Timeline for On a deceptively tricky calculus problem
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
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| Jan 21 at 15:00 | comment | added | matilda | @ThomasKojar- I have asked my original question here- mathoverflow.net/questions/462606/… I have also added it to this question. | |
| Jan 21 at 15:00 | history | edited | matilda | CC BY-SA 4.0 |
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| Jan 21 at 7:51 | comment | added | Thomas Kojar | I prefer to keep it here in MO because there are many experts here that can contribute. If you are concerned with sharing preliminary work, perhaps try to only mention the very particular technical estimate you think might be true but are having trouble proving. There is likely no need to mention which conjecture you are working on. | |
| Jan 20 at 22:29 | comment | added | matilda | @ThomasKojar- Would it be okay if I sent you an email about it? In fact the conjecture that I am trying to prove is very much in your field of research. I will be happy to post it here though, if you prefer to continue the discussion on MO. | |
| Jan 20 at 22:23 | comment | added | Thomas Kojar | It might be impossible to get rid off the integrals. Do you have some original problem that you are trying to solve? We can try to help you with that. Some estimate you are trying to obtain if true? If so, please edit your post to include those. | |
| Jan 20 at 22:09 | history | edited | matilda | CC BY-SA 4.0 |
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| S Jan 15 at 20:02 | history | bounty ended | CommunityBot | ||
| S Jan 15 at 20:02 | history | notice removed | CommunityBot | ||
| Jan 8 at 3:07 | history | edited | matilda | CC BY-SA 4.0 |
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| Jan 8 at 3:05 | comment | added | matilda | @WillieWong- Yes, the two are unrelated. I have now changed $A(u,t)$ to $X(u,t)$. | |
| S Jan 7 at 18:31 | history | bounty started | matilda | ||
| S Jan 7 at 18:31 | history | notice added | matilda | Draw attention | |
| Jan 7 at 14:41 | comment | added | matilda | @MichaelHardy- I have now edited the question to make it more explicit. Only the $\log$ term is being integrated with respect to $x$. | |
| Jan 7 at 14:40 | comment | added | matilda | @ThomasKojar- Ideally, $A(u,t)$ should be an expression without involving integrals. It should also be a norm of some kind. I have edited the question to include that condition. | |
| Jan 7 at 14:39 | history | edited | matilda | CC BY-SA 4.0 |
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| Jan 6 at 0:19 | comment | added | Michael Hardy | The integral expressed here as $$ \int u^s\log\left(\frac{u}{\|u\|_s}\right)-\langle Au,u^{s-1} \rangle$$ could easily be mistaken for $$ \int \left( u^s\log\left(\frac u {\|u\|_s}\right)-\langle Au,u^{s-1} \rangle \right) \, ds, $$ or for $$ \int u^s \left( \log\left(\frac u{\|u\|_s} \right) - \langle Au,u^{s-1}\rangle \right) \, dt. $$ But it appears that (maybe?) you intended $$ \int u^s \left( \log\left(\frac u{\|u\|_s} \right) - \langle Au,u^{s-1}\rangle \right) \, dx. $$ Explicitness about this could avoid confusion. | |
| Jan 5 at 21:56 | comment | added | Thomas Kojar | closed-form in terms of what? $A(u,t)=\int^{t}||u||^{1-s}... dt$ is a closed form since $u=e^{-tA}f$. | |
| Jan 5 at 21:32 | comment | added | matilda | @ThomasKojar- I would ideally like a closed-form expression for $A(u,t)$. | |
| Jan 5 at 21:32 | history | edited | matilda | CC BY-SA 4.0 |
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| Jan 5 at 20:11 | comment | added | Thomas Kojar | can you clarify what properties you want from $A(u,t)$? Because clearly by integrating $A(u,t)=\int^t...$. | |
| Jan 5 at 19:00 | history | edited | matilda | CC BY-SA 4.0 |
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| Jan 5 at 18:24 | history | asked | matilda | CC BY-SA 4.0 |