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Returned 97 matches (100 formulae, 88 docs)
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Found 153173708 tuple postings, 15155960 formulae, 4965759 documents
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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 1
0.1826, -32.0000, 9.0000, 0.1826
testing/NTCIR/xhtml5/9/1212.1982/1212.1982_1_48.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 2
0.1582, -37.0000, 8.0000, 0.1582
testing/NTCIR/xhtml5/10/hep-th9501047/hep-th9501047_1_4.xhtml
F
(
x
1
,
x
2
)
=
∂
∂
x
1
(
f
(
x
1
-
x
2
)
f
(
x
3
-
x
1
)
)
+
∂
∂
x
2
(
f
(
x
2
-
x
3
)
f
(
x
1
-
x
2
)
)
+
∂
∂
x
3
(
f
(
x
3
-
x
1
)
f
(
x
2
-
x
3
)
)
,
Doc 3
0.1582, -58.0000, 9.0000, 0.1582
testing/NTCIR/xhtml5/2/math-ph0110012/math-ph0110012_1_28.xhtml
f
t
(
x
)
=
u
t
(
x
)
v
t
(
x
)
,
∂
u
t
(
x
)
∂
t
=
∂
2
u
t
(
x
)
∂
x
2
,
∂
v
t
(
x
)
∂
t
=
-
∂
2
v
t
(
x
)
∂
x
2
.
Doc 4
0.1535, -41.0000, 6.0000, 0.2860
testing/NTCIR/xhtml5/9/1303.3381/1303.3381_1_47.xhtml
μ
±
∂
u
1
±
∂
x
2
=
∂
∂
x
1
f
±
(
x
1
)
:=
μ
±
∂
∂
x
1
(
ψ
±
(
x
1
)
∂
u
0
±
∂
x
1
)
,
Doc 5
0.1527, -32.0000, 7.0000, 0.2578
testing/NTCIR/xhtml5/7/1004.0320/1004.0320_1_21.xhtml
ℋ
(
x
→
)
=
-
1
2
g
2
(
∂
∂
A
j
a
(
x
→
)
)
2
+
1
2
g
2
(
B
j
a
(
x
→
)
)
2
,
Doc 6
0.1440, -25.0000, 5.0000, 0.1440
testing/NTCIR/xhtml5/2/hep-th0210204/hep-th0210204_1_23.xhtml
∂
∂
t
(
z
1
-
z
)
=
∂
ℓ
0
∂
η
(
z
1
,
η
1
)
-
∂
ℓ
0
∂
η
(
z
,
η
)
+
∂
V
~
∂
η
(
z
1
,
η
1
)
,
Doc 7
0.1440, -35.0000, 5.0000, 0.1440
testing/NTCIR/xhtml5/6/0912.4939/0912.4939_1_90.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 8
0.1440, -36.0000, 4.0000, 0.1440
testing/NTCIR/xhtml5/6/0910.0658/0910.0658_1_148.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 9
0.1440, -52.0000, 6.0000, 0.1440
testing/NTCIR/xhtml5/8/1204.1299/1204.1299_1_31.xhtml
U
i
(
x
,
y
)
=
∑
k
=
1
n
χ
i
k
(
y
)
∂
u
i
∂
x
k
(
x
)
+
γ
i
(
y
)
(
u
1
(
x
)
-
u
2
(
x
)
)
+
u
~
i
(
x
)
,
i
=
1
,
2
Doc 10
0.1388, -40.0000, 4.0000, 0.1388
testing/NTCIR/xhtml5/5/0710.5222/0710.5222_1_54.xhtml
+
∫
x
[
1
2
Z
0
(
u
x
)
(
∂
t
u
x
)
2
-
1
2
Z
1
(
u
x
)
(
∇
u
x
)
2
-
U
2
(
u
x
)
+
i
ϵ
u
x
2
]
,
Doc 11
0.1386, -34.0000, 4.0000, 0.1386
testing/NTCIR/xhtml5/2/cond-mat0108048/cond-mat0108048_1_21.xhtml
+
c
(
g
,
h
)
b
(
z
)
a
(
z
1
)
w
∂
∂
z
1
(
z
0
-
1
(
z
-
z
1
z
0
)
(
g
,
h
)
δ
(
z
-
z
1
-
z
0
)
)
Doc 12
0.1345, -34.0000, 6.0000, 0.2543
testing/NTCIR/xhtml5/1/math0006104/math0006104_1_67.xhtml
g
t
(
x
)
=
u
t
(
x
)
