bio | website | go.helms-net.de |
---|---|---|
location | Germany | |
age | 62 | |
visits | member for | 5 years |
seen | yesterday | |
stats | profile views | 1,344 |
Mathematics is only a hobby - although I have done undergrad courses in the 70s. But part of my job was doing statistics and this kept me near my favourite subject "linear algebra" (programmed factor-analysis and a matrix-orientated calculator MatMate). Around 2002 I came in contact with the internet community in math newsgroups and could improve my Collatz discussion. Next subject was the Bernoulli numbers, then integer matrices and since 2006 the problem of iterated exponentiation aka tetration. Serving half-time jobs in teaching here at the university I found time to fiddle with that subjects in depth - and found love with the exploratory approach and impulse of the 18'th century numbertheory, namely L. Euler, "the master of us all"... Due to lack of formal education I've to do my "research" widely on my own - but that's what I just like: to find structure, pattern, laws from the ground.
Jul 17 |
comment |
How to prove that this equation has only one solution?
@Anthony : didn't the argument of Rhin actually mean, that the approximation of the sum of logarithms to the nearest integer is actually bad instead of good so instead of "$\le$" in your formula you needed "$\ge$" ? (I don't have access to Rhin's paper, it seems just logical to me; also I found in a paper of J. Simons/B.de Weger the argument $ (K+l) \log2 - K \log3 \gt e^{-13.3(0.46057+ \log K)} \qquad $ with the reference to Rhin's result. ) |
Jul 17 |
awarded | Yearling |
Jun 25 |
answered | How to prove that this equation has only one solution? |
Jun 25 |
comment |
How to prove that this equation has only one solution?
This is very near related to an (open) conjecture of a detail in the Waring-problem of sums of like powers. I cannot at the moment show the exact relation/transformation, but you might search for keyword "waring" in MSE where I've given answers datailing this problem, sometimes to questins of the user Fred Kline there. I can come back to this possibly in the evening (west European time) |
Jun 10 |
accepted | Is there a systematic relation between the generating functions for the rows vs that for columns of infinite sized Carleman-matrices? |
Jun 10 |
comment |
Is there a systematic relation between the generating functions for the rows vs that for columns of infinite sized Carleman-matrices?
Ah, very good. This is in the spirit in which I hoped to find a general expression. In the earlier question math.stackexchange.com/questions/569751 I've described my pattern-detection solution for the iterated $f(x) = \exp(\exp(x)-1)-1$ and was surprised to find such typical products in the denominator in the gf's of the transpose. So I expected in some way derivatives occuring in the solution. And it is not too complicated - very good! Thank you very much. |
Jun 10 |
comment |
Is there a systematic relation between the generating functions for the rows vs that for columns of infinite sized Carleman-matrices?
I'll have to read that very accurate, thank you very much! One more focused question for generality: is it likely, that with the Carlemanmatrix for some function $f(x)$ the inverse function $f^{-1}(t)$ is always involved in the generating function for the transposed Carlemanmatrix? (say, simply for $f(x)=x-1/2x^2$ or the like) |
Jun 9 |
asked | Is there a systematic relation between the generating functions for the rows vs that for columns of infinite sized Carleman-matrices? |
May 7 |
awarded | Nice Answer |
Mar 26 |
comment |
On an example of an eventually oscillating function
I've found heuristically more properties of $d(x)$, detailed that aspects and gave some hypothetical explanations but still cannot provide proofs. So my followup-question (and possible answeres) might be interesting. Please see here mathoverflow.net/questions/201098 |
Mar 26 |
revised |
Oscillation aspects of two-way infinite alternating series (a followup from the MO-question “functions that eventually oscillate”)
added 262 characters in body |
Mar 26 |
revised |
Oscillation aspects of two-way infinite alternating series (a followup from the MO-question “functions that eventually oscillate”)
added 262 characters in body |
Mar 26 |
asked | Oscillation aspects of two-way infinite alternating series (a followup from the MO-question “functions that eventually oscillate”) |
Mar 16 |
revised |
3n+1 problem and cycles
added 16 characters in body |
Mar 16 |
revised |
3n+1 problem and cycles
added 16 characters in body |
Mar 16 |
answered | 3n+1 problem and cycles |
Mar 15 |
comment |
3n+1 problem and cycles
The "cycle" and the "divergence"-problem are likely unrelated. In the $5x+1$-problem we have cycles, and likely most trajectories diverge. In the $3x+1$-problem where we did not yet find any indication of a divergent trajectory, we have nontrivial cycles in the negative numbers. |
Mar 15 |
answered | Collatz property implying infinite “fall below” trajectories, is it known? |
Mar 10 |
revised |
On an example of an eventually oscillating function
rewrote the whole answer, deleted overcomplicated derivations |
Mar 4 |
revised |
On an example of an eventually oscillating function
added 124 characters in body |