Question

Q : Let $f : \mathbb Z\to \mathbb Z$ such that, for all $x,y\in\mathbb Z:$ $f(f(x) − y) = f(y) − f(f(x)).$ Show $f$ is bounded.

score 138 · Answer 1 · 2026-03-29 16:00:45

138

Views

Q : Let $f : \mathbb Z\to \mathbb Z$ such that, for all $x,y\in\mathbb Z:$ $f(f(x) − y) = f(y) − f(f(x)).$ Show $f$ is bounded.

Published on 29 Mar 2026 - 16:00

score 54 · Answer 2 · 2021-12-25 14:10:44

54

Views

If $g(x)=\frac1{1-2\sin^2x}$ and $f(x)=\sin 2x$ , what is the period of $\frac{f(x)}{g(x)}$?

Published on 25 Dec 2021 - 14:10

score 78 · Answer 3 · 2021-12-26 04:16:59

78

Views

Does the periodic and $C^1$ class $f$ satisfy Hölder condition for all $\alpha>0$?

Published on 26 Dec 2021 - 4:16

score 373 · Answer 4 · 2021-12-30 14:53:26

373

Views

Prove tha if $f:I\rightarrow\Bbb R$ is a periodic function then $\int_{x}^{x+T}f(t)\,dt=\int_0^T f(t)\,dt$ for any $x\in I$.

Published on 30 Dec 2021 - 14:53

score 114 · Answer 5 · 2026-03-30 22:13:36

114

Views

Log periodic power Law data-fiting

Published on 30 Mar 2026 - 22:13

score 50 · Answer 6 · 2022-01-03 14:30:04

50

Views

Can you approximate $\cos(x)$ on $\mathbb{R}$ in the space of periodic sawtooth functions?

Published on 03 Jan 2022 - 14:30

score 118 · Answer 7 · 2026-03-28 20:53:49

118

Views

Solving for Floquet multipliers: solving over multiple periods

Published on 28 Mar 2026 - 20:53

score 87 · Answer 8 · 2026-04-02 07:33:33

87

Views

Lipschitz continuity of $f(x)=|x|$ on $[-1,1]$ with period $2.$

Published on 02 Apr 2026 - 7:33

score 188 · Answer 9 · 2026-04-02 07:40:45

188

Views

If $f$ is periodic and $C^1$ class, then Lipschitz continuous.

Published on 02 Apr 2026 - 7:40

score 111 · Answer 10 · 2022-01-13 16:09:50

111

Views

Pendulum with Dirac Comb excitation

Published on 13 Jan 2022 - 16:09

score 48 · Answer 11 · 2026-03-30 07:05:19

48

Views

Finding a periodic function with this fundamental cycle

Published on 30 Mar 2026 - 7:05

score 39 · Answer 12 · 2022-01-17 09:04:09

39

Views

Finding family of functions satisfying equation

Published on 17 Jan 2022 - 9:04

score 38 · Answer 13 · 2022-01-18 16:07:20

38

Views

Intuition of $\left<f-a_0,f-a_0\right> =\left<f+a_0,f-a_0\right>$

Published on 18 Jan 2022 - 16:07

score 31 · Answer 14 · 2022-01-21 09:21:26

31

Views

[Sinusoidal Function Period]: demonstrate period of $f(x)=\sin(k\,x)$

Published on 21 Jan 2022 - 9:21

score 50 · Answer 15 · 2022-01-30 20:19:43

50

Views

Does the equality $\int _{[0,1]^n+a}f(x)d\lambda (x)=\int_{[0,1]^n}f(x)d\lambda (x)$ holds for all $a\in\mathbb{R}^n$ if $f$ is $1$-periodic?

Published on 30 Jan 2022 - 20:19

List Question

Q : Let $f : \mathbb Z\to \mathbb Z$ such that, for all $x,y\in\mathbb Z:$ $f(f(x) − y) = f(y) − f(f(x)).$ Show $f$ is bounded.

If $g(x)=\frac1{1-2\sin^2x}$ and $f(x)=\sin 2x$ , what is the period of $\frac{f(x)}{g(x)}$?

Does the periodic and $C^1$ class $f$ satisfy Hölder condition for all $\alpha>0$?

Prove tha if $f:I\rightarrow\Bbb R$ is a periodic function then $\int_{x}^{x+T}f(t)\,dt=\int_0^T f(t)\,dt$ for any $x\in I$.

Log periodic power Law data-fiting

Can you approximate $\cos(x)$ on $\mathbb{R}$ in the space of periodic sawtooth functions?

Solving for Floquet multipliers: solving over multiple periods

Lipschitz continuity of $f(x)=|x|$ on $[-1,1]$ with period $2.$

If $f$ is periodic and $C^1$ class, then Lipschitz continuous.

Pendulum with Dirac Comb excitation

Finding a periodic function with this fundamental cycle

Finding family of functions satisfying equation

Intuition of $\left<f-a_0,f-a_0\right> =\left<f+a_0,f-a_0\right>$

[Sinusoidal Function Period]: demonstrate period of $f(x)=\sin(k\,x)$

Does the equality $\int _{[0,1]^n+a}f(x)d\lambda (x)=\int_{[0,1]^n}f(x)d\lambda (x)$ holds for all $a\in\mathbb{R}^n$ if $f$ is $1$-periodic?

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