∂
v
t
(
x
)
∂
x
-
∂
u
t
(
x
)
∂
x
v
t
(
x
)
,
Doc 4
0.1535, -41.0000, 6.0000, 0.2860
testing/NTCIR/xhtml5/9/1303.3381/1303.3381_1_47.xhtml
1
2
∂
∂
t
(
u
0
(
x
+
t
)
+
u
0
(
x
-
t
)
)
+
1
2
(
u
1
(
x
+
t
)
-
u
1
(
x
-
t
)
)
Doc 13
0.1297, -28.0000, 6.0000, 0.1297
testing/NTCIR/xhtml5/4/math-ph0701058/math-ph0701058_1_60.xhtml
1
2
Z
0
(
n
)
(
u
x
)
(
∂
t
u
x
)
2
-
1
2
Z
1
(
n
)
(
u
x
)
(
∇
u
x
)
2
-
U
2
(
n
)
(
u
x
)
Doc 14
0.1244, -30.0000, 3.0000, 0.2397
testing/NTCIR/xhtml5/2/cond-mat0108048/cond-mat0108048_1_51.xhtml
g
(
1
)
(
x
)
∂
f
(
1
)
∂
x
i
(
x
)
f
(
2
)
g
(
2
)
=
g
(
1
)
(
x
)
∂
f
(
1
)
∂
x
i
(
x
)
g
(
2
)
f
(
2
)
Doc 15
0.1244, -33.0000, 6.0000, 0.1244
testing/NTCIR/xhtml5/8/1206.1718/1206.1718_1_71.xhtml
e
(
x
)
=
r
(
x
)
(
∂
u
1
∂
x
1
(
x
)
∂
u
2
∂
x
2
(
x
)
-
∂
u
1
∂
x
2
(
x
)
∂
u
2
∂
x
1
(
x
)
)
+
h
,
Doc 16
0.1244, -38.0000, 6.0000, 0.1244
testing/NTCIR/xhtml5/2/math-ph0212036/math-ph0212036_1_32.xhtml
(
α
=
(
2
,
1
)
,
i
=
1
,
j
=
2
)
:
-
1
3
∂
u
2
∂
x
1
(
x
)
∂
R
1212
∂
x
2
(
x
)
+
g
11
(
x
)
∂
4
u
1
∂
x
1
2
∂
x
2
2
(
x
)
+
Doc 17
0.1244, -49.0000, 6.0000, 0.3110
testing/NTCIR/xhtml5/10/dg-ga9411011/dg-ga9411011_1_61.xhtml
L
D
(
f
)
g
(
x
)
=
(
-
1
)
d
-
1
∑
j
=
1
d
∫
z
ˇ
j
≥
x
ˇ
j
∂
∂
x
j
[
a
j
j
(
x
j
)
∂
d
g
(
z
)
∂
z
1
⋯
∂
z
d
(
z
ˇ
j
,
x
j
)
]
d
z
ˇ
j
Doc 18
0.1244, -53.0000, 5.0000, 0.1244
testing/NTCIR/xhtml5/9/1304.1688/1304.1688_1_59.xhtml
=
(
∂
∂
x
)
2
-
k
x
(
s
-
1
)
∂
∂
x
-
∂
∂
x
k
x
(
s
-
1
)
+
k
x
(
s
-
1
)
k
x
(
s
-
1
)
Doc 19
0.1198, -35.0000, 8.0000, 0.1198
testing/NTCIR/xhtml5/1/math0004116/math0004116_1_29.xhtml
∂
∂
z
1
X
R
-
a
(
z
1
)
b
(
z
)
w
∂
∂
z
1
(
z
0
-
1
(
z
1
-
z
z
0
)
(
g
,
h
)
δ
(
z
1
-
z
z
0
)
)
Doc 12
0.1345, -34.0000, 6.0000, 0.2543
testing/NTCIR/xhtml5/1/math0006104/math0006104_1_67.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 20
0.1198, -39.0000, 4.0000, 0.1198
testing/NTCIR/xhtml5/8/1204.1299/1204.1299_1_27.xhtml
K
=
(
D
x
v
x
+
v
x
D
x
+
1
2
(
D
z
u
x
y
+
u
x
y
D
z
)
-
1
2
(
D
y
u
x
z
+
u
x
z
D
y
)
-
u
x
x
u
x
x
0
)
Doc 21
0.1198, -41.0000, 6.0000, 0.1198
testing/NTCIR/xhtml5/6/0904.3981/0904.3981_1_21.xhtml
+
μ
2
∂
∂
z
2
(
k
0
(
𝐫
+
𝐦
,
z
2
)
[
z
1
-
1
(
∂
∂
z
2
)
2
δ
(
z
2
z
1
)
]
)
Doc 22
0.1185, -29.0000, 3.0000, 0.2089
testing/NTCIR/xhtml5/2/math0201313/math0201313_1_196.xhtml
∂
r
+
1
u
j
∂
x
α
+
(
i
)
(
x
)
g
j
j
(
x
)
+
∂
r
+
1
u
i
∂
x
α
+
(
j
)
(
x
)
g
i
i
(
x
)
=
0
,
Doc 23
0.1185, -35.0000, 5.0000, 0.1185
testing/NTCIR/xhtml5/10/dg-ga9411011/dg-ga9411011_1_62.xhtml
∂
∂
t
