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seen Jun 18 '13 at 3:32

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Jun
13
comment Rigorous results on the method of multiple scales
Thank you, Jon, I'll check this out.
Jun
7
comment Rigorous results on the method of multiple scales
Jon, I've looked at p.360 and the following calculations but I did not see a theorem, if you meant that it should be possible to prove a theorem using the calculations in those pages, I am actually looking for a source where this is done. As for the two-scale approach being "well-supported by the adiabatic approximation", I'm not sure whether you are making a plausibility argument or claiming it should be possible to give proofs along those lines. If it is the latter case, once again, I would love to see a book/paper where this is done.
Jun
4
awarded  Scholar
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4
comment Rigorous results on the method of multiple scales
Thank you, Aleksey.
Jun
4
accepted Perturbation theory for the generalized eigenvalue problem
Jun
4
comment Rigorous results on the method of multiple scales
Thanks, Jon. I did a quick scan of Kevorkian and Cole and did not immediately see theorems of the sort I've mentioned (i.e. guarantees of accuracy). Do they have such theorems in the book?
Jun
4
comment Perturbation theory for the generalized eigenvalue problem
Thanks, Robert, that was an eye-opener.
Jun
4
comment Perturbation theory for the generalized eigenvalue problem
Various nice properties (e.g., orthogonality) of the eigenvectors follow easily from the Hermiticity of $A$ and $B$, and I was hoping that the perturbation theory would be better-behaved in this form. The general theory of perturbations of eigenvalues (of a possibly non-normal matrix, which $B^{-1}A$ may be) seemed a little scary, but maybe it will turn out to be ok, and I may end up trying that. The case of positive-definite $B$ was an almost trivial generalization of the usual perturbation theory for a Hermitian matrix with all the usual niceties, so I was hoping to have something similar.
Jun
4
comment Rigorous results on the method of multiple scales
@Steve Huntsman, I had read parts of Barenblatt's book years ago (I remember it as a fun and insightful book), does it have a discussion of the method of multiple scales, or did you cite it as a reference of general relevance along these lines?
Jun
4
asked Rigorous results on the method of multiple scales
Jun
4
asked Perturbation theory for the generalized eigenvalue problem
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9
awarded  Commentator
Feb
9
comment Rolling without slipping interpretation of torsion
David, do you know of a reference for a rigorous version (and proof) of the statement you give? (A semi-rigorous proof would also be helpful.)
Oct
28
awarded  Editor
Oct
28
revised Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature
added 78 characters in body
Oct
28
comment Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature
Thanks for catching that. The part I had replaced with the ellipsis said "so that the functions $K$ and $\|dK\|^2$ have independent differentials". The preceding theorem in the book states that these functions indeed have independent differentials for a generic Riemannian metric on a surface, and I had (perhaps partly due to the way the sentence was worded---with the "so that") falsely assumed it is true in general. I'm editing to fill in the missing part.
Oct
18
comment Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature
The OP's addendum, José's answer, and the OP's comment response convinced me that this theorem might be relevant.