tangent
Not Supported
w
=
{
w
*
if
w
*
>
1
2
,
1
2
if
w
*
≤
1
2
.
Search
Returned 90 matches (100 formulae, 80 docs)
Lookup 4.578 ms, Re-ranking 659.901 ms
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[ documents ]
[ documents-by-formula ]
Doc 1
1.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Nowcast_(Air_Quality_Index).html
w
=
{
w
*
if
w
*
>
1
2
,
1
2
if
w
*
≤
1
2
.
Doc 2
0.3545
3.6769
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Tobit_model.html
y
i
=
{
y
i
*
if
y
i
*
>
y
L
y
L
if
y
i
*
≤
y
L
.
y
i
=
{
y
i
*
if
y
i
*
>
0
0
if
y
i
*
≤
0
y
1
i
=
{
y
1
i
*
if
y
1
i
*
>
0
0
if
y
1
i
*
≤
0.
y
1
i
=
{
y
1
i
*
if
y
1
i
*
>
0
0
if
y
1
i
*
≤
0.
y
2
i
=
{
y
2
i
*
if
y
1
i
*
>
0
0
if
y
1
i
*
≤
0.
y
2
i
=
{
y
2
i
*
if
y
1
i
*
>
0
0
if
y
1
i
*
≤
0.
y
2
i
=
{
y
2
i
*
if
y
1
i
*
>
0
0
if
y
1
i
*
≤
0.
y
2
i
=
{
y
2
i
*
if
y
1
i
*
>
0
0
if
y
1
i
*
≤
0.
y
3
i
=
{
y
3
i
*
if
y
1
i
*
>
0
0
if
y
1
i
*
≤
0.
y
3
i
=
{
y
3
i
*
if
y
1
i
*
>
0
0
if
y
1
i
*
≤
0.
y
i
=
{
y
i
*
if
y
i
*
<
y
U
y
U
if
y
i
*
≥
y
U
.
I
(
y
j
)
=
{
0
if
y
j
=
y
L
1
if
y
j
≠
y
L
.
Doc 3
0.3011
0.3011
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/LTI_system_theory.html
Π
(
t
)
=
def
{
1
if
|
t
|
<
1
2
,
0
if
|
t
|
>
1
2
.
Doc 4
0.2527
0.6848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Binomial_regression.html
Y
=
{
0
,
if
Y
*
>
0
1
,
if
Y
*
<
0.
Y
n
=
{
1
,
if
U
n
>
0
,
0
,
if
U
n
≤
0
Y
n
=
{
1
,
if
U
n
>
0
,
0
,
if
U
n
≤
0
Doc 5
0.2362
0.4724
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Multivariate_probit_model.html
Y
1
=
{
1
if
Y
1
*
>
0
,
0
otherwise
,
Y
2
=
{
1
if
Y
2
*
>
0
,
0
otherwise
,
Doc 6
0.2255
0.2255
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Sparse_distributed_memory.html
𝐚
i
=
{
1
if
w
i
>
0
,
0
if
w
i
<
0.
Doc 7
0.2199
0.2199
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Monopsony.html
w
=
{
w
m
i
n
,
if
w
m
i
n
≥
w
(
L
)
w
(
L
)
,
if
w
m
i
n
≤
w
(
L
)
Doc 8
0.2160
0.2160
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Asymptote.html
f
(
x
)
=
{
1
x
if
x
>
0
,
5
if
x
≤
0.
Doc 9
0.2158
0.3527
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Rectangular_function.html
rect
(
t
)
=
Π
(
t
)
=
{
0
if
|
t
|
>
1
2
1
2
if
|
t
|
=
1
2
1
if
|
t
|
<
1
2
.
∴
rect
(
t
)
=
Π
(
t
)
=
lim
n
→
∞
,
n
∈
(
Z
)
1
(
2
t
)
2
n
+
1
=
{
0
if
|
t
|
>
1
2
1
2
if
|
t
|
=
1
2
1
if
|
t
|
<
1
2
.
