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Returned 96 matches (100 formulae, 97 docs)
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Found 49419779 tuple postings, 13120194 formulae, 4618385 documents
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A
(
u
,
v
)
=
-
1
3
log
(
f
(
u
)
+
g
(
v
)
)
+
1
2
log
(
f
′
(
u
)
g
′
(
v
)
)
+
1
3
(
f
(
u
)
+
g
(
v
)
)
2
+
a
Doc 1
0.2008, -32.0000, 10.0000, 0.2008
testing/NTCIR/xhtml5/1/hep-th0004206/hep-th0004206_1_33.xhtml
∂
∂
λ
j
F
n
(
λ
,
z
)
=
∂
f
λ
n
∂
λ
j
(
h
λ
(
z
)
)
+
(
f
λ
n
)
′
(
h
λ
(
z
)
)
∂
∂
λ
j
h
λ
(
z
)
-
∂
∂
λ
j
h
λ
(
z
)
.
Doc 2
0.1949, -41.0000, 9.0000, 0.1949
testing/NTCIR/xhtml5/4/math0606294/math0606294_1_133.xhtml
p
1
(
x
,
ξ
)
=
-
i
2
∂
g
j
k
∂
x
j
(
x
)
(
ξ
k
-
A
k
(
x
)
)
-
i
2
g
j
k
(
x
)
∂
A
k
∂
x
j
(
x
)
.
Doc 3
0.1826, -32.0000, 9.0000, 0.1826
testing/NTCIR/xhtml5/9/1212.1982/1212.1982_1_48.xhtml
Ω
n
(
x
,
ϵ
)
=
δ
J
n
δ
u
(
x
)
≡
∂
P
n
∂
u
(
x
)
-
∂
∂
x
∂
P
n
∂
u
x
(
x
)
+
∂
2
∂
x
2
∂
P
n
∂
u
x
x
(
x
)
-
…
Doc 4
0.1725, -43.0000, 7.0000, 0.1725
testing/NTCIR/xhtml5/10/solv-int9904004/solv-int9904004_1_32.xhtml
ϕ
(
t
,
σ
)
=
f
0
(
t
)
+
1
2
(
f
1
(
t
)
+
u
(
t
,
σ
)
)
σ
2
Doc 5
0.1668, -14.0000, 7.0000, 0.1668
testing/NTCIR/xhtml5/3/math0402201/math0402201_1_120.xhtml
G
2
(
t
0
,
y
,
B
1
+
u
t
0
(
1
)
(
y
)
)
-
∂
∂
t
1
(
B
1
+
u
t
0
(
1
)
(
y
)
)
-
∂
y
∂
t
2
Doc 6
0.1634, -28.0000, 6.0000, 0.1634
testing/NTCIR/xhtml5/6/0911.4990/0911.4990_1_91.xhtml
f
t
′
(
φ
s
,
t
(
z
)
)
∂
φ
s
,
t
∂
t
(
z
)
+
∂
f
t
∂
t
(
φ
s
,
t
(
z
)
)
Doc 7
0.1606, -22.0000, 7.0000, 0.1606
testing/NTCIR/xhtml5/6/0902.3116/0902.3116_1_201.xhtml
G
v
(
ψ
)
(
z
1
,
z
2
)
=
-
1
□
δ
8
(
z
1
-
z
2
)
+
1
4
□
(
ψ
(
z
1
)
D
¯
2
□
δ
8
(
z
1
-
z
2
)
)
+
O
(
Ψ
¯
)
Doc 8
0.1582, -37.0000, 8.0000, 0.1582
testing/NTCIR/xhtml5/10/hep-th9501047/hep-th9501047_1_4.xhtml
V
(
z
|
f
,
g
)
=
∫
d
u
u
A
(
∂
f
(
u
)
∂
u
A
g
(
u
)
-
σ
(
f
,
g
)
∂
g
(
u
)
∂
u
A
f
(
u
)
)
.
Doc 9
0.1527, -31.0000, 7.0000, 0.1527
testing/NTCIR/xhtml5/3/hep-th0401023/hep-th0401023_1_32.xhtml
G
(
s
,
t
)
=
f
(
𝐱
)
+
∂
f
∂
z
i
(
𝐱
)
s
+
∂
f
∂
z
j
(
𝐱
)
t
+
∂
2
f
∂
z
i
∂
z
j
(
𝐱
)
s
t
.
