user avatar
user avatar
user avatar
Yiorgos S. Smyrlis
  • Member for 9 years, 5 months
  • Last seen this week
39 votes
1 answer
3k views

If $\,\lim_{h\to 0}\frac{f(x+h)-f(x-h)}{2h}\,$ exists for every $x$, what does this imply for $f$?

34 votes
3 answers
1k views

Convergence of a series with repeated sines

29 votes
0 answers
539 views

The sequence $\,a_n=\lfloor \mathrm{e}^n\rfloor$ contains infinitely many odd and infinitely many even terms

24 votes
3 answers
5k views

$AB=BA$ implies $AB^T=B^TA$ when $A$ is normal

22 votes
6 answers
4k views

A problem V.I. Arnold solved as a primary school student

19 votes
2 answers
699 views

Show that $\int_0^{\pi/3} \big((\sqrt{3}\cos x-\sin x)\sin x\big)^{1/2}\cos x \,dx =\frac{\pi\sqrt{3}}{8\sqrt{2}}. $

18 votes
2 answers
716 views

Finding simply connected open sets between compact ones and general open ones in $\mathbb R^2$.

15 votes
2 answers
257 views

If $\,a_n\searrow 0\,$ and $\,\sum_{n=1}^\infty a_n<\infty,\,$ does this imply that $\,n\log n\, a_n\to 0$?

15 votes
1 answer
594 views

Is it true that $\,(1+\sin n)^{1/n}\to 1$?

13 votes
3 answers
599 views

A problem with 26 distinct positive integers

12 votes
1 answer
521 views

Integer parts of multiples of irrationals

11 votes
1 answer
2k views

Solutions of autonomous ODEs are monotonic

10 votes
1 answer
278 views

A functional relation which is satisfied by $\cos x$ and $\sin x$

10 votes
1 answer
371 views

If $f$ is continuous and $f'(x)\ge 0$, outside of a countable set, then $f$ is increasing

9 votes
0 answers
192 views

Does the series $\sum \frac{\sin p}{p}$, where $p$ prime, converge? [duplicate]

9 votes
3 answers
2k views

For which $s\in\mathbb R$, is $H^s(\mathbb T)$ a Banach algebra?

9 votes
1 answer
322 views

The grey area is equal to the white area

8 votes
2 answers
522 views

Existence of a simple closed curve which is not null-homotopic

8 votes
1 answer
183 views

How to fill up $(0,1)$ with disjoint closed intervals all total measure one

8 votes
4 answers
629 views

Area of a hexagon from the distances of the opposite sides

7 votes
1 answer
608 views

Lebesgue measurable but not Riemann integrable

7 votes
1 answer
236 views

For which values of $n$ the sum $\sum_{k=1}^n k^2$ is a perfect square?

6 votes
1 answer
222 views

Is there a function, continuous on the irrationals, with rational values, nowhere locally constant?

6 votes
1 answer
94 views

Uniqueness is a consequence of a non-vanishing autonomous flux

5 votes
1 answer
783 views

Functional equations leading to sine and cosine

5 votes
3 answers
196 views

Semigroup implies exponential

5 votes
3 answers
147 views

What is the value of the limit $\lim_{a\searrow 0}\sum_{n=1}^\infty\frac{(-1)^{n-1}}{n^{a}}$?

5 votes
1 answer
179 views

Characterisation of convergence of bounded sequences via ultra-filters

4 votes
1 answer
400 views

Odd and even square roots of $z^2-1$

4 votes
0 answers
115 views

Proof of the Three Utilities Problem with Complex Analysis?