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Contests
National and Regional Contests
China Contests
China Team Selection Test
2012 China Team Selection Test
2
find the maximum
find the maximum
Source: 2012 China TST Test 2 p5
March 20, 2012
function
inequalities
vector
inequalities proposed
Problem Statement
Given two integers
m
,
n
m,n
m
,
n
which are greater than
1
1
1
.
r
,
s
r,s
r
,
s
are two given positive real numbers such that
r
<
s
r<s
r
<
s
. For all
a
i
j
≥
0
a_{ij}\ge 0
a
ij
≥
0
which are not all zeroes,find the maximal value of the expression
f
=
(
∑
j
=
1
n
(
∑
i
=
1
m
a
i
j
s
)
r
s
)
1
r
(
∑
i
=
1
m
)
∑
j
=
1
n
a
i
j
r
)
s
r
)
1
s
.
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}}}.
f
=
(
∑
i
=
1
m
)
∑
j
=
1
n
a
ij
r
)
r
s
)
s
1
(
∑
j
=
1
n
(
∑
i
=
1
m
a
ij
s
)
s
r
)
r
1
.
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