you actually initiated created of the new tag, I thought that it would be polite to let you know about this, too. — Martin Sleziak 15 secs ago
3:01 PM
@MichaelGreinecker Since you are the local expert (at least in this chatroom) I will direct this to you. Should preference relations fall under the tag?
I see there a few posts about Debreu theorem which, as far as I know, is related to preference relations.
If yes, maybe it might be worth mentioning in the tag-info.
And perhaps if somebody who knows about economics could list a few topics which should fall under this tag, this would address Asaf's complaint that the tag-wiki is rather vague.
I am asking specifically about preferences since this is something I have heard about and I see that they are mentioned in the WP article Utility. (Of course, mentioning some other related topics in the tag info would be useful, too.)
3:49 PM
@MartinSleziak Yes, these posts are tagged correctly. The reason is basically that utility functions are at their most basic just a numerical way to represent preferences. Basically, you take a reflexive, complete, and transitive (usually not anti-symmetric) relation and find a function u from the underlying set to the reals such that xRy iff u(x) is at least as large as u(y).
But saying that in general, if there is a question about preference relations it belongs under (utility) tag would be incorrect?
You probably have better idea what should count as "stuff that belongs to utility theory". (Although I am not sure whether utility theory is really a name for somethings.)
I see that some questions about preference relations are tagged order-theory which is probably quite reasonable.
@MartinSleziak I would say so. One sometimes works with preferences that are not well-behaved enough to admit such a numerical representation.
Ok. I asked about preferences in the hope that adding some kind of list of topics under would make the tag-info less vague.
Does this sound reasonable (in terms of structure and form, not content): "For all questions involving utility function as used in economics and decision theory, including a study of their properties or how they can be used to represent preferences. "
But even though I know almost nothing about preference relations, at least after our conversation I will keep in mind that is (usually) the right tag for questions about them.
@MichaelGreinecker To me that sounds ok. (And it's definitely better than the current version.)
BTW after Asaf's post I browsed a few questions in the (utility) tag and I was surprised that the ones I looked at are tagged correctly. (I half-expected handful of questions like: Why is this theorem useful? What is the utility of the notion of ...?)
3:59 PM
@MartinSleziak Yes, I was rather surprised myself. I assumed a lot of people would use the tag for every economic problem in which utility functions are somewhere used in the problem formulation.
4:10 PM
I see that you have edited the tag-excerpt and the tag-wiki. Thanks for doing that!
The only suggestion I have that maybe including the Wikipedia link might be useful, too. (If only as a possible place where somebody reading that tag-info might go to get further information.)
But certainly it's not something really necessary.
Good idea. I included the wikipedia-link.
I am not sure whether it is related to your inquiry about partition calculus, but I have added in set theory chatroom the one post on meta I was able to find and which seemed related. (It is about book recommendations for infinitary combinatorics - not specifically partition calculus.)
And maybe Asaf will respond to you with some advice here (or elsewhere).
4:34 PM
Thank you!

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