Question

Find a function $\Phi$ such that $ \Phi(x)^{T}\Phi(y)=\exp(-\|x-y\|^2/(2\sigma^2))$

score 109 · Answer 1 · 2015-07-20 14:00:07

109

Views

Find a function $\Phi$ such that $ \Phi(x)^{T}\Phi(y)=\exp(-\|x-y\|^2/(2\sigma^2))$

Published on 20 Jul 2015 - 14:00

score 167 · Answer 2 · 2015-07-20 16:16:35

167

Views

Solve the functional equation $ q \, \frac{f(x+1)}{f(x)}=\frac{h(x+1)}{h(x)}. $

Published on 20 Jul 2015 - 16:16

score 674 · Answer 3 · 2015-07-20 19:35:29

674

Views

If $h(x)=f(g(f(x)))$ is bijective, what do we know about $f,g$?

Published on 20 Jul 2015 - 19:35

score 873 · Answer 4 · 2015-07-21 06:19:23

873

Views

Is a function $f:\mathbb R\to\mathbb R$ such that $f(x+y)=f(x)+f(y)$ always continuous?

Published on 21 Jul 2015 - 6:19

score 970 · Answer 5 · 2015-07-21 16:42:50

970

Views

Substitution with functional equations

Published on 21 Jul 2015 - 16:42

score 63 · Answer 6 · 2015-07-23 01:09:26

63

Views

A smooth function satisfying these functional constraints

Published on 23 Jul 2015 - 1:09

score 150 · Answer 7 · 2026-03-27 23:48:09

150

Views

Maximize $J[f] = \int_\mathbb{R} f(x)\log f(x)\,dx$ over smooth surjections $f : \mathbb{R}\to (0, \alpha)$ subject to $\int_\mathbb{R} f(x)\,dx = 1$.

Published on 27 Mar 2026 - 23:48

score 381 · Answer 8 · 2015-07-25 20:09:45

381

Views

Finding a function $h$ that satisfies $h \left ( \frac{x}{x^2+h(x)} \right )=1$

Published on 25 Jul 2015 - 20:09

score 1.8k · Answer 9 · 2015-07-26 08:04:12

1.8k

Views

given $2f(x) + f(1-x) = x^2$ find $f(-5)$

Published on 26 Jul 2015 - 8:04

score 467 · Answer 10 · 2015-07-27 09:19:51

467

Views

Find a polynomial from an equality

Published on 27 Jul 2015 - 9:19

score 1k · Answer 11 · 2015-07-27 21:14:09

Determine all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $xf(y)+yf(x)=(x+y)f(x^2+y^2)$ for all $x,y\in\mathbb{N}$ (contest question)

score 155 · Answer 12 · 2015-07-27 23:39:28

155

Views

What is meaning of this question and how to solve it?

Published on 27 Jul 2015 - 23:39

score 130 · Answer 13 · 2026-04-03 09:12:21

130

Views

Prove that $\lim_\limits{x\to 0}{f(x)}=0$

Published on 03 Apr 2026 - 9:12

score 139 · Answer 14 · 2015-07-28 20:30:19

139

Views

Example of a well defined functional integral?

Published on 28 Jul 2015 - 20:30

score 72 · Answer 15 · 2015-07-29 04:53:12

72

Views

A functional equation that is equal to 7x

Published on 29 Jul 2015 - 4:53

List Question

Find a function $\Phi$ such that $ \Phi(x)^{T}\Phi(y)=\exp(-\|x-y\|^2/(2\sigma^2))$

Solve the functional equation $ q \, \frac{f(x+1)}{f(x)}=\frac{h(x+1)}{h(x)}. $

If $h(x)=f(g(f(x)))$ is bijective, what do we know about $f,g$?

Is a function $f:\mathbb R\to\mathbb R$ such that $f(x+y)=f(x)+f(y)$ always continuous?

Substitution with functional equations

A smooth function satisfying these functional constraints

Maximize $J[f] = \int_\mathbb{R} f(x)\log f(x)\,dx$ over smooth surjections $f : \mathbb{R}\to (0, \alpha)$ subject to $\int_\mathbb{R} f(x)\,dx = 1$.

Finding a function $h$ that satisfies $h \left ( \frac{x}{x^2+h(x)} \right )=1$

given $2f(x) + f(1-x) = x^2$ find $f(-5)$

Find a polynomial from an equality

Determine all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $xf(y)+yf(x)=(x+y)f(x^2+y^2)$ for all $x,y\in\mathbb{N}$ (contest question)

What is meaning of this question and how to solve it?

Prove that $\lim_\limits{x\to 0}{f(x)}=0$

Example of a well defined functional integral?

A functional equation that is equal to 7x

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