bio | website | vmm.math.uci.edu |
---|---|---|
location | Univ. of California at Irvine | |
age | 83 | |
visits | member for | 4 years, 9 months |
seen | Mar 20 at 6:39 | |
stats | profile views | 6,972 |
I'm a Professor at UC Irvine, but spent most of my career at Brandeis. My research areas: Differential Topology, Transformation Groups, and Global Analysis. Recently I developed a math visualization program, 3D-XplorMath, freely available at http://3D-XplorMath.org) and a companion website, the Virtual Math Museum at http://VirtualMathMuseum.org. Last year I co-authored a differential equations text with my son Bob, most of which is downloadable from http://ode-math.com .
Jan 11 |
answered | Characterization of the exterior derivative |
Sep 30 |
awarded | Explainer |
Sep 29 |
awarded | Nice Answer |
Jul 4 |
awarded | Yearling |
Jul 2 |
awarded | Curious |
May 24 |
awarded | Enlightened |
May 24 |
awarded | Nice Answer |
Feb 3 |
awarded | Nice Question |
Nov 18 |
awarded | Good Answer |
Nov 2 |
awarded | Popular Question |
Sep 30 |
comment |
About Palais' remark that an isometry of Riemannian manifolds does not induce an isometry of the Hilbert manifolds of curves
The problem lies in the line above defining $g_\sigma(λ,μ)$. This is the metric for $H_0$, NOT the metric for $H_1$. The correct definition of the metric for $H_1$ uses $⟨λ'(t),μ'(t)⟩$ rather than $⟨λ(t),μ(t)⟩$ (see page 222 of my article where both metrics are defined), and with this change it is fairly obvious why my remark in the cited paper is in fact correct. |
Aug 23 |
comment |
Algorithm for finding inverse images of a local diffeomorphism
Yes! Newton's Method is clearly the way to go. For $k=1$, the algorithm I wrote in fact did use Newton's Method, (rather than bisection) since it is much faster. But I guess I forgot that Newton's Method works in higher dimensions too. Thanks Ryan. |
Aug 23 |
accepted | Algorithm for finding inverse images of a local diffeomorphism |
Aug 22 |
comment |
Algorithm for finding inverse images of a local diffeomorphism
@Nanda For the application I have in mind, F will be given by a formula. |
Aug 22 |
asked | Algorithm for finding inverse images of a local diffeomorphism |
Aug 4 |
awarded | Popular Question |
Aug 3 |
awarded | Good Answer |
Jul 11 |
comment |
What is a good method to find random points on the n-sphere when n is large?
@Mark Meckes Many thanks, Mark. In retrospect, if I had been more adept with my Googling I might have discovered that the Gaussian RV approach was a "well-known" answer to my question, and would not have needed to ask it on MO. But as usual, I have come away very impressed with the utility of this great website and learned a lot from the answers I received. |
Jul 11 |
accepted | What is a good method to find random points on the n-sphere when n is large? |
Jul 11 |
awarded | Nice Question |