Knowledge talk:WikiProject Mathematics/Archive/2015/Jul

2035:'s edit. Coming to the discussion late and reading the whole thing at once gave the impression that the edit was rash, but I now realize that the time element (this discussion had been going on for weeks) was missing. I was about to make the same edit and upon finding out that it had already been done my initial reaction was just re-enforced. Perhaps it would have been better if another editor had done it, but as Sławomir has pointed out, we (collectively) were late to the game and dropped the ball on this one. As to the substance of 1985:. That policy states "self-published media, such as books, patents, newsletters, personal websites, open wikis, personal or group blogs (as distinguished from newsblogs, above), Internet forum postings, and tweets, are largely not acceptable as sources." The weird interpretation of the policy that it's ok to use self-published sources in scientific articles as long as one is discussing one's own accomplishments falls well outside of any reasonable reading of it, especially taken in conjunction with the rest of our policies. 1800:

nothing to contradict that conclusion. Indeed, one of your arguments is "Look at my documentation referenced in this discussion above. It is actually better than several already existing table references and I have emails that confirm third-party (not me) verification of my results." Yes, that's true. But the other results were poorly-referenced as well. Surely it is not very surprising that the outcome would be their removal, rather than the inclusion of your own results in the table, given our apparent

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Another relatively recent development is the appearance of online lectures and screencasts. A role WP could play in this is as a kind of switchboard to these other resources. I'm not certain that the "External links" format we have now is up to the task though. When WP first started there were maybe a few other websites on specific topics, but nowadays you can take an entire lecture course (sans final exam), find a selection of textbooks for it and even get help with questions, all online and often free. --

2043:. If Rick314 publishes his results and an unrelated third party writes about them then we can include a discussion of them by sourcing the third party. Although many do chaff under these restrictions, they are necessary to prevent WP from devolving into yet another internet bulletin board. There are many breaches of these guidelines to be found in our articles, and when we come across them we need to act decisively, as Sławomir has done. 40: 3571: 2889: 4590:. This is a little more justifiable I think, because there was a proof already there and the new proof is somewhat more straightforward than the old one. Ideally, both proofs should be shortened and summarized. In fact, the new proof can more or less be reduced to a sentence or two. Something like: "Because the sequence of functions is uniformly bounded in absolute value by a summable sequence of numbers 3407: 5050:? Why is Minkowski geometry listed as a subset of affine geometry, and why is it included at all when we have no article specifically on that topic? Is the first group of topics really classified by axiomatization, rather than by symmetry groups (per the Erlangen program)? Why is Riemannian geometry listed as a top-level topic instead of being a subtopic of differential geometry? Where are 3168: 2064:

and more are now published in Wikimedia Commons. I can put them somewhere else if appropriate. I have emails with a third party and they checked everything there. My reviewer could have entered a row for my 1988 and 1992 records? (Slawomir please stop repeating your position and I will too. I hope we can get input from others and the amount of text here is unwieldy.)

4999:(which shows 7 articles now), hit "FIX" on any one of them, and see if you can identify which version of "matrix model" should be linked. If you don't know, just exit / delete the tab that has opened up. It is easy and fun to use this cool disambiguation-related tool, but you have to know something about the content area to fix these seven ones. TIA, -- 3418: 2736: 5282:

treated synthetically or analytically just as easily as Euclidean and the same goes for many other types. So while I'm not sure that the division in the article is wrong, the way the topics have been split between them seems arbitrary. Also, it's not clear how this article, when the missing branches are filled in, would differ meaningfully from

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Your choice of "(hyperbolic geometry)" violates the "whichever is simpler" part of the guidance you quote, so I don't think it is a good choice. I don't have a strong preference between the other two, but I tend to prefer "(geometry)", in part because we already have plenty of geometry disambiguators

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on Gowers's weblog on the future of Tricki and he was saying that he started Tricki before these sites had taken off, and they have taken away a lot of the potential online math market. But to extend your analogy, I think the space has enough dimensions for quite a few mutually orthogonal directions.

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and thinking how it serves a purpose almost completely orthogonal to Knowledge in helping with how things are done. I was wondering if there wasn't some way of getting a bit of synergy somehow where we continue along the current paths but people can easily find a way over to Tricki from the reference

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insisting that the article must cite your own unpublished work. This makes it essentially pointless to attempt discussion, since you are clearly using a very self-serving reading of policies, guidelines, discussions, and the article. For example, you apparently cannot be bothered to notice that the

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We already reference "e - the story of a number". And, in fact, according to that source, which contains almost no discussion of records, "In one sense the stories of e and π differ. Because of the longer history and greater fame of π, the urge to compute it to an ever greater number of digits over

1856:

Sorry, but this is a ridiculous number of words and policies to spout on a question of basic politeness and consensus-building. If you're discussing changes with someone and haven't reached consensus, it's rude to go and impose your version while discussion is ongoing. There was no particular rush,

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article slightly the benefit of the doubt by including two references to Gourdon concerning "algorithmic advances". Since you believe that I have "missed the algorithmic advances", now would be a good time to correct me by supplying sources to the secondary literature (peer reviewed journals, books,

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Probably a first step would be to have a WP article on it other than just a redirect to Timothy Gowers. Maybe a second step would be to jut start linking WP articles to Tricki where appropriate. For reference desk questions there's no reason you can't supplement an answer with a link to Tricki if it

2098:

Sorry that I did not make myself clear. When I say published, I mean published in a peer reviewed venue and not any form of self publication and the same holds for the third party source. Notice that no one here has criticized your work or even hinted that it might be incorrect, in fact I am working

2063:

Thank you Bill. You said "If Rick314 publishes his results and an unrelated third party writes about them then we can include a discussion of them by sourcing the third party." I asked about this way way back in the article Talk. My dated algorithm documentation and source code and execution metrics

1835:

Well, Rick314 had already announced his intention to make an edit, against consensus, guidelines and policies. There was a very clear consensus at the discussion page that the table entries were inappropriate. The discussion was ongoing for several weeks, during which time anyone at all could have

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here is that there are many reliable secondary sources concerning the quest for more digits of pi. For example, Arndt and Haenel spend a chapter discussing it. Papers in "Mathematics of computation" and "The American Mathematics Monthly" discuss new algorithms for computing π. Indeed, Borwein and

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page on June 23, designed to correct some basic mathematical flaws in the article. I am a genuine expert on the subject but I am now blind and totally inexperienced with Knowledge. So others need to carry out the actual edits. The suggestions don't correct everything in the article, but make a good

1351:

Our usual copyright tools failed to identify a problem because they tend to work with online materials. I tried invoking one tool which has access to off-line academic material but that failed to identify a problem. I don't believe the reader is making it up but I need some confirmation before I can

4485:

It seems like almost correct behaviour. \max is a maths operator which expects the next character as an argument. ( is the next character so that is taken as the argument. Running the the code through standard LaTeX produces an error and won't compile at all. It does not look like its new behaviour

4031:

Is such symbol in use (anywhere except, maybe, wikipedia)? I never saw it (as well as negated orthogonality, etc). Moreover, my experience with some economists shows that they tend to misunderstood the meaning of "not independent", mostly as "either positively dependent or negatively dependent" or

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who is urging against a series of ill-considered edits that go against policoes. I feel that the community has been negligent here. I shouldn't be the only one needing to comment there. I know this is a well-watched page. So where was everybody else? How come I was the only one holding the bag

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From the article "The number of known digits of e has increased substantially during the last decades. This is due both to the increased performance of computers and to algorithmic improvements." Two references are given. If you feel that details of the algorithmic improvements have been omitted,

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why Knowledge should not be in the business of record-keeping on the authority of Usenet posts and unpublished emails. I would have thought that was clear. There was evident consensus that these entries did not meet the requirements set forth at those policies and guidelines. Your arguments did

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There are certainly papers that study differential equations or dynamical systems intended to model the chemical kind of hypercycle. There are also papers about hypergraphs that call certain structures in them hypercycles. So yes, "mathematics" seems too ambiguous and this gives another reason to

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The theorem statement is a word-for-word copy of the one appearing in the source. The editor who added the material in question is correct that inevitable there will be some overlap in any two statements of the same theorem, but an exact match cannot have been a mere coincidence. I believe that

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I don't think the proofs are an improvement. Generally speaking, it's acceptable for Knowledge articles to summarize proofs, but not to give detailed proofs of statements. In the article under discussion, the proof is already summarized as the ε/3 trick. Filling in the details is routine. To

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This first thing that stood out for me was the division between geometry with different axioms vs other types. You can divide geometry by synthetic vs. analytic, and also by Euclidean vs. hyperbolic vs projective vs. whatever, but these are orthogonal classifications. Projective geometry can be

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The bottom line is, we are absolutely not going to cite your usenet posts and unpublished work. If you have a paper that is published in a peer reviewed place (typical of professional, as opposed to amateur, mathematicians), then please give a reference to that. Otherwise, I don't see further

