Activity for Pavel Kocourek
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Question | — |
Meta rep counting into the Math rep. > Can we agree on how much, if any, the meta reputation should account as part of the overall math reputation? It seems that currently the math.meta reputation counts equally to the math reputation. I feel like this spoils the quality of the math reputation. I understand that participating in the ... (more) |
— | over 1 year ago |
| Question | — |
Is there a "regular" quasi-convex function $f:\Bbb R^2 \to \Bbb R$ that is not a monotone transformation of any convex function? Question > Can you find an example of a differentiable quasi-convex function $f:\Bbb R^2 \to \Bbb R$ that is non-degenerate, but there does not exist any strictly increasing $\phi:\Bbb R \to \Bbb R$ such that $\phi \circ f$ is convex? >> Definition. We say that $f$ is non-degenerate iff $f'(x0)=... (more) |
— | over 1 year ago |
| Answer | — |
A: How can we grow this community? I'm new to math.codidact, and I'm relatively new (1 month) to MSE. I discovered this site after I found about how SE lacks respect to the community. Let me share my experience with this site. Cons 1. This is kind of a cosmetic detail, but the very thing that stroked me when I visited the si... (more) |
— | over 1 year ago |
| Question | — |
Is there a two variable quartic polynomial with two strict local minima and no other critical point? > Does there exist a degree 4 polynomial $p:\Bbb R^2 \to \Bbb R$ that has two strict local minima and no other critical point? This is the same as this question rock-star, except for that I'm only interested in quartic polynomials instead of general functions $f:\Bbb R^2 \to \Bbb R, C^\infty$. ... (more) |
— | over 1 year ago |
| Answer | — |
A: Is $f(x)=\sin(x)$ the unique function satisfying $f'(0)=1$ and $f^{(n)}(\Bbb R)\subset [-1,1]$ for all $n=0,1,\ldots$? This is not a complete answer, but only an attempt for it. It should not be surprising that considering the specific form $f(x)=k\sin(jx+y)$ , the condition $f'(0)=1$ fixes value of all the 3 paramters $k,j,y$: Since $1$ is the maximum value $f'(x)$ is allowed to attain, it must be that $y=0$ (o... (more) |
— | over 1 year ago |