u
(
t
,
x
)
=
-
1
2
∂
2
∂
x
2
Ψ
1
(
u
(
t
,
x
)
)
-
1
2
∂
∂
x
Ψ
2
(
u
(
t
,
x
)
)
Doc 24
0.1153, -34.0000, 5.0000, 0.1153
testing/NTCIR/xhtml5/7/1005.4757/1005.4757_1_42.xhtml
∂
→
∂
→
z
(
f
1
(
z
)
f
2
(
z
)
)
=
∂
→
f
1
(
z
)
∂
→
z
f
2
(
z
)
+
(
-
1
)
𝔞
(
f
1
)
f
1
∂
→
f
2
∂
→
z
,
Doc 25
0.1153, -39.0000, 6.0000, 0.1153
testing/NTCIR/xhtml5/2/hep-th0201074/hep-th0201074_1_23.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 26
0.1153, -45.0000, 7.0000, 0.1153
testing/NTCIR/xhtml5/8/1204.1299/1204.1299_1_32.xhtml
i
X
0
(
n
)
(
u
x
)
∂
t
-
X
1
(
n
)
(
u
x
)
ℰ
+
U
1
(
n
)
(
u
x
)
+
1
2
Y
0
(
n
)
(
u
x
)
(
∂
t
u
x
)
2
+
1
2
Y
1
(
n
)
(
u
x
)
(
∇
u
x
)
2
,
Doc 14
0.1244, -30.0000, 3.0000, 0.2397
testing/NTCIR/xhtml5/2/cond-mat0108048/cond-mat0108048_1_51.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 27
0.1153, -65.0000, 8.0000, 0.1153
testing/NTCIR/xhtml5/7/1103.2539/1103.2539_1_22.xhtml
u
t
1
=
-
u
x
,
u
t
2
=
-
u
u
x
+
(
∂
-
1
v
)
,
u
t
3
=
-
1
2
u
2
u
x
+
u
(
∂
-
1
v
)
+
∂
-
1
(
u
x
x
(
∂
-
2
v
)
)
,
⋮
.
Doc 28
0.1121, -47.0000, 8.0000, 0.1121
testing/NTCIR/xhtml5/3/nlin0401009/nlin0401009_1_8.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 29
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 30
0.1102, -18.0000, 4.0000, 0.1102
testing/NTCIR/xhtml5/3/math0312276/math0312276_1_13.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 31
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 33
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 32
0.1102, -29.0000, 3.0000, 0.1102
testing/NTCIR/xhtml5/10/hep-th9412230/hep-th9412230_1_31.xhtml
-
1
4
π
2
∫
𝒞
1
t
∫
𝒞
2
t
f
(
z
1
)
f
(
z
2
)
∂
2
∂
z
1
∂
z
2
𝒢
n
(
z
1
,
z
2
)
d
z
1
d
z
2
,
Doc 34
0.1102, -37.0000, 4.0000, 0.1102
testing/NTCIR/xhtml5/8/1208.5953/1208.5953_1_71.xhtml
∂
2
f
(
x
1
)
∂
2
x
1
2
+
∂
2
∂
x
1
2
h
(
x
1
,
x
2
,
t
)
=
2
∂
2
f
(
x
1
)
∂
x
1
2
(
1
-
f
(
x
2
)
)
Doc 35
0.1102, -40.0000, 6.0000, 0.1102
testing/NTCIR/xhtml5/9/1307.8252/1307.8252_1_5.xhtml
{
∂
u
∂
t
=
1
2
σ
2
∂
2
u
∂
x
1
2
+
μ
∂
u
∂
x
2
,
u
(
0
,
x
)
=
f
(
x
1
)
+
g
(
x
2
)
.
Doc 36
0.1102, -41.0000, 5.0000, 0.1102
testing/NTCIR/xhtml5/7/1012.0523/1012.0523_1_8.xhtml
Q
=
p
1
2
+
u
2
′
(
x
)
p
2
+
u
3
′
(
x
)
p
3
-
1
2
(
w
1
(
y
)
u
2
′′
(
x
)
+
v
1
(
z
)
u
3
′′
(
x
)
+
u
1
(
x
)
)
,
Doc 37
0.1102, -42.0000, 3.0000, 0.1102
testing/NTCIR/xhtml5/6/0812.2682/0812.2682_1_29.xhtml
v
x
(
x
,
0
)
=
(
a
(
u
-
1
)
x
+
b
(
u
-
1
)
t
)
x
=
-
(
b
(
u
-
1
)
x
t
+
c
(
u
-
1
)
t
t
)
=
-
b
u
x
-
c
u
t
=
f
(
x
)
.