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by mathematicians and computer scientists (such as myself) who spent significant time and effort advancing the state of the art using extended-precision approximations of e as an example problem. Someone with the authority, please correct him and undo his changes or explain the inconsistencies

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This is wrong. From the article: "The number of known digits of e has increased substantially during the last decades. This is due both to the increased performance of computers and to algorithmic improvements." I said as much above, and requested additional citations. References to the

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I agree with David and others that "(hyperbolic geometry)" is unnecessary complicate, as it does not help readers in their choice. On the other hand, my opinion is that "(mathematics)" must also be avoided in this case. In fact, I am not sure that "hypercycle" is not used in other parts of

3566:{\displaystyle T=e^{e^{-{\boldsymbol {\zeta }}\cdot \mathbf {J} }({\boldsymbol {\xi }}\cdot \mathbf {K} )e^{{\boldsymbol {\zeta }}\cdot \mathbf {J} }}=e^{-{\boldsymbol {\zeta }}\cdot \mathbf {J} }e^{{\boldsymbol {\xi }}\cdot \mathbf {K} }e^{{\boldsymbol {\zeta }}\cdot \mathbf {J} }} 2884:{\displaystyle T=e^{-{\boldsymbol {\zeta }}\cdot \mathbf {J} }e^{{\boldsymbol {\xi }}\cdot \mathbf {K} }e^{{\boldsymbol {\zeta }}\cdot \mathbf {J} }=e^{e^{-{\boldsymbol {\zeta }}\cdot \mathbf {J} }({\boldsymbol {\xi }}\cdot \mathbf {K} )e^{{\boldsymbol {\zeta }}\cdot \mathbf {J} }}} 1923:. So no apology from me, and both Slawomir's process and content are inappropriate. "Expert" and "amateur" are subjective terms to be avoided, and I think intentionally used in the article by Slawomir as an insult. Let's stick to Knowledge publishing guidelines. As I read 4015:.) I would suggest doing it in wikiformatting using the double up tack unicode character instead (⫫) but getting that to work well with a double-subscript-overbar is unlikely, not to mention that amazingly unicode seems to be missing the negated double up tack symbol. — 4800:: If there are several possible choices for parenthetical disambiguation, use the same disambiguating phrase already commonly used for other topics within the same class and context, if any. Otherwise, choose whichever is simpler. (no more specific guidance exist) 1732:. He just decided he was right and stopped the discussion by deleting much of the table. He also says "There are no recognized authorities for world record computations , unlike pi" without siting what those pi authorities are or why the history of pi precision at 1918:

to compute billions of digits of e." There is no mention of algorithmic improvements there. It refers to Alexander Yee as an example amateur. (He is not.) Similarly, amateur me improved expert Steve Wozniaks's algorithm 4 ways as explained on the first 2 pages of

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and substitute "Since that time, the proliferation of modern high-speed desktop computers has made it possible for amateurs to compute billions of digits of e". Please look at what he deleted. He is totally missing the documented and referenced and very important

3402:{\displaystyle e^{-{\boldsymbol {\zeta }}\cdot \mathbf {J} }({\boldsymbol {\xi }}\cdot \mathbf {K} )e^{{\boldsymbol {\zeta }}\cdot \mathbf {J} }=e^{\mathrm {ad} _{-{\boldsymbol {\zeta }}\cdot \mathbf {J} }}{\boldsymbol {\xi }}\cdot \mathbf {K} \in \mathbf {k} .} 4928:

mathematics. In any case, as "cycle" is used with various meanings, in particular in graph theory and topological algebra, it is useful to inform the reader that "hypercycle" is not a generalization of such cycles. Therefore my opinion is that the move done by

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weighed in. If we waited indefinitely for such discussions to be "done", nothing would ever happen on Knowledge, and we would be stuck in endless discussions with COI/SPAs. So I disagree very strongly that it was,"poor form". This is just an articulation of

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When the diagrams were created, Quondum provided no source, nor reference, nor even his own worded description, supporting his claim that Lorentz boosts in any direction do not preserve orthogonality of the spatial axes, he just accused YohanN7 of "unsourced"

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desk for instance. It doesn't fit in with Knowledge's content policies and I can't see an easy way of doing anything with it but it seems a shame not to have a way of guiding people who ask questions to a place that helps them with how to solve a problem.

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original research are false. Two of the sources are presented below. Normally Cushing should more than suffice, but since weight is needed versus authority, I added Weinberg as well, almost notorious for not making mistakes, both here and in the article.

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I've use \max as a subscript with no braces in Knowledge articles thousandds of times over quite a few years without seeing this problem. Will it suddenly be necessary to change all of them because of some change that just happened in the software?

1772:, although I have requested such sources, as they would certainly be most welcome if they existed. On the contrary, the portion of the table I removed was sourced to usenet posts and unpublished emails. Those are simply not acceptable sources, at 1615: 1433:

but I'm not sure if is related. As for a long-term plan, I agree it would make sense if someone else can take over running the bot (it should be so much easier to taking over the task than starting over), as apparently Jitse is no longer active. --

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Other Knowledge math experts please comment. Rather than continue discussion on the talk page he sites above, Slawomir took it upon himself on the same day he posted the comment above (9 July 2015) to delete much of the table of "Known Digits" at

1618: 3163:{\displaystyle e^{-{\boldsymbol {\zeta }}\cdot \mathbf {J} }({\boldsymbol {\xi }}\cdot \mathbf {K} )e^{{\boldsymbol {\zeta }}\cdot \mathbf {J} }=e^{\mathrm {ad} _{-{\boldsymbol {\zeta }}\cdot \mathbf {J} }}{\boldsymbol {\xi }}\cdot \mathbf {K} .} 3874: 2910: 5066:

supposed to fit? Is this a listing of branches of geometry, or a listing of geometrical branches of modern mathematics research, sweeping the parts of geometry that get taught to schoolchildren under the single Euclidean geometry link?

2103:". The editors of WP are not to be the judges of the content, they can only report on what the reliable secondary sources say about that content. If there are no such sources, then we do not say anything and don't include the content! 1410:

Jitse's bot hasn't updated the new articles list in almost two weeks. Four days ago I sent Jitse Niesen an email and I haven't heard anything. Will Knowledge be forever dependent on one person in that way? How should we proceed?

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I think the basic principle is that some or most of our math rendering pathways are not actually based on Knuth's TeX code and have occasional differences in parsing because of it, that can usually be fixed with more braces.

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move e and pi closer together in terms of leaving a history of precision improvements? The Table of Contents is available at that link, but I am not sure what content makes it more or less applicable to this discussion.

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Sławomir Biały, I think that L.Andrew Campbell probably has difficulty reading this page. I was thinking of sending your message to him as an e-mail, but I would only do that if you haven't done so already. Have you?

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I have posted suggestive changes with the above title to the JC talk page. An experienced math editor is needed. As a wrinkle, they include use of the name Druzkowski, which needs a dot over the letter z. Thanks,

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and took the report here. I blindly (as always) assumed I was wrong and others are correct, and thought I knew where Quondum came from and only blundered, about the LT matrix for a boost in any direction (no longer on

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I agree with Rick314 that it was rather poor form for Sławomir Biały to go make this edit in the middle of a discussion. But on substance I think Sławomir Biały is correct, for exactly the reasons he has given.

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there? Twould weeks went by, and made an edit, with clear reasons behind it. By any standards, those are reasonable actions. And calling other people names also isn't likely to make the world a better place.

1791:, you agreed that "Existing references already violate ." I agreed with this statement, and removed the portion of the table that did not agree with our guidelines. My edit summary clearly referenced 1728:

that made those increased approximations possible. His page change comment is "WP:SPS is pretty clear that we shouldn't have these entries..." when that was the very thing being discussed with me at

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To the right there is also an excerpt from Cushing's paper that verbatim verifies the disputed passage and diagrams in the article, and also my post on the talk page for which I am being reported.

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Since I have been reported for allegedly doing original research on a talk page, I feel I have to be my own lawyer and defend myself. I do thank Maschen for some moral support, here, and there.

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It looks like the problem only happens when the next character is a bracket, so most case are OK. I've run a search for equations with the bug and fixed the ten or so pages where it occurs.--

2272:(2014), p. 213, noting the use of the Rayleigh I and Rayleigh II equations for plotting wave scattering), which fit topically but differ in the equations used. What is the right answer here? 2145:

Can someone convert this disambiguation page into an article explaining the general concept of a correlation coefficient, and how all the types on the page fall into this concept? Cheers!

5097:

I may add to the points set by David that the relation between the different branches of geometry are much more complex that that suggested by the structure of this article. For example,

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It is also possible that some proofs are notable by themselves. I even wrote an article once because I thought the proof of something (at least in one direction) was extremely nifty.