Doc 10
0.2109
0.3725
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Convex_conjugate.html
{
x
*
log
(
x
*
)
-
x
*
if
x
*
>
0
0
if
x
*
=
0
{
x
*
log
(
x
*
)
-
(
1
+
x
*
)
log
(
1
+
x
*
)
if
x
*
>
0
0
if
x
*
=
0
Doc 11
0.2009
0.2009
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Homogeneous_distribution.html
x
+
α
=
{
x
α
if
x
>
0
0
otherwise
Doc 12
0.1900
0.3023
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/TSL_color_space.html
g
=
{
-
5
9
(
x
2
+
1
)
⋅
S
,
if
T
>
1
2
5
9
(
x
2
+
1
)
⋅
S
,
if
T
<
1
2
0
,
if
T
=
0
T
=
{
1
2
π
arctan
r
′
g
′
+
1
4
,
if
g
′
>
0
1
2
π
arctan
r
′
g
′
+
3
4
,
if
g
′
<
0
0
,
if
g
′
=
0
Doc 13
0.1896
0.3618
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Non-analytic_smooth_function.html
f
(
x
)
=
{
exp
(
-
1
/
x
)
if
x
>
0
,
0
if
x
≤
0
,
f
(
n
)
(
x
)
=
{
p
n
(
x
)
x
2
n
f
(
x
)
if
x
>
0
,
0
if
x
≤
0
,
Doc 14
0.1882
0.1882
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Lorentz_covariance.html
δ
b
a
=
{
1
if
a
=
b
,
0
if
a
≠
b
.
Doc 15
0.1875
0.1875
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Kronecker_delta.html
δ
i
j
=
{
0
if
i
≠
j
,
1
if
i
=
j
.
Doc 16
0.1852
0.1852
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Absolute_value.html
|
a
|
=
{
a
,
if
a
≥
0
-
a
,
if
a
≤
0
Doc 17
0.1839
0.1839
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Quadratic_integer.html
ω
=
{
D
if
D
≡
2
,
3
(
mod
4
)
1
+
D
2
if
D
≡
1
(
mod
4
)
Doc 18
0.1781
0.1781
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_coefficient.html
(
n
k
)
=
{
n
k
¯
/
k
!
if
k
≤
n
2
n
n
-
k
¯
/
(
n
-
k
)
!
if
k
>
n
2
.
Doc 19
0.1773
0.1773
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Logistic_regression.html
Y
i
=
{
1
if
Y
i
1
∗
>
Y
i
0
∗
,
0
otherwise.
Doc 20
0.1771
0.1771
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Multiset.html
𝟏
A
(
x
)
=
{
1
if
x
∈
A
,
0
if
x
∉
A
.
Doc 21
0.1771
0.1771
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Step_function.html
χ
A
(
x
)
=
{
1
if
x
∈
A
,
0
if
x
∉
A
.
Doc 22
0.1745
0.3245
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Smoothness.html
f
(
x
)
=
{
x
if
x
≥
0
,
0
if
x
<
0
f
(
x
)
=
{
x
2
sin
(
1
x
)
if
x
≠
0
,
0
if
x
=
0
Doc 23
0.1676
0.1676
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/McCarthy_91_function.html
M
(
n
)
=
{
n
-
10
,
if
n
>
100
M
(
M
(
n
+
11
)
)
,
if
n
≤
100
Doc 24
0.1619
0.1619
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Directed_infinity.html
a
z
∞
=
{
z
∞
if
a
>
0
,
-
z
∞
if
a
<
0.
Doc 25
0.1611
0.1611
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Comparator.html
V
o
=
{
1
,
if
V
+
>
V
-
0
,
if
V
+
<
V
-
Doc 26
0.1604
0.1604
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Uniform_integrability.html
I
|
X
|
≥
K
=
{
1
if
|
X
|
≥
K
,
0
if
|
X
|
<
K
.
Doc 27
0.1570
0.1570
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Lab_color_space.html
f
(
t
)
=
{
t
1
/
3
if
t
>
(
6
29
)
3
1
3
(
29
6
)
2
t
+
4
29
otherwise
Doc 28
0.1567
0.1567
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Legendre_symbol.html
(
x
2
p
)
=
{
1
if
p
∤
x
0
if
p
∣
x
.
Doc 29
0.1484
0.1484
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Incidence_algebra.html
δ
(
a
,
b
)
=
{
1
if
a
=
b
0
if
a
<
b
.
Doc 30
0.1478
0.1478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Character_theory.html
⟨
χ
i
,
χ
j
⟩
=
{
0
if
i
≠
j
,
1
if
i
=
j
.
Doc 31
0.1478
0.1478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Schur_orthogonality_relations.html
⟨
χ
i
,
χ
j
⟩
=
{
0
if
i
≠
j
,
1
if
i
=
j
.
Doc 32
0.1478
0.1478
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Character_table.html
⟨
χ
i
,
χ
j
⟩
=
{
0
if
i
≠
j
,
1
if
i
=
j
.
