Question

Cauchy–Schwarz inequality intuition

score 171 · Answer 1 · 2026-03-26 12:53:11

171

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Cauchy–Schwarz inequality intuition

Published on 26 Mar 2026 - 12:53

score 89 · Answer 2 · 2020-06-24 06:46:13

89

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Cauchy-Schwarz applied multiple times with difficulty on second application

Published on 24 Jun 2020 - 6:46

score 58 · Answer 3 · 2026-03-28 14:06:36

58

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$\left(\sum_i a_i\right)^2\ge (n-1)\sum_i a_i^2 + b\implies 2a_i a_j \ge b/(n-1) \quad (\forall i\ne j)$

Published on 28 Mar 2026 - 14:06

score 112 · Answer 4 · 2026-03-27 02:37:43

112

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Prove that $\int |\nabla u||\nabla v|+|u||v|\leq |u|_{H^1}|v|_{H^1}$

Published on 27 Mar 2026 - 2:37

score 242 · Answer 5 · 2026-03-25 22:06:34

242

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Prove that the cyclic sum over $a, b, c > 0$ $ \sum (\frac{a}{a+b})^3 >= \frac{3}{8}$

Published on 25 Mar 2026 - 22:06

score 236 · Answer 6 · 2020-06-25 00:36:06

236

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Rate of convegence of $\frac{E^2[X^n]}{ E[X^{n-1}] E[X^{n+1}]}$ as $n \to \infty$

Published on 25 Jun 2020 - 0:36

score 201 · Answer 7 · 2020-06-25 08:03:05

201

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combination of points in the open unit disk also lie in the unit disk

Published on 25 Jun 2020 - 8:03

score 65 · Answer 8 · 2026-03-28 12:32:46

65

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Prove that $ \sum_{k=0}^{n}\left\lvert x-\frac{k}{n}\right\rvert\binom{n}{k}x^k(1-x)^{n-k} \le \frac{1}{2\sqrt{n}} $

Published on 28 Mar 2026 - 12:32

score 345 · Answer 9 · 2020-06-26 15:11:10

345

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If $ 3a+2b+c=7$ then find minimum value of $ a^2+b^2+c^2$

Published on 26 Jun 2020 - 15:11

score 222 · Answer 10 · 2026-03-29 13:27:49

222

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Quantum-mechanical Schwarz inequality: Proving $\langle \psi \mid \phi \rangle^* \langle \psi \mid \phi \rangle \ge 0$ for 1D case.

Published on 29 Mar 2026 - 13:27

score 199 · Answer 11 · 2026-03-28 17:40:27

199

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For $a,b,c>0$ prove that $abc(a+b+c) \le a^3 b + b^3 c + c^3 a$

Published on 28 Mar 2026 - 17:40

score 54 · Answer 12 · 2020-07-03 23:05:57

54

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Cauchy Schwarz manipulation

Published on 03 Jul 2020 - 23:05

score 1k · Answer 13 · 2020-07-05 19:33:14

1k

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Show that if $f(z)$ is analytic for $|z| \leq R$, $f(0)=0$ and $|f(z)| \leq M$ then $|f(z)| \leq \frac{M|z|}{R}$.

Published on 05 Jul 2020 - 19:33

score 37 · Answer 14 · 2026-03-26 14:35:02

37

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Inequality of $( y_1 \cdot y_2 \cdot \ldots \cdot y_M )\log ( y_1 \cdot y_2 \cdot \ldots \cdot y_M )$?

Published on 26 Mar 2026 - 14:35

score 273 · Answer 15 · 2026-03-27 02:36:05

273

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Prove that $\int_0^1\left|f\left(x\right)\right|^2\text{d}x\le\frac12\int_0^1\left(1-x^2\right)\left|f'\left(x\right)\right|^2\text{d}x$.

Published on 27 Mar 2026 - 2:36

List Question

Cauchy–Schwarz inequality intuition

Cauchy-Schwarz applied multiple times with difficulty on second application

$\left(\sum_i a_i\right)^2\ge (n-1)\sum_i a_i^2 + b\implies 2a_i a_j \ge b/(n-1) \quad (\forall i\ne j)$

Prove that $\int |\nabla u||\nabla v|+|u||v|\leq |u|_{H^1}|v|_{H^1}$

Prove that the cyclic sum over $a, b, c > 0$ $ \sum (\frac{a}{a+b})^3 >= \frac{3}{8}$

Rate of convegence of $\frac{E^2[X^n]}{ E[X^{n-1}] E[X^{n+1}]}$ as $n \to \infty$

combination of points in the open unit disk also lie in the unit disk

Prove that $ \sum_{k=0}^{n}\left\lvert x-\frac{k}{n}\right\rvert\binom{n}{k}x^k(1-x)^{n-k} \le \frac{1}{2\sqrt{n}} $

If $ 3a+2b+c=7$ then find minimum value of $ a^2+b^2+c^2$

Quantum-mechanical Schwarz inequality: Proving $\langle \psi \mid \phi \rangle^* \langle \psi \mid \phi \rangle \ge 0$ for 1D case.

For $a,b,c>0$ prove that $abc(a+b+c) \le a^3 b + b^3 c + c^3 a$

Cauchy Schwarz manipulation

Show that if $f(z)$ is analytic for $|z| \leq R$, $f(0)=0$ and $|f(z)| \leq M$ then $|f(z)| \leq \frac{M|z|}{R}$.

Inequality of $( y_1 \cdot y_2 \cdot \ldots \cdot y_M )\log ( y_1 \cdot y_2 \cdot \ldots \cdot y_M )$?

Prove that $\int_0^1\left|f\left(x\right)\right|^2\text{d}x\le\frac12\int_0^1\left(1-x^2\right)\left|f'\left(x\right)\right|^2\text{d}x$.

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