Doc 10
0.1527, -33.0000, 5.0000, 0.1527
testing/NTCIR/xhtml5/8/1210.3231/1210.3231_1_189.xhtml
∂
∂
x
(
f
(
x
)
+
g
(
y
)
+
h
(
z
)
)
2
=
2
(
F
1
(
x
)
-
H
2
(
z
)
)
,
Doc 11
0.1466, -19.0000, 8.0000, 0.1466
testing/NTCIR/xhtml5/2/math-ph0205032/math-ph0205032_1_23.xhtml
X
2
=
f
3
(
z
2
)
∂
∂
z
3
,
X
1
=
g
1
(
z
1
)
∂
∂
z
1
+
∂
∂
z
2
+
g
3
(
z
1
,
z
2
)
∂
∂
z
3
,
Doc 12
0.1440, -36.0000, 4.0000, 0.1440
testing/NTCIR/xhtml5/6/0910.0658/0910.0658_1_148.xhtml
T
=
N
4
π
∫
∫
d
σ
d
x
v
(
σ
,
σ
)
𝒢
s
(
x
)
{
∂
u
(
σ
)
∂
σ
(
-
2
i
x
2
)
+
∂
u
(
σ
)
∂
σ
(
-
i
6
)
+
Doc 13
0.1440, -38.0000, 6.0000, 0.1440
testing/NTCIR/xhtml5/10/hep-th9705119/hep-th9705119_1_6.xhtml
u
ε
(
x
)
=
g
(
x
)
-
1
π
∫
∂
Ω
a
ln
|
x
-
z
|
∂
u
ε
(
z
)
∂
ν
d
σ
(
z
)
+
∫
∂
Ω
a
R
∂
Ω
(
x
,
z
)
∂
u
ε
(
z
)
∂
ν
d
σ
(
z
)
+
C
ε
.
Doc 14
0.1440, -49.0000, 6.0000, 0.2593
testing/NTCIR/xhtml5/6/1003.2275/1003.2275_1_20.xhtml
(
f
(
z
1
)
-
f
(
z
2
)
)
μ
o
d
(
z
1
,
z
2
)
=
(
f
(
z
1
)
+
c
)
g
(
z
1
)
+
(
f
(
z
2
)
+
c
)
g
(
z
2
)
-
1
2
Q
(
f
(
z
1
)
)
-
1
2
Q
(
f
(
z
2
)
)
,
Doc 15
0.1440, -52.0000, 6.0000, 0.1440
testing/NTCIR/xhtml5/8/1204.1299/1204.1299_1_31.xhtml
μ
∂
2
∂
t
2
u
(
x
p
,
t
)
=
Δ
2
m
(
h
)
u
(
x
p
,
t
)
,
Δ
2
m
(
h
)
u
p
=
-
∂
V
∂
u
p
,
Doc 16
0.1386, -33.0000, 7.0000, 0.1386
testing/NTCIR/xhtml5/9/1307.7688/1307.7688_1_27.xhtml
∂
f
t
(
z
)
∂
t
=
-
∂
f
t
(
z
)
∂
z
G
(
z
,
t
)
.
Doc 17
0.1325, -14.0000, 5.0000, 0.1325
testing/NTCIR/xhtml5/8/1112.2937/1112.2937_1_41.xhtml
Doc 18
0.1325, -14.0000, 5.0000, 0.1325
testing/NTCIR/xhtml5/8/1112.2937/1112.2937_1_3.xhtml
g
t
(
x
)
=
u
t
(
x
)
∂
v
t
(
x
)
∂
x
-
∂
u
t
(
x
)
∂
x
v
t
(
x
)
,
Doc 19
0.1325, -21.0000, 5.0000, 0.1325
testing/NTCIR/xhtml5/9/1303.3381/1303.3381_1_47.xhtml
V
𝕊
2
(
λ
1
,
λ
2
)
=
1
2
(
g
11
(
∂
W
∂
λ
1
)
2
+
g
22
(
∂
W
∂
λ
2
)
2
)
Doc 20
0.1297, -24.0000, 6.0000, 0.1297
testing/NTCIR/xhtml5/7/1009.0617/1009.0617_1_37.xhtml
1
2
∂
∂
t
(
u
0
(
x
+
t
)
+
u
0
(
x
-
t
)
)
+
1
2
(
u
1
(
x
+
t
)
-
u
1
(
x
-
t
)
)
Doc 21
0.1297, -28.0000, 6.0000, 0.1297
testing/NTCIR/xhtml5/4/math-ph0701058/math-ph0701058_1_60.xhtml
r
(
z
0
,
z
1
)
=
-
1
2
ln
(
f
′′
(
z
1
)
+
2
z
0
)
+
g
(
z
1
)
,
g
∈
C
2
(
ℝ
,
ℝ
)
.
Doc 22
0.1244, -28.0000, 6.0000, 0.1244
testing/NTCIR/xhtml5/10/solv-int9510001/solv-int9510001_1_19.xhtml
Doc 23
0.1244, -28.0000, 6.0000, 0.1244
testing/NTCIR/xhtml5/10/solv-int9510001/solv-int9510001_1_15.xhtml
=
-
∑
j
=
1
𝑛
∫
Ω
a
j
(
x
,
∂
r
s
∂
x
)
∂
∂
x
j
{
g
¯
(
x
)
[
u
s
(
x
)
-
h
s
(
x
)
+
g
s
(
x
)
]
}
d
x
,
Doc 24
0.1244, -38.0000, 5.0000, 0.1244
testing/NTCIR/xhtml5/2/math0010232/math0010232_1_95.xhtml
∂
∂
a
H
(
a
,
z
)
=
-
1
2
f
(
z
)
¯
f
′
(
a
)
1
-
f
(
z
)
¯
f
(
a
)
-
1
2
∂
∂
a
log
f
(
z
)
-
f
(
a
)
z
-
a
.
