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


May
7
comment Is nonlinear conjugate gradient a quasi-newton optimization technique?
@Dominique Interesting. Can you also tell me which part is erroneous? My guess is that you disagree with: "A quasi-Newton optimization technique use some approximation for the Hessian, or at least can be interpreted as implicitly using some approximation for the Hessian." Or do you disagree with my last "... not even implicitly"? In that case, could you please help me to also recognize the implicit Hessian you have in mind?
May
4
accepted Computing 2d radially symmetric Fourier transforms (with Wolfram Alpha)
May
4
reviewed Approve suggested edit on Completing the Square and Complex Coefficients
May
4
asked Computing 2d radially symmetric Fourier transforms (with Wolfram Alpha)
May
3
reviewed Approve suggested edit on Proving a circuit of a graph will have an edge in common with a cycle of the same graph.
May
3
accepted Can the consistency of ZF be proved in MK?
May
3
comment Can the consistency of ZF be proved in MK?
I didn't know about that question on MO. This certainly answers my question, even so I know from experience that it will take some time to digest the MO answers. However, there is no need to give simplified versions of the MO answers here, because I actually like digesting this sort of math.
May
2
asked Can the consistency of ZF be proved in MK?
May
2
revised What is so amazing about having least upper bound (and dually, the greatest lower bound)?
Tried to nail down what it is about lattice theory that feels wrong to me.
May
1
comment What is so amazing about having least upper bound (and dually, the greatest lower bound)?
@user89 I added parentheses "... as a bipartite graph (where the one set of nodes is given by the equations, the other by the variables, and an edge is there when the variable occurs in the equation)," and "like the Dulmage–Mendelsohn decomposition (in case of a perfect matching, this is just the strong component decomposition of the directed graph, which arises from identifying the matched nodes)." to the answer. I also wrote this answer once, but it isn't more detailed either. But the links from the wikipedia article contain nice pictures...
May
1
revised What is so amazing about having least upper bound (and dually, the greatest lower bound)?
added parentheses to the section about bipartite graphs and Dulmage-Mendelsohn
May
1
answered Locally small category whose collection of isomorphism classes cannot be a set
May
1
revised What is so amazing about having least upper bound (and dually, the greatest lower bound)?
missed to include the theme of bipartite graph and formal concept analysis
May
1
answered What is so amazing about having least upper bound (and dually, the greatest lower bound)?
Apr
27
comment Semantics and expressive power of generic element quantifiers
At least for $\mathbb R^n$, an idea for a possible semantics just occurred to me. The interior of the set of all $\xi$ for which the proposition is true should be dense in $\mathbb R^n$. So this type of semantics might work as soon as the model is required to have a topology. Doesn't look too bad for the moment.
Apr
27
asked Semantics and expressive power of generic element quantifiers
Apr
26
comment Locally small category whose collection of isomorphism classes cannot be a set
Thanks. I guess the term set is a bit too overloaded. I'm thinking of an "extensionally defined collection" when I hear set, in contrast to an "intensionally defined collection", which I associate more with the word class. A collection on the other hand doesn't even need to be well defined for me. You seem to think of set as a "somehow well defined collection", more or less. Tarski has published two different meta truth definitions, one in 1933 making no reference to any meta set notion, and one model-theoretic truth definition in 1956 (with Robert Vaught) using a meta set notion.
Apr
26
comment Locally small category whose collection of isomorphism classes cannot be a set
I will have to read the linked page in more detail to see whether this answers my question. However, your claim "In that framework, there is no unnatural category !" seems to rest on your special interpretation of "for any naive set", and I couldn't find a definition of "naive set" on the linked page. Note that for me, an isomorphism class of a typical natural category is as different from a "naive set" as possible, because the defining property of its members is that they are undefined, except for their "isomorphic properties".
Apr
26
asked Locally small category whose collection of isomorphism classes cannot be a set
Apr
26
revised Is every “almost” isomorphism an isomorphism?
One of the relations given in the question can be omitted, namely either hfg=1 or fgh=1.