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Mar 24, 2016 at 10:08 history edited Fedor Petrov CC BY-SA 3.0
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Mar 24, 2016 at 9:48 vote accept Ludwig
Mar 24, 2016 at 3:07 comment added Suvrit Very nice proof! (minor point: seems like the very first inequality has a minor typo in the location of $(Su_i,u_i)$, but it is inconsequential...)
Mar 24, 2016 at 0:28 history edited Fedor Petrov CC BY-SA 3.0
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Mar 23, 2016 at 19:12 comment added Fedor Petrov Yes, only the last step changes: for numbers $c_i=(T_i,\sum T_j)$ we may find positive numbers $\mu_i$ such that $\sum \mu_i=1$ and $\sum 1/c_i=1/\sum \mu_i^2 c_i$.
Mar 23, 2016 at 18:41 comment added jjcale Can you also prove the last inequality of the question ?
Mar 23, 2016 at 12:02 history edited Fedor Petrov CC BY-SA 3.0
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Mar 23, 2016 at 11:47 history answered Fedor Petrov CC BY-SA 3.0