10,349 reputation
14673
bio website vmm.math.uci.edu
location Univ. of California at Irvine
age 83
visits member for 4 years, 5 months
seen Nov 14 at 16:05
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 .

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awarded  Explainer
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awarded  Nice Answer
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awarded  Yearling
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awarded  Curious
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awarded  Enlightened
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awarded  Nice Answer
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awarded  Popular Question
Sep
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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
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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
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asked Algorithm for finding inverse images of a local diffeomorphism
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awarded  Popular Question
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awarded  Good Answer
Jul
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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
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awarded  Nice Question
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asked What is a good method to find random points on the n-sphere when n is large?