User kassandra - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T01:12:30Z http://mathoverflow.net/feeds/user/23509 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/126368/reference-needed-donskers-invariance-principle-for-riemannian-manifolds Reference needed: Donsker's Invariance Principle for Riemannian Manifolds kassandra 2013-04-03T11:03:00Z 2013-04-03T17:27:09Z <p>After an extensive unsuccessful search: I need a reference (preferably a book) for the Donsker's invariance principle for Riemannian manifolds. Thanks.</p> http://mathoverflow.net/questions/96343/the-left-hand-side-of-the-ricci-flow-equation-at-the-initial-value the left hand side of the Ricci flow equation at the initial value kassandra 2012-05-08T14:29:17Z 2013-02-19T16:46:03Z <p>I just started to learn about the Ricci flow and try to understand the Ricci flow evolution equation. It states that a one-parameter family $g_t$, $t\in[0,T)$ of Riemannian metrics on a smooth closed manifold $M$ is a solution of the equation $$\frac{\partial g_t}{\partial t}=-2 Ric_{g_t}.$$ But, in order to be able to write down the expression $$\frac{\partial g_t}{\partial t}$$ I need a little bit more than the fact that $g_t$ is a one-parameter family of Riemannian metrics. </p> <p>There are several ways to understand this expression, which probably are equivalent to each other. I think the most naive idea is to consider $g_t$ as a smooth curve in the infinite-dimensional vector space of all Riemannian metrics on $M$ and $\frac{\partial g_t}{\partial t}$ as tangent vectors to this curve.</p> <p>Now, my question is: How do I have to understand the left hand side of the Ricci flow equation at the initial value $t=0$?</p> <p>Does one consider $g_t$ as a smooth family at the open interval $(0,T)$ and requires continuity at the point $t=0$ or has one to deal with differentiability from the right? </p> <p>Thank you very much!</p> http://mathoverflow.net/questions/96219/do-you-use-the-mathematics-subject-classification-msc-when-searching-for-litera Do you use the Mathematics Subject Classification (MSC) when searching for literature? kassandra 2012-05-07T14:21:23Z 2012-05-12T05:14:35Z <p>I suppose most of you are familiar with the <a href="http://www.ams.org/mathscinet/msc/msc2010.html" rel="nofollow">Mathematics Subject Classification (MSC)</a>. Particularly, when submitting an article for publication one has to choose appropriate classification codes.</p> <p>But I am wondering if it does play a significant role in searching for literature on a specific subject, e.g. through MathSciNet or ZBMATH. Or do you prefer searching by subject terms?</p> <p>Thank you very much!</p> http://mathoverflow.net/questions/20551/sources-for-bibtex-entries/96212#96212 Answer by kassandra for Sources for Bibtex entries kassandra 2012-05-07T13:07:00Z 2012-05-07T13:31:33Z <p>I also use JabRef. In addition, there is an easy to use JabRef plugin for the <a href="http://gso.gbv.de/DB=2.1/" rel="nofollow">Union Catalogue (GVK)</a> of several German federal states participating in the so-called Common Library Network (GBV).</p> <p>For JabRef see <a href="http://jabref.sourceforge.net/" rel="nofollow">http://jabref.sourceforge.net/</a>.</p> <p>For downloading the JabRef-GBV-plugin see <a href="http://jabref.tempelb.de/" rel="nofollow">http://jabref.tempelb.de/</a>.