Doc 38
0.1102, -45.0000, 5.0000, 0.1102
testing/NTCIR/xhtml5/2/math0012254/math0012254_1_49.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 39
0.1102, -49.0000, 4.0000, 0.1102
testing/NTCIR/xhtml5/3/math0408227/math0408227_1_105.xhtml
(
α
=
(
2
,
1
)
,
i
=
j
=
2
)
:
-
1
3
∂
u
2
∂
x
1
(
x
)
∂
R
1212
∂
x
1
(
x
)
+
2
g
11
(
x
)
∂
4
u
2
∂
x
1
2
∂
x
2
2
(
x
)
=
0
,
Doc 17
0.1244, -49.0000, 6.0000, 0.3110
testing/NTCIR/xhtml5/10/dg-ga9411011/dg-ga9411011_1_61.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 40
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 41
0.1051, -21.0000, 6.0000, 0.1051
testing/NTCIR/xhtml5/3/nlin0304033/nlin0304033_1_75.xhtml
Φ
1
(
z
0
,
z
1
)
=
e
z
0
⋅
1
z
1
(
z
1
g
1
(
z
1
)
+
g
1
(
0
)
-
g
1
(
0
)
)
=
e
z
0
g
1
(
z
1
)
.
Doc 42
0.1051, -35.0000, 7.0000, 0.1051
testing/NTCIR/xhtml5/6/0912.3041/0912.3041_1_47.xhtml
u
1
+
-
u
1
-
=
g
(
x
1
)
:=
-
ϕ
(
x
1
)
(
∂
u
0
+
∂
x
2
-
∂
u
0
-
∂
x
2
)
=
-
ϕ
(
x
1
)
∂
u
0
+
∂
x
2
(
1
-
μ
+
μ
-
)
,
on
ζ
0
,
formulae-sequence
superscript
subscript
u
1
superscript
subscript
u
1
g
subscript
x
1
assign
ϕ
subscript
x
1
superscript
subscript
u
0
subscript
x
2
superscript
subscript
u
0
subscript
x
2
ϕ
subscript
x
1
superscript
subscript
u
0
subscript
x
2
1
subscript
μ
subscript
μ
on ζ0superscriptζ0\zeta^{0}
u_{1}^{+}-u_{1}^{-}=g(x_{1}):=-\phi(x_{1})\left(\frac{\partial u_{0}^{+}}{% \partial x_{2}}-\frac{\partial u_{0}^{-}}{\partial x_{2}}\right)=-\phi(x_{1})% \frac{\partial u_{0}^{+}}{\partial x_{2}}\left(1-\frac{\mu_{+}}{\mu_{-}}\right% ),\quad\text{on $\zeta^{0}$},
Doc 5
0.1527, -32.0000, 7.0000, 0.2578
testing/NTCIR/xhtml5/7/1004.0320/1004.0320_1_21.xhtml
g
t
(
x
)
=
-
∂
f
t
(
x
)
∂
x
,
h
t
(
x
)
=
∂
2
f
t
(
x
)
∂
x
2
Doc 43
0.1045, -22.0000, 5.0000, 0.1045
testing/NTCIR/xhtml5/9/1303.3381/1303.3381_1_41.xhtml
w
2
(
z
1
,
z
2
)
=
1
x
′
(
z
1
)
x
′
(
z
2
)
1
(
z
1
-
z
2
)
2
-
1
(
x
(
z
1
)
-
x
(
z
2
)
)
2
Doc 44
0.1045, -36.0000, 4.0000, 0.1045
testing/NTCIR/xhtml5/7/1009.1945/1009.1945_1_66.xhtml
x
k
0
(
x
)
+
g
0
(
λ
x
)
k
0
(
x
)
2
(
-
1
-
1
x
2
g
0
(
λ
x
)
k
0
(
x
)
)
≤
τ
x
k
0
(
x
)
(
λ
2
-
1
)
,
Doc 45
0.1045, -40.0000, 4.0000, 0.1045
testing/NTCIR/xhtml5/7/1108.0615/1108.0615_1_117.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 46
0.1045, -42.0000, 4.0000, 0.1045
testing/NTCIR/xhtml5/2/hep-th0211283/hep-th0211283_1_16.xhtml
u
u
t
=
-
∂
∂
x
[
α
u
p
+
2
(
p
+
2
)
+
β
(
u
u
2
x
-
1
2
u
x
2
)
+
γ
(
u
u
4
x
-
u
x
u
3
x
+
1
2
u
2
x
2
)
]
.