Doc 25
0.1244, -43.0000, 7.0000, 0.1244
testing/NTCIR/xhtml5/2/math0205106/math0205106_1_63.xhtml
-
∂
∂
x
(
A
(
x
,
y
)
u
x
)
-
∂
∂
y
(
A
(
x
,
y
)
u
y
)
+
B
(
x
,
y
)
u
x
=
F
,
Doc 26
0.1239, -25.0000, 7.0000, 0.1239
testing/NTCIR/xhtml5/1/0812.2769/0812.2769_1_43.xhtml
=
-
∂
H
∂
g
=
-
∂
∂
g
[
1
2
(
f
2
+
g
2
)
-
g
(
p
+
g
2
)
+
f
(
s
-
f
2
)
]
Doc 27
0.1239, -27.0000, 6.0000, 0.3444
testing/NTCIR/xhtml5/4/math-ph0506004/math-ph0506004_1_13.xhtml
V
(
q
,
t
)
=
v
+
i
u
=
1
μ
(
t
)
∂
S
∂
q
-
i
ℏ
2
μ
(
t
)
∂
∂
q
(
ln
ρ
)
,
Doc 28
0.1198, -26.0000, 7.0000, 0.1198
testing/NTCIR/xhtml5/1/1005.5059/1005.5059_1_11.xhtml
(
f
(
z
1
)
-
f
(
z
2
)
)
μ
e
v
(
z
1
,
z
2
)
=
g
(
z
1
)
+
g
(
z
2
)
-
1
2
Q
(
f
(
z
1
)
)
-
1
2
Q
(
f
(
z
2
)
)
,
Doc 29
0.1198, -39.0000, 4.0000, 0.1198
testing/NTCIR/xhtml5/8/1204.1299/1204.1299_1_27.xhtml
+
μ
2
∂
∂
z
2
(
k
0
(
𝐫
+
𝐦
,
z
2
)
[
z
1
-
1
(
∂
∂
z
2
)
2
δ
(
z
2
z
1
)
]
)
Doc 30
0.1185, -29.0000, 3.0000, 0.2089
testing/NTCIR/xhtml5/2/math0201313/math0201313_1_196.xhtml
∂
f
t
(
z
)
∂
t
=
-
∂
f
t
(
z
)
∂
z
z
1
+
k
(
t
)
z
1
-
k
(
t
)
z
,
t
∈
[
0
,
-
ln
A
)
.
Doc 31
0.1185, -33.0000, 5.0000, 0.1185
testing/NTCIR/xhtml5/8/1112.2937/1112.2937_1_64.xhtml
g
(
x
)
∂
∂
x
g
x
(
x
,
w
)
-
g
x
(
x
,
w
)
∂
∂
x
g
(
x
)
,
Doc 32
0.1153, -18.0000, 7.0000, 0.1153
testing/NTCIR/xhtml5/4/hep-th0510107/hep-th0510107_1_51.xhtml
u
ε
(
x
)
=
g
(
x
)
+
∫
∂
Ω
a
N
∂
Ω
(
x
,
z
)
∂
u
ε
(
z
)
∂
ν
z
d
σ
(
z
)
+
C
ε
,
x
∈
Ω
,
Doc 14
0.1440, -49.0000, 6.0000, 0.2593
testing/NTCIR/xhtml5/6/1003.2275/1003.2275_1_20.xhtml
-
∂
∂
x
(
a
u
x
)
-
∂
∂
y
(
a
u
y
)
-
∂
∂
z
(
a
u
z
)
+
d
u
x
+
e
u
y
+
f
u
z
=
0
,
Doc 33
0.1153, -32.0000, 6.0000, 0.1153
testing/NTCIR/xhtml5/1/0812.2769/0812.2769_1_48.xhtml
(
n
μ
o
d
(
z
1
,
z
2
)
+
g
(
z
2
)
-
g
(
z
1
)
+
1
2
b
2
(
f
(
z
1
)
-
f
(
z
2
)
)
)
(
ϕ
(
z
1
)
ψ
(
z
2
)
-
ψ
(
z
1
)
ϕ
(
z
2
)
)
Doc 34
0.1153, -45.0000, 7.0000, 0.1153
testing/NTCIR/xhtml5/8/1204.1299/1204.1299_1_32.xhtml
∂
D
^
∂
t
=
-
∂
D
^
∂
z
1
V
1
-
∂
D
^
∂
z
2
V
2
-
(
z
1
v
1
+
z
2
v
2
+
v
3
)
+
k
(
g
1
(
D
^
f
1
+
g
1
-
D
^
V
1
)
+
g
2
(
D
^
f
2
+
g
2
-
D
^
V
2
)
)
Doc 35
0.1153, -65.0000, 8.0000, 0.1153
testing/NTCIR/xhtml5/7/1103.2539/1103.2539_1_22.xhtml
∂
D
^
∂
t
=
-
∂
D
^
∂
z
1
(
f
1
+
Γ
HS
g
1
)
-
∂
D
^
∂
z
2
(
f
2
+
Γ
HS
g
2
)
-
(
z
1
v
1
+
z
2
v
2
+
v
3
)
+
k
(
1
-
D
^
Γ
HS
)
.
