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Guy Fsone's user avatar
Guy Fsone's user avatar
Guy Fsone
  • Member for 7 years, 8 months
  • Last seen this week
43 votes
5 answers
3k views

Proof only by transformation that : $ \int_0^\infty \cos(x^2) dx = \int_0^\infty \sin(x^2) dx $

23 votes
2 answers
2k views

A Gift Problem for the Year 2018 [duplicate]

19 votes
2 answers
4k views

Need good reference or a proof on regularity of solution to Neumann problem

13 votes
1 answer
835 views

How to prove that: $19.999<e^\pi-\pi<20$?

11 votes
1 answer
2k views

Proving that: $9.9998\lt \frac{\pi^9}{e^8}\lt 10$?

11 votes
1 answer
2k views

Let $A\in M_n(\Bbb R)$ prove that, $\|A^n\|\le \frac{n}{\ln 2}\|A\|^{n-1}$ when $\lambda_i<1.$

11 votes
1 answer
590 views

Trying to compute limit of singular integrals : $L= \lim_{s\to 1}(1-s)\int_{\Omega}\frac{(u(x)-u(y))}{|x-y|^{d+2s}} d y.$

10 votes
1 answer
469 views

How to find: $~\min\limits_{f\in E}(\int_0^1f(x) \,dx)$

10 votes
2 answers
777 views

Proving that, $|f'(x)-f'(y)|\le k|x-y| \implies (f'(x))^2< 2 kf(x) $

10 votes
3 answers
290 views

Existence of a sequence $\{\epsilon_n\}_{n\ge 1}$ such that $\sum\limits_{n=1}^{\infty}\frac{1}{n^{\varepsilon_n}} $ converges

10 votes
1 answer
381 views

On convergence of series of the generalized mean $\sum_{n=1}^{\infty} \left(\frac{a_1^{1/s}+a_2^{1/s}+\cdots +a_n^{1/s}}{n}\right)^s.$

9 votes
2 answers
355 views

computing $A_2=\sum_{k=1}^{n}\frac{1}{(z_k-1)^2} $ and $\sum_{k=1}^n \cot^2\left( \frac{k\pi}{n+1}\right)$

9 votes
2 answers
403 views

Computing a limit of a sum mixed with product.

9 votes
2 answers
777 views

If $M=M^{\perp\perp}$ for every closed subspace $M$ of a pre-Hilbert space then $H$ is complete

8 votes
2 answers
301 views

Example of function satisfying the growth condition: $\phi\big(\theta \frac{s}{t}\big) \leq \frac{\phi(s)}{\phi(t)}$

8 votes
2 answers
171 views

Proving that $\frac{f(b)-f(a)}{b-a}+ \left(\frac{g(b)-g(a)}{b-a}\right)^2\le \max_{t\in [a,b]}\{f'(t)+(g'(t))^2\}$

8 votes
1 answer
253 views

Proving that $\sum_{n=1}^{\infty} \left(\frac{a_1^{1/s}+a_2^{1/s}+\cdots +a_n^{1/s}}{n}\right)^s$ converges when $\sum_{n=1}^{\infty}a_n $ converges

7 votes
3 answers
6k views

How many number with 4 digits, beginning with $1$ and have exactly two identical digits?

7 votes
1 answer
444 views

What is an elegant way to find the third eigenvalue of $A=\left[\begin{smallmatrix} 51&-12 & -21\\ 60 & -40&28\\ 57&-68&1 \end{smallmatrix}\right]$?

6 votes
2 answers
2k views

Hausdorff distance: Prove that if $(E,d)$ is complete then, $(\mathcal{K}(E), \mathcal{H})$ is also complete

6 votes
1 answer
99 views

Among $2n-1$ irrationals there are $x_1,\dots,x_n$ such that for rationals $a_i\ge0$ with $\sum_{i=1}^{n}a_i>0$, $\sum_{i=1}^{n}a_ix_i$ is irrational

6 votes
2 answers
419 views

What is the value of $f(100)$?

6 votes
1 answer
128 views

Proving $\frac{B_1B_2}{A_1A_3}+ \frac{B_2B_3}{A_2A_4}+...+\frac{B_nB_1}{A_nA_2}>1$

6 votes
0 answers
601 views

Comparaison of two version of Fractional sobolev spaces: what do we have $W^{s,p}(\mathbb{R}^{n})=H^{s,p}(\mathbb{R}^{n})$?

6 votes
1 answer
123 views

How to prove that: $\forall a \in \Bbb R,$ $\|f+a\|_p\ge \frac12\|f\|_p$ when $\int_\Omega f(x)dx= 0$

6 votes
0 answers
79 views

Operator norm in Hilbert space, Schur criterion for infnite matrices

5 votes
1 answer
176 views

Computing a limit on the unit sphere: Riemann Lebesgue?

5 votes
1 answer
67 views

On Convolution: Show that $g_a *g_b = g_{\min(a,b)}$

5 votes
1 answer
220 views

Provig that the number $z_n$ of zero element of $A^{-1} $ satisfies $z_n\le n^2-2n$

5 votes
3 answers
296 views

How to prove that: $\lim_{n\to\infty}\frac1{n!}\int_0^ne^{-t}t^n\,dt.=\frac{1}{2}$

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