Doc 47
0.1045, -48.0000, 6.0000, 0.1045
testing/NTCIR/xhtml5/10/solv-int9710010/solv-int9710010_1_9.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 48
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 48
0.1045, -48.0000, 3.0000, 0.2090
testing/NTCIR/xhtml5/2/math0010232/math0010232_1_106.xhtml
-
1
6
∂
2
V
∂
x
2
+
1
2
(
V
(
x
)
)
2
+
4
3
v
3
f
0
2
(
x
)
+
4
v
f
0
2
(
x
)
V
(
x
)
,
Doc 49
0.1008, -34.0000, 5.0000, 0.1008
testing/NTCIR/xhtml5/8/1207.0942/1207.0942_1_31.xhtml
ω
(
z
^
)
-
ω
(
z
^
′
)
=
1
g
′
(
x
-
1
)
∂
x
h
(
z
-
1
)
-
1
g
′
(
x
-
1
′
)
∂
x
h
(
z
-
1
′
)
+
Doc 50
0.1008, -35.0000, 5.0000, 0.1008
testing/NTCIR/xhtml5/6/0911.2345/0911.2345_1_84.xhtml
∑
i
=
1
d
∂
x
i
(
A
i
(
x
)
T
l
(
u
n
)
(
x
)
)
=
f
n
(
x
)
+
∑
i
=
1
d
∂
x
i
(
A
i
(
x
)
(
T
l
(
u
n
)
(
x
)
-
u
n
(
x
)
)
)
,
Doc 51
0.1008, -44.0000, 3.0000, 0.1008
testing/NTCIR/xhtml5/6/0907.1373/0907.1373_1_43.xhtml
1
2
(
1
-
x
1
2
)
∂
2
V
x
1
∂
x
1
2
-
(
n
+
1
+
1
2
)
∂
V
x
1
∂
x
1
=
e
-
(
n
+
1
2
)
t
∂
∂
t
e
(
n
+
1
2
)
t
V
x
1
,
Doc 52
0.1008, -53.0000, 6.0000, 0.1008
testing/NTCIR/xhtml5/9/1303.0457/1303.0457_1_42.xhtml
c
32
=
-
u
∂
x
3
(
∂
X
∂
u
x
x
)
-
1
2
∂
X
∂
u
x
x
u
x
x
x
-
1
2
∂
x
2
(
∂
X
∂
u
x
x
)
u
x
Doc 53
0.0964, -37.0000, 5.0000, 0.1899
testing/NTCIR/xhtml5/2/nlin0108015/nlin0108015_1_288.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 54
0.0960, -27.0000, 4.0000, 0.0960
testing/NTCIR/xhtml5/7/1009.3151/1009.3151_1_26.xhtml
X
1
(
z
,
v
(
z
)
)
∂
v
∂
z
1
(
z
)
+
X
2
(
z
,
v
(
z
)
)
∂
v
∂
z
2
(
z
)
=
X
3
(
z
,
v
(
z
)
)
,
z
=
(
z
1
,
z
2
)
,
Doc 55
0.0960, -44.0000, 3.0000, 0.0960
testing/NTCIR/xhtml5/6/0912.0832/0912.0832_1_31.xhtml
L
(
f
,
n
)
g
(
x
)
=
1
2
(
g
(
x
+
f
(
x
)
+
1
n
)
+
g
(
x
+
f
(
x
)
-
1
n
)
)
-
g
(
x
)
-
f
(
x
)
g
′
(
x
)
1
n
+
f
(
x
)
2
Doc 56
0.0960, -51.0000, 6.0000, 0.0960
testing/NTCIR/xhtml5/4/math0511402/math0511402_1_86.xhtml
H
(
x
,
λ
)
=
(
a
1
(
x
)
+
∑
i
=
1
k
λ
i
∂
f
i
∂
x
1
(
x
)
,
…
,
a
n
(
x
)
+
∑
i
=
1
k
λ
i
∂
f
i
∂
x
n
(
x
)
,
f
1
(
x
)
,
…
,
f
k
(
x
)
)
.
