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bio website math.poly.edu/~yang
location New York, New York
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visits member for 5 years
seen 2 hours ago

2d
comment Why do we teach calculus students the derivative as a limit?
Depends on what you mean. If you need it for your work, you'll learn it properly through what you do. That's always the best way, because you understand why it's needed. If you just want to learn it, you succeed either by having a really good teacher or studying it on your own (and not being satisfied until you understand it inside out).
2d
comment Existence of minimizer in Sobolev space $H^{1,2}(\Omega)$
Sure it does. The functional is nonnegative and equal to zero if $u$ vanishes on the boundary but not in the interior.
Oct
18
awarded  Yearling
Oct
16
comment Regularity of the Minkowski functionnal of a convex
Use polar coordinates.
Oct
16
comment Source needed (at final-year undergrad level) for the double cover of SO(3) by SU(2)
Yes, but without discussing the topological aspect. Uses quaternions.
Oct
16
answered Source needed (at final-year undergrad level) for the double cover of SO(3) by SU(2)
Oct
15
comment How is this transformation related to the Legendre transform?
If you apply the Legendre transform to $-xf(x,y)$ in the $x$ variable and for fixed $y$, then you should get $s$ back. And, yes, it appears that $f$ is concave with respect to $y$ since it's obtained as an infimum over a family of concave functions.
Oct
15
comment How is this transformation related to the Legendre transform?
It looks to me like that, for each $y$, $-xf(x,y)$ is the Legendre transform of $-s(t,y)$.
Oct
11
awarded  Custodian
Oct
11
reviewed Leave Closed The periodic architecture underlying the natural numbers
Oct
11
comment Monge-Ampere type PDE
I agree with Robert that the question (and not just a comment) should contain an explicit description of how a Riemannian metric is constructed from the function $f$. Also, I don't recognize the PDE as written as an elliptic Monge-Ampere equation as it should be.
Oct
7
revised Variation of curvature with respect to immersion?
deleted 98 characters in body
Oct
7
answered Variation of curvature with respect to immersion?
Oct
7
revised Variation of curvature with respect to immersion?
deleted 16 characters in body
Oct
7
answered Variation of curvature with respect to immersion?
Oct
1
awarded  Favorite Question
Oct
1
comment The relation between Gromov hausdorff convergence and inverse limit of compact metric spaces
The question could be rephrased as follows: Does there exist a subset of Euclidean space that is isometric to the Gromov-Hausdorff limit?
Oct
1
comment Is the identification between symmetric tensors and homogeneous polynomials useful?
Sorry. I didn't read the question carefully. Your example is a question about tensors with respect to a single vector space, so it is a purely algebraic question. Differential geometry is effectively the study of tensors with respect to a smooth parameterized family of vector spaces. I don't see any need or use of differential geometry for a question like yours.
Sep
30
awarded  Explainer
Sep
30
comment Is the identification between symmetric tensors and homogeneous polynomials useful?
Arguably, the only point to tensors is as homogeneous polynomials or multilinear functions. A tensor is difficult to interpret geometrically. Typically, it's only when you evaluate it on on the right number of tangent vectors (or cotangent vectors) that you get a number that you can interpret. The most obvious example of this is the Riemann curvature tensor. I don't know any way to explain the full tensor geometrically, but if you evaluate it properly using two tangent vectors (which span a 2-d plane), then you get sectional curvature which does mean something geometrically.