4,782 reputation
917
bio website motls.blogspot.com
location Czech Republic
age 40
visits member for 3 years, 6 months
seen Aug 4 at 12:45

Hi, I am a string theorist and a publicist.


May
21
comment Interesting properties for numbers 1-20?
If you think that no numbers are interesting for any other reason, than 1 is the smallest positive integer that is uninteresting, 2 is the smallest positive integer among the uninteresting ones that is not the smallest uninteresting integer, 3 is the smallest positive integer among the uninteresting ones that is neither the smallest uninteresting integer, nor the smallest positive integer among the uninteresting ones that is not the smallest uninteresting integer, and so on. ;-)
May
21
answered Generalized “Worm on the rubber band ” problem
May
21
answered Binomial formula in $GF(2^m)$
May
21
answered Of two variables, which affects 'y' more?
May
21
revised Complex Exponential Expansion
added 16 characters in body
May
20
answered What are the finite subgroups of $SU_2(C)$?
May
20
revised I can't seem to simplify this trigonometric differential into the required form
added 68 characters in body
May
20
answered I can't seem to simplify this trigonometric differential into the required form
May
20
comment If $A\in M_{n}(\mathbb{C})$ is a Hermitian matrix so $I-iA$ is Invertible
Dear Nir, Hermitian matrices have purely real eigenvalues, that's why they're used by the physicists to express all real observables such as position or angular momentum. Compute $b(v,Av)$ for any normalized eigenvector $v$ - it's real because of hermiticity which makes it equal to $b(Av,v)=b(v,Av)^*$. This inner product is the eigenvalue, too. So it must be real.
May
19
revised Additive group of rational numbers
added 31 characters in body
May
19
awarded  Mortarboard
May
19
comment Additive group of rational numbers
You're right, it's a direct product.
May
19
answered Integrate in Mathematica takes forever
May
19
comment When does variété mean manifold?
I just want to confirm Ryan, click at "English" in the left column of these French Wikipedia articles: fr.wikipedia.org/wiki/Vari%C3%A9t%C3%A9_alg%C3%A9brique and fr.wikipedia.org/wiki/Vari%C3%A9t%C3%A9_(g%C3%A9om%C3%A9trie) - add the end-parenthesis by hand to the URL - Variete without adjectives is mostly manifold, but with the algebraic adjective it is mostly variety. In Czech, the difference is too subtle for all but 5-10 people haha but "manifold" is translated as "varieta", too.
May
19
answered How can there be multiple irreducible representations of a group each having distinct dimension?
May
19
answered Sturm-Liouville Problem
May
19
answered Additive group of rational numbers
May
19
answered How to project the surface of a hypersphere into the full volume of a sphere?
May
19
comment Is $\frac{m-1}{x}$ an unbiased estimator of $\theta$ for given pdf?
To prove that the Euler integral $\int_0^\infty dt\exp(-t)t^n$ is equal to $n!=\Gamma(n+1)$ for integer $n$, just integrate it by parts several times, so that the exponent above $t$ is always reduced by one. In this way, you will collect factors of $n, n-1$, and so on, and finally you collect the whole $n!$ and the remaining integral will be $\int_0^\infty dt \exp(-t)$ which is easily integrated to one.
May
19
comment Is $\frac{m-1}{x}$ an unbiased estimator of $\theta$ for given pdf?
I didn't do it with Mathematica first, it's just an ordinary Euler integral! Cardinal didn't do any extra steps to calculate the Euler integral, either. He just wrote that it's an elementary integral just like I did.