593 reputation
11327
bio website math.sunysb.edu/~myounsi
location Stony Brook, NY, USA
age
visits member for 5 years, 3 months
seen 2 hours ago

I am currently a NSERC postdoctoral fellow at Stony Brook University.


Jan
12
comment This inequality why can't solve it by now (Only four variables inequality)?
@AdamP.Goucher : But in your book "Mathematical Olympiad Dark Arts", you say "Hence [by Delzell's algorithm] it is theoretically possible to prove any inequality involving rational functions simply by reducing it to the sum of squares inequality. However, this approach is similar in its impracticality to building an automobile using Stone Age tools." As for the present problem, I would be quite interested to see the automobile built more efficiently..!
Jan
12
revised Analytic diffeomorphisms of the circle from complex domains
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Jan
12
revised Analytic diffeomorphisms of the circle from complex domains
added 803 characters in body
Jan
12
answered Analytic diffeomorphisms of the circle from complex domains
Dec
12
comment Bound areas of disks with respect to a quadratic differential
@DylanThurston : I'm glad I could help.
Dec
12
revised Bound areas of disks with respect to a quadratic differential
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Dec
12
revised Bound areas of disks with respect to a quadratic differential
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Dec
12
comment Bound areas of disks with respect to a quadratic differential
Yes, I made a silly mistake. I corrected my answer, hopefully it works now.
Dec
12
revised Bound areas of disks with respect to a quadratic differential
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Dec
12
answered Bound areas of disks with respect to a quadratic differential
Dec
8
accepted Is this infinite series related to some well-known special functions?
Dec
8
comment Is this infinite series related to some well-known special functions?
Great, thank you! +1
Dec
8
awarded  Good Answer
Dec
4
comment Starshapeness of polynomial tracts with respect to the (entire collection of) critical points contained in the tract
Do you assume that $G$ is connected?
Dec
3
comment Starshapeness of polynomial tracts with respect to the (entire collection of) critical points contained in the tract
There is also a simple proof using potential theory in the book "Potential theory in the complex plane" by Thomas Ransford, Theorem 5.5.8. I don't have access to Walsh's book right now, so I don't know if the proof is the same.
Nov
14
comment Applications of the Small and Great Theorems of Picard
@GHfromMO Ah, I didn't realize you were talking about meromorphic functions. Good point! The argument works for entire functions, but I don't know how to prove the result for meromorphic functions using Picard's theorem.
Nov
14
comment Applications of the Small and Great Theorems of Picard
@GHfromMO : From the factorization $1=\prod_{j=1}^n (f-\zeta_j g)$ where $\zeta_1,\dots,\zeta_n$ are the $n$ roots of $z^n+1=0$, it follows that $f/g$ is a meromorphic function that omits the values $\zeta_1,\dots,\zeta_n$, and hence must be constant by Picard's theorem. From this it follows easily that both $f$ and $g$ must be constant.
Nov
12
comment Non-trivial global solution for Dirichlet eigenvalue problem
I don't understand the new formulation... If $\Delta f = \lambda f$ almost everywhere, then $\Delta f = \lambda f$ everywhere just by continuity.
Nov
5
comment Is this infinite series related to some well-known special functions?
The formula looks correct, but I have no idea how to obtain it...
Nov
5
comment Is this infinite series related to some well-known special functions?
Whoa, where does that come from? :-)