bio | website | |
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age | ||
visits | member for | 4 years, 6 months |
seen | Jun 18 '13 at 3:32 | |
stats | profile views | 206 |
Aug 25 |
awarded | Populist |
Oct 10 |
awarded | Yearling |
Sep 30 |
awarded | Populist |
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 |
Jun 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 |
Feb 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. |