Question

Empirical Process and Azuma's Inequality

score 160 · Answer 1 · 2026-04-15 22:08:38

160

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Empirical Process and Azuma's Inequality

Published on 15 Apr 2026 - 22:08

score 89 · Answer 2 · 2026-04-15 18:48:07

89

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If $f(a)=f(b)=0$ and $|f''(x)|\le M$ prove $|\int_a^bf(x)\mathrm{d}x| \le \frac{M}{12}(b-a)^3$

Published on 15 Apr 2026 - 18:48

score 168 · Answer 3 · 2026-03-25 01:18:22

168

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Prove that $(a - 1)^3 + (b - 1)^3 + (c - 1)^3 \ge -\dfrac{3}{4}$ where $a+b+c=3$

Published on 25 Mar 2026 - 1:18

score 211 · Answer 4 · 2026-03-25 09:28:16

211

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Prove that $a\sqrt{b^3+1}+b\sqrt{c^3+1}+c\sqrt{a^3+1} \leq 5$

Published on 25 Mar 2026 - 9:28

score 61 · Answer 5 · 2026-04-17 00:33:13

61

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Prove the given inequality $\mid\sqrt{2}-c_{n+1}\mid <\frac{\mid\sqrt{2}-c_{n}\mid}{1+\sqrt{2}}$

Published on 17 Apr 2026 - 0:33

score 96 · Answer 6 · 2026-04-24 22:32:35

96

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Find the number of points in the region $x^{2}+y^{2}\leq4$ satisfying the equation $\tan^4x+\cot^4x+1=3\sin^2y$.

Published on 24 Apr 2026 - 22:32

score 108 · Answer 7 · 2026-04-12 05:39:19

108

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($x,y,z$ are positive real numbers)

Published on 12 Apr 2026 - 5:39

score 157 · Answer 8 · 2026-04-17 02:45:41

157

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Prove that $p_1\log(\frac{1}{p_1})+p_2\log(\frac{1}{p_2})\leq \log2$

Published on 17 Apr 2026 - 2:45

score 111 · Answer 9 · 2026-04-16 00:51:50

111

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Given $a+b+c+d=4$, find the minimum value of $\Sigma_{cyc}\frac{a}{b^3+4}$

Published on 16 Apr 2026 - 0:51

score 128 · Answer 10 · 2026-04-13 09:27:53

128

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How to use Chebyshev's inequality to find a lower bound?

Published on 13 Apr 2026 - 9:27

score 73 · Answer 11 · 2026-04-16 01:07:33

73

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$[a+b]\geq[a]+[b]$ for all a,b belongs to Real number

Published on 16 Apr 2026 - 1:07

score 59 · Answer 12 · 2026-04-15 22:51:56

59

Views

Given four real numbers $a_1<a_2<a_3<a_4$, rearrange them in such an order $a_{i_1}$, $a_{i_2}$, $a_{i_3}$, $a_{i_4}$ that the sum

Published on 15 Apr 2026 - 22:51

score 170 · Answer 13 · 2026-04-10 20:27:19

170

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Proof of an interesting inequality

Published on 10 Apr 2026 - 20:27

score 52 · Answer 14 · 2026-04-17 00:29:26

52

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Prove $\forall x,y \in \mathbb{R} \ $ $x^2+y^2 \geq x^2-y^2$

Published on 17 Apr 2026 - 0:29

score 40 · Answer 15 · 2026-04-12 15:12:46

40

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Why is a < 0 the only solution to the following inequality?

Published on 12 Apr 2026 - 15:12

List Question

Empirical Process and Azuma's Inequality

If $f(a)=f(b)=0$ and $|f''(x)|\le M$ prove $|\int_a^bf(x)\mathrm{d}x| \le \frac{M}{12}(b-a)^3$

Prove that $(a - 1)^3 + (b - 1)^3 + (c - 1)^3 \ge -\dfrac{3}{4}$ where $a+b+c=3$

Prove that $a\sqrt{b^3+1}+b\sqrt{c^3+1}+c\sqrt{a^3+1} \leq 5$

Prove the given inequality $\mid\sqrt{2}-c_{n+1}\mid <\frac{\mid\sqrt{2}-c_{n}\mid}{1+\sqrt{2}}$

Find the number of points in the region $x^{2}+y^{2}\leq4$ satisfying the equation $\tan^4x+\cot^4x+1=3\sin^2y$.

($x,y,z$ are positive real numbers)

Prove that $p_1\log(\frac{1}{p_1})+p_2\log(\frac{1}{p_2})\leq \log2$

Given $a+b+c+d=4$, find the minimum value of $\Sigma_{cyc}\frac{a}{b^3+4}$

How to use Chebyshev's inequality to find a lower bound?

$[a+b]\geq[a]+[b]$ for all a,b belongs to Real number

Given four real numbers $a_1<a_2<a_3<a_4$, rearrange them in such an order $a_{i_1}$, $a_{i_2}$, $a_{i_3}$, $a_{i_4}$ that the sum

Proof of an interesting inequality

Prove $\forall x,y \in \mathbb{R} \ $ $x^2+y^2 \geq x^2-y^2$

Why is a < 0 the only solution to the following inequality?

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