Timeline for Rotation invariant of surface
Current License: CC BY-SA 4.0
19 events
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| Aug 21, 2018 at 9:59 | comment | added | Qfwfq | Ah so it's $Hf\cdot \nabla f$, okay | |
| Aug 21, 2018 at 5:15 | comment | added | marimo | @Qfwfq It's the product of matrix $H$ and vector $\nabla f$. | |
| Aug 20, 2018 at 13:12 | comment | added | Qfwfq | By the way, what's $H\nabla f$? | |
| Aug 20, 2018 at 9:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jul 21, 2018 at 7:10 | answer | added | Ben McKay | timeline score: 2 | |
| Jul 20, 2018 at 10:08 | comment | added | marimo | @BenMcKay I defined these terms. | |
| Jul 20, 2018 at 10:08 | history | edited | marimo | CC BY-SA 4.0 |
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| Jul 20, 2018 at 10:00 | history | edited | marimo | CC BY-SA 4.0 |
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| Jul 20, 2018 at 9:54 | history | edited | marimo | CC BY-SA 4.0 |
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| Jul 20, 2018 at 9:41 | comment | added | Alex M. | @BenMcKay: Could the OP be asking for all the rotation-invariant differential operators in $\mathbb R^3$ (excluding the multiplication by functions)? Or maybe only those of order $2$? | |
| Jul 20, 2018 at 9:33 | comment | added | Ben McKay | Consider the invariant $I=1$ if $f>0$ everywhere and $I=0$ otherwise. This is a rotation invariant, not given as above. Please make a more precise definition of what you mean by a rotation invariant. Clearly you mean something like a nonlinear differential operator, but what is a combination, and do you require $f$ to belong to some particular function space? | |
| Jul 20, 2018 at 9:28 | comment | added | marimo | @BenMcKay If $T:(u, v)\mapsto (x,y)$ is a rotation, $(f_{xx}+f_{yy})(T(u,v)) = ((f\circ T)_{uu}+(f\circ T)_{vv})(u,v)$. | |
| Jul 20, 2018 at 9:26 | history | edited | marimo | CC BY-SA 4.0 |
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| Jul 20, 2018 at 9:26 | comment | added | Ben McKay | If $f(x,y)$ is not rotation invariant, and not linear, then surely $\Delta f$ is also not rotation invariant. What do you mean? | |
| Jul 20, 2018 at 9:24 | comment | added | Ben McKay | Are we rotating around the line $0=x=y$? | |
| Jul 20, 2018 at 9:24 | history | edited | marimo | CC BY-SA 4.0 |
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| Jul 20, 2018 at 9:08 | history | edited | marimo | CC BY-SA 4.0 |
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| Jul 20, 2018 at 8:11 | review | First posts | |||
| Jul 20, 2018 at 9:42 | |||||
| Jul 20, 2018 at 8:11 | history | asked | marimo | CC BY-SA 4.0 |