</p> http://mathoverflow.net/questions/126368/reference-needed-donskers-invariance-principle-for-riemannian-manifolds/126371#126371 Comment by kassandra kassandra 2013-04-03T18:49:43Z 2013-04-03T18:49:43Z @Carlo So far it looks very promising - and provides pretty much interesting reading material ... Thanks a lot! @Stephan Thank you very much for your helping hand. http://mathoverflow.net/questions/96219/do-you-use-the-mathematics-subject-classification-msc-when-searching-for-litera/96681#96681 Comment by kassandra kassandra 2012-05-14T08:14:01Z 2012-05-14T08:14:01Z Oh, Gerhard, you interestingly mentioned the term &quot;thesaurus&quot;. Many subjects do come up with sophisticated thesauri, but due to my knowledge there is no community established thesaurus (in its proper meaning) in mathematics. http://mathoverflow.net/questions/96219/do-you-use-the-mathematics-subject-classification-msc-when-searching-for-litera/96682#96682 Comment by kassandra kassandra 2012-05-14T08:13:05Z 2012-05-14T08:13:05Z Tom wrote &quot;Maybe there are other uses.&quot; Neil, here you brought a completely new aspect to the discussion: a use of the MSC in a certain project context. Does somebody know further projects involving the MSC or making use of it? http://mathoverflow.net/questions/96219/do-you-use-the-mathematics-subject-classification-msc-when-searching-for-litera/96740#96740 Comment by kassandra kassandra 2012-05-14T08:12:13Z 2012-05-14T08:12:13Z Joe, your answer confirms my impression that the idea of keeping up-to-date in a field that is outlined by a classification code is definitely worthwhile. http://mathoverflow.net/questions/96219/do-you-use-the-mathematics-subject-classification-msc-when-searching-for-litera/96677#96677 Comment by kassandra kassandra 2012-05-14T08:11:27Z 2012-05-14T08:11:27Z Neil, you wrote &quot;This is the only use ...&quot; but keeping up-to-date in a somewhat broader sense and not restricted to one's own specific research field seems to be more than most of us do today. http://mathoverflow.net/questions/96219/do-you-use-the-mathematics-subject-classification-msc-when-searching-for-litera/96679#96679 Comment by kassandra kassandra 2012-05-14T08:10:42Z 2012-05-14T08:10:42Z Tom, this is indeed a comprehensible argument, which is convincingly illustrated by a &quot;tasty&quot; example, but Yemon's comment beautifully shows that there is some evidence of the MSC in the case that one cannot use a known term search. http://mathoverflow.net/questions/96219/do-you-use-the-mathematics-subject-classification-msc-when-searching-for-litera/96683#96683 Comment by kassandra kassandra 2012-05-14T08:09:39Z 2012-05-14T08:09:39Z Henry, thank you very much for your response. I think the best that can happen to a question is that it sets off reflecting on something and gives way to a try. Obviously, there is a lot of agreement with your answer. http://mathoverflow.net/questions/96219/do-you-use-the-mathematics-subject-classification-msc-when-searching-for-litera Comment by kassandra kassandra 2012-05-11T15:05:39Z 2012-05-11T15:05:39Z I just realized that my question is reopened. Thanks. I am looking forward to seeing your opinions. http://mathoverflow.net/questions/96343/the-left-hand-side-of-the-ricci-flow-equation-at-the-initial-value/96363#96363 Comment by kassandra kassandra 2012-05-08T20:01:25Z 2012-05-08T20:01:25Z Otis, thanks particularly for your valuable references to the literature. http://mathoverflow.net/questions/96219/do-you-use-the-mathematics-subject-classification-msc-when-searching-for-litera Comment by kassandra kassandra 2012-05-08T19:49:53Z 2012-05-08T19:49:53Z I made it &quot;community wiki&quot;. Anton, thank you for your advice. http://mathoverflow.net/questions/96343/the-left-hand-side-of-the-ricci-flow-equation-at-the-initial-value Comment by kassandra kassandra 2012-05-08T18:30:47Z 2012-05-08T18:30:47Z Misha, that argument sounds plausible to me. Thank you very much! http://mathoverflow.net/questions/96219/do-you-use-the-mathematics-subject-classification-msc-when-searching-for-litera Comment by kassandra kassandra 2012-05-08T12:11:20Z 2012-05-08T12:11:20Z Honestly, I only wanted to get an impression on the actual use of MSC. I am not in the mood to hold a meta discussion on whether or not to reopen my question.