tangent
Not Supported
f
μ
=
-
8
π
G
3
c
4
(
A
2
T
α
β
+
B
2
T
η
α
β
)
(
δ
ν
μ
+
u
μ
u
ν
)
u
α
x
ν
u
β
Search
Returned 95 matches (100 formulae, 108 docs)
Lookup 1611.870 ms, Re-ranking 11385.948 ms
Found 17879151 tuple postings, 9680579 formulae, 3799102 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
(
1
2
g
μ
ν
-
u
μ
u
ν
)
ψ
∗
⋅
ψ
-
i
2
(
u
μ
ϵ
α
β
γ
ν
+
u
ν
ϵ
α
β
γ
μ
)
ψ
∗
α
ψ
β
u
γ
Doc 1
0.2523, -29.0000, 5.0000, 0.2523
testing/NTCIR/xhtml5/1/hep-th9704144/hep-th9704144_1_20.xhtml
τ
μ
ν
-
1
2
γ
μ
ν
γ
α
β
τ
α
β
=
(
δ
μ
α
δ
ν
β
+
1
2
γ
μ
ν
h
α
β
)
(
T
α
β
-
1
2
g
α
β
g
ρ
σ
T
ρ
σ
)
Doc 2
0.2453, -38.0000, 5.0000, 0.2453
testing/NTCIR/xhtml5/10/gr-qc9907027/gr-qc9907027_1_74.xhtml
G
μ
ν
=
(
c
1
-
c
3
)
[
1
2
T
μ
ν
f
+
1
4
f
2
u
μ
u
ν
]
Doc 3
0.2447, -17.0000, 5.0000, 0.2447
testing/NTCIR/xhtml5/5/0801.0516/0801.0516_1_48.xhtml
G
A
B
=
e
m
c
2
(
d
d
s
F
α
β
)
u
(
A
)
α
u
(
B
)
β
Doc 4
0.2292, -14.0000, 7.0000, 0.2292
testing/NTCIR/xhtml5/4/gr-qc0601002/gr-qc0601002_1_29.xhtml
G
μ
ν
=
1
2
T
μ
ν
f
+
1
4
f
2
u
μ
u
ν
Doc 5
0.2198, -11.0000, 5.0000, 0.2198
testing/NTCIR/xhtml5/5/0801.0516/0801.0516_1_37.xhtml
F
μ
ν
J
ν
+
1
τ
imp
(
δ
ν
μ
+
u
μ
u
ν
)
T
ν
γ
u
γ
.
Doc 6
0.2198, -15.0000, 9.0000, 0.2198
testing/NTCIR/xhtml5/5/0706.3215/0706.3215_1_53.xhtml
1
α
(
3
w
2
+
R
2
)
(
w
2
-
R
2
)
u
μ
u
ν
+
(
w
2
+
R
2
)
2
δ
ν
μ
,
Doc 7
0.2038, -25.0000, 7.0000, 0.2038
testing/NTCIR/xhtml5/6/1001.1039/1001.1039_1_107.xhtml
ρ
t
=
(
T
α
β
-
1
2
T
g
α
β
)
u
α
u
β
Doc 8
0.1947, -10.0000, 8.0000, 0.1947
testing/NTCIR/xhtml5/2/hep-th0210142/hep-th0210142_1_18.xhtml
∂
α
∂
μ
F
μ
β
-
∂
β
∂
μ
F
μ
α
+
A
-
1
2
∂
μ
2
F
α
β
-
B
2
m
2
F
α
β
=
0
,
Doc 9
0.1947, -30.0000, 7.0000, 0.1947
testing/NTCIR/xhtml5/6/0912.3716/0912.3716_1_6.xhtml
d
2
x
μ
d
s
2
+
Γ
α
β
μ
u
α
u
β
=
-
1
Λ
∇
ν
(
1
2
R
+
L
m
)
(
u
μ
u
ν
-
g
μ
ν
)
.
Doc 10
0.1947, -33.0000, 6.0000, 0.1947
testing/NTCIR/xhtml5/7/1008.4193/1008.4193_1_31.xhtml
β
2
2
m
2
(
∂
μ
F
μ
ν
)
2
+
β
m
2
ϵ
α
β
ν
μ
p
α
(
∂
β
A
ν
)
(
∂
ρ
F
ρ
μ
)
,
Doc 12
0.1858, -27.0000, 2.0000, 0.3119
testing/NTCIR/xhtml5/3/hep-th0304104/hep-th0304104_1_11.xhtml
β
2
2
m
2
(
∂
μ
F
μ
ν
)
2
+
β
m
2
ϵ
α
β
ν
μ
p
α
(
∂
β
A
ν
)
(
∂
ρ
F
ρ
μ
)
.