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and there had been no third opinion yet. You acted a bit like a jerk, unnecessarily. The world would have been a very slightly better place if you hadn't done so. That is all. --

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I started that page, on this page my idea was to construct some kind of scheme that sorts out the parent (less axioms) -child (more axioms) relations between the different (mostly

4514:

Would it be possible to find every case where \max occurs in a subscript or superscript to change it to {\max}, maybe even without needing to do each one by hand? And \min too.

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Regarding "amateurs", Yee's own website refers to this as a high school project. It's hard to defend your view that he was acting in a professional capacity as a mathematician.

5046:, but... Is there some sourcing for this structure, or is this just some editor's opinion of what the important topic groupings are? Why projective and affine geometry but not 4991:

Hello, math people! Me and i think most other wikipedians who are focusing on eliminating ambiguous links in Knowledge are stumped by a number of math-y articles that link to

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My understanding is that the purpose of parenthetical disambiguation is primarily for typing into the search box. As such, shorter is almost always better. I think

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several days ago and got no response. I will try again here. What does it take to run the bot? Does it run on the wikimedia foundation's server? I found this page

5312: 21: 49: 2490:. That would save valuable space in the article. But , alas, Quondum wouldn't have that to begin with, so, we have to go through this in depth in the article. 1875:

Excuse me, but I really think thus criticism of my behavior is way out of line, and I think you should apologize. As far as I can tell, I'm the only editor at

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For clarity... YohanN7 has, as always, provided painfully detailed explanations and Quondum walked off, because "bully boy" YohanN7 was being too "energetic".

1787:

Finally, regarding the rather childish observation that you made "He just decided he was right and stopped the discussion by deleting much of the table", in

1776:. So there aren't "different standards ... applied to the two", rather I have applied the same strict standards of sourcing to the one article as the other. 4715:

I got rid of the proof that Riemann integration commutes with uniform limits. This is geometrically obvious, and the given proof was very unenlightening.

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Why not simply add these to the stub and push it out into main space? If someone is interested, then the article will expand in the natural Wiki fashion.

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would help; there are a couple of occasions where a question was answered with a link to math.stackexchange.com or mathoverflow.net. I browsed an article,

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this does qualify as a copyvio from the rather stringent conditions of Knowledge. The article should be deleted, and replaced with an untainted version.

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concerning a question of whether we should cite someone's self-published and unpublished computer programs (including a rather novel interpretation of

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he comments "Anyone with a computer can compute billions of digits of e, as the case of Alexander Yee shows." Again, he is minimizing and missing the

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I am trying to track down and alleged copyright violation. A reader wrote to the Wikimedia foundation noting that the text of the following article:

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something like this. The exact meaning of this negation seems to be clear only to mathematicians; but these do not need such notion (I think so).

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literature are welcome. Tendentious lies like this are not constructive, and could potentially result in having your editing privileges revoked.

1297:. Normally that would cause the new title to appear in the new articles list tomorrow. But it won't unless someone finally rescues Jitse' bot. 3592:

on a sphere is transitive, the claim in the by Quondum disputed is proved (once the remaining easy details left to the reader are filled in).

2082:, e.g. by going through peer review and getting it published in an academic journal. It doesn't mean merely making something available online. — 17: 4761:

there is been some discussion about "Parenthetical disambiguation" and we would like to have that discussion in a more general place (here).

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of your suggestions were promptly implemented. I'm more than happy to help, but could you please be clearer what still needs to be done?

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remove it. I'm hoping that there is some reader of this wiki project who happens to have a copy of the text handy and can check it out.--

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between the pi and e articles in such a way that makes it obvious why such different standards should be applied to the two. Thank you.

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Dear mathematicians: There appear to be quite a few book references that could be added to make this stub into an article, for example

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start. Someone must know how to bring this to the attention of previous editors of the page.Please use email to contact me if desired.

2391:, see its history if you care). Quondum has also claimed we were "not giving room to speak", which is clearly false because he has and 5286:

if some of the clutter was removed from that article. In other words it seems like we now have two articles with the same purpose. --

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If one follows the action of the successive transformations on the spatial coordinate axes, it is apparent what is going on. Rotate,

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At least in theory, it is thus a possibility that Quondum is incorrect in real life. But this matters little. He is most certainly

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Another reference supporting orthogonality under Lorentz transformations (rotation and boost) is Goldstein, 2nd edition, page 285.

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Strangely, this had the effect of causing BOTH "max" and the left parenthesis to appear in subscript. So I changed it to this:

3729:, that you might find it useful to watch and/or check regularly, since that's where things like this should eventually appear. — 2300:

Folks, those with an interest in relativity, please take a look at what I believe is unjustifiable, unsourced OR in progress at

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under the assumption that it is perfectly fine – the objections have to do with how statements that appear on WP are backed up "

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that the main branches of geometry, and their relations should be described. Therefore, I suggest to merge this article in

4548:". Neither mathematics nor English are free of errors. But more important is the question, do we need these proofs at all? 5010: 2486:

is possibly true. We can, as is done in most (actually all) of the relevant literature, toss the whole issue off as being

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Borwein have and entire book on this subject. As far as I am aware, no such sources exists concerning the computation of

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Thanks for the response, now deleted. (and a candidate for a new article, if someone is looking for something to do :)--

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I would do it with a few more slash-bangs, as David suggests. Also, I would probably use the built-in symbol \amalg (

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It's already a link on the page. Correct me if I'm wrong, but I presume that a correlation coefficient is merely a

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I think you misunderstood something. In this context, "publishes" means to publish in a way that makes something a

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I don't know where to begin. For one thing, such classifications are usually original research, in my experience.

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appear in a few papers by at least two authors. We are filling in the gaps where these papers are unclear, so by

1876: 1720: 1679: 1347:

Hoffman, Kenneth; Kunze, Ray (1971). Linear algebra (2nd ed.). Englewood Cliffs, N.J.: Prentice-Hall, Inc. p. 231

4970: 4804:

So what is the best parenthetical disambiguated name for this page? The options are (add when there are more):

4716: 4694: 4648: 4569: 4216: 4105: 2002: 1881: 1841: 1805: 1702: 1654: 1639: 1568: 1525: 1371: 1217: 5248: 5072: 4952: 4914: 4461: 4153: 4141: 4020: 3734: 3716: 2087: 1920: 1494: 1254: 5215:

Maybe it is not the right page for a page about this, but I think such a page would be an good addition to WP

4872: 4808: 4012: 1932: 3750:

Talk:Infinite_monkey_theorem#RfC:_Which_of_these_versions_of_the_lead_is_the_more_accurate_and_informative.3F

2698:{\displaystyle {\mathfrak {so}}(3,1)={\mathfrak {so}}(3)\subset {\mathfrak {so}}(3,1)\oplus {\mathfrak {k}},} 1607: 5283: 5043: 5032: 4519: 4476: 4445: 4243: 4174: 4053: 3886: 3704: 2139: 1862: 1826: 1593: 1550: 1502: 1476: 1416: 1325: 1302: 1265: 1257:

page. If you need to contact me, please use email, as I have difficulties navigating to my user talk page.

2499: 2479:, because my statement is verifiable. According to Knowledge policy, verifiability weighs more than truth. 2263: 5151: 5059: 4780: 4212: 2899: 2388: 1439: 4966: 4826: 4813: 4754: 4568:

applies. Detailed proofs are the sort of thing one looks for in textbooks, not encyclopedia articles.

4565: 4197: 4166: 2527: 1666: 1628: 4000:{\displaystyle (Z\perp \!\!\!\perp Y)_{G_{\overline {X}}}\qquad (Z\not \!\!{\perp \!\!\!\perp }X)_{G}} 3179: 2039:'s objections, I find no merit in the argument and see this as falling squarely under the umbrella of 5220: 5021: 4893: 4860: 4505: 4491: 2259: 1940: 1392: 1358: 1261: 2123:

OK, and thanks for all your help and explanations. I better understand Knowledge content rules now.