Doc 57
0.0960, -57.0000, 4.0000, 0.0960
testing/NTCIR/xhtml5/6/0903.2137/0903.2137_1_15.xhtml
c
21
=
u
∂
x
2
(
∂
X
∂
u
x
)
-
1
2
∂
X
∂
u
x
u
x
x
+
1
2
∂
x
(
∂
X
∂
u
x
)
u
x
Doc 53
0.0964, -37.0000, 5.0000, 0.1899
testing/NTCIR/xhtml5/2/nlin0108015/nlin0108015_1_288.xhtml
-
∂
V
(
u
1
)
∂
u
1
-
∂
W
(
u
2
-
u
1
)
∂
u
1
+
A
sin
(
ω
t
)
+
ξ
1
(
t
)
,
Doc 58
0.0904, -28.0000, 3.0000, 0.1808
testing/NTCIR/xhtml5/3/cond-mat0410320/cond-mat0410320_1_13.xhtml
-
∂
V
(
u
2
)
∂
u
2
-
∂
W
(
u
2
-
u
1
)
∂
u
2
+
A
sin
(
ω
t
)
+
ξ
2
(
t
)
,
Doc 58
0.0904, -28.0000, 3.0000, 0.1808
testing/NTCIR/xhtml5/3/cond-mat0410320/cond-mat0410320_1_13.xhtml
+
μ
2
(
∂
∂
z
2
)
2
(
k
0
(
𝐫
+
𝐦
,
z
2
)
[
z
1
-
1
∂
∂
z
2
δ
(
z
2
z
1
)
]
)
Doc 22
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 59
0.0904, -32.0000, 3.0000, 0.0904
testing/NTCIR/xhtml5/6/0910.0658/0910.0658_1_114.xhtml
G
(
z
1
,
z
2
)
=
G
(
z
1
-
z
2
)
=
-
1
(
z
1
-
z
2
)
2
+
κ
2
4
1
sinh
2
κ
(
z
1
-
z
2
)
2
Doc 60
0.0904, -37.0000, 4.0000, 0.0904
testing/NTCIR/xhtml5/5/0804.0198/0804.0198_1_10.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 61
0.0904, -41.0000, 5.0000, 0.0904
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 62
0.0904, -41.0000, 4.0000, 0.0904
testing/NTCIR/xhtml5/6/0906.3305/0906.3305_1_94.xhtml
S
(
g
)
|
g
(
ξ
,
x
)
=
Exp
(
ξ
ω
(
x
)
)
=
-
1
6
ξ
-
2
(
∂
x
3
F
∂
x
F
-
3
2
(
∂
x
2
F
∂
x
F
)
2
)
+
⋯
Doc 63
0.0904, -42.0000, 3.0000, 0.0904
testing/NTCIR/xhtml5/9/hep-th9207048/hep-th9207048_1_39.xhtml
u
(
x
,
t
)
=
1
4
π
t
∫
S
t
(
x
)
(
v
0
(
x
′
)
+
1
t
u
0
(
x
′
)
+
∇
u
0
(
x
′
)
⋅
n
x
(
x
′
)
)
d
S
(
x
′
)
,
Doc 64
0.0904, -43.0000, 3.0000, 0.0904
testing/NTCIR/xhtml5/4/math-ph0508044/math-ph0508044_1_72.xhtml
e
(
z
1
-
z
)
∂
∂
x
1
e
(
z
2
-
z
)
∂
∂
x
2
Sing
x
1
,
x
2
(
Y
-
(
Y
-
(
u
,
x
1
-
x
2
)
v
,
x
2
+
z
)
e
z
∂
w
)
Doc 65
0.0904, -45.0000, 3.0000, 0.0904
testing/NTCIR/xhtml5/2/math0209310/math0209310_1_98.xhtml
v
t
=
1
2
(
v
u
x
-
u
v
x
)
-
A
k
-
1
[
v
x
A
k
(
u
)
+
u
x
A
k
(
v
)
+
1
2
v
A
k
(
u
x
)
+
1
2
u
A
k
(
v
x
)
]
,
Doc 66
0.0904, -47.0000, 3.0000, 0.0904
testing/NTCIR/xhtml5/3/math-ph0305013/math-ph0305013_1_31.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 67
0.0901, -28.0000, 7.0000, 0.0901
testing/NTCIR/xhtml5/5/0803.0261/0803.0261_1_12.xhtml
{
u
(
x
1
)
,
v
(
x
2
)
}
=
∂
∂
x
1
(
(
u
v
)
(
x
1
)
)
x
1
-
1
δ
(
x
1
x
2
)
+
(
u
v
+
v
u
)
(
x
1
)
∂
∂
x
1
x
1
-
1
δ
(
x
1
x
2
)
.