Doc 11
0.1858, -27.0000, 2.0000, 0.3119
testing/NTCIR/xhtml5/3/hep-th0304104/hep-th0304104_1_6.xhtml
δ
x
μ
=
ε
μ
+
ε
μ
x
ν
ν
=
ε
μ
+
1
2
ε
α
β
(
δ
α
μ
η
ν
β
-
δ
β
μ
η
ν
α
)
x
ν
,
Doc 13
0.1858, -29.0000, 5.0000, 0.1858
testing/NTCIR/xhtml5/2/hep-th0201074/hep-th0201074_1_33.xhtml
R
α
β
γ
μ
u
α
u
β
N
γ
+
1
2
(
R
α
β
γ
;
δ
μ
-
R
γ
δ
α
;
β
μ
)
u
α
u
β
N
γ
N
δ
Doc 14
0.1858, -29.0000, 4.0000, 0.1858
testing/NTCIR/xhtml5/3/gr-qc0309058/gr-qc0309058_1_19.xhtml
P
⟂
ν
μ
=
δ
ν
μ
+
u
μ
u
ν
Doc 15
0.1845, -6.0000, 8.0000, 0.1845
testing/NTCIR/xhtml5/7/1010.1861/1010.1861_1_34.xhtml
d
Q
T
=
-
i
2
(
∂
α
u
β
+
∂
β
u
α
-
η
α
β
∂
λ
u
λ
)
(
2
a
t
α
β
+
b
η
α
β
t
μ
μ
)
Doc 16
0.1705, -29.0000, 4.0000, 0.1705
testing/NTCIR/xhtml5/5/0711.3749/0711.3749_1_9.xhtml
P
ν
μ
=
1
2
(
δ
ν
μ
+
R
ν
μ
)
Doc 17
0.1696, -7.0000, 6.0000, 0.1696
testing/NTCIR/xhtml5/2/hep-th0202069/hep-th0202069_1_27.xhtml
P
ν
μ
=
1
2
(
δ
ν
μ
+
R
ν
μ
)
,
Doc 18
0.1696, -8.0000, 6.0000, 0.1696
testing/NTCIR/xhtml5/2/hep-th0202069/hep-th0202069_1_15.xhtml
1
2
g
α
β
∂
α
x
μ
∂
β
x
ν
G
μ
ν
+
i
2
ψ
¯
μ
ρ
α
D
α
ψ
ν
G
μ
ν
Doc 19
0.1696, -24.0000, 3.0000, 0.1696
testing/NTCIR/xhtml5/3/hep-th0305028/hep-th0305028_1_13.xhtml
∫
d
Ω
4
=
8
π
2
3
,
∫
d
Ω
4
n
α
n
β
=
8
π
2
15
(
η
α
β
+
u
α
u
β
)
,
Doc 20
0.1696, -27.0000, 4.0000, 0.1696
testing/NTCIR/xhtml5/6/0907.3087/0907.3087_1_29.xhtml
Doc 21
0.1696, -27.0000, 4.0000, 0.1696
testing/NTCIR/xhtml5/6/0907.3079/0907.3079_1_24.xhtml
H
μ
ν
=
-
R
μ
α
R
α
ν
+
2
3
R
R
μ
ν
+
(
1
2
R
α
β
R
α
β
-
1
4
R
2
)
g
μ
ν
Doc 22
0.1696, -31.0000, 3.0000, 0.1696
testing/NTCIR/xhtml5/8/1211.4628/1211.4628_1_24.xhtml
1
2
(
δ
μ
ν
J
α
β
+
δ
α
β
J
μ
ν
)
-
1
2
δ
μ
ν
δ
α
β
Doc 23
0.1653, -17.0000, 6.0000, 0.3027
testing/NTCIR/xhtml5/10/hep-th9611226/hep-th9611226_1_24.xhtml
-
1
2
(
∂
μ
A
~
ν
)
(
∂
μ
A
~
ν
)
+
e
θ
2
ϵ
α
β
∂
α
A
~
μ
∂
β
A
~
ν
ℱ
~
μ
ν
Doc 24
0.1653, -25.0000, 4.0000, 0.1653
testing/NTCIR/xhtml5/6/0911.3461/0911.3461_1_17.xhtml
-
1
2
(
∂
μ
A
~
ν
)
(
∂
μ
A
~
ν
)
+
e
θ
2
ϵ
α
β
∂
α
A
~
μ
∂
β
A
~
ν
ℱ
~
μ
ν
+
𝒪
(
(
e
θ
)
2
)
,
Doc 25
0.1653, -32.0000, 4.0000, 0.1653
testing/NTCIR/xhtml5/6/0911.3461/0911.3461_1_16.xhtml
-
i
2
(
δ
α
μ
δ
ν
β
+
η
μ
β
η
ν
α
)
,
Doc 26
0.1597, -12.0000, 5.0000, 0.1597
testing/NTCIR/xhtml5/10/hep-th9801028/hep-th9801028_1_22.xhtml
K
ν
μ
=
κ
2
2
(
-
σ
3
δ
ν
μ
+
1
κ
4
2
G
~
ν
μ
(
4
)
)
,
Doc 27
0.1597, -21.0000, 3.0000, 0.1597
testing/NTCIR/xhtml5/4/hep-th0503191/hep-th0503191_1_4.xhtml
L
=
1
2
(
x
˙
μ
+
x
˙
α
A
α
μ
)
g
μ
ν
(
x
˙
ν
+
A
β
ν
x
˙
β
)
+
1
2
x
˙
α
g
α
β
x
˙
β
-
U
q
(
x
)
.