Doc 36
0.1121, -51.0000, 7.0000, 0.1121
testing/NTCIR/xhtml5/7/1103.2539/1103.2539_1_35.xhtml
g
(
u
0
(
0
)
)
=
∂
u
0
+
∂
x
(
0
)
-
∂
u
0
-
∂
x
(
0
)
,
Doc 37
0.1102, -18.0000, 4.0000, 0.1102
testing/NTCIR/xhtml5/3/math0312276/math0312276_1_13.xhtml
Δ
K
=
1
f
K
2
(
χ
)
∂
∂
χ
(
f
K
2
(
χ
)
∂
∂
χ
)
+
1
f
K
2
(
χ
)
Δ
,
Doc 38
0.1102, -25.0000, 5.0000, 0.1102
testing/NTCIR/xhtml5/9/1304.5645/1304.5645_1_26.xhtml
u
i
(
x
)
=
0
g
i
i
(
x
)
∂
u
i
∂
x
j
(
x
)
+
g
j
j
(
x
)
∂
u
j
∂
x
i
(
x
)
=
0
,
Doc 39
0.1102, -29.0000, 4.0000, 0.1102
testing/NTCIR/xhtml5/10/dg-ga9411011/dg-ga9411011_1_46.xhtml
N
2
G
2
c
(
z
1
,
z
2
)
=
∂
2
∂
z
1
∂
z
2
Log
[
u
(
z
1
)
-
u
(
z
2
)
z
1
-
z
2
]
Doc 41
0.1102, -29.0000, 3.0000, 0.1102
testing/NTCIR/xhtml5/10/hep-th9412230/hep-th9412230_1_10.xhtml
N
2
G
2
c
(
z
1
,
z
2
)
=
∂
2
∂
z
1
∂
z
2
Log
(
u
(
z
1
)
-
u
(
z
2
)
z
1
-
z
2
)
Doc 40
0.1102, -29.0000, 3.0000, 0.1102
testing/NTCIR/xhtml5/10/hep-th9412230/hep-th9412230_1_31.xhtml
=
-
∂
H
∂
f
=
-
∂
∂
f
[
1
2
(
f
2
+
g
2
)
-
g
(
p
+
g
2
)
+
f
(
s
-
f
2
)
]
Doc 27
0.1239, -27.0000, 6.0000, 0.3444
testing/NTCIR/xhtml5/4/math-ph0506004/math-ph0506004_1_13.xhtml
=
∂
H
∂
p
=
∂
∂
p
[
1
2
(
f
2
+
g
2
)
-
g
(
p
+
g
2
)
+
f
(
s
-
f
2
)
]
=
-
g
Doc 27
0.1239, -27.0000, 6.0000, 0.3444
testing/NTCIR/xhtml5/4/math-ph0506004/math-ph0506004_1_13.xhtml
ℳ
(
φ
,
∂
u
¯
δ
∂
δ
δ
)
=
-
φ
t
-
(
A
(
x
)
(
φ
+
∂
u
¯
δ
∂
δ
δ
)
)
x
+
(
B
(
x
)
(
φ
x
+
∂
u
¯
x
δ
∂
δ
δ
)
x
-
∂
u
¯
δ
∂
δ
δ
˙
Doc 42
0.1102, -49.0000, 4.0000, 0.1102
testing/NTCIR/xhtml5/3/math0408227/math0408227_1_105.xhtml
(
f
⋆
g
)
x
(
y
)
=
f
x
(
y
)
g
x
(
y
)
+
ϵ
∑
i
,
j
=
1
d
α
x
i
j
(
y
)
∂
f
x
(
y
)
∂
y
i
∂
g
x
(
y
)
∂
y
j
+
⋯
Doc 43
0.1088, -40.0000, 5.0000, 0.1088
testing/NTCIR/xhtml5/2/math0012228/math0012228_1_55.xhtml
F
(
z
1
,
z
2
)
=
1
2
(
F
(
z
1
)
+
F
(
z
2
)
-
(
z
1
2
-
z
2
2
)
2
)
Doc 44
0.1051, -21.0000, 6.0000, 0.1051
testing/NTCIR/xhtml5/3/nlin0304033/nlin0304033_1_75.xhtml
V
(
ϕ
,
χ
)
=
1
2
(
∂
W
∂
ϕ
)
2
+
1
2
(
∂
W
∂
χ
)
2
-
1
3
W
2
.
Doc 45
0.1051, -24.0000, 4.0000, 0.1051
testing/NTCIR/xhtml5/6/0912.4712/0912.4712_1_33.xhtml
V
(
ϕ
,
χ
)
=
1
8
(
∂
W
∂
ϕ
)
2
+
1
8
(
∂
W
∂
χ
)
2
-
1
3
G
(
5
)
W
2
Doc 46
0.1051, -26.0000, 4.0000, 0.1051
testing/NTCIR/xhtml5/6/0901.3543/0901.3543_1_35.xhtml
f
(
z
0
,
z
1
)
=
e
z
0
(
z
1
g
1
(
z
1
)
+
g
1
(
0
)
)
Doc 47
0.1045, -16.0000, 5.0000, 0.1045
testing/NTCIR/xhtml5/6/0912.3041/0912.3041_1_47.xhtml
m
0
=
ω
u
(
∂
∂
z
1
,
∂
∂
z
¯
1
)
=
u
1
1
¯
(
0
)
+
μ
.