5252: 5098: 5068: 4948: 4910: 4852: 4784: 4545: 4457: 4232: 4149: 4016: 3757: 3730: 3712: 2217: 2175: 2083: 1928: 1486: 1454: 3869:{\displaystyle (Z\perp \!\!\!\perp Y)_{G_{\overline {X}}}\qquad (Z\not {\perp \!\!\!\perp }X)_{G}} 5240: 5202: 5174: 5166: 5159: 5144: 5126: 5106: 5063: 5047: 5028: 4937: 4587: 4515: 4472: 4441: 4170: 4123: 4049: 3882: 2895: 2443: 2108: 2048: 2028: 1858: 1822: 1546: 1472: 1412: 1321: 1298: 1223: 4620: 5269: 5256: 5189: 5155: 5110: 5055: 5005: 4976: 4738: 4722: 4700: 4654: 4575: 4222: 4111: 4071: 3677: 3642: 3622: 2576: 2422: 2355: 2326: 2305: 2301: 2294: 2128: 2069: 2008: 1948: 1887: 1847: 1811: 1750: 1708: 1645: 1574: 1531: 1435: 1377: 1736:

is included in Knowledge but the page on e somehow doesn't warrant such information. Also in

5291: 5188:(Orig.-Ausg., 12. durchges. Aufl. ed.). München: Dt. Taschenbuch-Verl. p. 128-129, 136-137. 5088: 4676: 4553: 4193: 4087: 4037: 3685: 2515: 2495: 2454: 2282: 2236: 2202: 2155: 1662: 1624: 1221: 1219: 39: 5236: 5216: 5170: 5102: 5051: 4929: 4889: 4856: 4593: 4501: 4487: 2564: 2556: 2540: 1910:

Notice after Slawomir's edit the article reads "...the proliferation of modern high-speed

1387: 1353: 5259:. Also, one might look at the AMS classification to see other areas that we've missed. 1493:

I really need some help from experienced math editors. I posted some suggestions to the

5147:, but haven't found a lot of time for this yet (and also became confused, to name two: 3753: 3665: 3634: 2334: 2213: 2171: 1837: 5113:, and none; of these branches are uniquely defined by sets of axioms. IMO, this is in 1606: 5306: 5122: 4996: 4933: 4881: 4797: 4668: 2104: 2044: 1989: 1982: 1924: 1792: 1694: 5262: 5000: 4992: 4851:

The subject (as described in the article ) is rather sopecialised and only used in

4734: 4140:) actually works without spacing hacks, but unfortunately that's the wrong symbol: 4067: 3638: 2405: 2383: 2338: 2124: 2079: 2065: 2040: 2036: 2032: 1944: 1796: 1746: 1290: 3899:(Z \perp\!\!\!\perp Y)_{G_{\overline{X}}} \qquad(Z \not\!\!{\perp\!\!\!\perp} X)_G 1931:(look at the details) the original table entries seem fine. Regarding books, does 4066:

That double up tack unicode character doesn't display for us with old computers.

5287: 5084: 4672: 4549: 4048:

I've seen this symbol used for probabilistic independence used in other places.

4033: 3681: 2273: 2227: 2212:

Yes, that's right - it is a quantitative measure of correlation (of some type).

2193: 2185: 2146: 1658: 1517: 1516:

It looks to me like some of those suggestions have already been implemented by

4788: 4776: 4189: 3772:(Z \perp\!\!\!\perp Y)_{G_{\overline{X}}} \qquad(Z \not{\perp\!\!\!\perp} X)_G 2724:

is, by definition, an arbitrary pure boost. Claim: For any rotation parameter

1760:

you are welcome to supply additional references to reliable secondary sources.

4647:. So the Cauchy criterion implies that the series of functions converges." 4301:

That's how it stands now. Let's try it both ways and see how it looks here:

1253:

One or more math editors are needed to deal with suggestions I posted to the

3661: 4693:

I don't object to that one. The test is rather baffling without a proof.

2442: 1738:

Talk:E (mathematical constant)#287,000 digits in 1988 and 1,000,000 in 1992

1730:

Talk:E (mathematical constant)#287,000 digits in 1988 and 1,000,000 in 1992

1691:

Talk:E (mathematical constant)#287,000 digits in 1988 and 1,000,000 in 1992

1583:

Just saw those changes, thanks. I will try to make further changes myself.

5118: 5114: 4262: 3619:

The interpretation is not unsourced original research, see Cushing above

3637:, put this in a footnote in the article, unless someone spots an error. 4145: 1978:." So, if anything, this source actually supports the opposite stance. 4104:) instead of hacking TeX to produce such a symbol out of other ones. 2593:

So that wasn't original research, whether unsourced or unjustifiable.

2519: 1318:

Draft:Hierarchical testing of variables in high dimensional datasets

4855:

and I think the most precise parenthetical disambiguation is best.

3703:

is undergoing an AfD suggesting that it should be merged back into

2464:

First off, everything is in order because Quondum's claim's about

1974:

the years has become something of a race... No such craze befell

1471:

I think Jitse Niesen will probably look at this within 48 hours.

3700: 1610:- references available if someone knowledgeable can apply them 1520:

several days before this post. In fact, unless I'm mistaken,

1224: 33: 1431: 4909:

and in part because it was the one that was already used. —

4211:

The perennial upright d issue has been raised once more at

3616:

boost (leaving coordinate axes intact), then rotate back.

1733: 1685:

Two separate editors have requested some outside input at

3657: 1699:

Talk:E (mathematical constant)#Exponential-like functions

1623:, but I don't know how to apply them. Can someone help? — 4768:

There is a need to have a parenthetical disambiguation:

4440:

Just a bug, or is there some sensible reason for this?

1804:

that the references used in the table are unsuitable?

1788: 4834:

Historical, the article was named this way previously

1964:

There is no mention of algorithmic improvements there.

4623: 4596: 4377: 4310: 4126: 4090: 3907: 3780: 3633:. Since references are scanty on proofs, I might, by 3421: 3274: 3182: 3043: 2913: 2739: 2606: 4486:

as you get the lower bracket in PNG, and MathJax. --

4430:{\displaystyle \sigma _{y}^{2}\leq 2y_{\max }(A-H),} 1993:

article does mention algorithmic improvements, even

1933:

e: The Story of a Number (Princeton Science Library)

