User talk:R.e.b./Archive 5

2539:

attacked as incoherent, without making a distinction between different types of non-Archimedean fields. An infinitesimal is by definition an element of a non-archimedean field that violates the archimedean axiom. To what extent these can be exploited in the calculus is a separate issue, and depends on the power of the field to handle various arithmetic operations, to what extent one has a transfer principle, etcetera. The infinitesimal navbox is intended to cover all notions of infinitesimals. I am not sure what you mean when you say that it is a coincidence that non-standard analysis and Dehn both used non-Archimedean fields. There is certainly no reason to limit the navbox to non-standard analysis. leibniz was not a non-standard analyst. Levi-Civita fields naturally belong here, as well, and for all I know Dehn might have used a Levi-Civita field in his construction.

4809:, which is the same thing as a slight generalisation of Diff ( S) that several authors have studied (including your friend from UCSC, who seems to have published a corrected version of the infamous paper that did not get slated in Maths Reviews). The matrix coefficient in the projective representation of Diff ( S) is expressed as a Fredholm determinant which arises in geometric function theory (called Fredholm eigenvalues of a planar domain) and has been calculated explicitly. Anyway, just so that you are warned (I thought quite long about what title the article should have). I liked the bio on Grunsky, which I had contemplated writing myself. Regards, A. 2425:

infinitesimals from mathematics. Thus, in Dehn's time, there was active research going on in non-Archimedean fields, for instance Stolz, du Bois-Reymond, Borel, Levi-Civita, and others. I am not sure which theory exactly Dehn used, but it must have been somewhat powerful to be able to handle square roots. There is definite continuity among all these theories of infinitesimals. There is no reason to limit the navbox to surreals and hyperreals. In short, I am puzzled by your comment.

31: 6486: 1834: 723:

variables course, but until I saw your new article here tonight I didn't know that name for it. A philosophy professor to whom I posed this question suggested this: a closed loop of string enters a hole drilled in the picture, goes through to the other side and returns back out through the hole. So there's an end of the loop on each side that you can hang on a nail. It works. But that's not what was intended by the question.

2700: 629:

scattered over several other articles, with the result that almost every redirect in the area was wrong anyway (so a few more or less made little difference). I didnt explain at the time because I hadnt decided exactly what to, but I think everything is now more or less in the right place. There is usually no need to fix double redirects as there are bots that do it automatically if you wait a day or two.

7358: 7270: 4551: 2383:"Plane" can mean "2-dimensional geometry", as in "projective plane" or "hyperbolic plane". "Semi-Euclidean" does not sound like "Semi-Riemannian" to me, and is the name that Dehn and Hilbert use for it. I suggest moving the present article to "Semi-Euclidean geometry", writing a new article on Dehn's "Non-Legendrian geometry", and making "Dehn plane" a disambiguation page pointing to both. 7452:

terminology seems to be torn between the current refs and the article... I will not argue about or change any terminology, but it would be great if you added at least one ref using the term "decomposable", as well as more refs furthering the definitions of "reducible/irreducible representations" as opposed to "decomposable/indecomposable".

613:

am even more so now) because of the double redirect problems that arise. Maybe the best thing would be to ignore the seductive "click here to perform the move" link on the template, just do the deletion, and then say to the tagger "Right, I've deleted it, now you sort out the rest of what you want to do". Regards,

529:

must be the same thing, and all very "well-knowable", but not the best sort of citation given that the connection may be somewhat folkloric, or reliant on the old papers of Schwartz and Klein. I first came across this business in papers of Nick Katz. So I wonder if there is a sensible modern reference.

4999:

Consider the set of rational numbers. Its natural extension, the hyperrationals, contains the hyperfinite grid used in the definition of the counting measure v. Therefore the rationals would have full measure if the definition you presented is interpreted naively. What one has to do instead is the

2401:

There really isn't enough material here for two separate articles. Whenever someone gets around to reading Dehn's German, it would be helpful to add something on his non-Legendian example here, as well. I have no evidence that anyone after Hilbert called this "semi-Euclidean", so that term is a bit

1901:

on MathOverflow recently. I've done some editing on Knowledge so I figured that the 'reb' there might be you. Could you please answer the question raised by Joel Hamkins there(if indeed it is you)? I thought that your answer was very interesting, so I would like to know more. Again, I'm sorry for the

1768:

Both the MO thread and the wikipedia article are quite long, and there seem to be several different definitions of linear disjointness in the literature, so I'm not quite sure in what way they are incompatible. Z-S seems the best reference for this sort of stuff, though its a long time since I looked

1381:

Thanks. It seems little more than superficial speculation by someone who does not appear to know what etale cohomology is. It is fairly clear to anyone who works with etale cohomology that the vast set theoretic structures are not really necessary, but that eliminating them would be more trouble than

612:

to that title, so I did that and then conscientiously fixed all the resulting double redirects, thinking I was being helpful, and was worried to see that you had to change them all back. Did I misunderstand, or were you engaged in a more complex reshuffle? I have tended to be rather shy of db-g6 (and

7626:

Greetings. Because you have already cast a vote for the 2013 Arbitration Committee Elections, I regret to inform you that due to a misconfiguration of the SecurePoll we've been forced to strike all votes and reset voting. This notice is to inform you that you will need to vote again if you want to

4572:

is currently developing new tools to make new page patrolling much easier. Whether you have patrolled many pages or only a few, we now need to know about your experience. The survey takes only 6 minutes, and the information you provide will not be shared with third parties other than to assist us

4285:

b) A more conceptual q-n: to the best of my understanding, Mehler-Heine is a complement to simpler asymptotics (Laplace-Heine for Legendre and Darboux for Jacobi pol-s). Returning to even more basic stuff, I did not find a single wiki-article on asymptotics of OP (even in the classical case!) So the

