All Questions

What is $$p_*:=\inf\big\{p\in\mathbb R\colon\,\inf_{n\in\mathbb N}n^p\,\inf_{k\in\mathbb N} |2\sqrt{3n}-9\pi/4-k\pi|>0\big\},$$ where $\mathbb N:=\{1,2,\dots\}$? In other words, I would like to ...

Let $n \geq 3$ and consider two sequences of strictly monotone functions $\{\mu_l(t)\}_{l=1}^{n}$ and $\{\lambda_l(t)\}_{l=1}^n$ on the interval $[-1,1]$ with $\mu_l(0)=0$ and $\lambda_l(0)=1$ for all ...

Suppose that I have a sequence of $n$ numbers $x_1, \ldots, x_n$ all taken from the real interval $[0,1]$. I am interested in minimizing the infinity norm of the vector $$ v = \left( \frac{x_{1}}{x_2},...

I have questions about the integral $$F(a,b,c)=\sqrt{\frac{a}{\pi}}\int_{0}^{\infty}e^{-bx^4+cx^3-ax^2}dx$$ for $a,b,c>0$. What is the asymptotic behavior of $F(a,b,c)$ for small $a,b,c$? In ...