network profile
| bio | website | motls.blogspot.com |
|---|---|---|
| location | Czech Republic | |
| age | 39 | |
| visits | member for | 2 years |
| seen | Jan 14 at 12:36 | |
| stats | profile views | 1,855 |
Hi, I am a string theorist and a publicist.
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May 22 |
comment |
The graph of $x^{n}+y^{n}=r^{n}$ for sufficiently large $n$ Let me say an answer using basic maths. Without a loss of generality, assume $r=1$; a different value of $r$ simply scales the picture. More importantly, If $n$ is very large and $x$ or $y$ are smaller than one, then $x^n$ and $y^n$ are much smaller than one - they're virtually zero, unless $x$ or $y$ are extremely close to one. For example, $0.9^{100}$ is still close to zero. So if $x^n+y^n=1$, then either $x$ or $y$ or both have to be extremely close to 1 from below so that the high power contributes almost one. |
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May 21 |
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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. ;-) |
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May 21 |
answered | Generalized “Worm on the rubber band ” problem |
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May 21 |
answered | Binomial formula in $GF(2^m)$ |
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May 21 |
answered | Of two variables, which affects 'y' more? |
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May 21 |
revised |
Complex Exponential Expansion added 16 characters in body |
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May 20 |
answered | What are the finite subgroups of $SU_2(C)$? |
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May 20 |
revised |
I can't seem to simplify this trigonometric differential into the required form added 68 characters in body |
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May 20 |
answered | I can't seem to simplify this trigonometric differential into the required form |
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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. |
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May 19 |
revised |
Additive group of rational numbers added 31 characters in body |
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May 19 |
awarded | Mortarboard |
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May 19 |
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Additive group of rational numbers You're right, it's a direct product. |
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May 19 |
answered | Integrate in Mathematica takes forever |
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May 19 |
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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. |
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May 19 |
answered | How can there be multiple irreducible representations of a group each having distinct dimension? |
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May 19 |
answered | Sturm-Liouville Problem |
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May 19 |
answered | Additive group of rational numbers |
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May 19 |
answered | How to project the surface of a hypersphere into the full volume of a sphere? |
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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. |
