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.

Jul
25
awarded Custodian
Jul
22
comment Why are box topology and product topology different on infinite products of topological spaces?
@MathsLover The set theoretical topological spaces where defined by Felix Hausdorff in his book "Grundzüge der Mengenlehre", which appeared in 1914. In 1912, Jan Brouwer had started intuitionism, but Felix Hausdorff's work is not really based on it. The linked publication page of Dirk van Dalen is a good source for the connections between formal intuitionistic logic and topological spaces. If the links in that page don't work in your browser, copy the desired "link address" and replace "papers.html" in the current addresss by "articles/..." from the copied "link address".
Jul
21
answered Negative impact of wrong or non-rigorous proofs
Jul
20
answered Why are box topology and product topology different on infinite products of topological spaces?
Jul
18
comment Can a biased physical random source be post-processed to control the bias?
@Did Thanks, now I see where I made a mistake in the description of the method. Should be fixed now. This also answers part of my initial confusion, i.e. why I asked this sort of questions in the first place.
Jul
18
revised Can a biased physical random source be post-processed to control the bias?
OK, now I see my mistake in the description of the method
Jul
18
comment Can a biased physical random source be post-processed to control the bias?
@Did You mean I made a mistake in my description of the procedure? Or you mean you simply don't believe that such a can procedure work? Or is it just that you can't recognize the well known situation (produce unbiased random bits with the help of a single biased coin) behind my complicated and overly formal description?
Jul
17
revised Can a biased physical random source be post-processed to control the bias?
Thought a bit about how this problem can be pragmatically addressed, and modified question accordingly
Jul
15
comment How is the theory of partial coherent light related to quantum-mechanics?
The spectral lines of atoms and molecules are a strange phenomena explained by quantum-mechanics. We might try to explain it by computing the eigenstates and eigenvalues of an appropriate Hermitian operator. At this point there isn't necessarily a quantum-mechanical measurement involved, but the indistinguishablilty of quantum-particles certainly enters into this explanation (hence there is a reference to particles). Roger Penrose tried to explain the strange phenomena of conciousness by reference to quantum-measurement processes (what he calls "objective reduction"). Just an example...
Jul
15
comment How can molecule of a few angstroms absorb visible light of a few hundred nanometers?
@fibonatic This general question is already answered more or less by Marty Green, but I need to check his answer thoroughly before accepting it, because it references his own blog instead of more "conventional" sources.
Jul
15
comment How is the theory of partial coherent light related to quantum-mechanics?
This is a nice and informative answer, but it doesn't even mention partial coherence. I therefore expanded the text in the question a bit, to explain what I actually would like to learn. Don't know whether you can help there...
Jul
15
comment How is the theory of partial coherent light related to quantum-mechanics?
I have nearly finished reading the links now. They are nice links indeed. I was really impressed by the blog entry, both for the nice coverage of the subject, but also by the aggressive tone of its author. Yes, I was also initially misguided with respect to quantum-mechanics, because of the way the subject was treated in the textbooks I read at the time. However, the author somehow seems to imply that I should feel ashamed for having read these textbooks. Or maybe not, but why does he writes so aggressively?
Jul
15
revised How is the theory of partial coherent light related to quantum-mechanics?
Found a nice link to the theory of partial coherent light, and added my puzzlement about Mueller calculus for further motivation
Jul
14
asked How can molecule of a few angstroms absorb visible light of a few hundred nanometers?
Jul
14
awarded Curious
Jul
13
asked How is the theory of partial coherent light related to quantum-mechanics?
Jul
13
answered Why is there readonly (const) in C++, but not writeonly (sink)?
Jul
12
comment Which natural number predicates can be defined in Robinson arithmetic?
My initial expectation for a function "definition" (and my statement "...exponentiation cannot be defined in Robinson arithmetic!") were based on the requirements for eliminating an additional function symbol in the non-logical language by a suitably defined predicate (i.e. a first order formula). But because Robinson arithmetic seems to be unable to prove totality, it seems like a good idea to omit the totality requirement. (After all, some logics also have terms and function symbols without existential import. Totality isn't a "Horn property" either...) I updated the question accordingly.
Jul
12
comment Which natural number predicates can be defined in Robinson arithmetic?
Here is an explicit formula for $E(x,y,z)$. It's only 6 lines, but it uses abbreviations/auxiliary predicate definitions. But I agree that even if these abbreviations would be expanded, the resulting formula would still not be that complicated.
Jul
12
revised Which natural number predicates can be defined in Robinson arithmetic?
Now I understood the point which Asaf and Peter raised...
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