3,186 reputation
1833
bio website jakitoimgeisterhaus.blogspot.…
location Munich, Germany
age 38
visits member for 3 years, 1 month
seen 15 mins 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.


Aug
15
answered A question about convolution of two distributions
Aug
11
awarded  Fanatic
Aug
3
comment Continuity equation on manifolds
The following (non-English) presentation gives answers to this question on the last two slides.
Aug
2
comment Determining sparse frequency distribution via discrete Fourier transform
I assumed that it is known that the signal has period $2\pi$. I further assumed that it is known that uniform sampling with a spacing smaller than $\frac{\pi}{400}$ is sufficient.
Aug
2
revised Determining sparse frequency distribution via discrete Fourier transform
updated to v2 of cited paper and included updated information in the answer
Aug
2
answered Determining sparse frequency distribution via discrete Fourier transform
Jul
15
answered How can I intuit the role of the central limit theorem in breaking the curse of dimensionality for Monte Carlo integration
Jul
12
answered Fourier transform eigenvalues
Jul
11
answered viscosity solution vs. weak solution
Jul
11
comment viscosity solution vs. weak solution
For nonlinear PDEs like a Hamilton-Jacobi equation or a hyperbolic systems of conservation laws, a weak solution need not be unique. For a Hamilton-Jacobi equation, the viscosity solution is a special weak solution which turns out to exist and be unique. For hyperbolic systems of conservation laws, a similar concept is the entropy solution, which can be shown to exist and be unique in a number of "sufficiently well understood" situations.
Jul
11
comment How can I intuit the role of the central limit theorem in breaking the curse of dimensionality for Monte Carlo integration
This answer cites a very readable survey article about sparse grids and the course of dimensionality. Regarding your questions, "including a variety of length scales" goes in the right direction, but there are many other intuitive explanations. You could work with space filling curves, investigate enumeration schemes for $\mathbb Z^n$ or look at multivariate polynomials of a fixed degree. What would you prefer for an answer?
Jul
11
revised Why Monte Carlo integration is not affected by curse of dimensionality?
added 57 characters in body
Jul
9
accepted Weak categoricity in first order logic
Jul
9
comment Weak categoricity in first order logic
Thanks for your answer. I have some questions/remarks: I don't understand what you mean with your first sentence. I don't understand the example with the additive group of integers. I don't understand the notion of "primal model", and couldn't find it via googling. Is it correct that if the minimal model exists and is unique, then it is also a prime model? Does infinitary logic requires a sufficiently strong set theory (like required for second order logic)?
Jul
9
asked Weak categoricity in first order logic
Jun
29
answered Is there a name for a semigroup whose idempotents form a subsemigroup?
Jun
25
comment Mathematical Discoveries that were made or supported by savants
What are the advantages of savants over computers for the purpose of mathematical discoveries? Of course, according to Roger Penrose they should have some, but in this case the savants are probably real mathematicians and will be able to successfully hide that they are savants.
Jun
25
asked Is the universal inverse semigroup of a commutative semigroup an embedding?
Jun
24
answered what means a integral exists in the distributional sense?
Jun
24
revised What are some (or even one) interesting examples of (non-group) semigroups?
deleted 28 characters in body