Doc 48
0.1045, -20.0000, 4.0000, 0.1045
testing/NTCIR/xhtml5/6/0906.3548/0906.3548_1_92.xhtml
g
t
(
x
)
=
-
∂
f
t
(
x
)
∂
x
,
h
t
(
x
)
=
∂
2
f
t
(
x
)
∂
x
2
Doc 49
0.1045, -22.0000, 5.0000, 0.1045
testing/NTCIR/xhtml5/9/1303.3381/1303.3381_1_41.xhtml
f
x
y
(
q
)
=
∂
l
i
∂
x
(
q
)
l
y
(
q
)
+
∂
l
i
∂
y
l
x
(
q
)
.
Doc 50
0.1045, -22.0000, 4.0000, 0.1045
testing/NTCIR/xhtml5/9/1306.3483/1306.3483_1_32.xhtml
(
∂
1
,
1
f
2
)
(
z
1
,
z
2
)
=
f
1
(
z
1
)
-
f
1
(
z
2
)
z
1
-
z
2
.
Doc 51
0.1045, -24.0000, 5.0000, 0.1045
testing/NTCIR/xhtml5/3/math0306172/math0306172_1_133.xhtml
m
0
=
χ
u
(
∂
∂
z
1
,
∂
∂
z
¯
1
)
=
u
1
1
¯
(
0
)
+
χ
1
1
¯
(
0
)
.
Doc 52
0.1045, -25.0000, 4.0000, 0.1045
testing/NTCIR/xhtml5/6/0910.1851/0910.1851_1_86.xhtml
-
g
l
k
(
∂
∂
x
i
(
f
h
j
l
)
+
∂
∂
x
j
(
f
h
i
l
)
-
∂
∂
x
l
(
f
h
i
j
)
)
.
Doc 53
0.1045, -30.0000, 6.0000, 0.1045
testing/NTCIR/xhtml5/4/math0611906/math0611906_1_15.xhtml
q
=
-
∂
θ
¯
∂
y
(
∂
w
∂
x
+
∂
u
∂
z
)
+
∂
(
v
+
f
x
,
θ
′
)
∂
(
x
,
z
)
.
Doc 54
0.1045, -30.0000, 5.0000, 0.1045
testing/NTCIR/xhtml5/8/1211.2067/1211.2067_1_26.xhtml
c
i
j
(
x
)
=
-
1
2
[
∂
f
i
∂
u
j
(
x
,
U
(
x
)
)
+
∂
f
j
∂
u
i
(
x
,
U
(
x
)
)
]
Doc 55
0.1045, -30.0000, 3.0000, 0.1045
testing/NTCIR/xhtml5/8/1206.3926/1206.3926_1_105.xhtml
∂
P
n
(
λ
;
z
)
∂
λ
=
∂
k
n
(
λ
)
∂
λ
(
z
-
z
0
)
n
+
∂
Q
n
-
1
(
λ
,
z
0
;
z
)
∂
λ
.
Doc 56
0.1045, -34.0000, 6.0000, 0.1045
testing/NTCIR/xhtml5/6/0901.2639/0901.2639_1_19.xhtml
N
f
(
z
1
,
z
2
)
=
ln
(
f
′
(
0
)
z
1
-
z
2
(
1
(
f
(
0
)
-
f
(
z
2
-
1
)
)
-
1
(
f
(
0
)
-
f
(
z
1
-
1
)
)
)
)
,
Doc 57
0.1045, -42.0000, 4.0000, 0.1045
testing/NTCIR/xhtml5/2/hep-th0211283/hep-th0211283_1_16.xhtml
∑
j
=
1
𝑛
∫
Ω
[
a
j
(
x
,
∂
u
0
∂
x
)
-
f
j
(
x
)
]
∂
g
(
x
)
∂
x
j
d
x
-
∫
Ω
c
(
x
,
f
(
x
)
-
u
0
(
x
)
)
g
(
x
)
d
x
=
0
Doc 58
0.1045, -48.0000, 3.0000, 0.2090
testing/NTCIR/xhtml5/2/math0010232/math0010232_1_106.xhtml
∑
j
=
1
𝑛
∫
Ω
[
a
j
(
x
,
∂
u
0
∂
x
)
-
f
j
(
x
)
]
∂
g
(
x
)
∂
x
j
d
x
-
∫
Ω
c
(
x
,
f
(
x
)
-
u
0
(
x
)
)
g
(
x
)
d
x
⩾
0.