1701:concerning whether original research is permitted. 4363:{\displaystyle \sigma _{y}^{2}\leq 2y_{\max(}A-H),} 2325:YohanN7 and myself have been creating diagrams for 4749:Naming convention for Parenthetical disambiguation 4639: 4609: 4429: 4362: 4132: 4096: 3999: 3868: 3727:Knowledge:WikiProject Deletion sorting/Mathematics 3725:Also, there's a fairly new deletion sorting page, 3565: 3401: 3234: 3162: 3009: 2883: 2697: 4404: 4337: 3705:Trigonometric_functions#Sine, cosine and tangent 2894:is a pure boost (equality is by property of the 3978: 3976: 3974: 3968: 3966: 3921: 3919: 3917: 3847: 3845: 3843: 3794: 3792: 3790: 1763:The reason there is a difference between π and 4787:neither one should be the primary subject for 4165:I've implemented David Eppstein's solution at 1450:Knowledge:Bot_owners' noticeboard#Jietse's bot 5177:in particular every two points are on a line) 4987:Help on disambiguating "matrix models" needed 3881:How can we get this negation to look better? 1426:Actually I responded at the very top section 1232:This page has archives. Sections older than 57: 8: 5207:: CS1 maint: multiple names: authors list ( 4783:and a mathematical one that is only used in 3576:is a pure boost, again by definition. Since 1795:, and I also referred in that discussion to 1335:Need a math person with some hard copy texts 5186:Dtv-Atlas zur Mathematik : Tafeln und Texte 5184:Soeder, Fritz Reinhardt ; Heinrich (2001). 4586:I see the same editor has added a proof to 3748:Comments would be appreciated on this RfC: 4837:Shortest parenthetical disambiguation name 1661:has done just that. Thanks to you both. — 64: 50: 4631: 4622: 4601: 4595: 4564:readers for whom it is not routine, then 4403: 4387: 4382: 4376: 4336: 4320: 4315: 4309: 4125: 4089: 3991: 3970: 3959: 3938: 3933: 3906: 3860: 3839: 3832: 3811: 3806: 3779: 3556: 3548: 3547: 3536: 3528: 3527: 3516: 3508: 3504: 3488: 3480: 3479: 3467: 3459: 3449: 3441: 3437: 3432: 3420: 3391: 3383: 3375: 3366: 3358: 3354: 3346: 3344: 3330: 3322: 3321: 3309: 3301: 3291: 3283: 3279: 3273: 3224: 3213: 3205: 3197: 3189: 3181: 3152: 3144: 3135: 3127: 3123: 3115: 3113: 3099: 3091: 3090: 3078: 3070: 3060: 3052: 3048: 3042: 2980: 2979: 2969: 2961: 2960: 2948: 2940: 2930: 2922: 2918: 2912: 2872: 2864: 2863: 2851: 2843: 2833: 2825: 2821: 2816: 2802: 2794: 2793: 2782: 2774: 2773: 2762: 2754: 2750: 2738: 2686: 2685: 2658: 2657: 2636: 2635: 2608: 2607: 2605: 4880:(no reasons yet) , but is this not what 3549: 3529: 3509: 3481: 3460: 3442: 3376: 3359: 3323: 3302: 3284: 3206: 3190: 3145: 3128: 3092: 3071: 3053: 2962: 2941: 2923: 2865: 2844: 2826: 2795: 2775: 2755: 88: 5200: 5182:The only reference I have till now is 5042:It does seem a bit less unwieldy than 3631:For strikeout, see above small comment 2718:be an arbitrary boost parameter. Then 2552: 2548: 2536: 2525: 2001:discussion as remotely constructive. 1721:E (mathematical_constant)#Known_digits 18:Knowledge talk:WikiProject Mathematics 5313:WikiProject Mathematics archives/2015 2188:that illustrates correlation (in the 7: 4271:\sigma_y^2 \le 2y_\text{max} (A - H) 3709:Knowledge:Articles for deletion/Sine 3656:I was just looking around Tricki at 2027:My initial reaction was the same as 1427: 3625:(ref in article) for stretching by 2984: 2981: 2687: 2662: 2659: 2640: 2637: 2612: 2609: 5150:There are different opinions what 5027:Any opinions of this new article? 3606:Oops, this is wrong, the boost is 3350: 3347: 3119: 3116: 1784:etc.) that discuss these advances. 1343:is a copy of the source material: 45:WikiProject Mathematics archives ( 32: 4995:disambiguation page. Please see 4759:hypercycle (hyperbolic geometry) 4669:Ratio test#Proof of Kummer's Test 3235:{\displaystyle \in \mathbf {k} ,} 2258:I disambiguated "Rayleigh II" at 2031:'s but I in no way disagree with 1405: 1236:may be automatically archived by 4902:hypercycle (hyperbolic geometry) 4844:hypercycle (hyperbolic geometry) 4819:hypercycle (hyperbolic geometry) 4295:\sigma_y^2 \le 2y_{\max} (A - H) 3557: 3537: 3517: 3489: 3468: 3450: 3392: 3384: 3367: 3331: 3310: 3292: 3225: 3214: 3198: 3153: 3136: 3100: 3079: 3061: 2970: 2949: 2931: 2873: 2852: 2834: 2803: 2783: 2763: 2500:"Vector Lorentz Transformations" 2482:Quondum's allegation that it is 38: 1997:it has been pointed out to you! 1793:the guideline that they violate 1734:Pi#Modern_quest_for_more_digits 4764:The facts (add when needed) : 4421: 4409: 4354: 4340: 4283:\sigma_y^2 \le 2y_\max (A - H) 3988: 3953: 3930: 3908: 3857: 3826: 3803: 3781: 3472: 3456: 3314: 3298: 3218: 3183: 3083: 3067: 3001: 2989: 2953: 2937: 2856: 2840: 2679: 2667: 2651: 2645: 2629: 2617: 2451:Vector Lorentz transformations 1687:Talk:E (mathematical constant) 1: 3951: 3824: 3767:Independence and its negation 2708:vector space direct sum. Let 1295:uncorrelated random variables 1285:uncorrelated random variables 4257:Anomalous MathJax rendering. 4190:Talk:Ratio#Split mathematics 4184:Ratios always dimensionless? 4133:{\displaystyle \not \amalg } 3960: 3943: 3833: 3816: 2569:The Quantum Theory of Fields 2304:. Look at , for example. — 1406:Is Jitse's bot dead forever? 1341:Cyclic decomposition theorem 2269:Novel 3D Media Technologies 5329: 5245:pseudo-Riemannian geometry 4775:There are two meanings of 4640:{\displaystyle \sum M_{n}} 3896:Even more negative space? 3588:, and since the action of 2573:Cambridge University Press 2226:Ok, that will do. Thanks! 2190:correlation and dependence 2168:correlation and dependence 1988:Finally, you have a clear 1779:In fact, I have given the 5296:21:21, 29 July 2015 (UTC) 5277:13:32, 29 July 2015 (UTC) 5235:The list is also missing 5225:09:44, 29 July 2015 (UTC) 5131:08:34, 29 July 2015 (UTC) 5093:00:28, 29 July 2015 (UTC) 5077:00:24, 29 July 2015 (UTC) 5037:00:09, 29 July 2015 (UTC) 5016:07:03, 29 July 2015 (UTC) 4981:12:14, 27 July 2015 (UTC) 4957:23:46, 27 July 2015 (UTC) 4942:09:25, 27 July 2015 (UTC) 4919:06:39, 27 July 2015 (UTC) 4898:05:57, 27 July 2015 (UTC) 4865:05:57, 27 July 2015 (UTC) 4743:14:52, 27 July 2015 (UTC) 4727:12:38, 26 July 2015 (UTC) 4705:13:11, 26 July 2015 (UTC) 4681:11:52, 26 July 2015 (UTC) 4659:11:31, 26 July 2015 (UTC) 4580:11:19, 26 July 2015 (UTC) 4558:11:00, 26 July 2015 (UTC) 4544:is adding proofs to the " 4524:19:48, 25 July 2015 (UTC) 4510:11:20, 25 July 2015 (UTC) 4496:08:59, 25 July 2015 (UTC) 4481:07:11, 25 July 2015 (UTC) 4466:20:57, 24 July 2015 (UTC) 4450:20:25, 24 July 2015 (UTC) 4252:23:03, 24 July 2015 (UTC) 4227:17:02, 24 July 2015 (UTC) 4215:. Opinions are welcome. 