3,196 reputation
1833
bio website jakitoimgeisterhaus.blogspot.…
location Munich, Germany
age 38
visits member for 3 years, 1 month
seen 9 hours ago

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
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
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
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
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
comment Which natural number predicates can be defined in Robinson arithmetic?
@hardmath I tied to clarify this now. It turns out that I just want to know whether transitivity, reflexivity and antisymmetry can be proved for a suitable definition (by a first order formula in $Q$) of $x\leq y$. I'm quite convinced that this isn't possible for the definition given in the question, so either one has to come up with a definition for which this can be proved, or show that no such definition can exist.
Jul
7
comment Which biased random sources can be obtained from an unbiased one?
The expanded answer is even more awesome. And it is actually a quite canonical procedure, in a certain sense.
Jul
7
comment Which biased random sources can be obtained from an unbiased one?
Cool, I'm glad I asked. But you surely mean one can get every $p\in \mathbb Q\cap[0,1]$, not every $p\in[0,1]$. Or what would you do for $p=1/\sqrt{2}$?
Jun
9
comment Trying to calculate length of one parameter in complex geometrical object (polygon)
If you have to program this for some "real" application, you might also have to take care about the case H2 >> R. So a max(T/2, X) might be a good idea.
Jun
9
comment Is there a (foundational) type theory with the features I'm looking for?
@MaliceVidrine I wouldn't necessary agree to your statements about NF(U), but you are right that I will need at least "Inf" in addition to TST, and that "Choice" won't really hurt. I don't know how to parse "Small Ordinals", but I guess it's something harmless similar to "Choice". I think the reason why Holmes and I discuss TST is that it is a baseline, which already has a quite significant consistency strength, but can be directly traced back to a philosophical position with corresponding explicit ontological commitments.
Jun
7
comment Is there a (foundational) type theory with the features I'm looking for?
@user18921 I think that yes, it has support for (primitive?) recursively defined sets. To see this, try to start with the constant $0$ and the successor relation $S$, and then recursively define addition, multiplication and exponentiation. Then decide for yourself, whether the support for recursive definitions is good enough. I haven't checked whether $\mu$-recursion is also available, but I guess that it is indeed.
Jun
3
comment How do I turn a “broken” plot into a smooth curve
@Lee There are some options for making such methods "reproducible, repeatable and programmable". The method with the exponential function already satisfies this property without any further modification. For the method with the cubic polynomial, I added a suggestion how to make it reproducible. I'm not sure why you stress VBA.
Jun
1
comment Can the divergence theorem be restricted to flat surfaces?
Oh man, you really seem to have problems with the English language. Even a flat surface is still not restricted to $\mathbb R^2$. The non-mathematical meaning the word "surface" is the outer face of an object. What you probably mean is called an "area" or a (two dimensional) "domain".
May
24
comment Does every function with $f_x,f_y>0,f_{xx},f_{yy}<0$ with particular condition have to satisfy $f_{xy}/f_{xx} = -x/y$?
No, this should definitively not be posted at mathoverflow. Your condition $f(\lambda x, \lambda y)=\lambda f(x,y)$ forces the derivative in x-direction along the x-axis to be constant, so that you limes conditions cannot be satisfied everywhere. So of course nobody can give a counterexample, because there is no example at all to satisfy these conditions.
May
22
comment Understanding properties and criticisms of a (specific) sequent calculus
To be honest, I don't really see how this "intended reading" is any different from the rules themselves, except for the turnstile. Also, I guess the main part of Peter Smith's criticism referred to the (missing) subformula property of (PC) and (Ctr). This answer doesn't mention (PC) and (Ctr) explicitly, but it seems as if they are unchanged.
May
19
comment Difference between bound and free variable
philosophy.stackexchange.com/questions/7827/…
May
19
comment Difference between bound and free variable
math.andrej.com/2012/12/25/…
May
19
comment Difference between bound and free variable
@MauroALLEGRANZA I tried to incorporate your suggestiongs into my anser. I agree that $P(x)$ has no fixed meaning. There are many reasonable ways to assign meaning to it. It makes most sense to strive for functoriality of truth values for these meanings. The drawback of the definition I gave is that it hides the fact that even $\forall x (P(x)\implies Q(x))$ can take truth values in a Boolean algebra. But I hope that it might be relatively easy to understand for somebody with a "bivalued" classical mindset.
May
17
comment Not enough memory for GMRES
While computing the vector product, you might also consider using your existing Gauss-Seidel as a preconditioner, because the memory consumption of GMRES is proportional to the number of GMRES iterations (once you avoid the "obvious" mistakes).
May
17
comment Not enough memory for GMRES
You can just replace all instances of "A*v" in that code by a callback to "your code", which computes this matrix vector product (and uses a more appropriate representation of "A" internally). Many of the common numerical C++ frameworks (like PETSc or Trilinos) will also have implementations of GMRES. However, if you are interested in this sort of answer, please ask on Computational Science instead. People "closer associated" to these frameworks are active there, and they would probably correct misleading answers (which probably won't happen here, even if you get answers).