1,705 reputation
313
bio website
location Atlanta (GA)
age
visits member for 2 years, 7 months
seen Jan 27 at 4:59

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.


Jan
26
answered Is this a bounded linear map?
Jan
26
asked Tangential derivative vs covariant derivative
Dec
10
revised Understanding weighted inner product and weighted norms
Write a statement more precisely
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