Timeline for Are we able to estimate the fraction of the domain where $\cos (ax)+2\cos (b x)$ with $\frac ab \notin\mathbb{Q}$ is positive?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 13, 2021 at 19:31 | vote | accept | CommunityBot | ||
| May 13, 2021 at 18:21 | history | edited | GH from MO |
edited tags
|
|
| May 13, 2021 at 18:16 | answer | added | Noam D. Elkies | timeline score: 11 | |
| May 13, 2021 at 18:07 | comment | added | Gro-Tsen | PS: The mean motion theorem and the references given in this question is relevant to a closely related question (computing the number of zeros of this function in a given interval). | |
| May 13, 2021 at 18:06 | history | edited | Iosif Pinelis |
edited tags
|
|
| May 13, 2021 at 18:04 | answer | added | Iosif Pinelis | timeline score: 3 | |
| May 13, 2021 at 18:04 | comment | added | Gro-Tsen | I guess the answer is of the form “mumble ergodic mumble fraction of $(u,v) \in (\mathbb{R}/2\pi\mathbb{Z})^2$ such that $\cos(u) + 2\cos(v) > 0$, which is equal to mumble”, but I don't know the magic words with which to replace the first two “mumble” and I don't have the patience to compute the value of the last “mumble”. 😔 | |
| S May 13, 2021 at 17:18 | history | suggested | Jukka Kohonen | CC BY-SA 4.0 |
cleaning up formulas: if integrating with respect to x, don't reuse x as the upper limit
|
| May 13, 2021 at 16:36 | comment | added | Jukka Kohonen | Interesting question. If the amplitudes were equal, i.e. the function was $\cos(ax)+\cos(bx)$, it could be rewritten as a product $2\cos(Ax)\cos(Bx)$ with $A=(a+b)/2$, $B=(a-b)/2$, and one would only have to worry about the signs of the two cosines. But with the different amplitudes it "beats" me. (Pun intended, en.wikipedia.org/wiki/Beat_(acoustics) ) | |
| May 13, 2021 at 16:05 | review | Suggested edits | |||
| S May 13, 2021 at 17:18 | |||||
| May 12, 2021 at 11:03 | comment | added | user215601 | @LSpice Yes, that is true, thanks. | |
| May 12, 2021 at 1:28 | comment | added | LSpice | I found "the ratio of the domain" confusing; I think you meant something like "the fraction of the domain". I have edited accordingly, hopefully without changing the meaning. | |
| May 12, 2021 at 1:28 | history | edited | LSpice | CC BY-SA 4.0 |
I think clearer wording
|
| May 12, 2021 at 1:20 | review | First posts | |||
| May 12, 2021 at 5:58 | |||||
| May 12, 2021 at 1:16 | history | asked | user215601 | CC BY-SA 4.0 |