2538:

Since the previous thread seems to be focusing on the page dealing with Dehn's counterexamples, I am starting a separate thread on infinitesimals. Does Dehn's paper use the term "infinitesimal"? Whether he used Stolz's, du Bois-Reymond's, or Veronese's infinitesimals, he was using work that Cantor

2344:

Where did you find two different Dehn planes? Are you referring to the two geometries discussed by Dehn, as I elaborated on the talkpage? The other one may not be a plane at all; I suspect it is a sphere of an infinite radius, but I have not gotten around to applying Google translate to his German

528:

Since you are working over the hypergeometric function, I thought I'd go back to the reference I know about the finite monodromy case (an old book by Poole on differential equations). What in fact is there is a "Schwartz list" of 15 spherical triangles, classified by the resulting finite group. This

6587:

Is there any chance at least one of the cited papers can be described as "to appear" or something like that? I suspect what might happen is the article gets deleted because the papers are not refereed, then in a few months one or more of the papers gets published and then we'll have to remember to

3601:

hmmm... I have had another look, there are more serious problems in the Tauberian article. For example, it is not clear from what is written there that the theorems in L1 and L2 are different statements, which do not follow from one another (or have I gone crazy)? The L1 statement is what I thought

2599:

Yes, Berkovits was motivated by his pure-spinor string theory, but the idea is actually a natural generalization of twistors to any even dimension (possibly odd ones too, but that is not obvious). The relevant reference is a paper titled "Higher-dimensional twistor transforms using pure spinors" by

2558:

Despite what Penrose intended, twistors actually do generalize to higher dimensions in a natural way (see Berkovits on "pure spinors"). Further, your articles on this are full of mathematical jargon that is extremely obfuscatory considering that twistors are concrete accessible computational tools.

2198:

No. 0 is a branch point in general. This is not obvious from the series, but a contour that starts at 0, circles around 1, and comes back to 0 will in general hit a branch point at 0. (Infinity is also a branch point, but a contour of integration in the complex plane by definition avoids infinity.)

1961:

Hi, thanks for your edits to the Reynolds operator page. I did have one point of contention, though, about your non-English sources. Since the article is on the English Knowledge, English sources are preferred. Are there any English versions or translations of the citation you listed (reproduced

6630:

I am sorry that the template posted a Teahouse link and treated you like a new user...I just wanted to drop by to tell you I'd added that tag. When it comes to BLP (I am not sure whether or not this is one based on the ref and my quick Google search), I probably apply tags a little more liberally.

3095:

You write: "Let's use the most common standard convention." Such a convention is fine and everyone giving a lecture or writing a book should fix his use unambiguously. However, I think it is not the mission of an encyclopedia to fix conventions. Rather, to inform about different conventions and to

1996:

As it states in the text, the purpose of the references is to give the earliest use of the phrase "Reynolds operator" (or rather its French version) and the original precise definition. There are several references because I have not yet made up my mind which is the best one. I agree that English

4390:

I have put an "underconstruction" template on the Classical OP page: obviously, it needs a major revision, but I am not sure I understand what to keep there and what to move to the OP page. Since you are still editing the 2 pages, I do not want to create a mess by simultaneous editing, so I won't

1977:

If not, could you give some indication as to the purpose the references serve? I'm guessing from the location in the text that they're the references where J. Kampé de Fériet first named these operators "Reynolds operators", but it would be a little more clear if they were a footnote, esp. given

722:

nail is removed, the picture falls? The answer is this curve (the nails are the deleted points and the picture is located somewhere along the curve). I thought at first I couldn't figure this out without some effort and then a few seconds later this curve came to mind. I'd seen it in a complex

5861:

and the "General Science Journal" as part of a couple of deletion discussions, I can definitively say that you perhaps underestimate the breadth of crackpottery: it's really a choose-your-own-adventure out there.) Anyway, I'm not going to make a big deal out of it either way, although if I were

1752:

What we currently do is to reference the EoM. MO's thread (at answer #4) references Zariski-Samuel, which is accessible to me; otherwise I'm not quite sure how to make the discussion there (which I'm sure is pretty good) verifiable: probably everything is known but where is it written down? This

1724:

I have no objection to moving it. In fact I'm not even sure what the difference between "references" and "bibliography" is; one possibility would be to amalgamate them to save having to think about the difference. Some biographies list the person's works under "publications" and put articles by

2766:

deletion, if the page meets the criterion, it may be deleted without delay. Please do not remove the speedy deletion tag yourself, but don't hesitate to add information to the page that would render it more in conformance with Knowledge's policies and guidelines. If the page is deleted, you can

7451:

However - at the points where I originally wrote "reducible/irreducible" and you changed to "decomposable/indecomposable", the inline citations (including Wigner) use the former terms and not the latter, unless I have somehow complete misread them (the books are not to hand right now). So, the

7091:

Unipotent representations are supposed to be the basic "building blocks" out of which one can construct all other representations in the following sense. Unipotent representations should form a small (preferably finite) set of irreducible representations for each reductive group, such that all

4180:

0." That identifies one particular linear functional. I'd have thought that the theorem says that if there is some such three-term recurrence, then there is some linear functional for which the sequence is orthogonal; not that if there is some such three-term recurrence, then the sequence is

628:

No problem, and thanks for the deletion. It was part of a complicated multiple reshuffle to sort out a complete mess: the article titled "hypergeometric function" was largely about the generalized hypergeometric function, and meanwhile the information on the hypergeometric function itself was

6953:: The "nbsp" non-breakable space prevents line breaks when it precedes and follows a minus sign, but not when it precedes and follows an en-dash. On the browser I'm using a minus sign does not otherwise look different from an en-dash, but there you have a reason to distinguish between them. 2325:

Sorry, I can't, since this now requires admin tools. Since there has been a recent edit war, I would suggest waiting a few weeks before doing anything, to give everyone time to lose interest. "Semi-Euclidean geometry" might be a better title since there seem to be two different Dehn planes.