Doc 58
0.1045, -48.0000, 3.0000, 0.2090
testing/NTCIR/xhtml5/2/math0010232/math0010232_1_106.xhtml
∫
d
θ
∂
f
(
θ
)
∂
θ
g
(
θ
)
=
-
(
-
1
)
ε
(
f
)
∫
d
θ
f
(
θ
)
∂
g
(
θ
)
∂
θ
,
Doc 59
0.0960, -27.0000, 6.0000, 0.0960
testing/NTCIR/xhtml5/2/hep-th0202192/hep-th0202192_1_13.xhtml
+
g
ℓ
(
u
x
)
-
g
ℓ
(
v
x
)
u
x
-
v
x
f
ℓ
(
u
)
+
f
ℓ
(
v
)
2
(
u
x
-
v
x
)
Doc 60
0.0960, -27.0000, 4.0000, 0.0960
testing/NTCIR/xhtml5/7/1009.3151/1009.3151_1_26.xhtml
(
u
u
t
)
t
-
u
t
2
-
∂
∂
x
i
(
u
a
i
j
u
x
j
)
+
u
x
i
a
i
j
(
x
)
u
x
j
+
u
6
Doc 61
0.0960, -30.0000, 5.0000, 0.1777
testing/NTCIR/xhtml5/6/1003.1820/1003.1820_1_4.xhtml
+
1
2
(
f
′
(
r
)
g
(
r
)
+
f
(
r
)
g
′
(
r
)
)
∂
S
1
∂
r
=
0
,
Doc 62
0.0904, -22.0000, 5.0000, 0.1808
testing/NTCIR/xhtml5/5/0805.2220/0805.2220_1_13.xhtml
+
1
2
(
f
′
(
r
)
g
(
r
)
+
f
(
r
)
g
′
(
r
)
)
∂
S
0
∂
r
=
0
,
Doc 62
0.0904, -22.0000, 5.0000, 0.1808
testing/NTCIR/xhtml5/5/0805.2220/0805.2220_1_13.xhtml
=
ρ
a
¨
(
t
)
+
(
∂
∂
x
i
g
(
z
)
)
f
(
z
)
+
g
(
z
)
∂
∂
x
i
f
(
z
)
Doc 63
0.0904, -24.0000, 5.0000, 0.1808
testing/NTCIR/xhtml5/7/1005.3651/1005.3651_1_22.xhtml
F
(
λ
,
t
)
=
L
(
t
,
u
(
t
)
+
λ
v
(
t
)
,
∂
u
∂
t
(
t
)
+
λ
∂
v
∂
t
(
t
)
)
Doc 64
0.0904, -28.0000, 3.0000, 0.0904
testing/NTCIR/xhtml5/4/math0510438/math0510438_1_15.xhtml
+
μ
2
(
∂
∂
z
2
)
2
(
k
0
(
𝐫
+
𝐦
,
z
2
)
[
z
1
-
1
∂
∂
z
2
δ
(
z
2
z
1
)
]
)
Doc 30
0.1185, -29.0000, 3.0000, 0.2089
testing/NTCIR/xhtml5/2/math0201313/math0201313_1_196.xhtml
X
1
=
g
1
(
z
1
)
∂
∂
z
1
+
g
2
(
z
1
)
∂
∂
z
2
+
g
3
(
z
1
,
z
2
)
∂
∂
z
3
,
Doc 65
0.0904, -32.0000, 3.0000, 0.0904
testing/NTCIR/xhtml5/6/0910.0658/0910.0658_1_114.xhtml
[
f
,
g
]
(
z
)
=
(
-
1
)
ε
A
ϵ
(
f
)
∂
∂
z
A
(
f
(
z
)
ω
A
B
∂
∂
z
B
g
(
z
)
)
-
2
f
Δ
g
(
z
)
,
Doc 66
0.0904, -36.0000, 5.0000, 0.0904
testing/NTCIR/xhtml5/7/1011.5807/1011.5807_1_49.xhtml
b
i
j
e
,
s
(
x
)
=
-
1
2
(
∂
f
i
∂
u
j
(
|
x
|
,
U
(
x
)
)
+
∂
f
i
∂
u
j
(
|
x
|
,
U
σ
e
(
x
)
)
)
Doc 67
0.0904, -38.0000, 3.0000, 0.0904
testing/NTCIR/xhtml5/8/1209.5581/1209.5581_1_86.xhtml
Doc 68
0.0904, -38.0000, 3.0000, 0.0904
testing/NTCIR/xhtml5/8/1209.5581/1209.5581_1_88.xhtml
+
(
∂
∂
x
i
g
(
z
)
)
C
i
∑
j
=
2
m
f
(
z
)
γ
j
+
g
(
z
)
∂
∂
x
i
(
∑
j
=
2
m
f
(
z
)
γ
j
)
+
ρ
F
i
(
t
)
Doc 63
0.0904, -24.0000, 5.0000, 0.1808
testing/NTCIR/xhtml5/7/1005.3651/1005.3651_1_22.xhtml
ρ
(
1
|
2
)
(
z
1
,
z
2
)
=
(
z
2
∂
∂
z
2
+
1
2
)
ρ
(
1
|
1
)
(
z
1
)
-
ρ
(
1
|
1
)
(
z
2
)
z
1
-
z
2
Doc 69
0.0904, -41.0000, 4.0000, 0.0904
testing/NTCIR/xhtml5/6/0906.3305/0906.3305_1_94.xhtml
u
t
-
u
t
x
x
=
-
3
2
∂
x
(
u
2
)
-
1
2
∂
x
(
u
x
2
)
+
1
2
∂
x
3
(
u
2
)
Doc 70
0.0901, -28.0000, 7.0000, 0.0901
testing/NTCIR/xhtml5/5/0803.0261/0803.0261_1_12.xhtml
𝒜
4
(
0
,
0
)
=
0
,
∂
𝒜
4
∂
Ψ
x
=
c
2
(
ρ
¯
+
)
-
u
¯
+
2
2
u
¯
+
(
x
0
)
,
∂
𝒜
4
∂
Ψ
=
-
a
′
u
¯
-
2
a
(
x
0
)
.
