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Mathematics
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Feng
  • Member for 7 years, 4 months
  • Last seen more than a week ago
  • China
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How to study math?

Don't just read it; fight it!

-------Paul Halmos

An interesting figure

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23
compute $\int_0^1\sqrt{x(1-x)}dx$.
Nov 16, 2022
22
How to show analytically that $x^4-4x^3-2x^2+16x+24=0$ has no solutions in $\mathbb{R}$?
Jul 19, 2022
19
Let $ f(x)=\frac{1+\cos(2\pi x)}2$ and $f^n=f\circ f^{n-1}$. Is it true that for almost every $x$, $\lim_{n \to \infty} f^n(x)=1$?
Oct 23, 2022
14
Given a sequence with $a_1=1$ and $a_{n+1}=a_n-\frac13a_n^2$. Is there an easier way to get an upper bound of $1/a_{100}$?
Jun 19, 2022
12
If $L^1$ average of $f$ is smaller than $t^2$ then $f=0$ a.e.
Aug 20, 2019
11
Compute $\prod^{100}_{n=1} \left(5-4 \cos \left(\frac{\pi (2n-1)}{100} \right) \right)$.
Aug 26, 2023
10
A random series has infinitely many zeros in $[0,1)$ almost surely.
May 11, 2019
10
Prove $\liminf_{n\to\infty} \left(n^2(4a_n(1-a_{n-1})-1)\right)\leq\frac14$ for any non-negative seqence $\{a_n\}$.
Jul 22, 2022
9
$a_n>0$, $\sum a_n^2<+\infty$, and $\sum a_{n_k}=+\infty$ whenever $\lim\limits_{k\to\infty}\frac{n_{k+1}}{n_k}=1\;?$
Dec 25, 2023
8
Why is the plot of $|x|^N + |y|^N =2$ almost a square when $N$ is large?
Sep 2, 2023

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9
What is the optimal constant for $\|f\|_{L^\infty}\leq C\|f\|_{L^2}^{1/2}\|f'\|_{L^2}^{1/2}$?
7
High dimensional Fekete's subadditive lemma: does $|\vec x_{n+m}|\leq |\vec x_n+\vec x_m|$ imply the convergence of $\{\vec x_n/n\}$?
7
Energy of harmonic maps from $\mathbb R^2$ to $S^2$ is quantized
7
Estimate the Hilbert–Schmidt norm of $\mathrm e^{\mathrm itA}-\mathrm e^{\mathrm itB}$
6
If an initial value problem has a solution on $[0,a)$ for all $a>0$, will it have a solution on the whole $[0,\infty)$?