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Omni-MATH / Given two integers m,n which are greater than 1. r,s are two given positive real numbers such that r<s. For all a_(ij)≥0 which are not all zeroes,find the maximal value of the expr…

Problem

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problem

Given two integers

m,n

which are greater than

1

r,s

are two given positive real numbers such that

r<s

. For all

a_{ij}\ge 0

which are not all zeroes,find the maximal value of the expression

f=\frac{(\sum_{j=1}^{n}(\sum_{i=1}^{m}a_{ij}^s)^{\frac{r}{s}})^{\frac{1}{r}}}{(\sum_{i=1}^{m})\sum_{j=1}^{n}a_{ij}^r)^{\frac{s}{r}})^{\frac{1}{s}}}.

Plain-text mathematical notation (without MathML)

Given two integers m,n which are greater than 1. r,s are two given positive real numbers such that r<s. For all a_(ij)≥0 which are not all zeroes,find the maximal value of the expression
f=((∑_(j=1)^(n)(∑_(i=1)^(m)a_(ij)^(s))^((r)/(s)))^((1)/(r)))/((∑_(i=1)^(m))∑_(j=1)^(n)a_(ij)^(r))^((s)/(r)))^((1)/(s))).

Original LaTeX notation

Given two integers $m,n$ which are greater than $1$. $r,s$ are two given positive real numbers such that $r<s$. For all $a_{ij}\ge 0$ which are not all zeroes,find the maximal value of the expression
\[f=\frac{(\sum_{j=1}^{n}(\sum_{i=1}^{m}a_{ij}^s)^{\frac{r}{s}})^{\frac{1}{r}}}{(\sum_{i=1}^{m})\sum_{j=1}^{n}a_{ij}^r)^{\frac{s}{r}})^{\frac{1}{s}}}.\]

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task_id: edac7fee-1381-5145-a241-7a733c75f710
task_key: test--edac7fee-1381-5145-a241-7a733c75f710
task_revision_id: 4
config / split: / test

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