Doc 71
0.0901, -47.0000, 3.0000, 0.0901
testing/NTCIR/xhtml5/7/1107.5856/1107.5856_1_20.xhtml
∂
u
∂
t
+
∑
k
A
k
(
x
)
∂
u
∂
x
k
+
B
(
x
)
u
=
0
,
u
(
0
,
x
)
=
u
0
(
x
)
,
Doc 72
0.0862, -29.0000, 5.0000, 0.0862
testing/NTCIR/xhtml5/3/math0407210/math0407210_1_5.xhtml
W
∂
S
[
f
,
g
]
=
∫
∂
S
(
f
(
t
)
∂
g
∂
n
(
t
)
-
∂
f
∂
n
(
t
)
g
(
t
)
)
d
σ
(
t
)
,
Doc 73
0.0862, -30.0000, 4.0000, 0.0862
testing/NTCIR/xhtml5/10/math9906021/math9906021_1_29.xhtml
∂
u
x
∂
t
=
1
2
{
u
x
(
x
)
,
H
-
2
}
2
=
-
1
2
(
u
x
)
2
-
u
u
x
x
-
1
2
ρ
2
∂
ρ
∂
t
=
1
2
{
ρ
(
x
)
,
H
-
2
}
2
=
-
(
u
ρ
)
x
Doc 74
0.0862, -56.0000, 3.0000, 0.0862
testing/NTCIR/xhtml5/4/nlin0507062/nlin0507062_1_38.xhtml
g
x
x
(
u
h
)
+
g
x
x
′
(
u
h
)
(
u
-
u
h
)
+
…
,
Doc 75
0.0817, -15.0000, 5.0000, 0.0817
testing/NTCIR/xhtml5/4/hep-th0605191/hep-th0605191_1_30.xhtml
∂
x
u
N
(
x
,
t
)
=
u
j
+
1
(
t
)
-
u
j
(
t
)
h
.
Doc 76
0.0817, -16.0000, 3.0000, 0.0817
testing/NTCIR/xhtml5/4/math0701150/math0701150_1_77.xhtml
∂
ϕ
∂
z
k
(
z
)
+
ϕ
(
z
)
Φ
(
z
)
∂
Φ
∂
z
k
(
z
)
Doc 77
0.0817, -17.0000, 5.0000, 0.0817
testing/NTCIR/xhtml5/7/1011.1650/1011.1650_1_11.xhtml
=
∂
α
∂
ζ
(
0
,
p
)
∂
V
∂
p
(
y
)
-
∂
V
∂
x
(
y
)
+
p
.
Doc 78
0.0817, -21.0000, 6.0000, 0.0817
testing/NTCIR/xhtml5/7/1007.0199/1007.0199_1_35.xhtml
cos
(
v
(
z
)
)
∂
v
∂
z
1
(
z
)
+
sin
(
v
(
z
)
)
∂
v
∂
z
2
(
z
)
=
0
,
Doc 79
0.0817, -23.0000, 5.0000, 0.0817
testing/NTCIR/xhtml5/6/0912.0832/0912.0832_1_41.xhtml
∂
∂
t
(
u
u
t
)
-
∂
∂
x
i
(
u
a
i
j
u
x
j
)
+
|
∇
g
u
|
g
2
+
u
6
-
u
t
2
.
Doc 61
0.0960, -30.0000, 5.0000, 0.1777
testing/NTCIR/xhtml5/6/1003.1820/1003.1820_1_4.xhtml
ς
m
(
g
s
(
z
)
,
g
s
(
z
)
¯
)
=
ς
m
(
z
,
z
¯
)
∂
g
s
(
z
)
∂
z
+
∂
g
s
(
z
)
∂
q
m
.
Doc 80
0.0817, -33.0000, 3.0000, 0.0817
testing/NTCIR/xhtml5/8/1211.3280/1211.3280_1_15.xhtml
(
z
1
(
f
,
g
x
)
w
z
2
a
z
3
)
+
L
g
¯
g
(
(
z
1
(
f
¯
X
)
z
2
a
z
3
)
-
(
z
1
(
f
¯
X
)
z
2
a
z
3
)
)
Doc 81
0.0817, -37.0000, 2.0000, 0.0817
testing/NTCIR/xhtml5/7/1009.0196/1009.0196_1_80.xhtml
Δ
Re
u
1
(
z
)
=
(
d
d
J
c
z
1
)
y
(
z
)
(
∂
u
∂
x
(
z
)
,
J
∂
u
∂
x
(
z
)
)
.
