4,147 reputation
1024
bio website shapetales.wordpress.com
location Prague, Czech Republic
age 29
visits member for 4 years, 1 month
seen 4 hours ago

Math PhD. student and functional programming enthusiast.


Feb
18
comment Continuous surjective functions from the unit disk to itself that agree nowhere
Please be more specific. Beyond superficial connection with isomorphisms of the unit disk I don't see any relevance of your answer to the OP.
Feb
15
comment Summation using residues
$\sinh(z)$ has zeros on the imaginary axis. I don't see how you account for them.
Feb
13
answered Limit sequence sets
Feb
13
comment $\sum a_n$ converges $\iff \sum (\sqrt{1+a_n}-1)$ converges
When $a_n$ is small (a necessary condition for the convergence of the sum), $\sqrt{1 + a_n} = 1 + a_n / 2 + O(a_n^2)$. So, up to a sum over $a_n^2$ (which converges), these sums are similar. Your job is to find precise estimates.
Feb
13
answered Issue while applying Master Theorem
Feb
13
comment Issue while applying Master Theorem
@chersanya: again, true. But for the function you've written, you can bound $f(n)$ between $n^2 \log n$ and $3 n^2 \log n$. Both of them are regular, and so you can apply the master theorem. Then you get the master theorem for $f(n)$ by sandwiching between these two results (which are equal).
Feb
13
comment Issue while applying Master Theorem
@chersanya: that's true of course, but the additional terms can't spoil the asymptotic behavior (the regularity only needs to hold for $n$ big enough, not for all $n$). So when $n$ is big enough, it's okay (and this can be made rigorous) to assume that $f(n)$ actually is $C n^2 \log(n)$.
Feb
13
revised How to prove this result about connectedness?
Fixed a letter switch
Feb
13
comment How to prove this result about connectedness?
@Stefan: indeed I switched the letters. Thank you :)
Feb
13
answered Uniform and point wise convergence
Feb
13
comment Issue while applying Master Theorem
Why do you think $f$ is not regular? We have $af(n/b) \leq (5/9) f(n)$.
Feb
13
answered Homogenous Polynomial Functions and the Symbol of a Differential Operator
Feb
13
answered How to prove this result about connectedness?
Feb
13
comment On surjectivity of exponential map for Lie groups
Thank you, nice example.
Feb
12
comment On surjectivity of exponential map for Lie groups
@David: correct me if I am wrong, but the sphere is not a local object, is it? I mean, for every point of the sphere, we can find a ball in $\mathfrak g$ around that point it that still maps to an open set.
Feb
12
revised On surjectivity of exponential map for Lie groups
More detailed proof of exp being closed and open
Feb
12
comment On surjectivity of exponential map for Lie groups
@David: thank you for the first example, I'll think about it. As for the second, I don't follow. Where does the set you've given lie and how is it related to the property of local homeomorphism?
Feb
12
asked On surjectivity of exponential map for Lie groups
Feb
12
comment Universal Covering Group of $SO(1,3)^{\uparrow}$
Thanks, that's a nice argument. The adjoint rep. won't work in general, but finding any isomorphism of Lie algebras will, so I guess that's good enough.
Feb
12
comment Universal Covering Group of $SO(1,3)^{\uparrow}$
I'd say it's purely coincidental and follows from identification of vectors and antisymmetric matrices in dimensions $3$. In any case, could you elaborate how does the adjoint rep. of $su(2)$ help us prove that $SU(2)$ is a universal cover of $SO(3)$?