Doc 28
0.1597, -36.0000, 5.0000, 0.1597
testing/NTCIR/xhtml5/2/hep-th0102117/hep-th0102117_1_59.xhtml
L
G
=
1
2
x
˙
α
g
α
β
([
g
])
x
˙
β
+
1
2
(
x
˙
μ
+
x
˙
α
A
α
μ
(
g
)
)
g
μ
ν
(
g
)
(
x
˙
ν
+
A
β
ν
(
g
)
x
˙
β
)
Doc 29
0.1597, -40.0000, 3.0000, 0.1597
testing/NTCIR/xhtml5/2/hep-th0102115/hep-th0102115_1_77.xhtml
Λ
ν
μ
≃
δ
ν
μ
+
ω
2
(
δ
α
μ
g
β
ν
-
δ
β
μ
g
α
ν
)
Doc 30
0.1593, -16.0000, 2.0000, 0.1593
testing/NTCIR/xhtml5/4/hep-th0504132/hep-th0504132_1_30.xhtml
P
7
μ
ν
α
β
=
1
4
(
δ
[
μ
α
δ
ν
]
β
+
1
2
ϕ
μ
ν
α
β
)
.
Doc 31
0.1593, -21.0000, 5.0000, 0.1593
testing/NTCIR/xhtml5/10/hep-th9705138/hep-th9705138_1_12.xhtml
Γ
α
β
μ
=
1
2
(
u
α
f
β
μ
+
u
β
f
α
μ
)
-
1
2
(
u
α
,
β
+
u
β
,
α
)
u
μ
.
Doc 32
0.1593, -28.0000, 4.0000, 0.1593
testing/NTCIR/xhtml5/5/0801.0516/0801.0516_1_34.xhtml
Γ
α
β
μ
=
γ
α
β
μ
+
1
2
(
u
α
f
β
μ
+
u
β
f
α
μ
)
-
1
2
u
μ
(
u
α
|
β
+
u
β
|
α
)
.
Doc 33
0.1593, -33.0000, 3.0000, 0.1593
testing/NTCIR/xhtml5/4/gr-qc0512037/gr-qc0512037_1_23.xhtml
Doc 34
0.1593, -33.0000, 3.0000, 0.1593
testing/NTCIR/xhtml5/4/hep-th0505268/hep-th0505268_1_7.xhtml
=
-
i
2
(
u
ν
,
μ
+
u
μ
,
ν
-
η
μ
ν
u
α
,
α
)
Doc 35
0.1524, -15.0000, 3.0000, 0.1524
testing/NTCIR/xhtml5/10/hep-th9903055/hep-th9903055_1_6.xhtml
d
u
ν
d
s
=
-
Γ
α
β
ν
u
α
u
β
+
∂
μ
(
ln
m
)
(
g
μ
ν
-
u
μ
u
ν
)
Doc 36
0.1524, -23.0000, 6.0000, 0.1524
testing/NTCIR/xhtml5/8/1111.0912/1111.0912_1_72.xhtml
R
μ
ν
=
8
π
G
(
T
α
β
(
m
)
+
T
α
β
(
ϕ
)
+
T
α
β
(
u
)
)
(
δ
μ
α
δ
ν
β
-
1
2
g
μ
ν
g
α
β
)
.
Doc 37
0.1524, -35.0000, 6.0000, 0.1524
testing/NTCIR/xhtml5/5/0809.3847/0809.3847_1_32.xhtml
K
ν
μ
+
β
ℓ
2
3
(
9
2
J
ν
μ
-
J
δ
ν
μ
-
3
P
α
ν
β
μ
K
α
β
+
P
α
ρ
β
ρ
K
α
β
δ
ν
μ
)
Doc 38
0.1524, -35.0000, 5.0000, 0.1524
testing/NTCIR/xhtml5/4/gr-qc0604071/gr-qc0604071_1_13.xhtml
-
K
ν
μ
-
2
ℓ
2
3
(
9
2
J
ν
μ
-
J
δ
ν
μ
-
3
P
α
ν
β
μ
K
α
β
+
P
α
ρ
β
ρ
K
α
β
δ
ν
μ
)
Doc 39
0.1524, -36.0000, 2.0000, 0.2967
testing/NTCIR/xhtml5/4/hep-th0605122/hep-th0605122_1_37.xhtml
h
ν
μ
=
δ
ν
μ
-
u
μ
u
ν
Doc 40
0.1443, -5.0000, 7.0000, 0.1443
testing/NTCIR/xhtml5/9/1305.2334/1305.2334_1_57.xhtml
Doc 41
0.1443, -5.0000, 7.0000, 0.1443
testing/NTCIR/xhtml5/9/1305.2334/1305.2334_1_92.xhtml
R
α
β
+
1
2
η
α
β
R
=
-
8
π
G
T
α
β
.