7027:

A while ago I had been drafting an article for torsion-free module, but I did not find the time to finish it. I'm glad you dug into it. I was wondering: is the general definition using regular elements the one Matlis used? I know that most (all?) the theory works for a slightly more general

3102:

And the article does in my opinion a good job to explain the differences of the two definitions; not only in the section 'definition' much care is taken to explain both versions, also in numerous other places, for example where the different ranges of validity of representations is stated.

3133:=−1/2 as Neukirch, and almost everyone else such as the standard references Abramovich-Stegun and Olver. The article should use this standard convention, which is now used almost everywhere in number theory, and make a passing mention of the fact that a few authors use other conventions. 2221:

I restored the referenced material you removed, which was not "trivia", but referenced material, one from the Mathematical biographies page (ultimately from Wiener's famous autobiography, which was cited by page) and the other from a recent historian's book, which cites archival sources.

5722: 3091:

It is about the convention B_1 = 1/2 or B_1 = -1/2. You are right that B_1 = 1/2 is the more common one. But we have to acknowledge that there are major writers which use B_1 = -1/2. See for example Neukirch, Jürgen, Algebraic Number Theory, Grundlehren der mathematischen Wissenschaften.

2424:

Regarding the infinitesimal navbox: what do you mean when you say that Dehn did not use infinitesimals "in this sense"? There are several theories of infinitesimals, old and new, represented in the navbox. Contrary to popular belief, Cantor, Dedekind, and Weierstrass did not eliminate

1096: 5996:

It is a glossary of terms used in old (=pre-Grothendieck) algebraic geometry books. As you have correctly pointed out, some of them are still widely used, and so are strictly speaking not really archaic. I guess you could change the word "archaic" to "old" if it upsets you that much.

3688:

How widespread is the terminology "finite algebra"? It doesn't seem to be explained in wiki, and the only hits I can find online give the (obvious) interpretation that the underlying set is finite. If less than three references use this term, we should consider not propagating it.

1972:

Kampé de Fériet, J. (1949), "Sur un problème d'algèbre abstraite posé par la définition de la moyenne dans la théorie de la turbulence", Annales de la Societé Scientifique de Bruxelles. Série I. Sciences Mathématiques, Astronomiques et Physiques 63: 165–180, MR0032718, ISSN

3659:, to which you seem to have been the earliest contributor. I'm kind of confused by this phrase: "...an integral domain A is called an N-1 ring if its integral closure in its quotient field is a finite A module." Should "finite A module" be "finitely generated A module"? 1708:

to the related entry: do you worry if I move it to the "Bibliography" section? I think it would be a better place, since there you'll find other biographical notices about him. Thank you for your attention (and of course for your help in the making of the entry! :D ):

201:

It's a potential embarrassment, since great chunks of non-encyclopedic material are now being added. I can handle the adminstrator's angle. Over-claiming on the mathematical front is not going to be good for Yau, though, either. You'll probably see why I'm concerned.

5022:

I was a bit sloppy in describing the construction. The measure v cannot be applied to the "inverse shadow" because the latter is not internal. Instead, we take an outer measure generated by v, and apply that. That's the best I can do without opening some books.

3578:

well, there are many formulations of the Tauberian theorem, 1/f being one of them (the one which appears in the article can be deduced from it and vice versa). That's what I mean by "the same". Anyhow, thanks for your comment -- I think I will follow your advise.

3106:

To help the user to distinguish different viewpoints and to enable him to draw his own conclusions about the relative merits of different conventions is an important point of a good article; not only in an encyclopedia, but in an encyclopedia in particular.

2252:

I agree with the removal since the added stuff creates drastically undue weight in the article for a narrow sensationalistic aspect of the subject's overall life and work. Also, discussion of the article content should normally go on the article talk page.

6307:

According to Sylvester, a covariant is "a function which stands in the same relation to the primitive function from which it is derived as any of its linear transforms to a similarly derived transform of its primitive". I hope this makes everything clear.

4483:, who unfortunately often try to delete articles they do not understand. If you want to keep the article, I suggest taking a copy, adding a couple more references, and recreating it when all the editors who know nothing about the topic have lost interest. 5842:

His book has been called "the second major revolution in the history of the Elliptic Functions". The only problem is that the person who called it that was Eagle himself. So he is notable for being the world's first (and only) elliptic function crackpot.

3249:. Last I checked (three or four years ago?) there was not yet an infallible decree from the Roman Pontiff or Oprah Winfrey or Miss Manners or whoever that we should do the same with polynomial sequences. Do you have any particular opinion on this one? 7216:

Cuspidal representations are the basic building blocks for parabolic induction. For more refined types of induction such as cohomological induction or Deligne-Lusztig's construction one expects the basic building blocks to be unipotent representations.

908: 7382: 7294: 6779:

I haven't fully digested the definition of this concept yet . . . . Would I be right if I guessed that a hyper-finite field is any field satisfying the same first-order sentences in the language of fields that are satisfied by all finite fields?

2948: 2732:, because the article appears to be about a person or group of people, but it does not indicate how or why the subject is important or significant: that is, why an article about that subject should be included in an encyclopedia. Under the 2578:

rather than an article on (classical) twistor theory, which is an established area of mathematical research that predates string theory. It's actually a little alarming that we don't yet seem to have an article on twistor-string theory.

5540: 5249: 3767:, you wrote that "It is only defined for field theories on a lattice, and not field theories on a continuum.". Do you remember why you said that? Glancing thru a textbook on statistical mechanics, I see that it assumes a continuum. 452:

but only as a "see also", except two articles that are lists. So if there are others that should link there or if it can be included within the body of the text rather than as a "see also", you might think about adding those links.

