Behnam Esmayli - StackExchange and M.O.

Check out my profiles on Stackexchange and Mathoverflow.

Sample of questions/answers.

ALL Orthogonality preserving linear maps from $\mathbb R^n$ to $\mathbb R^n$?That is we have a linear transformation, i.e. an $ n\times n $ matrix $A$, such that for every pair of vectors $ v $ and $ w $ we have $$ \langle v,w\rangle=0 \ \ \ \implies \ \ \ \ \ \langle...

A surprising inequality about a $\limsup$ for any sequence of positive numbersI think I remember this from either Apostol's or Rudin's principles of Analysis. Claim: Let $\{x_n\}_{n=1}^{\infty}$ be a sequence of positive real numbers. Then $$ \limsup \frac{x_1+x_2+...+x_n+x...

Evaluation of $\cos\left(\frac{\pi}{2n}\right)\cdot \cos\left(\frac{2\pi}{2n} \right)....\cos\left(\frac{(n-1)\pi}{2n}\right)$Evaluation of $$\lim_{n\rightarrow \infty}\left(\tan \frac{\pi}{2n}\cdot \tan \frac{2\pi}{2n}\cdot \tan \frac{\pi}{3n}\cdot ...............\tan \frac{(n-1)\pi}{2n}\right)^{\frac{1}{n}} = $$ without...

The following question lead to a key part of my paper the Coarea Inequality!

Bounding an "integral" from below by the Hausdorff measure of the domainLet $(X,d)$ be an arbitrary metric space and $E \subset X$ also arbitrary. Fix $s \in (0,\infty)$. Is it true that for any $ \delta > 0 $ and any collection of pairs $\{(A_i,a_i)\}_{i \in \

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