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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeAug 27th 2011

    created gradient

    • CommentRowNumber2.
    • CommentAuthordomenico_fiorenza
    • CommentTimeAug 31st 2011
    • (edited Aug 31st 2011)

    created stubs for curl and divergence

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 31st 2011

    Thanks!

    I have added more links and a TOC.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeAug 31st 2011

    I added redirect rotation of a vector field to the more cryptic anglosaxon alternative curl (and which I could prefer to be a title in fact, wikipedia givee 2.1 mil hits, for curl of a vactor field 320 thousand hits).

  1. added a link to and created a stub for symplectic gradient. By trhe way, I notice now that moment map is still very stubby; i hope to be able to expand that soon.

    • CommentRowNumber6.
    • CommentAuthorTobyBartels
    • CommentTimeAug 31st 2011

    People are forgetting that you need an orientation, not just a metric, to do Hodge duals (and thus, for example, to define the curl of a vector field as a vector field on a Riemannian 33-fold).

    • CommentRowNumber7.
    • CommentAuthorzskoda
    • CommentTimeAug 31st 2011

    go on, jump in, I seem not to have time these days to reconcentrate on this topic, which I started

    • CommentRowNumber8.
    • CommentAuthorzskoda
    • CommentTimeSep 1st 2011

    Anyway, I did expand moment map following Joel Robbin’s notes (well, I think I have learned the first steps into the subject from my advisor, so I follow his notes). Still not much there but at least the basic reasoning leading to the definition is produced (and the literature).

    • CommentRowNumber9.
    • CommentAuthorTobyBartels
    • CommentTimeSep 2nd 2011

    Unhappy that we had the curl only in the classical 33 dimensions, I discussed its relation to the cross product and described nonclassical cross products. The latter page is now massively general!

    • CommentRowNumber10.
    • CommentAuthorzskoda
    • CommentTimeSep 2nd 2011

    Well, a further justification should go from the Stokes theorem. I mean, there is a limit of an integral formula for the rotation of the vector field, similar to the one for the divergence.

    • CommentRowNumber11.
    • CommentAuthorzskoda
    • CommentTimeSep 2nd 2011
    • (edited Sep 2nd 2011)

    I mean

    rot𝒜=lim volD01volD Dn×𝒜dS rot \vec\mathcal{A} = lim_{vol D\to 0} \frac{1}{vol D} \oint_{\partial D} \vec{n}\times \vec\mathcal{A} d S div𝒜=lim volD01volD Dn𝒜dS div \vec\mathcal{A} = lim_{vol D\to 0} \frac{1}{vol D} \oint_{\partial D} \vec{n}\cdot \vec\mathcal{A} d S

    where DD runs over the domains with smooth boundary containing point xx at which the rotation or the divergence of the vector field is calculated. These formulas are invariant.

    • CommentRowNumber12.
    • CommentAuthorzskoda
    • CommentTimeSep 2nd 2011

    I added the above remarks in the case of divergence (in which case this works in any dimension).

    • CommentRowNumber13.
    • CommentAuthorzskoda
    • CommentTimeSep 2nd 2011

    New entry nabla and additions to rotation of a vector field.

    • CommentRowNumber14.
    • CommentAuthorTobyBartels
    • CommentTimeSep 5th 2011

    I’ve generalised nabla to discuss all applications of the operator, defined using the integral formula in a very general way, and moved the formula originally there (for the gradient only) to gradient.

    • CommentRowNumber15.
    • CommentAuthorzskoda
    • CommentTimeSep 5th 2011

    Right, I have left it in a rudimentary form, planning something similar and I am happy with your way of finishing the job!

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeSep 5th 2011

    There is something funny going on with the rendering: at least on my system that

      \nabla \odot T
    

    in the entry sometimes (such as in the big displayed formula) comes out as “boxT\nabla box T”.

    • CommentRowNumber17.
    • CommentAuthorTobyBartels
    • CommentTimeSep 5th 2011

    You probably caught this while I was in the midst of editing for itex’s capabilities. Reload the page and check again.

    • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeSep 5th 2011

    Ah, right, now it dsiplays correctly.

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