21,673 reputation
31557
bio website
location
age
visits member for 2 years, 11 months
seen 18 mins ago

21h
comment Can the inequality $a^3 + b^3 + c^3 \ge a^2b + ac^3 + b^2c$ be derived from arithmetic-geometric means?
Is $ac^3$ a typo for $ac^2$ ?
1d
revised Tightenning Interval Mapping
added 151 characters in body
1d
answered Tightenning Interval Mapping
2d
comment convergence in probability induced by a metric
@mathmath8128 The function $f(t)=\frac{t}{1+t}=1-\frac{1}{1+t}$ is increasing on $(0,\infty)$, so that $|X_n-X|\geq \varepsilon$ yields $f(|X_n-X|) \geq f(\varepsilon)$
2d
comment Prove $\left(\sum_{1 \le i <j \le n} |x_i-x_j|\right)^2 \ge (n-1)\sum_{1\le i<j \le n} (x_i-x_j)^2.$
@math110 you use $x_k=x_1+\sum_{j=2}^k y_j$ : you replace $x_2$ by $x_1+y_2$, you replace $x_3$ by $x_1+y_2+y_3$ etc.
Aug
17
awarded  Nice Question
Aug
16
comment Every endomorphims is a linear combination of how many idempotents in infinite dimensions?
At the very end of the proof of(II), shouldn't it be ${\rm ker}(\pi_1)+{\rm ker}(\pi_2)$ rather than ${\rm ker}(\pi_2)+{\rm ker}(\pi_3)$ ?
Aug
16
awarded  real-analysis
Aug
15
answered If a polynomial has only real zeros then $a_{0}+a_{1}+\cdots+a_{n}\le\frac{(n+1)^n}{\binom{n}{s}(n-s)^{n-s}(s+1)^s}\cdot\max_{k}a_{k}$
Aug
15
comment A “repeated roots allowed” version of the continuity of roots
The reordering issue is easy : the functions $\min$ and $\max$ are continuous ${\mathbb R}^2 \to {\mathbb R}$, because $\min(x,y)=\frac{x+y-|x-y|}{2}$ and $\max(x,y)=\frac{x+y+|x-y|}{2}$
Aug
15
comment How to find the minimum value of $\sum_{1\le i<j\le 6}[a_{i}+a_{j}]$
Thank you for taking the time to write such an elaborate answer.
Aug
15
asked A “repeated roots allowed” version of the continuity of roots
Aug
15
answered Determining if a recursively defined sequence converges and finding its limit
Aug
14
comment Prove that the length of segment on tangent is constant for $y=\frac a2\ln{\frac{a+\sqrt{a^2-x^2}}{a-\sqrt{a^2-x^2}}}-\sqrt{a^2-x^2}$
You’re right, I was mistaken
Aug
14
answered How prove that $q \geq b+d$ for $ad-bc = 1$ and $\frac{a}{b} > \frac{p}{q} > \frac{c}{d}$?
Aug
14
comment What is the set with characteristic function $\chi_A(x) + \chi_B(x)-\chi_A(x)\chi_B(x)$?
You are correct, the "answer given" is false.
Aug
14
comment What is the connection between $\rho$ and $\sigma$ if $\rho\rho^T=\sigma\sigma^T$?
@WillNelson I believe you’re mistaken, it does necessarily follow. First, if $\sigma=\rho R$ then $R$ is $\rho^{-1}\sigma$ not $\sigma\rho^{-1}$ as you wrote. Also, $\alpha=\rho^{-1}$ is orthogonal if $\rho$ is, so that if we put $R=\alpha\sigma$, we have $R^{T}=\sigma^{T}\alpha^{T}$ so that $RR^{T}=\alpha\sigma\sigma^{T}\alpha^{T}=\alpha\rho\rho^{T}\alpha^{T}=I$ since $\alpha=\rho^{-1}$.
Aug
13
comment Every endomorphims is a linear combination of how many idempotents in infinite dimensions?
@GeorgeLowther I understand that you do not have the time to put it all in Internet-readable form. If you’re willing to produce a reasonably elaborate sketch of proof (even with many missing details), I’d be quite happy to put a bounty on this question. I hope you'll let me know :-)
Aug
13
revised if $ax-2by+cz=0$ and $ac-b^2>0$ , Prove $zx-y^2\leq0$
deleted 11 characters in body
Aug
13
answered if $ax-2by+cz=0$ and $ac-b^2>0$ , Prove $zx-y^2\leq0$