bio | website | go.helms-net.de |
---|---|---|
location | Germany | |
age | 62 | |
visits | member for | 4 years, 9 months |
seen | 5 hours ago | |
stats | profile views | 1,287 |
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.
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”)
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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
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Mar 16 |
revised |
3n+1 problem and cycles
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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
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Mar 3 |
revised |
On an example of an eventually oscillating function
added 535 characters in body |
Mar 2 |
revised |
On an example of an eventually oscillating function
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Mar 2 |
revised |
On an example of an eventually oscillating function
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Mar 2 |
revised |
On an example of an eventually oscillating function
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Mar 2 |
revised |
On an example of an eventually oscillating function
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Mar 2 |
answered | On an example of an eventually oscillating function |
Feb 28 |
comment |
On an example of an eventually oscillating function
Hmm,I just tried to get some advantage from a reformulation for $x$ near $1$, so using $x=1-t$ and then to centralize (+ smooth) the oscillation of the result around $1/2$ by writing $g(t)=((1-t)-1) - ((1-t)^2-1)+((1-t)^4-1) - ... + ... $ and $f(x)=g(1-x)+1/2 $), then expand the binomial expressions (by the powers of $(1-t)$ and collect like powers of $t$. This gives at each power of $t$ an infinite divergent series but which is alternating and can be normalized by decomposition into geometric series. This gives vanishing coefficients at the $g(t)$-series. But I've not yet arrived anywhere... |
Feb 21 |
revised |
A question on Collatz's conjecture
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Feb 21 |
answered | A question on Collatz's conjecture |