Doc 82
0.0777, -26.0000, 4.0000, 0.0777
testing/NTCIR/xhtml5/3/math0310474/math0310474_1_154.xhtml
d
d
τ
(
∂
L
∂
q
˙
j
)
-
∂
L
∂
q
j
=
f
j
i
e
(
τ
)
+
f
j
c
e
(
τ
)
+
f
j
d
e
(
τ
,
𝒒
e
)
Doc 83
0.0777, -34.0000, 3.0000, 0.0777
testing/NTCIR/xhtml5/3/math0410286/math0410286_1_49.xhtml
(
-
∂
ρ
∂
z
2
(
a
)
,
∂
ρ
∂
z
1
(
a
)
)
Doc 84
0.0763, -13.0000, 4.0000, 0.0763
testing/NTCIR/xhtml5/6/0910.5331/0910.5331_1_133.xhtml
Doc 85
0.0763, -13.0000, 4.0000, 0.0763
testing/NTCIR/xhtml5/7/1009.2414/1009.2414_1_55.xhtml
∂
u
0
∂
η
(
x
)
=
u
0
(
x
)
∂
g
∂
η
(
x
,
0
)
Doc 86
0.0763, -16.0000, 3.0000, 0.0763
testing/NTCIR/xhtml5/6/0902.4531/0902.4531_1_53.xhtml
Doc 87
0.0763, -16.0000, 3.0000, 0.0763
testing/NTCIR/xhtml5/6/0902.4531/0902.4531_1_55.xhtml
∂
u
∂
z
1
(
z
)
+
u
(
z
)
∂
u
∂
z
2
(
z
)
=
0
,
Doc 88
0.0763, -17.0000, 3.0000, 0.0763
testing/NTCIR/xhtml5/6/0912.0832/0912.0832_1_31.xhtml
-
(
∂
f
l
Cas
∂
V
)
β
=
-
1
4
π
r
2
(
∂
f
l
Cas
(
r
)
∂
r
)
β
,
Doc 89
0.0763, -24.0000, 3.0000, 0.0763
testing/NTCIR/xhtml5/10/gr-qc9710100/gr-qc9710100_1_6.xhtml
β
(
2
u
u
x
2
-
u
2
u
x
x
)
+
β
γ
u
x
(
∂
-
1
u
)
+
γ
2
2
(
∂
-
2
u
)
2
-
u
4
2
]
x
.
Doc 90
0.0763, -37.0000, 4.0000, 0.0763
testing/NTCIR/xhtml5/4/math-ph0606063/math-ph0606063_1_5.xhtml
D
H
2
f
(
z
)
=
(
N
+
𝟏
)
-
1
(
∂
f
∂
z
1
(
z
)
…
,
∂
f
∂
z
d
(
z
)
)
=
(
N
+
𝟏
)
-
1
∇
f
(
z
)
Doc 91
0.0763, -37.0000, 3.0000, 0.0763
testing/NTCIR/xhtml5/3/math0502388/math0502388_1_144.xhtml
∂
∂
z
¯
2
(
∂
u
1
∂
z
1
+
∂
u
2
∂
z
2
)
=
∂
∂
z
1
(
∂
u
1
∂
z
¯
2
-
∂
u
2
∂
z
¯
1
)
+
f
2
.
Doc 92
0.0763, -44.0000, 4.0000, 0.0763
testing/NTCIR/xhtml5/2/math0112065/math0112065_1_135.xhtml
-
∂
(
D
(
x
,
y
)
u
x
)
∂
x
-
∂
(
D
(
x
,
y
)
u
y
)
∂
y
+
a
u
x
+
b
u
y
=
1
,
Doc 93
0.0713, -30.0000, 5.0000, 0.0713
testing/NTCIR/xhtml5/1/0812.2769/0812.2769_1_35.xhtml
R
(
1
)
=
R
+
u
y
∂
∂
u
x
-
u
x
∂
∂
u
y
,
Doc 94
0.0672, -16.0000, 4.0000, 0.0672
testing/NTCIR/xhtml5/5/math0703698/math0703698_1_16.xhtml
∂
2
v
1
∂
x
2
=
u
¨
1
(
∂
g
∂
x
)
2
+
u
˙
1
(
∂
2
g
∂
x
2
)
Doc 96
0.0672, -25.0000, 3.0000, 0.0672
testing/NTCIR/xhtml5/1/math0606723/math0606723_1_19.xhtml
∂
2
v
1
∂
y
2
=
u
¨
1
(
∂
g
∂
y
)
2
+
u
˙
1
(
∂
2
g
∂
y
2
)
Doc 95
0.0672, -25.0000, 3.0000, 0.0672
testing/NTCIR/xhtml5/1/math0606723/math0606723_1_21.xhtml
-
u
(
∂
∂
u
x
x
A
2
)
u
x
u
t
x
+
⋯
-
(
∂
∂
u
x
A
5
)
u
t
x
=
0
,
Doc 97
0.0622, -28.0000, 3.0000, 0.0622
testing/NTCIR/xhtml5/5/0803.0387/0803.0387_1_9.xhtml