3782:

Sorry, I can't remember offhand. My guess is that there are several different things called cluster expansions, some of which only work for lattices, and some for continuums. You may remove my comment if you think it is misleading.

2054:. There is a good reason why we are trying to include two sets of page numbers in some refs (one for UK edition, one for US edition), and I was hoping otherpage might offer something more clever than just putting "pp=238 (209–10)". 5974:

You have not answered to my post on the talk page: Many of the terms you have introduced in this page are not archaic at all. Several appear in the title of publications of XXIth century. What is your project? To rename the page

5000:

following. Given a real set X, we look at the inverse image of the standard part function restricted to the hyperfinite grid. Then we apply v to the inverse image of X, and take standard part to get the Lebesgue measure of X.

7060:

Ah, ok well in that case, I think I will cite the general definition given in Lam's Lectures on Modules and Rings so that there is a reference for it. I'm curious about other places where similar definitions are given also.

6676:

tools, as having some issues to fix. Judging from the only source, I'm not sure if this is a BLP or not, but nevertheless, additional sources and claims to notability would be helpful. Thank you. Feel free to contact me on

516:. If you can convince me here as well that's fine- it looks like you know what you're doing, I just don't want a situation where one editor thinks it should be one way, then the next one to come along thinks the other etc. 7539:

is missing a description and/or other details on its image description page. If possible, please add this information. This will help other editors make better use of the image, and it will be more informative to readers.

4945:

It is a plausible correction as the new matrix is skew symmetric (as it should be) and the old one was not. Whether the matrix is now correct I have no idea. It really needs a reliable source as checking it is tiresome.

7519: 2512:. In this case, there are already well-established terms for what is under discussion (see R.e.b.'s post above). There is no need to invent our own very idiosyncratic terms to denote them, hence my comment above. 1793:, is the affine map from the torus to itself thought of as a map from a 2-dimensional real space rather than as a 1-dimensional complex space (so the composition of the three things is not in general holomorphic)? 753:

I guess that explains why people do not hire philosophy professors as interior decorators. I dont see why you shouldnt add your observations to the article. It really needs a picture but I'm too lazy to draw one.

935: 2267:

Please see the talk page for a longer response. I shortened this section, which is now no longer than the on-line biography at St. Andrews. The longer version has been on the Swedish WP without challenge, btw.

4432: 4425: 2046:

and I'm hoping you might tell me where I can find the parameter otherpage explained (it looks to me like a never-implemented feature, but I'm just stumbling around in the code without fully understanding it).

7632: 3228:

I have proposed elsewhere, and I think it got mentioned in a style manual, possibly as a not-universally-agreed rule, that an article about a sequence of polynomials should usually have a plural title as in

2479:

Dehn's paper does not use infinitesimals in the sense of calculus or non-standard analysis. There is no real connection, except that Dehn and non-standard analysis both happen to use non-archimedean fields.

4804:

of univalent functions corresponding to the conformal welding of the diffeomorphism. In that context the Grunsky matrices become corners of a unitary matrix. They also appear as part of the smooth model of

2989: 2768: 3060:. Also, note that the terminology is kind of a mess with different people calling different things by the same name. For a nice discussion of the modern take on these ideas see chapter 1 of Colmez's book 2756:(just below the existing speedy deletion, or "db", tag; if no such tag exists, then the page is no longer a speedy delete candidate and adding a hang-on tag is unnecessary), coupled with adding a note on 7486: 3635:. (If articles on closely related topics were always merged, wikipedia would end up with just one vast article.) Though merging some of these articles is also fine as they are short and closely related. 6291:

seems to have a much more restricted definition. I'm really unfamiliar with any texts relevant to the notion of covariant, so I was hoping you might be able to fix up the entry in the glossary. Thanks.

4286:

missing Laplace-Heine is perhaps not the major problem, and I do not even know where to start. If you have ideas how this should work, perhaps we can discuss it a bit and then start filling the gap.

1172: 7150: 6190: 6088: 3602:

is called the Wiener Tauberian theorem, and it is obviously equivalent to the 1/f thm. The L2 thm is also true and also due to Wiener, but I am not sure it even appears in the same paper of Wiener.

4800:

article (using the Cauchy transform for existence for sufficiently smooth curves/diffeomorphisms and the Beltrami equation more generally), and the Grunsky matrices fit into that, this time for a

3997: 7445: 6186: 6084: 3209:. What quite "Lichtenbaum conjecture" means to the experts now I'm not so sure: without saying that things have got out of hand, some consolidation of what the literature says would be welcome. 1861:

You may edit the article during the discussion, including to address concerns raised in the discussion. However, do not remove the article-for-deletion template from the top of the article. --

7621: 6232:

It seems to me that the phrase "conjugate with respect to some conic" ought to link somewhere. Whether the place it ought to link to currently exists is another question. I looked briefly at

6240:, and I thought I could probably figure out where among several articles would be the best article or section to link to. But I haven't done so yet and maybe you already know. Or maybe not. 4436: 7558: 4309:

b) If you are looking for things to write about related to orthogonal polynomials, Szego's book has lots of stuff that is not yet on Knowledge, and there are still plenty of red links at

7378: 7199: 3344: 7092:

irreducible representations can be obtained from unipotent representations of possibly smaller groups by some sort of systematic process, such as (cohomological or parabolic) induction.

3719:

OK thanks for clearing that up then. This usage really should be clarified within wikipedia somewhere, though. It seems that it will trip up anyone without a commutative algebra text!

7500: 5366: 3088:

Recently you made a change in the article 'Bernoulli number' which I reversed. You again reversed. So let me explain to you why I did so and why I think it should be reversed again.

