My past research interests included differential algebraic equations, nonlinear analysis and relations between symmetries and structural properties.

I recently investigated hierarchical structures, starting from group cohomology, continuing with semi-group theory and ending with lattices and universal algebra.

2h
answered What is the difference between non-determinism and randomness?
3h
answered Why is non-determinism useful concept?
18h
answered Is mathematics as pure as originally thought?
1d
reviewed Leave Open Did I correctly apply Ockham's razor?
1d
reviewed Close About the possibility of A.I. systems
1d
reviewed Leave Open Resources for learning Indian Philosophy
2d
comment Why is mathematics fond of infinity, but dismissive towards partially (un)defined operations?
I would normally upvote such an answer. However, as this is your first post here, it would probably set wrong expectations. If you look at the question marks in the question, can you really say that your answer addresses any of these explicit questions? Your answer doesn't even mention the words "context" or "infinite". On the other hand, you emphasize the words "should" and "existence", but I don't really know why, i.e. I see nobody else here even mentioning these words.
Jan
21
awarded Custodian
Jan
21
reviewed Approve suggested edit on Error propagation on GSL eigenvalues computation
Jan
21
awarded Yearling
Jan
21
awarded Yearling
Jan
18
comment How does non-linear behaviour arise from the inherently linear QM framework?
There are at least two points where it can enter: (1) A linear PDE can have a close relation to a non-linear ODE. Classical Hamilton-Jacobi theory allows you to formulate classical mechanics in the form of a linear PDE. (2) If you describe a subsystem by a density matrix, the evolution equation for the density matrix can have non-linear terms modeling the interaction of the subsystem with the environment. (I don't want to prevent anybody from writing a proper answer by this comment, even if it should use the same examples. I'm just too lazy to write a detailed answer.)
Jan
18
asked Is square removal easier than factoring?
Jan
17
awarded Talkative
Jan
17
reviewed Close Real in Mathematics Vs Real in Philosophy
Jan
17
reviewed Close Is there a cogent argument for whether there are objective moral facts?
Jan
14
comment Eigenvectors of a symmetric positive definite Toeplitz matrix
"... which makes me expect that the solutions to this problem won't be substantially faster than the solution of the problem for general matrices" You are mixing theoretical and practical questions here! In theory, it's easy to get an $O(n^2\log n)$ algorithm using Lancoz tridiagonalization based on FFT and a QR like diagonalization of the tridiagonal matrix, but see scicomp.stackexchange.com/questions/2975/… and scicomp.stackexchange.com/questions/10842/…
Jan
12
comment Importance of zero and non-zero eigenvalues of density matrix
For example, a 193 nm ArF laser produces unpolarized quasi-monochromatic light with a small narrow bandwidth around 193.3 nm. At least two eigenvalues are needed to model the unpolarized light. Whether you need additional eigenvalues to model the quasi-monochromatic light (or its very narrow bandwidth) depends on what you do with it. If you spilt it up such that it travels on completely different paths, then you need additional eigenvalues for it. If the small difference in wavelength never has any appreciable consequences, then you also don't need to model it by additional eigenvalues.
Jan
12
comment Importance of zero and non-zero eigenvalues of density matrix
@Martin Well, you could say that there is exactly one zero-eigenvalue, namely "0", or you could say that there are infinitely many zero-eigenvalues (because the canonical commutator relations can only be satisfied in an infinite-dimensional Hilbert space), but both answers are pretty useless. That's what I mean by "The number of zero eigenvalues has no significance". You might object that the number of non-zero eigenvalues is infinite too. However, if we are satisfied with a certain accuracy (say 1%), then a "well-defined" number of non-zero eigenvalues is sufficient to get that accuracy.
Jan
11
answered Wavelength used in manufacturing of integrated circuits (IC)
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