1,655 reputation
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location Atlanta (GA)
age
visits member for 2 years, 5 months
seen Nov 18 at 19:51

I am a PhD candidate in applied math. My research interests are in numerical approximation of PDE's, CFD, optimization, inverse problems, Data Assimilation, HPC, C/C++ programming. I'm a senior developer of a C++ finite element library, with MPI parallelization.

Other areas of math that I like are analysis, matrix analysis, differential geometry and numerical analysis.


Nov
12
comment Absolute Maximum of the integral
Nice animation. What did you use to create it?
Oct
28
answered Low-rank matrix approximation in terms of entry-wise $L_1$ norm
Oct
28
comment Fractional Sobolev embedding into $L^\infty$
I don't understand the first inequality in the first line: how can you get rid of the absolute value of $e^{ix\cdot\xi}$ if you don't know that $\xi$ is real? For a general function, the F-transform may be defined for complex values of $\xi$. Am I missing something?
Oct
3
answered Applying Rouché's Theorem
Oct
3
comment Residue Calculus (Computing an Improper Integral)
Notice that, in order to use contour integrals, you must prove that the integral over the semi-circle vanishes as $R\to\infty$...
Sep
24
awarded  Autobiographer
Sep
9
awarded  Revival
Sep
9
comment A topological function with only removable discontinuities
I think you're right. It seems an obvious requirement, but that's because I think about nice topological (and actually metric) spaces.
Sep
7
comment Questions about weak derivatives
@PhoemueX, in order to do that you have to be considering a particular type of distributions, namely $L^1_{loc}$ functions and appeal to the Lebesgue differentiation theorem (aka, the Lebesgue version of the Lagrange theorem for Riemann integral). But even then, the pairing would be a "small" number, since $\varphi$ is constant on a small interval. Also, I don't understand what you mean with "$f$ is locally $C^\infty$ at $x$"... The function $\chi_\mathbb{Q}$ defines a distribution (since it's locally integrable), but it is nowhere continuous.
Aug
29
answered Questions about weak derivatives
Aug
29
comment Computing the derivative of a transformation matrix
Yes, you need a sum. Otherwise that's a pointwise cost, and you would have different optimization problems at each point, with infinitely many solutions. But since the function $f$ is only one, you need $f$ to work for every point, considering as a cost, the sum of $CF$ over all the points.
Aug
29
revised For what $a \in \mathbb{R}$ does $f_a(x) := \sin x + ax$ attain every value exactly three times?
Fixed an error in a formula
Aug
29
answered For what $a \in \mathbb{R}$ does $f_a(x) := \sin x + ax$ attain every value exactly three times?
Aug
29
comment What is $\operatorname{Ei}(x)$?
Why did someone voted down this question? Looks perfectly legit to me.
Aug
28
comment A topological function with only removable discontinuities
I guess you meant $g(y_U)\in \overline{V}$ (notice that $V\subset Y$, while $y_U\in X$). You had a strong point there. I modified the proof, to distinguish between the two cases. I'm 99% sure it works now, but you may want to double check.
Aug
28
revised A topological function with only removable discontinuities
explained better a concept
Aug
28
revised A topological function with only removable discontinuities
explained better a concept
Aug
26
comment A topological function with only removable discontinuities
Why you say that I need that? I'm thinking but I can't see it. Yes, if $X$ is not Hausdorff, then what I said is not true.
Aug
26
answered Approximation by definite integrals
Aug
26
comment A topological function with only removable discontinuities
Yeah, sorry, I meant $\forall x \in U\setminus \{x_0\}$. That slipped in somehow. ;-) Notice that singletons are indeed closed, since they contain all limit points of sequences that lie in the set (which, of course, can only be constant sequences, with elements equal to the singleton element).