Doc 42
0.1443, -13.0000, 5.0000, 0.1443
testing/NTCIR/xhtml5/10/gr-qc9611023/gr-qc9611023_1_49.xhtml
S
μ
ν
=
1
2
T
T
μ
ν
-
1
4
T
μ
α
T
ν
α
+
3
T
α
β
T
α
β
-
T
2
24
g
μ
ν
,
Doc 43
0.1443, -31.0000, 2.0000, 0.1443
testing/NTCIR/xhtml5/7/1105.2605/1105.2605_1_22.xhtml
Doc 44
0.1443, -31.0000, 2.0000, 0.1443
testing/NTCIR/xhtml5/7/1005.3101/1005.3101_1_12.xhtml
=
-
κ
5
2
2
(
T
ν
μ
-
1
3
T
δ
ν
μ
)
+
α
2
κ
5
2
κ
4
2
(
R
ν
μ
-
1
6
R
δ
ν
μ
)
,
Doc 39
0.1524, -36.0000, 2.0000, 0.2967
testing/NTCIR/xhtml5/4/hep-th0605122/hep-th0605122_1_37.xhtml
(
R
ν
μ
-
1
2
δ
ν
μ
R
)
+
m
g
2
2
(
δ
ν
μ
+
g
μ
α
γ
α
ν
-
1
2
δ
ν
μ
g
α
β
γ
α
β
)
=
8
π
T
ν
μ
Doc 45
0.1443, -41.0000, 2.0000, 0.1443
testing/NTCIR/xhtml5/1/hep-th9711147/hep-th9711147_1_3.xhtml
Δ
μ
ν
α
β
=
1
2
(
δ
μ
α
δ
ν
β
+
δ
μ
β
δ
ν
α
)
Doc 46
0.1374, -14.0000, 3.0000, 0.1374
testing/NTCIR/xhtml5/4/hep-th0503231/hep-th0503231_1_33.xhtml
{
g
α
β
,
π
μ
ν
}
=
1
2
(
δ
α
μ
δ
β
ν
+
δ
α
ν
δ
β
μ
)
,
Doc 47
0.1374, -18.0000, 3.0000, 0.1374
testing/NTCIR/xhtml5/4/hep-th0510260/hep-th0510260_1_15.xhtml
1
2
{
J
μ
β
,
J
α
ν
}
+
T
2
(
δ
μ
β
J
α
ν
-
δ
α
ν
J
μ
β
)
Doc 23
0.1653, -17.0000, 6.0000, 0.3027
testing/NTCIR/xhtml5/10/hep-th9611226/hep-th9611226_1_24.xhtml
-
δ
α
β
μ
ν
,
δ
α
β
μ
ν
=
1
2
(
δ
α
μ
δ
β
ν
+
δ
α
ν
δ
β
μ
)
,
Doc 48
0.1374, -22.0000, 3.0000, 0.1374
testing/NTCIR/xhtml5/3/hep-th0306233/hep-th0306233_1_12.xhtml
{
h
α
β
,
p
μ
ν
}
=
1
2
(
δ
α
μ
δ
β
ν
+
δ
α
ν
δ
β
μ
)
≡
Δ
α
β
μ
ν
Doc 49
0.1374, -23.0000, 3.0000, 0.1374
testing/NTCIR/xhtml5/5/0710.1430/0710.1430_1_38.xhtml
{
g
α
β
,
π
μ
ν
}
=
1
2
(
δ
α
μ
δ
β
ν
+
δ
α
ν
δ
β
μ
)
≡
Δ
α
β
μ
ν
Doc 50
0.1374, -23.0000, 3.0000, 0.1374
testing/NTCIR/xhtml5/5/0808.2623/0808.2623_1_27.xhtml
[
1
-
M
4
2
ℰ
G
0
]
γ
δ
μ
ν
H
α
β
γ
δ
=
1
2
(
δ
μ
α
δ
ν
β
+
δ
μ
β
δ
ν
α
)
.