7290: 6407:" entry you created, and I'm writing this just to say you that I'm positively impressed: it's nice work, precise, compact and well documented, and Knowledge deserves such articles. 4462:

is in immediate danger of being deleted without more references that substantially address the topic. I was hoping you might have better luck with this than I did. Happy editing,

6985: 2758: 2017:

Greetings to all. There's an article on arXiv that you might want to add to the Virasoro algebra references. Best wishes for the New Year (even if you're asleep when it happens),

1409: 5299: 7096:

My understanding was that it was not unipotent representations, but cuspidal representations, which form the basic building blocks. For instance in the representation theory of

6474: 3385: 3080: 2688: 1668:

It's written that “ω is a volume form on the boundary”, so it should be n-1–form, shouldn't it? Fot example in case of n = 2 ω = r dφ in standard polar coordinat system (r, φ).

6981: 3482:, and since you are one of the latest contributors, I thought it was a nice thing to ask for your opinion. If you do not like its present shape, please feel free to change it. 1366:

The subject came up on your talk page a while back. I don't understand the article myself. I look at the FOM mailing list archives sometimes and I found the reference there.

7514: 2069:"Otherpage" is a deprecated parameter that will not help for your problem. It allows you to link to a harvard citation on a different wikipedia page, if I remember correctly. 5043:

It is possible to construct Lebesgue measure on the reals using Loeb measures. In this case a subset of the reals is Lebesgue measurable if and only if its inverse shadow is

804: 6882: 1753:

issue is actually why I got interested in MO in the first place, but I don't seem to have made progress (in other words I have got distracted by the Recent Changes there).

487:

Laziness rather than a "typo". It's easy enough to describe explicit examples as variations of the Peano curve, but the topic is so obscure it didnt seem worth the bother.

4659: 2752: 2725: 2693: 7201:, and so unipotence is in some sense orthogonal to the notion of being a building block. Could you clarify what you meant; are there other induction processes at play? 6878: 2804: 1492: 100:

is a new article written by someone clearly unfamiliar with Knowledge usage conventions. It seems to be about group representation theory. Can you help clean it up?

7639: 6579: 217:

I would wait a couple of weeks for everyone to lose interest, then quietly clean it up. As long as no-one is adding anything libelous it is not worth worrying about.

5047:

Loeb measurable, and then they have the same measure. Perhaps this is what you are trying to say. However this is not needed for constructing general Loeb measures.

3205:(zeta-values up to powers of 2, as I understand it). On googling "Lichtenbaum's original conjecture" it seems clear that there is a relationship; as there is to the 3119: 3115: 2168: 2022: 1382:

it is worth. (One might be able do this painlessly by using the fact that ZFC can prove the existence of universes for any finitely axiomatizable fragment of ZFC.)

6721: 6287:. For instance, the work of Davenport and Heilbronn studies binary cubic forms and their quadratic covariant, the Hessian. However, the entry for covariant in the 1442: 1428: 6439: 5400: 5109: 2365:

Actually, it might be a plane, since Dehn is trying to build counterexamples to show independence of plane axioms. The appropriate title is then "Dehn planes".

1540:

has a big fat red flag: it's a brand-new thing (introduced during 2010) that cites no refereed source. I won't be surprised if it arouses suspicions about "OR".

6967: 6864: 5964: 2575: 2784: 6421: 6011:

I understand that you consider as "archaic" or "old" the large part of algebraic geometry which does not use scheme theory. If I understand correctly, this is

4857: 2660: 6435: 6172: 6056: 5857:

While that's very interesting, I'm not sure it rises to the level of having an article about the person. (And after recently being subjected to a barrage of

4424: 6416: 2192: 1639:

You added an proof of Brouwer fixed point theorem via Stokes theorem. Could you please explain me, why is the exterior ederivative of volume form is zero?

6343: 5881: 4853: 2345:

text in the Annalen. The problem with "semi-Euclidean" is that it is too similar to "semi-Riemannian", which has an altogether different meaning today.

1847:. While contributions are welcome, an article may be deleted if it is inconsistent with Knowledge policies and guidelines for inclusion, explained in the 734:

deleted point, winding around the Pochhammer curve and returning to where it started. Then put another closed loop like that where it passes through the

6396: 6769: 6361: 5990: 5899: 4661:. Do you happen to know a good reference (here on Knowledge) or a simple explanation, that might be suitable for inclusion in the article? Many thanks! 4446: 7246: 7015: 6912: 5681:

I advise dropping the topic, even though I agree with you. Remember the old curse: "May you be involved in a lawsuit in which you know you are right".

4409:

I havn't yet figured out what to move to the OP page or how to organize the 2 pages either. Feel free to edit either page: your edits on OPs are fine.

6469: 3300:

It looks as if you wrote \mathrm{max} rather than \max in TeX. These don't always give identical results. Thus, \mathrm{max}_{a \in A} yields this:

2289: 2262: 555: 7505:

to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you.

6615: 6597: 6220: 6136: 4725: 1762: 317: 275: 6808: 6391: 6357: 5929: 5895: 2970:

I'm not sure. It's taken from Quillen's paper, which does not seem to make sense: I've either misunderstood something or there is a misprint in it.

2618:

I am not currently editing articles on this topic. If you have a suggestion about some article I suggest putting it on the corresponding talk page.

2609: 2590: 2439:

What about putting it back to the title I moved it to after the first move "Dehn non-parallel planar geometry", or perhaps "Dehn planar geometry" ?

2121:

as an example, which, if I understand the term correctly, is not a finite geometry. Am I right in concluding that the article should start with "In

1887: 1718: 481: 377: 7533: 7520: 7492: 4778: 3233:, on the grounds that it's about a set of things rather than about the individual things. Thus, for example, no same person would call an article 6739: 4199:

You could phrase it like that, but it is trivial to see that any linear functional for which the sequence is orthogonal must be the functional Λ.