Doc 68
0.0901, -52.0000, 4.0000, 0.0901
testing/NTCIR/xhtml5/5/0708.1551/0708.1551_1_15.xhtml
-
1
2
(
1
+
ϵ
(
z
1
2
-
z
2
2
)
)
∂
∂
z
1
-
ϵ
z
1
z
2
∂
∂
z
2
,
Doc 69
0.0862, -25.0000, 5.0000, 0.1625
testing/NTCIR/xhtml5/3/math-ph0305021/math-ph0305021_1_61.xhtml
H
=
L
1
=
1
f
1
(
x
1
)
+
f
2
(
x
2
)
(
∂
x
1
2
+
∂
x
2
2
+
v
1
(
x
1
)
+
v
2
(
x
2
)
,
Doc 70
0.0862, -33.0000, 4.0000, 0.0862
testing/NTCIR/xhtml5/7/1101.5292/1101.5292_1_8.xhtml
R
1
k
(
t
,
x
)
≜
-
1
2
(
(
u
k
v
k
-
u
x
k
v
x
k
)
x
-
(
u
k
v
x
k
-
u
x
k
v
k
)
)
m
k
-
b
u
x
k
Doc 71
0.0862, -38.0000, 4.0000, 0.0862
testing/NTCIR/xhtml5/9/1306.0417/1306.0417_1_34.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 72
0.0862, -56.0000, 3.0000, 0.0862
testing/NTCIR/xhtml5/4/nlin0507062/nlin0507062_1_38.xhtml
∂
F
∂
λ
(
λ
,
t
)
=
(
∇
x
L
(
t
,
u
(
t
)
+
λ
v
(
t
)
,
∂
u
∂
t
(
t
)
+
λ
∂
v
∂
t
(
t
)
)
,
v
(
t
)
)
Doc 73
0.0817, -39.0000, 4.0000, 0.0817
testing/NTCIR/xhtml5/4/math0510438/math0510438_1_16.xhtml
Δ
Re
u
1
(
z
)
=
(
d
d
J
c
z
1
)
y
(
z
)
(
∂
u
∂
x
(
z
)
,
J
∂
u
∂
x
(
z
)
)
.
Doc 74
0.0777, -26.0000, 4.0000, 0.0777
testing/NTCIR/xhtml5/3/math0310474/math0310474_1_154.xhtml
-
ϵ
z
1
z
2
∂
∂
z
1
-
1
2
(
1
-
ϵ
(
z
1
2
-
z
2
2
)
)
∂
∂
z
2
,
Doc 69
0.0862, -25.0000, 5.0000, 0.1625
testing/NTCIR/xhtml5/3/math-ph0305021/math-ph0305021_1_61.xhtml
S
(
z
1
,
z
)
=
(
z
-
1
z
)
2
(
z
1
-
1
z
1
)
(
z
-
z
1
)
(
z
-
1
z
1
)
Doc 75
0.0763, -29.0000, 4.0000, 0.0763
testing/NTCIR/xhtml5/7/1105.0453/1105.0453_1_43.xhtml
V
1
(
1
)
=
V
1
+
η
x
(
1
)
∂
∂
u
x
+
η
y
(
1
)
∂
∂
u
y
+
η
t
(
1
)
∂
∂
u
t
,
Doc 76
0.0763, -32.0000, 4.0000, 0.0763
testing/NTCIR/xhtml5/5/math0703698/math0703698_1_21.xhtml
(
u
1
,
v
1
,
w
1
)
=
(
p
(
z
f
1
(
x
)
+
x
g
1
(
x
)
)
x
,
x
,
z
f
1
(
x
)
+
x
g
1
(
x
)
)
Doc 77
0.0763, -34.0000, 3.0000, 0.0763
testing/NTCIR/xhtml5/7/1106.4580/1106.4580_1_112.xhtml
Doc 78
0.0763, -34.0000, 3.0000, 0.0763
testing/NTCIR/xhtml5/7/1106.4580/1106.4580_1_133.xhtml
e
(
z
1
-
z
2
)
∂
∂
x
0
e
(
z
1
-
z
0
)
∂
∂
x
1
e
(
z
2
-
z
0
)
∂
∂
x
2
(
Y
(
v
,
x
2
)
Y
(
u
,
x
1
)
w
)
Doc 79
0.0763, -44.0000, 3.0000, 0.2290
testing/NTCIR/xhtml5/8/1210.5733/1210.5733_1_70.xhtml
e
(
z
1
-
z
2
)
∂
∂
x
0
e
(
z
1
-
z
0
)
∂
∂
x
1
e
(
z
2
-
z
0
)
∂
∂
x
2
(
Y
(
u
,
x
1
)
Y
(
v
,
x
2
)
w
)
Doc 79
0.0763, -44.0000, 3.0000, 0.2290
testing/NTCIR/xhtml5/8/1210.5733/1210.5733_1_70.xhtml
e
(
z
1
-
z
2
)
∂
∂
x
0
e
(
z
1
-
z
0
)
∂
∂
x
1
e
(
z
2
-
z
0
)
∂
∂
x
2
(
Y
(
Y
(
u
,
x
0
)
v
,
x
2
)
w
)
Doc 79
0.0763, -44.0000, 3.0000, 0.2290
testing/NTCIR/xhtml5/8/1210.5733/1210.5733_1_70.xhtml
(
α
=
(
3
,
0
)
,
i
=
1
,
j
=
2
)
:
g
22
(
x
)
∂
4
u
2
∂
x
1
4
(
x
)
+
g
11
(
x
)
∂
4
u
1
∂
x
1
3
∂
x
2
(
x
)
=
0
,
Doc 17
0.1244, -49.0000, 6.0000, 0.3110
testing/NTCIR/xhtml5/10/dg-ga9411011/dg-ga9411011_1_61.xhtml
(
1
2
u
2
,
1
n
+
2
α
(
t
)
u
n
+
2
+
β
(
t
)
(
u
u
x
x
-
1
2
u
x
2
)
+
σ
(
t
)
(
u
u
x
x
x
x
-
u
x
u
x
x
x
+
1
2
u
x
x
2
)
)
.
