Timeline for Why were these constants picked in this Lyapunov function and how did the author arrive at the final form of the Lyapunov function?
Current License: CC BY-SA 4.0
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| S Feb 25, 2022 at 15:03 | history | bounty ended | CommunityBot | ||
| S Feb 25, 2022 at 15:03 | history | notice removed | CommunityBot | ||
| Feb 22, 2022 at 13:40 | comment | added | Math | @CarloBeenakker Yes, I also did not understand how they got this.. Maybe things will cancel? | |
| Feb 21, 2022 at 18:45 | comment | added | Carlo Beenakker | I looked at that paper and the equations make little sense to me; consider the second equality on page 167, there is the term $-(m_1\Lambda/S^\ast)x^{-1}$. It is the only term $\propto 1/x$. In the next equality they set $m_1=S^\ast$, so that term should just read $-\Lambda/x$. Instead, it has expanded to 10 (!) terms... | |
| Feb 21, 2022 at 14:42 | history | edited | Math | CC BY-SA 4.0 |
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| Feb 17, 2022 at 14:56 | history | edited | Math | CC BY-SA 4.0 |
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| Feb 17, 2022 at 14:41 | history | edited | Sam Hopkins | CC BY-SA 4.0 |
improved URL link to DOI which should be more stable
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| Feb 17, 2022 at 14:11 | history | edited | Math | CC BY-SA 4.0 |
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| Feb 17, 2022 at 14:00 | history | edited | Math | CC BY-SA 4.0 |
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| S Feb 17, 2022 at 13:55 | history | bounty started | Math | ||
| S Feb 17, 2022 at 13:55 | history | notice added | Math | Canonical answer required | |
| Feb 17, 2022 at 13:55 | history | edited | Math | CC BY-SA 4.0 |
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| Feb 17, 2022 at 13:28 | comment | added | Math | @PiyushGrover I believe the the author makes the variable terms($xu, xv, z, u, v, yu, yv$) equal to zero at the top of page 167 in journal. when I try solving these, it outputs $m_i$'s equal to zero.. | |
| Feb 15, 2022 at 15:49 | comment | added | Piyush Grover | looks like a contrived problem:the solution was the written down first and then the problem was created | |
| Feb 14, 2022 at 14:54 | comment | added | Math | @CarloBeenakker I understand we need the lyapunov function to be negative semi definite but this doesn't explain why they picked these coefficients in particular. Granted these coefficients worked, but why these? or better, how were they deduced? | |
| Feb 14, 2022 at 14:22 | comment | added | Carlo Beenakker | they need $dH_1/dt\leq 0$, and that fixes these coefficients in the expression for $H_1$. | |
| Feb 14, 2022 at 13:14 | history | edited | Ben McKay | CC BY-SA 4.0 |
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| Feb 14, 2022 at 13:05 | history | asked | Math | CC BY-SA 4.0 |