2523: 2464: 6930:. Seeing as you're the one who started that page I thought you might know if there exist an english translation. Thanks in advance for any help. 5965: 4970:

and it seems to me that the passage from v to mu is not completely correct. Shouldn't there be an application of the inverse shadow somewhere?

4751: 2225:

Please expand on Carleman's mathematics, but do not remove referenced sentences. Please consider discussing at the Wikiproject mathematics. Mvh,

1823: 7258: 3605:

Sorry for bothering you again, I just do not want to change anything before I understand the rationale of what appears in the two articles now.

3506: 1855: 1778: 1734: 593: 263: 226: 6684:

The tags can be removed by you or another editor once the issues they mention are addressed. If you have questions, you can leave a comment on

2600:

Berkovits. The explicit relationship between complex structures and pure spinors is extremely illuminating, and it is phrased concretely there.

7226: 6939: 6735: 6716: 5873: 5852: 4927: 4739: 4492: 2651: 1699: 1496: 1091:{\displaystyle \displaystyle (1-e^{2\pi i\alpha })(1-e^{2\pi i\beta })\mathrm {B} (\alpha ,\beta )\int _{C}t^{\alpha -1}(1-t)^{\beta -1}\,dt.} 428: 414: 6828: 5599: 4756: 4263: 4249: 4208: 4190: 4157: 3465: 3451: 3437: 3287: 3273: 3160: 3142: 3041: 2979: 1946: 1928: 1817: 1568: 1391: 1310: 1224: 763: 302: 176: 124: 4955: 2964: 2627: 2006: 1478: 1462: 314: 7232: 4908: 4712: 4395: 4369: 4337: 4292: 3606: 3580: 3531: 1740: 730:

Picture a new curve running at a right angle to the plane through one of the deleted points, then turning so that it gets farther from the

3491: 3176: 2503: 2448: 2208: 681: 5947:, and consider incorporating them (adding categories, stub templates, talk page assessments) to your article creation process? Thanks! -- 4535: 4282:

a) I saw you switched notation from theta to z in the generalisation, so I did the same in the Legendre part -- I hope you don't object.

4221:

What's the rook polynomial-orthogonal polynomial connection? I didn't see anything in the rook polynomial article to suggest a link. --

3258: 2568: 1693: 1677: 1663: 1598: 7210: 7070: 7055: 6050: 6032: 6006: 4887: 3806: 3792: 3748: 3728: 3714: 3698: 3683: 2092: 2078: 1750: 551:"Ueber diejenigen Fälle in welchen die Gaussichen hypergeometrische Reihe eine algebraische Function ihres vierten Elementes darstellt" 501: 4833: 2163: 6538: 6335: 6317: 5704: 5690: 5672: 5654: 5640: 5090: 5074: 5056: 5032: 5009: 4994: 4691: 3644: 3151:=1/2 (not −1/2 as stated in your message), but says that this is an unusual convention. Maybe you switched +1 and −1 in your message. 3023: 2489: 2434: 2411: 2392: 2374: 2354: 2335: 2051: 638: 191: 161: 139: 109: 6995: 6892: 6749: 6449: 6371: 6200: 6072: 5909: 4867: 4418: 4345: 4322: 3623:

A good rule of thumb is to have one wikipedia article for each named concept. So it would be reasonable to have separate articles on

3588: 1919:

Sorry, but I don't know any good references. The best I can suggest is looking at some of the papers on Harvey Friedman's home page.

1648: 582: 6859: 5811: 5578: 3614: 3218: 3075: 2063: 248: 6660: 6178: 6080: 6020: 4839: 7481: 7616: 6962: 6917: 6789: 6167: 4473: 2246: 1610: 7631:. You do not have to perform any additional actions other than voting again. If you have any questions, please direct them at 3776: 1526: 1375: 538: 6559: 4334:

well, I guess wikifying all of Szego's book is a project I won't finish in my lifetime, so I will start with more modest goals.

3828: 2789: 2772: 2689: 664: 287: 6988:). Such links are almost always unintended, since a disambiguation page is merely a list of "Did you mean..." article titles. 6885:). Such links are almost always unintended, since a disambiguation page is merely a list of "Did you mean..." article titles. 6742:). Such links are almost always unintended, since a disambiguation page is merely a list of "Did you mean..." article titles. 6442:). Such links are almost always unintended, since a disambiguation page is merely a list of "Did you mean..." article titles. 6364:). Such links are almost always unintended, since a disambiguation page is merely a list of "Did you mean..." article titles. 6193:). Such links are almost always unintended, since a disambiguation page is merely a list of "Did you mean..." article titles. 5902:). Such links are almost always unintended, since a disambiguation page is merely a list of "Did you mean..." article titles. 4860:). Such links are almost always unintended, since a disambiguation page is merely a list of "Did you mean..." article titles. 4824:

I have no strong feelings about this and only a passing interest in the topic, so feel free to do whatever you think is best.

4306:

a) I have no preference for θ or z and have no objection to your change: I was only changing notation to fix a minor misprint.

4138: 2026: 1990: 1353: 1295: 1251: 1209: 778: 747: 399: 6991: 6888: 6745: 6445: 6367: 6249: 6196: 6068: 6065:. Such links are almost always unintended, since a disambiguation page is merely a list of "Did you mean..." article titles. 5905: 5762: 4863: 4403: 4230: 3668: 3047: 7040: 6493: 6479: 5836: 4673: 211: 7046:

Matlis in his book works only over integral domains, and uses the definition that does not generalize well to other rings.