4202:05:49, 22 July 2015 (UTC) 4179:21:18, 20 July 2015 (UTC) 4158:16:12, 19 July 2015 (UTC) 4116:12:22, 19 July 2015 (UTC) 4076:11:29, 19 July 2015 (UTC) 4058:21:19, 20 July 2015 (UTC) 4042:04:25, 19 July 2015 (UTC) 4025:01:28, 19 July 2015 (UTC) 3891:00:38, 19 July 2015 (UTC) 3762:10:29, 20 July 2015 (UTC) 3739:07:39, 18 July 2015 (UTC) 3721:00:35, 18 July 2015 (UTC) 3690:17:45, 16 July 2015 (UTC) 3670:10:20, 15 July 2015 (UTC) 3647:17:03, 13 July 2015 (UTC) 2431:16:34, 16 July 2015 (UTC) 2364:18:08, 12 July 2015 (UTC) 2309:17:39, 12 July 2015 (UTC) 2288:17:37, 15 July 2015 (UTC) 2242:16:12, 13 July 2015 (UTC) 2222:15:43, 13 July 2015 (UTC) 2208:15:25, 13 July 2015 (UTC) 2180:14:57, 13 July 2015 (UTC) 2161:14:13, 13 July 2015 (UTC) 2133:18:10, 11 July 2015 (UTC) 2113:03:17, 11 July 2015 (UTC) 2092:03:04, 11 July 2015 (UTC) 2074:01:23, 11 July 2015 (UTC) 2053:18:22, 10 July 2015 (UTC) 2013:18:03, 10 July 2015 (UTC) 1957:17:22, 10 July 2015 (UTC) 1914:has made it possible for 1892:15:56, 10 July 2015 (UTC) 1877:E (mathematical constant) 1867:15:14, 10 July 2015 (UTC) 1852:15:04, 10 July 2015 (UTC) 1831:13:53, 10 July 2015 (UTC) 1816:13:37, 10 July 2015 (UTC) 1755:04:43, 10 July 2015 (UTC) 1680:E (mathematical constant) 1671:13:25, 10 July 2015 (UTC) 1444:00:17, 29 June 2015 (UTC) 1421:23:27, 26 June 2015 (UTC) 1255:talk: Jacobian conjecture 5249:non-commutative geometry 4947:stick with "geometry". — 4873:hypercycle (mathematics) 4809:hypercycle (mathematics) 4142:conditional independence 3707:. Please participate at 2445:File:Cushing Excerpt.JPG 1981:You're just wrong about 1713:12:55, 9 July 2015 (UTC) 1650:13:42, 9 July 2015 (UTC) 1633:01:28, 9 July 2015 (UTC) 1602:23:31, 9 July 2015 (UTC) 1579:22:42, 9 July 2015 (UTC) 1555:14:48, 9 July 2015 (UTC) 1536:13:26, 9 July 2015 (UTC) 1511:00:53, 9 July 2015 (UTC) 1495:talk:Jacobian conjecture 1481:03:59, 9 July 2015 (UTC) 1464:18:55, 3 July 2015 (UTC) 1398:17:16, 4 July 2015 (UTC) 1382:15:41, 4 July 2015 (UTC) 1364:15:05, 4 July 2015 (UTC) 1330:20:30, 3 July 2015 (UTC) 1307:19:07, 3 July 2015 (UTC) 1278:00:40, 3 July 2015 (UTC) 5284:List of geometry topics 5105:are both considered in 5044:list of geometry topics 4265:, some code said this: 4097:{\displaystyle \amalg } 2140:Correlation coefficient 5152:non-Euclidean geometry 5060:computational geometry 4781:hypercycle (chemistry) 4755:hypercycle (geometry) 4641: 4611: 4431: 4364: 4277:I changed it to this: 4134: 4098: 4001: 3870: 3567: 3403: 3265:works by composition) 3236: 3164: 3011: 2885: 2699: 2458: 2389:Talk:Thomas precession 2337:it should be allowed. 1608:Draft:Thaine's theorem 1239:Lowercase sigmabot III 5173:? (Not all axioms of 4967:hypercycle (geometry) 4827:hypercycle (geometry) 4814:hypercycle (geometry) 4642: 4612: 4610:{\displaystyle M_{n}} 4432: 4365: 4167:Instrumental variable 4135: 4099: 4002: 3871: 3623:A. Ben-Menahem (1985) 3614:coordinate axes alone 3568: 3404: 3237: 3165: 3012: 2886: 2700: 2448: 1990:conflict of interests 1448:I've raised it here: 5022:Branches of geometry 4621: 4594: 4375: 4308: 4124: 4088: 3905: 3778: 3744:Request for Comment 3419: 3272: 3180: 3041: 2911: 2898:). By a property of 2737: 2604: 2260:Wave field synthesis 1840:, which is policy. 1742:algorithmic advances 1726:algorithmic advances 5253:elliptical geometry 5160:spherical geometry 5145:synthetic geometrys 5099:projective geometry 4997:this "dablink-list" 4853:hyperbolic geometry 4785:hyperbolic geometry 4757:which I renamed to 4546:Uniform convergence 4536:Uniform convergence 4392: 4325: 4233:Jacobian conjecture 4207:Perennial upright d 3964: 3837: 1921:my 1992 source code 1487:Jacobian conjecture 1249:Jacobian conjecture 5241:geometric analysis 5175:incidence geometry 5167:Minkowski geometry 5162:also a part of it. 5107:synthetic geometry 5064:synthetic geometry 5048:inversive geometry 4932:must be reverted. 4637: 4607: 4588:Weierstrass M-test 4427: 4378: 4360: 4311: 4130: 4094: 3997: 3979: 3977: 3975: 3969: 3967: 3952: 3922: 3920: 3918: 3866: 3848: 3846: 3844: 3825: 3795: 3793: 3791: 3563: 3399: 3232: 3160: 3007: 2896:matrix exponential 2881: 2695: 2547:Unknown parameter 2459: 2293:OR in progress at 2264:Rayleigh–Jeans law 5275: 5257:tropical geometry 5156:absolute geometry 5111:analytic geometry 5056:discrete geometry 4542:Sergey Liflandsky 4244:L.Andrew Campbell 3963: 3946: 3836: 3819: 3632: 3615: 3597:then stretch the 2589:Original research 2520:10.1119/1.1974267 2449:Excerpt from ref 2327:Thomas precession 2302:Thomas precession 2295:Thomas precession 2101:in the literature 1960: 1943:comment added by 1912:desktop computers 1594:L.Andrew Campbell 1503:L.Andrew Campbell 1457: 1281: 1266:L.Andrew Campbell 1264:comment added by 1246: 1245: 95:Nov 2002–Dec 2003 5320: 5274: 5272: 5260: 5212: 5206: 5198: 5013: 5008: 5003: 4973: 4719: 4697: 4651: 4646: 4644: 4643: 4638: 4636: 4635: 4616: 4614: 4613: 4608: 4606: 4605: 4572: 4436: 4434: 4433: 4428: 4408: 4407: 4391: 4386: 4369: 4367: 4366: 4361: 4344: 4343: 4324: 4319: 4219: 4144:uses the double 4139: 4137: 4136: 4131: 4108: 4103: 4101: 4100: 4095: 4006: 4004: 4003: 3998: 3996: 3995: 3983: 3965: 3961: 3950: 3949: 3948: 3947: 3939: 3875: 3873: 3872: 3867: 3865: 3864: 3852: 3838: 3834: 3823: 3822: 3821: 3820: 3812: 3630: 3628: 3605: 3602: 3591: 3587: 3583: 3579: 3572: 3570: 3569: 3564: 3562: 3561: 3560: 3552: 3542: 3541: 3540: 3532: 3522: 3521: 3520: 3512: 3496: 3495: 3494: 3493: 3492: 3484: 3471: 3463: 3455: 3454: 3453: 3445: 3408: 3406: 3405: 3400: 3395: 3387: 3379: 3374: 3373: 3372: 3371: 3370: 3362: 3353: 3336: 3335: 3334: 3326: 3313: 3305: 3297: 3296: 3295: 3287: 3264: 3251:, so (recalling 3250: 3241: 3239: 3238: 3233: 3228: 3217: 3209: 3201: 3193: 3169: 3167: 3166: 3161: 3156: 3148: 3143: 3142: 3141: 3140: 3139: 3131: 3122: 3105: 3104: 3103: 3095: 3082: 3074: 3066: 3065: 3064: 3056: 3032: 3027: 3016: 3014: 3013: 3008: 2988: 2987: 2975: 2974: 2973: 2965: 2952: 2944: 2936: 2935: 2934: 2926: 2902: 2890: 2888: 2887: 2882: 2880: 2879: 2878: 2877: 2876: 2868: 2855: 2847: 2839: 2838: 2837: 2829: 2808: 2807: 2806: 2798: 2788: 2787: 2786: 2778: 2768: 2767: 2766: 2758: 2729: 2723: 2717: 2704: 2702: 2701: 2696: 2691: 2690: 2666: 2665: 2644: 2643: 2616: 2615: 2584: 2560: 2554: 2550: 2544: 2538: 2533: 2531: 2523: 2455:James T. Cushing 2446: 2280: 2234: 2200: 2153: 2105:Bill Cherowitzo 2045:Bill Cherowitzo 2005: 1959: 1937: 1884: 1844: 1808: 1705: 1657:, It seems that 1642: 1571: 1567:No, I haven't. 1528: 1453: 1428:#No_new_articles 1395: 1390: 1374: 1361: 1356: 1280: 1258: 1241: 1225: 66: 59: 52: 42: 34: 5328: 5327: 5323: 5322: 5321: 5319: 5318: 5317: 5303: 