User talk:Igny/Math

Please vote on list of lists, a featured list candidate
Please vote at Featured list candidates/List of lists of mathematical topics. Michael Hardy 20:29, 13 October 2005 (UTC)

Gagliardo--Nirenberg--Sobolev
Hi Igny. I would like your help if possible on the GNS inequality. I am onaraighl and I am the one who edited your article, but I am an applied mathematician and not an expert here.

It's just I have a problem with the GNS inequality if you don't subtract off a constant term: taking u=constant\neq0 on the open unit disc would satisfy the conditions of the theorem, yet gives constant\leq0, which seems to be a contradiction. I have spoken to some of my professors about the GNS inequality and consulted the functional analysis book by Kantorovich, and they all say that you need to subtract off the mean of the function in the GNS inequality.

I would dearly like it if it were the case that you did not have to subtract off the mean, since then some estimates that I am working on for the Cahn--Hilliard equation would work out a lot nicer, yet I just don't see how you can do that.

Also, perhaps the article would benefit from a discussion on the optimal constants for the bound, which clearly depends on the domain in question.

Thanks.

Hi again Igny. Thanks for reference - very useful. I can see where the compact support comes into the proof now. So the variant of the GNS you provide is restricted to functions that are C_1 on the whole of R^n, but with compact support. This limits one to a narrow class of functions indeed.

I have checked the literature and GNS applies to broader classes of functions:


 * C_1 functions with the norm of whose gradient is finite - see http://citeseer.ist.psu.edu/590313.html.
 * Functions defined on a compact, open domain of R^n with Lifshitz boundary. The function need not be C_1 on the whole of R^n then - it can be zero outside the domain in question.  Then you have to subtract off the mean.  See Kantorovich, p. 338.
 * Periodic functions on the n-torus. Then the mean is subtracted off.  See Gibbon and Doering, appendix I.  This latter case is a generalization of the Poincare inequality.

These variations also go by the name of GNS and maybe merit a discussion??

Thanks again for the reference, and for the article on wikipedia. I have fixed my estimates now :-)

Mathematics CotW
Hey Igny, I am writing you to let you know that the Mathematics Collaboration of the week(soon to "of the month") is getting an overhaul of sorts and I would encourage you to participate in whatever way you can, i.e. nominate an article, contribute to an article, or sign up to be part of the project. Any help would be greatly appreciated, thanks--Cronholm144 21:42, 13 May 2007 (UTC)

Request for edit summary
Hi Igny. It could be nice if you could use the edit summary more often, especially for edits like this where it is not clear why you removed the link. Thanks. You can reply here if you have comments. Oleg Alexandrov (talk) 15:02, 11 July 2007 (UTC)
 * Hi Oleg, I am sorry for my laziness regarding the summaries and thank you for keeping an eye on the articles. The reason I deleted the link was that the Russian and English versions of Kolmogorov theorem were about different theorems by Kolmogorov. The Russian version actually refers to the Kolmogorov's result regarding Kolmogorov-Smirnov test rather that Hahn-Kolmogorov theorem (Igny 16:08, 11 July 2007 (UTC))
 * Cool. :) Thanks. Oleg Alexandrov (talk) 03:16, 12 July 2007 (UTC)

Kernel density
Hi Igny. I reverted this edit because I don't think it is correct, and because you did not explain why you made the change (please do that in the future). You can reply here if you have comments. Cheers, Oleg Alexandrov (talk) 16:17, 22 July 2007 (UTC)


 * Sigma was superfluous because there is parameter h. Regards, Igny.
 * Thanks, that makes sense. And again, it is good if you summarize what you changed, and especially, why you change something. That saves time and effort in the long run. Cheers, Oleg Alexandrov (talk) 03:42, 23 July 2007 (UTC)

Probability articles
Hi, Igny!

I notice that you've been doing quite a bit of rearranging of articles about probability, like Donsker's theorem and empirical process and Glivenko-Cantelli theorem, among others. That's good.

The difficulty I have is that sometimes your command of English idiom is not quite perfect. I know that has to be tough – especially with words like "the" (which has no equivalent in Russian). Anyway, I'm going to put some effort into making those articles read more smoothly, and I just want to give you a heads up before I get started in earnest.

I can see that you know the math extremely well (better than I do, no doubt). I just want to make the articles easier for native English speakers to read.

Thanks for all your good efforts! DavidCBryant 23:12, 9 August 2007 (UTC)


 * Thank you for correcting my English, I appreciate this. The thing is that I have all these math books lying around and all these lecture notes which I kept from my college, it is my dream to organize it all in accessible form and Wikipedia is perfect for that. I just wish I had more time for that. (Igny 00:37, 10 August 2007 (UTC))

Ref Desk
Thanks for all your help - but I still think we're missing something: 70.169.186.78 (talk) 03:51, 31 July 2009 (UTC)
 * Thus "E"? 70.169.186.78 (talk) 04:28, 31 July 2009 (UTC)


 * Looks that way. (Igny (talk) 04:37, 31 July 2009 (UTC))

empirical mean
(Sorry this is nearly a year old, but...) in talk:arithmetic mean I seconded Hv's objection to an unexplained redirect. Consider the situation of a Wikipedia user who is reading the article on principal component analysis or the one on empirical measure and encounters the term empirical mean but is unfamiliar with it. Such a user would likely click through the link and find himself inexplicably confronted with an article not about emprical means, but about arithmetic means.

Your reply to our perplexity was a suggestion to read about empirical measures. The first problem with that reply is that, residing as it does on a talk page, it will likely never be seen by our hapless user. A further problem is that even the article to which you referred us does not unambiguously define empirical mean. And the worst problem with your suggestion is that the empirical-measure article may well be where some of our hapless users encountered the unfamiliar term to begin with!

I'd fix the problem if I thought myself qualified, but I don't. So I'm appealing to you to do so. Could you please edit the arithmetic mean article to make clear (1) why any user expecting to land on an article about empirical means ends up here instead and (2) the meaning of empirical mean, or at least the relationship between empirical and arithmetic means.

Thanks in advance.—PaulTanenbaum (talk) 01:59, 3 September 2009 (UTC)