List questions from mixing-variables

Published on 24 Jun 2023 - 16:11

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$P=\frac{4 a^3+3 b^3+2 c^3-3 b^2 c}{(a+b+c)^3}\ge\frac{4}{25}$

Published on 24 Jun 2023 - 17:29

107

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How to solve this step and are there any tips for this method?

Published on 04 Jul 2023 - 13:32

45

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Can I write an Abel Summation Formula for this?

Published on 13 Jul 2023 - 7:42

146

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Follow-up question on Abel Summation

Published on 13 Jul 2023 - 15:34

114

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For $x+y+z=3,$ prove $\frac{1}{x^2+4}+\frac{1}{y^2+4}+\frac{1}{z^2+4}\le \frac{3}{5}.$

Published on 09 Aug 2023 - 10:13

73

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Prove $f(a,b,c)\le f\left(\frac{a+b}{2},\frac{a+b}{2},c\right)$

Published on 06 Nov 2023 - 1:24

30

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Power law distribution of Mixed Poisson random variable

Published on 09 Feb 2024 - 15:33

88

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If $a+b+c=x+y+z=ax+by+cz=0$, then find value of $\frac{a^2}{a^2+b^2+c^2}+\frac{x^2}{x^2+y^2+z^2}$

Published on 23 Mar 2024 - 13:40

176

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Find the minimize value of $P=\sum_{cyc}\frac{1}{\sqrt{a^2+b^2}}$

Published on 06 Aug 2017 - 16:45

190

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Find all the natural solutions of (a+b+c)a-3bc=0

Published on 28 Sep 2017 - 20:54

367

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Gaussian mixture: zero correlation implies independence?

Published on 03 Nov 2017 - 13:06

162

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Example of a distribution that is ergodic but not $\phi$-mixing?

Published on 18 Dec 2017 - 15:08

48

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Defining variables for optimization problem

Published on 23 Dec 2017 - 12:57

40

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3D graph out of two 2D graphs

Published on 02 Jan 2018 - 3:44

List Question

Prove that: $\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}-\frac{2}{abc}\geq1$

$P=\frac{4 a^3+3 b^3+2 c^3-3 b^2 c}{(a+b+c)^3}\ge\frac{4}{25}$

How to solve this step and are there any tips for this method?

Can I write an Abel Summation Formula for this?

Follow-up question on Abel Summation

For $x+y+z=3,$ prove $\frac{1}{x^2+4}+\frac{1}{y^2+4}+\frac{1}{z^2+4}\le \frac{3}{5}.$

Prove $f(a,b,c)\le f\left(\frac{a+b}{2},\frac{a+b}{2},c\right)$

Power law distribution of Mixed Poisson random variable

If $a+b+c=x+y+z=ax+by+cz=0$, then find value of $\frac{a^2}{a^2+b^2+c^2}+\frac{x^2}{x^2+y^2+z^2}$

Find the minimize value of $P=\sum_{cyc}\frac{1}{\sqrt{a^2+b^2}}$

Find all the natural solutions of (a+b+c)a-3bc=0

Gaussian mixture: zero correlation implies independence?

Example of a distribution that is ergodic but not $\phi$-mixing?

Defining variables for optimization problem

3D graph out of two 2D graphs

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