Doc 51
0.1374, -28.0000, 3.0000, 0.1374
testing/NTCIR/xhtml5/5/0711.2072/0711.2072_1_7.xhtml
Q
ν
μ
=
-
λ
δ
ν
μ
+
1
ℓ
2
[
(
q
-
1
)
μ
α
g
α
ν
-
1
2
(
q
-
1
)
α
β
g
α
β
δ
ν
μ
]
Doc 52
0.1374, -31.0000, 6.0000, 0.1374
testing/NTCIR/xhtml5/5/0811.1272/0811.1272_1_10.xhtml
f
ν
μ
=
1
2
s
μ
+
ν
1
2
a
μ
,
ν
Doc 53
0.1348, -12.0000, 5.0000, 0.1348
testing/NTCIR/xhtml5/5/0707.4437/0707.4437_1_133.xhtml
L
β
α
=
δ
β
α
+
1
2
(
δ
ν
α
η
β
μ
-
δ
μ
α
η
β
ν
)
ω
μ
ν
,
Doc 54
0.1348, -23.0000, 3.0000, 0.1348
testing/NTCIR/xhtml5/10/math-ph9804011/math-ph9804011_1_53.xhtml
Doc 55
0.1348, -23.0000, 3.0000, 0.1348
testing/NTCIR/xhtml5/10/math-ph9805004/math-ph9805004_1_90.xhtml
=
1
2
ϵ
μ
ν
α
β
∂
μ
u
ν
ξ
α
∂
β
μ
+
1
2
ϵ
μ
ν
α
β
u
ν
∂
μ
ξ
α
∂
β
μ
Doc 56
0.1348, -30.0000, 3.0000, 0.1348
testing/NTCIR/xhtml5/7/1104.5245/1104.5245_1_68.xhtml
Λ
(
ω
)
=
𝕀
+
i
2
ω
μ
ν
M
μ
ν
and
Λ
ν
μ
=
p
μ
+
i
2
(
ω
α
β
M
α
β
)
ν
μ
p
ν
=
δ
ν
μ
+
ω
ν
μ
Doc 57
0.1348, -39.0000, 5.0000, 0.1348
testing/NTCIR/xhtml5/3/quant-ph0307107/quant-ph0307107_1_26.xhtml
Δ
μ
ν
α
β
≡
1
2
(
δ
μ
α
δ
ν
β
+
δ
ν
α
δ
μ
β
)
Doc 59
0.1322, -15.0000, 3.0000, 0.1322
testing/NTCIR/xhtml5/7/1010.2887/1010.2887_1_9.xhtml
Δ
μ
ν
α
β
=
1
2
(
δ
μ
α
δ
ν
β
+
δ
ν
α
δ
μ
β
)
Doc 58
0.1322, -15.0000, 3.0000, 0.1322
testing/NTCIR/xhtml5/4/hep-th0510031/hep-th0510031_1_10.xhtml
-
1
2
V
μ
∂
⋅
A
-
1
2
(
E
ν
μ
-
A
2
4
δ
ν
μ
)
∂
ν
C
,
Doc 60
0.1322, -21.0000, 4.0000, 0.1322
testing/NTCIR/xhtml5/2/hep-th0109202/hep-th0109202_1_42.xhtml
d
d
s
(
m
g
μ
ν
u
ν
)
-
1
2
m
(
∂
μ
g
α
β
)
u
α
u
β
-
∂
μ
m
=
0
Doc 61
0.1322, -24.0000, 2.0000, 0.1322
testing/NTCIR/xhtml5/8/1111.0912/1111.0912_1_46.xhtml
{
g
α
β
,
π
μ
ν
}
=
{
G
α
β
,
Π
μ
ν
}
=
1
2
(
δ
α
μ
δ
β
ν
+
δ
β
μ
δ
α
ν
)
,
Doc 62
0.1322, -28.0000, 3.0000, 0.1322
testing/NTCIR/xhtml5/4/hep-th0605193/hep-th0605193_1_13.xhtml
T
^
α
β
=
(
ρ
+
p
c
2
)
u
^
α
u
^
β
-
p
g
^
α
β
,
Doc 63
0.1261, -14.0000, 4.0000, 0.1261
testing/NTCIR/xhtml5/3/gr-qc0304058/gr-qc0304058_1_7.xhtml
Doc 64
0.1261, -14.0000, 4.0000, 0.1261
testing/NTCIR/xhtml5/2/gr-qc0101126/gr-qc0101126_1_10.xhtml
Doc 65
0.1261, -14.0000, 4.0000, 0.1261
testing/NTCIR/xhtml5/2/astro-ph0203164/astro-ph0203164_1_9.xhtml
δ
(
μ
ν
)
α
β
:=
1
2
(
δ
μ
α
δ
ν
β
+
δ
μ
β
δ
ν
α
)
Doc 66
0.1261, -22.0000, 3.0000, 0.1261
testing/NTCIR/xhtml5/2/gr-qc0104081/gr-qc0104081_1_66.xhtml
Doc 67
0.1261, -22.0000, 3.0000, 0.1261
testing/NTCIR/xhtml5/3/gr-qc0306034/gr-qc0306034_1_40.xhtml
Doc 68
0.1261, -22.0000, 3.0000, 0.1261
testing/NTCIR/xhtml5/3/gr-qc0306036/gr-qc0306036_1_9.xhtml
G
μ
+
ν
(
K
μ
-
ν
δ
ν
μ
K
)
,
y
+
1
2
δ
ν
μ
(
K
2
+
K
α
β
K
α
β
)
Doc 69
0.1261, -25.0000, 3.0000, 0.1261
testing/NTCIR/xhtml5/6/0904.3899/0904.3899_1_11.xhtml
T
α
β
=
T
2
(
:
∂
α
X
μ
∂
β
X
μ
-
1
2
η
α
β
∂
γ
X
μ
∂
γ
X
μ
:
)
Doc 70
0.1261, -26.0000, 4.0000, 0.1261
testing/NTCIR/xhtml5/2/hep-th0102003/hep-th0102003_1_22.xhtml
1
2
(
∂
ν
u
μ
-
∂
μ
u
ν
+
u
μ
u
α
∂
α
u
ν
-
u
ν
u
α
∂
α
u
μ
)
.
