Timeline for Sequence tending to modulus function
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| May 11, 2021 at 22:32 | comment | added | Dagobert Duck | @WillieWong thank you, that worked out nicely. | |
| May 11, 2021 at 20:22 | comment | added | Willie Wong | ... and to satisfy 3, you also just need to normalize. To satisfy 2 the normalization gives you what $g_n(x)|_{N_n}$ must be. To satisfy 3 also, you need to choose the normal derivative appropriately. Try the ansatz $$ f_n(x) = (x_2 - \sqrt{x^2_1 + 1/n}) g_n(x_1) + (x_2 - \sqrt{x^2_1 + 1/n})^2 h_n(x_1) $$ (You may also need to cut-off away from $N_n$ to makes sure that the quadratic doesn't generate another branch of $f_n^{-1}(\{0\})$. | |
| May 11, 2021 at 20:09 | comment | added | Dagobert Duck | @WillieWong I accidentally swapped numerator and denominator. But the derivation of a function satisfying 1 and 2 is easy, you just take an ansatz $f_n(x)=(x_2-\sqrt{x_1^2+1/n})g_n(x)$ and normalize. | |
| May 11, 2021 at 20:08 | history | edited | Dagobert Duck | CC BY-SA 4.0 |
edited body
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| May 11, 2021 at 19:47 | comment | added | Dagobert Duck | @WillieWong sorry, its norm | |
| May 11, 2021 at 19:47 | history | edited | Dagobert Duck | CC BY-SA 4.0 |
added 11 characters in body
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| May 11, 2021 at 19:29 | comment | added | Willie Wong | $\nabla f_n$ is a vector. What does it mean for it to equal 1? | |
| May 11, 2021 at 19:25 | review | First posts | |||
| May 11, 2021 at 21:20 | |||||
| May 11, 2021 at 19:23 | history | asked | Dagobert Duck | CC BY-SA 4.0 |