5302: 5270: 5265: 5261: 5237:global analysis 5199: 5195: 5183: 5171:affine geometry 5103:affine geometry 5052:convex geometry 5025: 5011: 5006: 5001: 4989: 4971: 4888:Please join in 4751: 4717: 4695: 4673:Boris Tsirelson 4649: 4627: 4619: 4618: 4597: 4592: 4591: 4570: 4550:Boris Tsirelson 4538: 4399: 4373: 4372: 4332: 4306: 4305: 4259: 4237: 4217: 4209: 4186: 4122: 4121: 4106: 4086: 4085: 4034:Boris Tsirelson 3987: 3934: 3929: 3903: 3902: 3856: 3807: 3802: 3776: 3775: 3769: 3746: 3698: 3654: 3626: 3598: 3589: 3585: 3581: 3577: 3543: 3523: 3500: 3475: 3433: 3428: 3417: 3416: 3345: 3340: 3317: 3275: 3270: 3269: 3258: 3252: 3246: 3178: 3177: 3114: 3109: 3086: 3044: 3039: 3038: 3030: 3025: 2956: 2914: 2909: 2908: 2900: 2859: 2817: 2812: 2789: 2769: 2746: 2735: 2734: 2725: 2719: 2709: 2602: 2601: 2591: 2582: 2563: 2546: 2534: 2524: 2494: 2444: 2441: 2427: 2360: 2321:an overreaction 2298: 2274: 2256: 2228: 2194: 2147: 2143: 2080:reliable source 2003: 1938: 1882: 1842: 1806: 1703: 1683: 1640: 1612: 1569: 1526: 1491: 1462: 1408: 1393: 1388: 1372: 1359: 1354: 1337: 1320:notable? Best, 1314: 1287: 1259: 1251: 1237: 1226: 1220: 1211: 1097: 87: 86: 73: 70: 30: 29: 28: 12: 11: 5: 5326: 5324: 5316: 5315: 5305: 5304: 5301: 5300: 5299: 5298: 5268: 5263: 5232: 5231: 5230: 5229: 5228: 5227: 5213: 5193: 5180: 5179: 5178: 5163: 5136: 5135: 5134: 5133: 5109:as well as in 5080: 5079: 5069:David Eppstein 5024: 5019: 4988: 4985: 4984: 4983: 4972:Sławomir Biały 4963: 4962: 4961: 4960: 4959: 4949:David Eppstein 4922: 4921: 4911:David Eppstein 4900:(ps I prefer 4886: 4885: 4868: 4867: 4839: 4838: 4835: 4822: 4821: 4816: 4811: 4802: 4801: 4794: 4793: 4792: 4791: 4770: 4769: 4750: 4747: 4746: 4745: 4730: 4729: 4718:Sławomir Biały 4712: 4711: 4710: 4709: 4708: 4707: 4696:Sławomir Biały 4686: 4685: 4684: 4683: 4662: 4661: 4650:Sławomir Biały 4634: 4630: 4626: 4604: 4600: 4583: 4582: 4571:Sławomir Biały 4566:WP:NOTTEXTBOOK 4537: 4534: 4533: 4532: 4531: 4530: 4529: 4528: 4527: 4526: 4498: 4458:David Eppstein 4438: 4437: 4426: 4423: 4420: 4417: 4414: 4411: 4406: 4402: 4398: 4395: 4390: 4385: 4381: 4370: 4359: 4356: 4353: 4350: 4347: 4342: 4339: 4335: 4331: 4328: 4323: 4318: 4314: 4299: 4298: 4297: 4296: 4287: 4286: 4285: 4284: 4275: 4274: 4273: 4272: 4258: 4255: 4236: 4230: 4218:Sławomir Biały 4208: 4205: 4188:Pls weigh in: 4185: 4182: 4163: 4162: 4161: 4160: 4150:David Eppstein 4129: 4107:Sławomir Biały 4093: 4082: 4081: 4080: 4079: 4078: 4064: 4063: 4062: 4061: 4060: 4017:David Eppstein 4011:(As discussed 4009: 4008: 4007: 3994: 3990: 3986: 3982: 3973: 3958: 3955: 3945: 3942: 3937: 3932: 3928: 3925: 3916: 3913: 3910: 3900: 3879: 3878: 3876: 3863: 3859: 3855: 3851: 3842: 3831: 3828: 3818: 3815: 3810: 3805: 3801: 3798: 3789: 3786: 3783: 3773: 3768: 3765: 3745: 3742: 3731:David Eppstein 3713:David Eppstein 3697: 3694: 3693: 3692: 3653: 3650: 3574: 3573: 3559: 3555: 3551: 3546: 3539: 3535: 3531: 3526: 3519: 3515: 3511: 3507: 3503: 3499: 3491: 3487: 3483: 3478: 3474: 3470: 3466: 3462: 3458: 3452: 3448: 3444: 3440: 3436: 3431: 3427: 3424: 3410: 3409: 3398: 3394: 3390: 3386: 3382: 3378: 3369: 3365: 3361: 3357: 3352: 3349: 3343: 3339: 3333: 3329: 3325: 3320: 3316: 3312: 3308: 3304: 3300: 3294: 3290: 3286: 3282: 3278: 3254: 3245:for arbitrary 3243: 3242: 3231: 3227: 3223: 3220: 3216: 3212: 3208: 3204: 3200: 3196: 3192: 3188: 3185: 3171: 3170: 3159: 3155: 3151: 3147: 3138: 3134: 3130: 3126: 3121: 3118: 3112: 3108: 3102: 3098: 3094: 3089: 3085: 3081: 3077: 3073: 3069: 3063: 3059: 3055: 3051: 3047: 3018: 3017: 3006: 3003: 3000: 2997: 2994: 2991: 2986: 2983: 2978: 2972: 2968: 2964: 2959: 2955: 2951: 2947: 2943: 2939: 2933: 2929: 2925: 2921: 2917: 2892: 2891: 2875: 2871: 2867: 2862: 2858: 2854: 2850: 2846: 2842: 2836: 2832: 2828: 2824: 2820: 2815: 2811: 2805: 2801: 2797: 2792: 2785: 2781: 2777: 2772: 2765: 2761: 2757: 2753: 2749: 2745: 2742: 2706: 2705: 2694: 2689: 2684: 2681: 2678: 2675: 2672: 2669: 2664: 2661: 2656: 2653: 2650: 2647: 2642: 2639: 2634: 2631: 2628: 2625: 2622: 2619: 2614: 2611: 2590: 2587: 2586: 2585: 2580: 2561: 2549:|subscription= 2496:Cushing, J. T. 2477:wiki-incorrect 2440: 2437: 2436: 2435: 2434: 2433: 2425: 2399: 2398: 2397: 2396: 2376: 2375: 2374: 2373: 2367: 2366: 2358: 2297: 2291: 2255: 2252: 2251: 2250: 2249: 2248: 2247: 2246: 2245: 2244: 2142: 2137: 2136: 2135: 2121: 2120: 2119: 2118: 2117: 2116: 2115: 2084:David Eppstein 2061: 2060: 2059: 2058: 2057: 2056: 2055: 2018: 2017: 2016: 2015: 2004:Sławomir Biały 1998: 1986: 1979: 1971: 1968: 1908: 1907: 1906: 1905: 1904: 1903: 1902: 1901: 1900: 1899: 1898: 1897: 1896: 1895: 1894: 1883:Sławomir Biały 1843:Sławomir Biały 1807:Sławomir Biały 1797:policy reasons 1785: 1777: 1774:either article 1761: 1704:Sławomir Biały 1682: 1677: 1676: 1675: 1674: 1673: 1655:Sławomir Biały 1641:Sławomir Biały 1611: 1605: 1591: 1590: 1589: 1588: 1587: 1586: 1585: 1584: 1570:Sławomir Biały 1560: 1559: 1558: 1557: 1539: 1538: 1527:Sławomir Biały 1501: 1490: 1484: 1469: 1468: 1467: 1466: 1458: 1455:JohnBlackburne 1407: 1404: 1403: 1402: 1401: 1400: 1373:Sławomir Biały 1349: 1348: 1336: 1333: 1313: 1312:AfC submission 1310: 1286: 1283: 1250: 1247: 1244: 1243: 1231: 1228: 1227: 1222: 1218: 1216: 1213: 1212: 1210: 1209: 1154: 1098: 1096: 1095: 1040: 985: 930: 875: 820: 765: 710: 655: 600: 545: 490: 435: 380: 325: 270: 215: 160: 105: 84: 83: 82: 79: 78: 75: 74: 69: 68: 61: 54: 46: 43: 37: 31: 15: 14: 13: 10: 9: 6: 4: 3: 2: 5325: 5314: 5311: 5310: 5308: 5297: 5293: 5289: 5285: 5280: 5279: 5278: 5273: 5267: 5258: 5254: 5250: 5246: 5242: 5238: 5234: 5233: 5226: 5222: 5218: 5214: 5210: 5204: 5196: 5194:3-423-03007-0 5191: 5187: 5181: 5176: 5172: 5168: 5164: 5161: 5157: 5154:means: Is it 5153: 5149: 5148: 5146: 5142: 5141: 5140: 5139: 5138: 5137: 5132: 5128: 5124: 5120: 5116: 5112: 5108: 5104: 5100: 5096: 5095: 5094: 5090: 5086: 5082: 5081: 5078: 5074: 5070: 5065: 5061: 5057: 5053: 5049: 5045: 5041: 5040: 5039: 5038: 5034: 5030: 5029:Michael Hardy 5023: 5020: 5018: 5017: 5014: 5009: 5004: 4998: 4994: 4986: 4982: 4978: 4974: 4968: 4964: 4958: 4954: 4950: 4945: 4944: 4943: 4939: 4935: 4931: 4926: 4925: 4924: 4923: 4920: 4916: 4912: 4907: 4906: 4905: 4903: 4899: 4895: 4891: 4883: 4879: 4878: 4877: 4876: 4874: 4866: 4862: 4858: 4854: 4850: 4849: 4848: 4847: 4845: 4836: 4833: 4832: 4831: 4830: 4828: 4820: 4817: 4815: 4812: 4810: 4807: 4806: 4805: 4799: 4796: 4795: 4790: 4786: 4782: 4778: 4774: 4773: 4772: 4771: 4767: 4766: 4765: 4762: 4760: 4756: 4748: 4744: 4740: 4736: 4732: 4731: 4728: 4724: 4720: 4714: 4713: 4706: 4702: 4698: 4692: 4691: 4690: 4689: 