Doc 71
0.1261, -28.0000, 3.0000, 0.1261
testing/NTCIR/xhtml5/6/0907.2583/0907.2583_1_9.xhtml
R
μ
ν
=
-
1
2
g
μ
ν
-
F
α
β
δ
μ
α
δ
ν
β
-
π
u
α
β
2
r
δ
μ
α
δ
ν
β
,
Doc 72
0.1261, -29.0000, 2.0000, 0.1261
testing/NTCIR/xhtml5/8/1205.0120/1205.0120_1_22.xhtml
d
(
2
K
ν
α
E
α
μ
-
3
2
K
E
ν
μ
-
1
2
K
β
α
E
α
β
δ
ν
μ
+
C
α
ν
β
μ
K
α
β
Doc 73
0.1261, -32.0000, 3.0000, 0.1261
testing/NTCIR/xhtml5/4/hep-th0506152/hep-th0506152_1_30.xhtml
ω
μ
ν
=
1
2
(
∂
μ
u
ν
-
∂
ν
u
μ
)
+
1
2
(
u
μ
u
α
∂
α
u
ν
-
u
ν
u
α
∂
α
u
μ
)
,
Doc 74
0.1261, -33.0000, 3.0000, 0.1261
testing/NTCIR/xhtml5/7/1011.5895/1011.5895_1_32.xhtml
M
μ
ν
α
β
=
c
1
g
α
β
g
μ
ν
+
c
2
δ
μ
α
δ
ν
β
+
c
3
δ
ν
α
δ
μ
β
+
c
4
u
α
u
β
g
μ
ν
.
Doc 75
0.1261, -36.0000, 0.0000, 0.1261
testing/NTCIR/xhtml5/9/1212.1040/1212.1040_1_3.xhtml
d
2
ξ
a
d
s
2
+
8
π
G
N
(
n
-
4
)
(
T
¯
μ
ν
u
μ
u
ν
+
1
2
T
¯
)
ξ
a
+
K
¯
α
β
a
u
α
u
β
=
0.
Doc 76
0.1261, -39.0000, 3.0000, 0.2523
testing/NTCIR/xhtml5/4/gr-qc0608071/gr-qc0608071_1_10.xhtml
d
2
ξ
a
d
s
¯
2
+
8
π
G
N
(
n
-
4
)
(
T
¯
μ
ν
u
¯
μ
u
¯
ν
+
1
2
T
¯
)
ξ
a
+
K
¯
α
β
a
u
¯
α
u
¯
β
=
0
,
Doc 76
0.1261, -39.0000, 3.0000, 0.2523
testing/NTCIR/xhtml5/4/gr-qc0608071/gr-qc0608071_1_10.xhtml
β
4
F
μ
ν
F
μ
ν
+
1
2
ϵ
α
β
ν
μ
p
α
(
∂
β
A
ν
)
A
μ
-
1
2
m
2
(
ϵ
α
β
ν
μ
p
α
(
∂
β
A
ν
)
)
2
Doc 11
0.1858, -27.0000, 2.0000, 0.3119
testing/NTCIR/xhtml5/3/hep-th0304104/hep-th0304104_1_6.xhtml
Doc 12
0.1858, -27.0000, 2.0000, 0.3119
testing/NTCIR/xhtml5/3/hep-th0304104/hep-th0304104_1_11.xhtml
Doc 77
0.1261, -40.0000, 2.0000, 0.1261
testing/NTCIR/xhtml5/3/hep-th0304104/hep-th0304104_1_13.xhtml
T
μ
μ
=
0
and
T
ν
α
T
α
μ
=
1
4
(
T
α
β
T
α
β
)
δ
ν
μ
Doc 78
0.1188, -20.0000, 5.0000, 0.1188
testing/NTCIR/xhtml5/4/gr-qc0507109/gr-qc0507109_1_8.xhtml
Doc 79
0.1188, -20.0000, 5.0000, 0.1188
testing/NTCIR/xhtml5/3/hep-th0303112/hep-th0303112_1_14.xhtml
1
2
(
u
;
μ
α
P
μ
β
+
u
;
μ
β
P
μ
α
)
-
1
2
Θ
P
α
β
,
Doc 80
0.1188, -22.0000, 4.0000, 0.1188
testing/NTCIR/xhtml5/9/gr-qc9306012/gr-qc9306012_1_8.xhtml
-
K
μ
α
K
α
ν
+
K
K
ν
μ
+
1
2
δ
ν
μ
(
K
α
β
K
α
β
-
K
2
)
Doc 81
0.1188, -23.0000, 4.0000, 0.1188
testing/NTCIR/xhtml5/7/1103.1703/1103.1703_1_8.xhtml
K
ν
μ
=
κ
2
2
(
-
σ
3
δ
ν
μ
-
T
~
ν
μ
+
1
κ
4
2
G
~
ν
μ
(
4
)
)
,
Doc 82
0.1188, -26.0000, 4.0000, 0.1188
testing/NTCIR/xhtml5/3/hep-th0501232/hep-th0501232_1_10.xhtml
+
b
4
2
u
μ
α
u
ν
β
h
μ
ν
+
b
5
u
μ
μ
u
ν
α
h
β
ν
-
(
α
↔
β
)
.