Doc 80
0.0763, -56.0000, 3.0000, 0.0763
testing/NTCIR/xhtml5/9/1309.7161/1309.7161_1_58.xhtml
-
[
∂
x
1
(
δ
(
u
x
1
)
u
x
1
x
1
)
+
∂
x
2
(
δ
(
u
x
2
)
u
x
1
x
2
)
+
γ
Δ
u
x
1
]
=
-
u
t
x
1
Doc 81
0.0748, -35.0000, 6.0000, 0.0748
testing/NTCIR/xhtml5/9/1303.1655/1303.1655_1_41.xhtml
∂
2
v
1
∂
x
2
=
u
¨
1
(
∂
g
∂
x
)
2
+
u
˙
1
(
∂
2
g
∂
x
2
)
Doc 82
0.0672, -25.0000, 3.0000, 0.0672
testing/NTCIR/xhtml5/1/math0606723/math0606723_1_19.xhtml
1
2
[
Λ
σ
,
(
u
1
+
u
2
)
]
∂
x
v
+
1
2
[
Λ
σ
,
v
]
∂
x
(
u
1
+
u
2
)
+
u
2
Λ
σ
∂
x
v
+
v
Λ
σ
∂
x
u
1
.
Doc 83
0.0672, -44.0000, 3.0000, 0.0672
testing/NTCIR/xhtml5/6/0812.1825/0812.1825_1_107.xhtml
-
1
2
∂
∂
x
2
(
σ
(
x
2
)
-
σ
(
x
1
)
x
2
-
x
1
)
+
R
2
(
x
1
;
x
2
)
M
(
x
1
)
Doc 84
0.0622, -36.0000, 3.0000, 0.0622
testing/NTCIR/xhtml5/3/hep-th0407261/hep-th0407261_1_54.xhtml
=
-
1
2
t
(
∂
2
∂
v
1
2
+
∂
2
∂
x
1
2
)
-
α
2
t
(
∂
2
∂
u
1
2
+
∂
2
∂
y
1
2
)
Doc 85
0.0622, -38.0000, 3.0000, 0.0622
testing/NTCIR/xhtml5/10/hep-th9901100/hep-th9901100_1_15.xhtml
-
ψ
b
+
1
(
y
(
z
1
)
;
a
)
ψ
c
+
1
(
y
(
P
(
z
1
)
)
;
a
)
ln
y
(
z
1
)
-
ln
y
(
P
(
z
1
)
)
⋅
∂
x
1
∂
z
1
x
1
,
Doc 86
0.0622, -46.0000, 3.0000, 0.0622
testing/NTCIR/xhtml5/6/0910.4320/0910.4320_1_21.xhtml
∂
1
φ
=
-
x
2
(
x
1
)
2
+
(
x
2
)
2
,
∂
2
φ
=
x
1
(
x
1
)
2
+
(
x
2
)
2
-
2
π
θ
(
x
1
)
δ
(
x
2
)
,
Doc 87
0.0525, -41.0000, 3.0000, 0.0525
testing/NTCIR/xhtml5/4/hep-th0608216/hep-th0608216_1_18.xhtml
∂
t
(
u
x
)
=
∂
x
(
u
t
)
-
∂
x
(
u
x
)
=
c
∂
x
(
u
t
)
+
d
∂
t
(
u
t
)
,
Doc 88
0.0480, -29.0000, 2.0000, 0.0480
testing/NTCIR/xhtml5/4/math0610766/math0610766_1_50.xhtml