4688: 4687: 4682: 4678: 4674: 4670: 4666: 4665: 4664: 4663: 4660: 4656: 4652: 4632: 4628: 4624: 4602: 4598: 4589: 4585: 4584: 4581: 4577: 4573: 4567: 4562: 4561: 4560: 4559: 4555: 4551: 4547: 4543: 4535: 4525: 4521: 4517: 4516:Michael Hardy 4513: 4512: 4511: 4507: 4503: 4499: 4497: 4493: 4489: 4484: 4483: 4482: 4478: 4474: 4473:Michael Hardy 4469: 4468: 4467: 4463: 4459: 4454: 4453: 4452: 4451: 4447: 4443: 4442:Michael Hardy 4424: 4418: 4415: 4412: 4400: 4396: 4393: 4388: 4383: 4379: 4371: 4357: 4351: 4348: 4345: 4333: 4329: 4326: 4321: 4316: 4312: 4304: 4303: 4302: 4294: 4293: 4292: 4291: 4290: 4282: 4281: 4280: 4279: 4278: 4270: 4269: 4268: 4267: 4266: 4264: 4256: 4254: 4253: 4249: 4245: 4241: 4234: 4231: 4229: 4228: 4224: 4220: 4214: 4206: 4204: 4203: 4199: 4195: 4191: 4183: 4181: 4180: 4176: 4172: 4171:Michael Hardy 4168: 4159: 4155: 4151: 4147: 4143: 4127: 4119: 4118: 4117: 4113: 4109: 4091: 4083: 4077: 4073: 4069: 4065: 4059: 4055: 4051: 4050:Michael Hardy 4047: 4046: 4045: 4044: 4043: 4039: 4035: 4030: 4029: 4028: 4027: 4026: 4022: 4018: 4014: 4010: 3992: 3984: 3980: 3971: 3956: 3940: 3935: 3926: 3923: 3914: 3911: 3901: 3898: 3897: 3895: 3894: 3893: 3892: 3888: 3884: 3883:Michael Hardy 3877: 3861: 3853: 3849: 3840: 3829: 3813: 3808: 3799: 3796: 3787: 3784: 3774: 3771: 3770: 3766: 3764: 3763: 3759: 3755: 3751: 3743: 3741: 3740: 3736: 3732: 3728: 3723: 3722: 3718: 3714: 3710: 3706: 3702: 3695: 3691: 3687: 3683: 3678: 3674: 3673: 3672: 3671: 3667: 3663: 3658: 3651: 3649: 3648: 3644: 3640: 3636: 3629: 3624: 3617: 3613: 3609: 3604: 3601: 3593: 3580:is onto both 3553: 3544: 3533: 3524: 3513: 3505: 3501: 3497: 3485: 3476: 3464: 3446: 3438: 3434: 3429: 3425: 3422: 3415: 3414: 3413: 3396: 3388: 3380: 3363: 3355: 3341: 3337: 3327: 3318: 3306: 3288: 3280: 3276: 3268: 3267: 3266: 3262: 3257: 3249: 3229: 3221: 3210: 3202: 3194: 3186: 3176: 3175: 3174: 3157: 3149: 3132: 3124: 3110: 3106: 3096: 3087: 3075: 3057: 3049: 3045: 3037: 3036: 3035: 3033: 3023: 3004: 2998: 2995: 2992: 2976: 2966: 2957: 2945: 2927: 2919: 2915: 2907: 2906: 2905: 2903: 2897: 2869: 2860: 2848: 2830: 2822: 2818: 2813: 2809: 2799: 2790: 2779: 2770: 2759: 2751: 2747: 2743: 2740: 2733: 2732: 2731: 2728: 2722: 2716: 2712: 2692: 2682: 2676: 2673: 2670: 2654: 2648: 2632: 2626: 2623: 2620: 2600: 2599: 2598: 2596: 2588: 2583: 2581:0-521-55001-7 2578: 2575:, pp. 68–69, 2574: 2570: 2566: 2562: 2558: 2542: 2529: 2521: 2517: 2513: 2509: 2505: 2501: 2497: 2493: 2492: 2491: 2489: 2485: 2484:unjustifiable 2480: 2478: 2473: 2470: 2467: 2462: 2456: 2452: 2447: 2438: 2432: 2429: 2428: 2421: 2419: 2416: 2412: 2411: 2410: 2403: 2402: 2401: 2400: 2394: 2390: 2385: 2380: 2379: 2378: 2377: 2371: 2370: 2369: 2368: 2365: 2362: 2361: 2354: 2352: 2349: 2345: 2344: 2343: 2336: 2332: 2328: 2324: 2320: 2316: 2313: 2312: 2311: 2310: 2307: 2303: 2296: 2292: 2290: 2289: 2286: 2285: 2281: 2279: 2278: 2271: 2270: 2265: 2261: 2253: 2243: 2240: 2239: 2235: 2233: 2232: 2225: 2224: 2223: 2219: 2215: 2211: 2210: 2209: 2206: 2205: 2201: 2199: 2198: 2191: 2187: 2183: 2182: 2181: 2177: 2173: 2169: 2165: 2164: 2163: 2162: 2159: 2158: 2154: 2152: 2151: 2141: 2138: 2134: 2130: 2126: 2122: 2114: 2110: 2106: 2102: 2097: 2096: 2095: 2094: 2093: 2089: 2085: 2081: 2077: 2076: 2075: 2071: 2067: 2062: 2054: 2050: 2046: 2042: 2038: 2034: 2030: 2026: 2025: 2024: 2023: 2022: 2021: 2020: 2019: 2014: 2010: 2006: 1999: 1996: 1991: 1987: 1984: 1980: 1977: 1972: 1969: 1965: 1962: 1961: 1958: 1954: 1950: 1946: 1942: 1934: 1930: 1926: 1922: 1917: 1913: 1909: 1893: 1889: 1885: 1878: 1874: 1873: 1872: 1871: 1870: 1869: 1868: 1864: 1860: 1855: 1854: 1853: 1849: 1845: 1839: 1834: 1833: 1832: 1828: 1824: 1819: 1818: 1817: 1813: 1809: 1803: 1798: 1794: 1790: 1786: 1782: 1778: 1775: 1771: 1766: 1762: 1758: 1757: 1756: 1752: 1748: 1743: 1739: 1735: 1731: 1727: 1722: 1717: 1716: 1715: 1714: 1710: 1706: 1700: 1696: 1692: 1688: 1681: 1678: 1672: 1668: 1664: 1660: 1656: 1653: 1652: 1651: 1647: 1643: 1637: 1636: 1635: 1634: 1630: 1626: 1622: 1619: 1616: 1609: 1604: 1603: 1599: 1595: 1582: 1581: 1580: 1576: 1572: 1566: 1565: 1564: 1563: 1562: 1561: 1556: 1552: 1548: 1543: 1542: 1541: 1540: 1537: 1533: 1529: 1523: 1519: 1515: 1514: 1513: 1512: 1508: 1504: 1499: 1496: 1488: 1485: 1483: 1482: 1478: 1474: 1473:Michael Hardy 1465: 1461: 1456: 1451: 1447: 1446: 1445: 1441: 1437: 1432: 1429: 1425: 1424: 1423: 1422: 1418: 1414: 1413:Michael Hardy 1399: 1396: 1391: 1385: 1384: 1383: 1379: 1375: 1368: 1367: 1366: 1365: 1362: 1357: 1346: 1345: 1344: 1342: 1334: 1332: 1331: 1327: 1323: 1322:FoCuSandLeArN 1319: 1311: 1309: 1308: 1304: 1300: 1299:Michael Hardy 1296: 1292: 1289:I just moved 1284: 1282: 1279: 1275: 1271: 1267: 1263: 1256: 1248: 1240: 1235: 1230: 1229: 1215: 1214: 1208: 1204: 1200: 1196: 1192: 1188: 1184: 1180: 1176: 1172: 1168: 1164: 1160: 1159: 1155: 1153: 1149: 1145: 1141: 1137: 1133: 1129: 1125: 1121: 1117: 1113: 1109: 1105: 1104: 1100: 1099: 1094: 1090: 1086: 1082: 1078: 1074: 1070: 1066: 1062: 1058: 1054: 1050: 1046: 1045: 1041: 1039: 1035: 1031: 1027: 1023: 1019: 1015: 1011: 1007: 1003: 999: 995: 991: 990: 986: 984: 980: 976: 972: 968: 964: 960: 956: 952: 948: 944: 940: 936: 935: 931: 929: 925: 921: 917: 913: 909: 905: 901: 897: 893: 889: 885: 881: 880: 876: 874: 870: 866: 862: 858: 854: 850: 846: 842: 838: 834: 830: 826: 825: 821: 819: 815: 811: 807: 803: 799: 795: 791: 787: 783: 779: 775: 771: 770: 766: 764: 760: 756: 752: 748: 744: 740: 736: 732: 728: 724: 720: 716: 715: 711: 709: 705: 701: 697: 693: 689: 685: 681: 677: 673: 669: 665: 661: 660: 656: 654: 650: 646: 642: 638: 634: 630: 626: 622: 618: 614: 610: 606: 605: 601: 599: 595: 591: 587: 583: 579: 575: 571: 567: 563: 559: 555: 551: 550: 546: 544: 540: 536: 532: 528: 524: 520: 516: 512: 508: 504: 500: 496: 495: 491: 489: 485: 481: 477: 473: 469: 465: 461: 457: 453: 449: 445: 441: 440: 436: 434: 430: 426: 422: 418: 414: 410: 406: 402: 398: 394: 390: 386: 385: 381: 379: 375: 371: 367: 363: 359: 355: 351: 347: 343: 339: 335: 331: 330: 326: 324: 320: 316: 312: 308: 304: 300: 296: 292: 288: 284: 280: 276: 275: 271: 269: 265: 261: 257: 253: 249: 245: 241: 237: 233: 229: 225: 221: 220: 216: 214: 210: 206: 202: 198: 194: 190: 186: 182: 178: 174: 170: 166: 165: 161: 159: 155: 151: 147: 143: 139: 135: 131: 127: 123: 119: 115: 111: 110: 106: 104: 100: 96: 92: 89: 85:Earlier years 81: 80: 77: 76: 72: 67: 62: 60: 55: 53: 48: 47: 41: 36: 35: 27: 23: 19: 5185: 5026: 4993:Matrix model 4990: 4887: 4870: 4869: 4841: 4840: 4824: 4823: 4803: 4763: 4752: 4539: 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