2683: 2553: 2143: 1488: 1132: 622: 7099: 3840: 3188: 2319: 1913: 1446: 6709: 6648: 3223: 3111: 3099:

Note that this approach is common on Knowledge in all cases where different definition or viewpoints or theories exists.

2138: 2031: 2018: 1634: 1367: 672:

Not sure. I moved a lot to different articles, and deleted some unsourced ones that were either trivial or not notable.

605: 3905: 1802: 7437: 6834: 3422: 2790: 2601: 2560: 2254: 1881: 1583: 1549: 1438: 1424: 7589: 5631:

I prefer not to jump into cesspits. It would be better to delete this article, but there seems little chance of this.

3705:

It is (unfortunately) standard in commutative algebra and algebraic geometry. Check any commutative algebra textbook.

1453:

I don't know how to transfer files to wiki commons, but if you can figure this out you are welcome to do it yourself.

575: 7253: 7078: 6655: 4598: 3473: 2574:

Could you please be more specific? On first glance, references to Berkovits would seem to more befit an article on

2548: 1629: 462: 7432: 6508:. None of this has been peer-reviewed, cited in Google scholar by anybody other than Mochizuki himself, reviewed in 5770: 3674:

Yes. The terminology is confusing: an algebra over a ring is called finite if it is finitely generated as a module.

3569: 1316:

Oh.... It's not the integral that blows up; it's the quotient of the integral by one of those differences. So when

7346: 4377: 3539: 2180:(section Hypergeometric series) says the function has branch points at 0 and 1? Shouldn't that be 1 and infinity? 2106: 660: 513: 354: 92: 5959: 4916: 4520: 4300: 3760: 1181:

and to the right of "=" an expression including an integral along the Pochhammer curve, but what's there includes

7553: 6973: 6563: 6301: 6259:

From the little I know about covariants and from the article you created on Hermite reciprocity, it seems like a

4979: 4382: 3754: 1844: 1898: 604:

I'm sorry if I caused confusion in your hypergeometric rearrangements two days ago: I thought your db-g6 tag on

5976: 5096: 4939: 4818: 4769:". Do you have strong feelings one way or the other concerning this? (I changed "a" to "an" in the article.) 3198: 368:, and it seems not altogether impossible that the first one is the wrong one, so you may want to look at that. 323: 7594: 7155: 5625: 4806: 4125:(which normally one would specify in the statement of the theorem) the sequence is orthogonal with respect to 3413:

and I think in some instances that also gives different results, and is also standard for certain situations.

3306: 496: 7464: 6972:

Hi. Thank you for your recent edits. Knowledge appreciates your help. We noticed though that when you edited

6869:

Hi. Thank you for your recent edits. Knowledge appreciates your help. We noticed though that when you edited

6726:

Hi. Thank you for your recent edits. Knowledge appreciates your help. We noticed though that when you edited

6233: 5869: 5832: 4613: 4469: 2647: 2586: 2519: 2460: 7381:

again to fix it. If I misunderstood what happened, or if you have any questions, you can leave a message on

7293:

again to fix it. If I misunderstood what happened, or if you have any questions, you can leave a message on

4720: 7496: 6673: 6288: 5798:. I dealt with this one by creating an "Algebra" section with "Linear algebra" as a subsection. For now, 4577:

If this invitation also appears on other accounts you may have, please complete the survey once only.

3650: 3428:

You may have confused me with someone else. I do not recall using any of these constructions on wikipedia.

3032:

I think it is sorted out now. Quillen's paper seems to confuse the cohomology group with its coefficients.

2709: 2659: 2285: 2242: 1574:...but it still might be prudent to find something to cite that will impress suspiciously inclined people. 599: 390:

In the above-mentioned article, you only define a Kirillov model, not a Whittaker model. Is this a typo? --

342: 334: 167:

You should not worry so much. Anyone looking up "multiplicity-one theorem" probably knows what a field is.

7543: 6023:, but this implies to rewrite the lead and add the mention of "archaic" for the entries which really are. 5332: 4597:

You are receiving this invitation because you have patrolled new pages. For more information, please see

3201:

is promising, but what with various reformulations it is not easy to see the relationship to the original

7628: 7020: 6944: 6870: 6774: 6551: 6497: 6475: 6141: 3624: 3557: 3525: 3193: 2297: 1588: 903:{\displaystyle \displaystyle \mathrm {B} (\alpha ,\beta )=\int _{0}^{1}t^{\alpha -1}(1-t)^{\beta -1}\,dt} 232: 4602: 3845: 2667: 718:

Once upon a time I heard this question: How can one hang a picture from two nails in such a way that if

7604: 7569: 7438: 6926:

need an english translation of Homologie nicht-additiver Funktore by Dold & Puppe. Here's the link

6555: 6412: 4451: 3487: 3214: 2100: 2040: 1758: 1714: 1620:

Thanks for your note. I'm glad somebody is actually using zeteo! I fixed the two issues you mentioned.

1504: 1358: 589: 534: 244: 207: 84: 72: 67: 59: 38: 6225: 5277: 4433:

Knowledge:Categories for discussion/Log/2011 September 9#Category:Mathematicians who committed suicide

4144:

No. The numbers c and d are not specified in the theorem, though they are determined by the sequence y

3442:

I see what happened now: I was copying a paragraph written by someone else (as my edit summary says).

523: 145: 4788:

Hi R. Since the theory of Grunsky matrices involves interpreting them as operators, I will be making

4735: 4362: 3479: 3355: 3184: 1954: 1848: 1625: 1594: 341:

and vice-versa. So far there's only one link to the new article besides the bot-added link from the

269: 7204:

Thanks for your time, and also for all the beautiful mathematics you've contributed to Knowledge. --

5613: 7600: 7084: 6950: 6935: 6611: 6575: 6062: 5863: 5826: 5645:

It does seem to be "notable". However they are currently trying to add more scurrilous material.

