Erik Satie

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reputation
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Empress Elisabeth of Austria did maths .

She is famous for this integral :

$$\int_{0}^{\pi}Si(x)Si(x)dx$$

Wich is an unsolved problem .(lol)

Well I like maths at a amateur level and also Monty Python .My god in music is JS Bach played by Glenn Gould.I dislike philosophy .Now...I sleep.

Hard nut :

Let :

$$b=\frac{xp\left(x+y\right)}{x+z},c=\frac{pb\left(v+y\right)}{v+y}$$

Then define :

$$f\left(x,y,z,p\right)=\frac{1}{133+\frac{81p^{3}\left(x+y\right)^{3}}{\left(x+z\right)^{3}}}$$

And :

$$a\left(x,y,z,v,p\right)=2f\left(\frac{\left(x+\frac{x\cdot p\cdot\left(x+y\right)}{x+z}\right)}{2},y,z,p\right)+\frac{\left(\frac{x\cdot p\left(x+y\right)}{x+z}\frac{p\left(v+y\right)}{v+z}\right)^{4}}{133\left(\frac{x\cdot p\left(x+y\right)}{x+z}\frac{p\left(v+y\right)}{v+z}\right)^{3}+81x^{3}}-\frac{\left(\frac{x\cdot p\left(x+y\right)}{x+z}+\frac{x\cdot p\left(x+y\right)}{x+z}\frac{p\left(v+y\right)}{v+z}+x\right)}{214}$$

Then we have for $x,y,z>0$:

$$a(1,x+y+1,1+x+y+z,1+x,1+x+y+z+1)\geq 0$$

Where all the coefficients are positives

Where we have used :

$f\left(x,y,z,p\right)=\frac{1}{133+\frac{81p^{3}\left(x+u\right)^{3}}{\left(x+k\right)^{3}}}$ wich seems to be convex for $0<u\leq k\leq 1$ and $p\geq 1$