Doc 83
0.1188, -26.0000, 3.0000, 0.1188
testing/NTCIR/xhtml5/5/0711.0869/0711.0869_1_12.xhtml
δ
ν
μ
+
1
3
R
μ
ξ
α
α
β
ν
ξ
β
+
1
12
∇
γ
R
μ
ξ
α
α
β
ν
ξ
β
ξ
γ
Doc 84
0.1188, -27.0000, 2.0000, 0.1188
testing/NTCIR/xhtml5/3/hep-th0312064/hep-th0312064_1_15.xhtml
1
D
-
2
(
δ
ν
μ
𝒯
α
β
-
δ
β
μ
𝒯
ν
α
-
g
α
ν
𝒯
β
μ
+
g
α
β
𝒯
ν
μ
)
Doc 86
0.1188, -27.0000, 0.0000, 0.1188
testing/NTCIR/xhtml5/7/1105.4750/1105.4750_1_18.xhtml
1
D
-
2
(
δ
ν
μ
T
α
β
-
δ
β
μ
T
ν
α
-
g
α
ν
T
β
μ
+
g
α
β
T
ν
μ
)
Doc 85
0.1188, -27.0000, 0.0000, 0.1188
testing/NTCIR/xhtml5/7/1105.4750/1105.4750_1_20.xhtml
+
1
2
∂
α
h
β
ν
∂
α
h
μ
β
-
1
2
∂
α
h
β
ν
∂
β
h
μ
α
+
1
4
∂
ν
h
α
β
∂
μ
h
α
β
Doc 87
0.1188, -36.0000, 4.0000, 0.1188
testing/NTCIR/xhtml5/10/hep-th9807071/hep-th9807071_1_16.xhtml
M
α
β
=
μ
ν
c
1
g
α
β
g
μ
ν
+
c
2
δ
μ
α
δ
ν
β
+
c
3
δ
ν
α
δ
μ
β
+
c
4
u
α
u
β
g
μ
ν
.
Doc 88
0.1188, -37.0000, 4.0000, 0.1188
testing/NTCIR/xhtml5/7/1104.2889/1104.2889_1_12.xhtml
K
μ
ν
=
α
β
c
1
g
μ
ν
g
α
β
+
c
2
δ
α
μ
δ
β
ν
+
c
3
δ
β
μ
δ
α
ν
-
c
4
u
μ
u
ν
g
α
β
,
Doc 89
0.1188, -37.0000, 2.0000, 0.1188
testing/NTCIR/xhtml5/5/0801.0516/0801.0516_1_4.xhtml
R
¯
α
ν
β
μ
=
[
δ
ν
μ
η
α
β
-
δ
β
μ
η
α
ν
]
ℋ
2
,
Doc 90
0.1099, -18.0000, 3.0000, 0.1099
testing/NTCIR/xhtml5/2/hep-th0107233/hep-th0107233_1_45.xhtml
+
(
ζ
-
2
3
η
)
(
g
(
0
)
α
β
+
u
α
u
β
c
2
)
∂
u
σ
∂
x
σ
)
}
Doc 92
0.1099, -26.0000, 3.0000, 0.1099
testing/NTCIR/xhtml5/4/math-ph0503027/math-ph0503027_1_89.xhtml
+
(
ζ
-
2
3
η
)
(
g
(
0
)
α
β
+
u
α
u
β
c
2
)
∂
u
σ
∂
x
σ
}
.
