Question

Showing inequality: $pe^{s(1-p)} + (1-p)e^{-sp} \leq e^{s^2 (3/2) p }$

score 161 · Answer 1 · 2026-03-25 22:03:36

161

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Showing inequality: $pe^{s(1-p)} + (1-p)e^{-sp} \leq e^{s^2 (3/2) p }$

Published on 25 Mar 2026 - 22:03

score 48 · Answer 2 · 2026-03-26 03:10:43

48

Views

Inequalities for linear optimization confusion

Published on 26 Mar 2026 - 3:10

score 249 · Answer 3 · 2026-03-29 22:33:57

249

Views

Are positive Vieta's equations sufficient for negative roots?

Published on 29 Mar 2026 - 22:33

score 150 · Answer 4 · 2026-03-29 09:09:54

150

Views

Triangle inequality with the exradii $r_{a}$, $r_{b}$, $r_{c}$, the medians $m_{a}$, $m_{b}$, $m_{c}$

Published on 29 Mar 2026 - 9:09

score 114 · Answer 5 · 2026-03-25 23:42:13

114

Views

Payley-Zygmund Inequality Application $Pr\left(|\sum_{i=1}^m y_i x_i | > \frac 1 2 \sqrt {\sum_{i=1}^m {y_i}^2}\right) \ge K$

Published on 25 Mar 2026 - 23:42

score 95 · Answer 6 · 2026-03-25 22:30:51

95

Views

$ x^{2}- x- 4+ \frac{4\left ( x- 1 \right )^{2}}{\sqrt{3+ 2x-x^{2}}+ x+ 1}> 0 $

Published on 25 Mar 2026 - 22:30

score 49 · Answer 7 · 2026-03-31 21:29:01

49

Views

Algebra integral solutions

Published on 31 Mar 2026 - 21:29

score 153 · Answer 8 · 2026-03-25 06:04:05

153

Views

Markov's inequality, unclear Wikipedia intuition

Published on 25 Mar 2026 - 6:04

score 295 · Answer 9 · 2026-03-25 07:45:50

295

Views

Showing inequality: $pe^{x(1-p)}+(1-p)e^{-xp} \leq e^{x^2(3/4)p}$ for $0 \leq p \leq 1/2, 0 \leq x \leq 1$?

Published on 25 Mar 2026 - 7:45

score 140 · Answer 10 · 2018-03-28 15:22:05

140

Views

Test if a system of linear inequalities has a solution

Published on 28 Mar 2018 - 15:22

score 69 · Answer 11 · 2026-03-25 16:39:17

69

Views

counter example for $\mathbb{E}[\log(x)] <\mathbb{E}[\log(y)]$ when $\mathbb{E}[x]< \mathbb{E}[y]$ and vice versa

Published on 25 Mar 2026 - 16:39

score 116 · Answer 12 · 2026-03-25 22:06:22

116

Views

$\sum_{1}^{n}\left ( a_{i}b_{i} \right )\geq \prod_{1}^{n}\left ( a_{i}^{b_{i}} \right )$

Published on 25 Mar 2026 - 22:06

score 89 · Answer 13 · 2018-03-29 01:42:22

89

Views

Find the maximal number of elements of such subset $S$

Published on 29 Mar 2018 - 1:42

score 385 · Answer 14 · 2026-03-25 20:36:12

385

Views

Proving $\frac{a}{a+ b}+ \frac{b}{b+ c}+ \frac{c}{2c+ 5a}\geq \frac{38}{39}$

Published on 25 Mar 2026 - 20:36

score 75 · Answer 15 · 2026-03-25 05:59:57

75

Views

Banach fixed point theorem without using cauchy criterion

Published on 25 Mar 2026 - 5:59

List Question

Showing inequality: $pe^{s(1-p)} + (1-p)e^{-sp} \leq e^{s^2 (3/2) p }$

Inequalities for linear optimization confusion

Are positive Vieta's equations sufficient for negative roots?

Triangle inequality with the exradii $r_{a}$, $r_{b}$, $r_{c}$, the medians $m_{a}$, $m_{b}$, $m_{c}$

Payley-Zygmund Inequality Application $Pr\left(|\sum_{i=1}^m y_i x_i | > \frac 1 2 \sqrt {\sum_{i=1}^m {y_i}^2}\right) \ge K$

$ x^{2}- x- 4+ \frac{4\left ( x- 1 \right )^{2}}{\sqrt{3+ 2x-x^{2}}+ x+ 1}> 0 $

Algebra integral solutions

Markov's inequality, unclear Wikipedia intuition

Showing inequality: $pe^{x(1-p)}+(1-p)e^{-xp} \leq e^{x^2(3/4)p}$ for $0 \leq p \leq 1/2, 0 \leq x \leq 1$?

Test if a system of linear inequalities has a solution

counter example for $\mathbb{E}[\log(x)] <\mathbb{E}[\log(y)]$ when $\mathbb{E}[x]< \mathbb{E}[y]$ and vice versa

$\sum_{1}^{n}\left ( a_{i}b_{i} \right )\geq \prod_{1}^{n}\left ( a_{i}^{b_{i}} \right )$

Find the maximal number of elements of such subset $S$

Proving $\frac{a}{a+ b}+ \frac{b}{b+ c}+ \frac{c}{2c+ 5a}\geq \frac{38}{39}$

Banach fixed point theorem without using cauchy criterion

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