Question

Upper bound for the integral $\int_{\mathbb R} \frac{dx}{(1+x^2)^a}$ when $a\in (1/2, 1)$

score 53 · Answer 1 · 2023-11-28 00:25:18

53

Views

Upper bound for the integral $\int_{\mathbb R} \frac{dx}{(1+x^2)^a}$ when $a\in (1/2, 1)$

Published on 28 Nov 2023 - 0:25

score 111 · Answer 2 · 2023-11-29 21:41:28

111

Views

Prove that if $f: \mathbb{R} \to \mathbb{R}$ is convex and bounded from above, then $f$ is constant.

Published on 29 Nov 2023 - 21:41

score 50 · Answer 3 · 2026-02-23 21:56:59

50

Views

Bounded second derivative also bounds the function

Published on 23 Feb 2026 - 21:56

score 30 · Answer 4 · 2023-11-30 08:18:51

30

Views

Use $\Pr(|Y-\mathbb EY| \le a) > 1-\delta$ to simplify $\Pr(X \le Y \mid Y = y) > 1-\delta$.

Published on 30 Nov 2023 - 8:18

score 88 · Answer 5 · 2026-04-02 07:59:28

88

Views

Prove $r^3 = 2$ where $r = \sup\, E$

Published on 02 Apr 2026 - 7:59

score 38 · Answer 6 · 2026-03-30 13:24:59

38

Views

Properites of Lattices imply eachother.

Published on 30 Mar 2026 - 13:24

score 23 · Answer 7 · 2026-02-23 06:24:22

23

Views

The lower bound of Frobenius norm of matrices product.

Published on 23 Feb 2026 - 6:24

score 36 · Answer 8 · 2026-03-30 21:11:26

36

Views

Bound from below the probability to go beyond a certain point in a zero mean random walk

Published on 30 Mar 2026 - 21:11

score 94 · Answer 9 · 2023-12-04 21:00:21

94

Views

If $\sum_{i=1}^n x_i \ge a$, then what can we know about $\sum_{i=1}^n \frac{1}{x_i}$?

Published on 04 Dec 2023 - 21:00

score 84 · Answer 10 · 2026-03-26 09:16:27

84

Views

Inequalities for the solution of $x = (x-a) e^{x+a}$.

Published on 26 Mar 2026 - 9:16

score 207 · Answer 11 · 2026-03-25 23:52:22

207

Views

Control $\int_0^\infty |\psi(x)|^2 dx$ by $\int_0^\infty \int_0^\infty K(x+y)\psi(x) \psi(y) dxdy$

Published on 25 Mar 2026 - 23:52

score 122 · Answer 12 · 2026-03-29 04:10:56

122

Views

Show that $\left\{\frac{m}{mn+1}: m,n\in\Bbb N*\right\}$ is bounded

Published on 29 Mar 2026 - 4:10

score 96 · Answer 13 · 2023-12-18 16:56:27

96

Views

Application of the fundamental theorem of Calculus?

Published on 18 Dec 2023 - 16:56

score 121 · Answer 14 · 2026-03-30 10:11:40

121

Views

A good upper bound for the infinite product $\prod_{i=0}^\infty (1+p/2^i)$

Published on 30 Mar 2026 - 10:11

score 24 · Answer 15 · 2026-03-30 23:21:20

24

Views

Showing upper and lower Bayesian method of survival function

Published on 30 Mar 2026 - 23:21

List Question

Upper bound for the integral $\int_{\mathbb R} \frac{dx}{(1+x^2)^a}$ when $a\in (1/2, 1)$

Prove that if $f: \mathbb{R} \to \mathbb{R}$ is convex and bounded from above, then $f$ is constant.

Bounded second derivative also bounds the function

Use $\Pr(|Y-\mathbb EY| \le a) > 1-\delta$ to simplify $\Pr(X \le Y \mid Y = y) > 1-\delta$.

Prove $r^3 = 2$ where $r = \sup\, E$

Properites of Lattices imply eachother.

The lower bound of Frobenius norm of matrices product.

Bound from below the probability to go beyond a certain point in a zero mean random walk

If $\sum_{i=1}^n x_i \ge a$, then what can we know about $\sum_{i=1}^n \frac{1}{x_i}$?

Inequalities for the solution of $x = (x-a) e^{x+a}$.

Control $\int_0^\infty |\psi(x)|^2 dx$ by $\int_0^\infty \int_0^\infty K(x+y)\psi(x) \psi(y) dxdy$

Show that $\left\{\frac{m}{mn+1}: m,n\in\Bbb N*\right\}$ is bounded

Application of the fundamental theorem of Calculus?

A good upper bound for the infinite product $\prod_{i=0}^\infty (1+p/2^i)$

Showing upper and lower Bayesian method of survival function

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