4463: 3245:

used in the singular, the article title is nonetheless plural. That much I think is prescribed in

2716: 2641: 2580: 2513: 2454: 2214: 2012: 1746: 687: 424: 395: 97: 4706: 3512: 2943:{\displaystyle E_{2}^{pq}=H_{\text{etale}}^{p}({\text{Spec }}A)=0(q{\text{ odd}}),Z_{l}(i)(q=-2i)} 7612: 7549: 7414:

the inverse images of elements of ''C'' are groupoids. Some authors use the word "stack" to refer

7408:

is called a '''stack in groupoids''' if it is also fibered in groupoids, meaning that its fibers

6958: 6804: 6785: 6700: 6685: 6678: 6639: 6593: 6353: 6245: 6163: 5807: 5799: 5776: 5574: 4774: 4507:

article. I heard once in an offhand conversation that the original "oh-sharp" term derived from

4259: 4226: 4214: 4186: 4134: 3836: 3461: 3418: 3283: 3254: 2960: 2303: 1942: 1909: 1798: 1606: 1579: 1545: 1522: 1371: 1349: 1291: 1247: 1205: 774: 743: 700: 506: 477: 458: 383: 373: 350: 283: 187: 157: 135: 105: 5660: 4761:

I've been accustomed to thinking of the "H" in "Hermite" as silent, so that one would write "an

7563: 6427: 6158:.) It seems possible that you know of other articles that should be listed there and are not. 4935: 4580:

If this has been sent to you in error and you have never patrolled new pages, please ignore it.

3202: 2743:

If you think that this notice was placed here in error, you may contest the deletion by adding

2674:

I have restored it, and now notify you in case you wish to consider taking it to AfD. Regards,

2671: 2637: 2605: 2564: 2533: 2509: 2258: 2114: 1986: 1875: 738:

deleted point. You get Borromean links. Do you think that's worth mentioning in the article?

4573:

in analyzing the results of the survey; the WMF will not use the information to identify you.

1997:

sources are preferred, but in the case of original documents are sometimes not yet available.

7251: 7242: 6977: 6874: 6839:

Hi, thanks a lot for all your contributions! I have one request: could you write a little at

6408: 6115: 5816: 5757: 5754:

and others. Your efforts to improve the encyclopedia for the public are greatly appreciated.

5535:{\displaystyle \sum {\frac {f_{xx}f_{y}^{2}-2f_{xy}f_{x}f_{y}+f_{yy}f_{x}^{2}}{f_{y}^{3}}}=0} 5244:{\displaystyle \sum {\frac {f_{xx}f_{y}^{2}-2f_{xy}f_{x}f_{y}+f_{yy}f_{x}^{2}}{f_{y}^{3}}}=0} 4628: 4622: 4353: 3628: 3521: 3483: 3210: 3206: 2271: 2228: 1754: 1710: 1397: 1113: 609: 585: 550: 530: 502: 240: 203: 5979:

or removing the non-archaic terms? What about old terms which are still in use but rarely?

4845: 3899:

0. Favard's theorem states that if these polynomials satisfy the 3-term recurrence relation

7573: 7510: 7428: 7342: 5939:

Thanks for your stubs on Polish mathematicians. May I suggest that you look at my edits to

5791: 5780: 5712: 4892: 4793: 4443: 4271: 4237: 3814: 3180: 2737: 2499: 2444: 2188: 2159: 1892: 1621: 1434: 656: 648: 320: 6840: 8: 7370: 7205: 7021: 6931: 6855: 6607: 6571: 6567: 6151: 6015:

and does not correspond to the reality of modern research (see the list of text books in

5944: 4516: 3736: 3545: 3234: 3230: 2122: 1673: 1644: 445: 420: 391: 233: 196: 7607:. If you know of any others that should be there and are not, could you add those too? 6606:

article. So I added it as well to the inter-universal article and removed my own prod. —

1601:. If you know of any others that should be there but are not, could you add those too? 512:

You've probably got them on your watchlist, but anyway you'll probably be interested in

7608: 7238: 7222: 7066: 7051: 7036: 6954: 6824: 6800: 6781: 6693: 6689: 6632: 6589: 6313: 6254: 6241: 6182: 6159: 6046: 6028: 6016: 6002: 5986: 5940: 5934: 5848: 5803: 5736:

Thanks for creating the new mathematics- and mathematician-related articles, including

5686: 5636: 5570: 5086: 5052: 4990: 4961: 4951: 4829: 4770: 4687: 4531: 4488: 4459: 4452: 4414: 4318: 4255: 4245: 4222: 4204: 4182: 4153: 4130: 3832: 3802: 3788: 3772: 3744: 3724: 3710: 3694: 3679: 3664: 3640: 3565: 3502: 3457: 3447: 3433: 3414: 3279: 3269: 3250: 3166: 3156: 3138: 3037: 2975: 2956: 2780: 2623: 2485: 2388: 2331: 2204: 2110: 2088: 2074: 2059: 2002: 1938: 1924: 1905: 1813: 1794: 1784: 1774: 1730: 1689: 1659: 1602: 1575: 1564: 1541: 1518: 1514: 1474: 1458: 1387: 1345: 1306: 1287: 1243: 1220: 1201: 770: 759: 739: 677: 634: 571: 492: 473: 454: 410: 369: 346: 298: 279: 259: 222: 183: 172: 153: 131: 120: 101: 7320:'''Q'''/'''Z''' canonically. The invariant ''a''(''P'') is the image of the element 1/ 4541: 4437:

Knowledge:Categories for discussion/Log/2011 October 3#Category:Suicides by occupation

4077:), it follows that the functional Λ is positive definite if (and only if) the numbers 2733: 7585: 7473: 7351: 7011: 7002: