bio | website | www-irma.u-strasbg.fr/… |
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location | Strasbourg | |
age | 37 | |
visits | member for | 2 years, 9 months |
seen | 2 hours ago | |
stats | profile views | 1,532 |
I'm working on complex dynamical systems, more specifically on the local/global aspect of singular holomorphic foliations in the complex plane
Mar 18 |
reviewed | Approve hyperbolic metrics |
Mar 17 |
revised |
Are all rational exactly solvable differential equations known?
added 286 characters in body |
Mar 17 |
comment |
Automorphisms of $\mathbb{C}$ and meromorphic functions
Ok, thank you for the precision. |
Mar 17 |
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Automorphisms of $\mathbb{C}$ and meromorphic functions
Maybe there is something I don't understand, but the $\sin$ function both defines $\mathbb Z=\{z : \sin (z)=0\}$ and $\mathbb R=\{z : \sin (z)=\overline{\sin (z)}\}$. |
Mar 17 |
comment |
Are all rational exactly solvable differential equations known?
Nothing, I understood what you said. I just included the second piece because if you want to achieve effective, concrete algorithms then the issue pops up (although it also does in the first piece). But I understood your concern was at a higher-level of calculability. That being said, I still somehow believe that a lot of undecidability lies down there ;) |
Mar 17 |
answered | Are all rational exactly solvable differential equations known? |
Mar 17 |
comment |
Are all rational exactly solvable differential equations known?
You must specify what you mean by both «decide» (and therefore what conditions you put on the coefficients of the differential equation, e.g. belonging to a field where you can decide the equality to $0$ with a halting turing machine) and «exactly solvable» (I assume you mean integrability by quadrature in the sense of Liouville). Even being granted the two defaulted meanings above, I fear that there are no known answer to your question, although it is believed by some that the Poincaré question (solvable by rational first-integral) is undecidable. The key-word is differential Galois theory. |
Mar 17 |
reviewed | Approve Is it true that for each bounded continuous function we can find a set of analytic functions to uniformly converge it? |
Mar 16 |
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the impossibility of exactly computing eigenvalues
It is sufficient to take $p$ with non-solvable Galois group. Take your favorite non-solvable real quintic polynomial. Now the diagonal matrix with diagonal entries the real roots of this polynomial is hermitian. This question is not research level in its present form. E.g. you should precise what you mean by "explicit formula" and on which field you work, to avoid stupid trivial answers as the one I just gave. |
Mar 15 |
reviewed | Approve Motivation for concepts in Algebraic Geometry |
Mar 11 |
reviewed | Approve More recently published comprehensive reference on inequalities in the spirit of Hardy-Littlewood-Pólya |
Feb 20 |
reviewed | Approve Extension of Sobolev Functions |
Feb 19 |
comment |
Interesting integral
Yep, sorry, my mistake. |
Feb 19 |
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Interesting integral
Are you sure the LHS is an anti-derivative, or is the bound $z$ mistaken for some other value? Otherwise you might as well differentiate both sides... |
Feb 18 |
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Is this a $C^0$ foliation of $\mathbb{R}^2$?
@foliations Yes indeed, your requirement is stronger. I will amend my answer. |
Feb 18 |
revised |
Is this a $C^0$ foliation of $\mathbb{R}^2$?
added 510 characters in body |
Feb 18 |
awarded | Cleanup |
Feb 18 |
revised |
Is this a $C^0$ foliation of $\mathbb{R}^2$?
rolled back to a previous revision |
Feb 18 |
revised |
Is this a $C^0$ foliation of $\mathbb{R}^2$?
added 86 characters in body |
Feb 18 |
answered | Is this a $C^0$ foliation of $\mathbb{R}^2$? |