Doc 91
0.1099, -26.0000, 3.0000, 0.1099
testing/NTCIR/xhtml5/4/math-ph0503027/math-ph0503027_1_88.xhtml
=
-
i
d
Q
T
α
+
2
m
u
μ
(
u
μ
ν
v
α
ν
-
u
ν
α
v
μ
ν
+
u
β
β
v
β
α
)
Doc 93
0.1099, -28.0000, 2.0000, 0.1099
testing/NTCIR/xhtml5/5/0711.0869/0711.0869_1_17.xhtml
Π
ν
μ
(
2
)
=
A
1
T
μ
α
T
ν
α
+
A
2
T
T
ν
μ
+
A
3
T
α
β
T
α
β
δ
ν
μ
+
A
4
T
2
δ
ν
μ
,
Doc 94
0.1099, -37.0000, 3.0000, 0.1099
testing/NTCIR/xhtml5/4/astro-ph0601220/astro-ph0601220_1_23.xhtml
m
u
˙
μ
=
e
F
μ
ν
u
ν
+
2
3
(
u
¨
μ
+
u
μ
u
˙
2
)
,
Doc 95
0.1084, -16.0000, 8.0000, 0.1084
testing/NTCIR/xhtml5/2/hep-th0112110/hep-th0112110_1_8.xhtml
D
2
η
μ
D
τ
2
+
R
ν
α
β
μ
η
ν
u
α
u
β
=
q
η
ν
∇
ν
∇
μ
ϕ
,
Doc 96
0.1084, -22.0000, 3.0000, 0.1084
testing/NTCIR/xhtml5/4/hep-th0702166/hep-th0702166_1_98.xhtml
Δ
μ
ν
α
β
≡
1
2
(
δ
μ
α
δ
ν
β
-
η
α
β
η
μ
ν
)
.
Doc 97
0.0992, -18.0000, 2.0000, 0.0992
testing/NTCIR/xhtml5/1/hep-th0107008/hep-th0107008_1_5.xhtml
-
1
2
-
h
h
α
β
∂
α
X
μ
∂
β
X
ν
g
μ
ν
+
1
2
ϵ
α
β
∂
α
X
μ
∂
β
X
ν
B
μ
ν
Doc 98
0.0992, -33.0000, 4.0000, 0.0992
testing/NTCIR/xhtml5/3/hep-th0302127/hep-th0302127_1_35.xhtml
d
u
¯
μ
d
s
+
Γ
α
β
μ
u
¯
α
u
¯
β
Doc 99
0.0929, -10.0000, 3.0000, 0.0929
testing/NTCIR/xhtml5/3/gr-qc0408004/gr-qc0408004_1_5.xhtml
+
K
K
μ
+
ν
1
2
δ
ν
μ
(
K
α
β
K
α
β
-
K
2
)
,
Doc 100
0.0929, -18.0000, 3.0000, 0.0929
testing/NTCIR/xhtml5/3/gr-qc0311074/gr-qc0311074_1_7.xhtml
u
α
μ
u
β
ν
R
λ
ρ
α
β
=
R
α
β
μ
ν
u
λ
α
u
ρ
β
Doc 101
0.0929, -18.0000, 3.0000, 0.0929
testing/NTCIR/xhtml5/5/0810.1114/0810.1114_1_33.xhtml
C
4
2
2
M
(
u
)
A
B
(
u
-
ψ
)
A
(
u
-
ψ
)
B
+
9
2
M
(
u
)
α
β
u
α
u
β
Doc 102
0.0929, -28.0000, 2.0000, 0.0929
testing/NTCIR/xhtml5/6/0904.0503/0904.0503_1_44.xhtml
-
1
2
∂
α
h
β
ν
∂
α
h
μ
β
+
1
2
∂
α
h
β
ν
∂
β
h
μ
α
-
1
4
∂
μ
h
α
β
∂
ν
h
α
β
Doc 103
0.0929, -37.0000, 3.0000, 0.0929
testing/NTCIR/xhtml5/7/1006.0984/1006.0984_1_45.xhtml
Doc 104
0.0929, -37.0000, 3.0000, 0.0929
testing/NTCIR/xhtml5/7/1103.5963/1103.5963_1_38.xhtml
δ
I
b
=
-
μ
2
∫
∂
Σ
d
t
h
δ
h
α
β
(
u
α
u
β
u
μ
u
ν
h
μ
ν
-
h
α
β
u
μ
u
ν
h
μ
ν
)
.
Doc 105
0.0929, -41.0000, 3.0000, 0.0929
testing/NTCIR/xhtml5/4/hep-th0605068/hep-th0605068_1_50.xhtml
(
8
π
G
c
4
T
μ
ν
+
L
2
R
;
α
β
μ
α
ν
β
)
;
ν
=
0.
Doc 106
0.0848, -21.0000, 4.0000, 0.0848
testing/NTCIR/xhtml5/8/1205.3088/1205.3088_1_20.xhtml
R
μ
ν
-
1
2
g
μ
ν
R
=
8
π
G
c
4
T
μ
ν
+
L
2
R
;
α
β
μ
α
ν
β
Doc 107
0.0848, -28.0000, 2.0000, 0.0848
testing/NTCIR/xhtml5/8/1205.3088/1205.3088_1_8.xhtml
-
4
m
2
u
ν
μ
h
μ
β
h
ν
β
+
2
m
2
u
μ
u
μ
ν
u
~
ν
Doc 108
0.0661, -20.0000, 2.0000, 0.0661
testing/NTCIR/xhtml5/5/0711.0869/0711.0869_1_18.xhtml