Doc 33
0.1476
0.1476
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Kronecker_symbol.html
(
a
-
1
)
=
{
-
1
if
a
<
0
,
1
if
a
≥
0.
Doc 34
0.1423
0.1423
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Discrete_space.html
ρ
(
x
,
y
)
=
{
1
if
x
≠
y
,
0
if
x
=
y
Doc 35
0.1405
0.1405
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Floor_and_ceiling_functions.html
{
x
}
+
{
-
x
}
=
{
0
if
x
∈
ℤ
1
if
x
∉
ℤ
.
Doc 36
0.1394
0.2787
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Uniformly_most_powerful_test.html
ϕ
(
T
)
=
{
1
if
T
>
t
0
0
if
T
<
t
0
ϕ
(
x
)
=
{
1
if
x
>
x
0
0
if
x
<
x
0
Doc 37
0.1389
0.1389
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Conditional_probability_distribution.html
𝟏
A
(
ω
)
=
{
1
if
ω
∈
A
,
0
if
ω
∉
A
,
Doc 38
0.1385
0.1385
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Construction_of_t-norms.html
f
p
SS
(
x
)
=
{
-
log
x
if
p
=
0
1
-
x
p
p
otherwise.
Doc 39
0.1350
0.2688
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Derivative.html
f
(
x
)
=
{
+
x
2
,
if
x
≥
0
-
x
2
,
if
x
≤
0.
f
′
(
x
)
=
{
+
2
x
,
if
x
≥
0
-
2
x
,
if
x
≤
0.
Doc 40
0.1339
0.1339
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Rao–Blackwell_theorem.html
δ
0
=
{
1
if
X
1
=
0
,
0
otherwise,
Doc 41
0.1338
0.1338
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_distribution.html
f
(
k
;
p
)
=
{
p
if
k
=
1
,
1
-
p
if
k
=
0.
Doc 42
0.1320
0.1320
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/First-order_hold.html
=
{
1
T
(
1
+
t
T
)
if
0
≤
t
<
T
1
T
(
1
-
t
T
)
if
T
≤
t
<
2
T
0
otherwise
Doc 43
0.1319
0.1319
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Guard_(computer_science).html
f
(
x
)
=
{
1
if
x
>
0
0
otherwise
Doc 44
0.1319
0.1319
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Discrete_choice.html
y
n
i
=
{
1
,
if
U
n
i
>
U
n
j
,
j
≠
i
,
0
,
otherwise
Doc 45
0.1310
0.1310
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Linear_search.html
{
n
if
k
=
0
n
+
1
k
+
1
if
1
≤
k
≤
n
.
Doc 46
0.1292
0.2583
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Average_absolute_deviation.html
𝐈
O
:=
{
1
if
x
>
median
,
0
otherwise
.
𝐈
O
:=
{
1
if
x
>
μ
,
0
otherwise
.
Doc 47
0.1285
0.1285
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Inclusion–exclusion_principle.html
𝟏
S
(
x
)
:=
{
1
if
x
∈
S
,
0
if
x
∉
S
.
Doc 48
0.1285
0.1285
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Indicator_function.html
𝟏
A
(
x
)
:=
{
1
if
x
∈
A
,
0
if
x
∉
A
.
Doc 49
0.1284
0.1284
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Microcanonical_ensemble.html
f
(
x
)
=
{
1
,
if
|
x
|
<
1
2
,
0
,
otherwise
.
Doc 50
0.1278
0.1278
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Meridian_arc.html
B
2
k
=
{
c
0
,
if
k
=
0
,
c
k
/
k
,
if
k
>
0
,
Doc 51
0.1266
0.1266
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Lovász_number.html
u
i
T
u
j
=
{
1
,
if
i
=
j
,
0
,
if
i
j
∉
E
.
Doc 52
0.1265
0.1265
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Parseval's_identity.html
⟨
e
m
,
e
n
⟩
=
{
1
if
m
=
n
0
if
m
≠
n
.
Doc 53
0.1263
0.1263
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Limit_superior_and_limit_inferior.html
d
(
x
,
y
)
:=
{
0
if
x
=
y
,
1
if
x
≠
y
.
Doc 54
0.1262
0.4932
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Word_problem_for_groups.html
f
(
P
,
w
)
=
{
0
if
w
≠
1
in
G
undefined/does not halt
if
w
=
1
in
G
f
(
w
)
=
{
0
if
w
≠
1
in
H
undefined/does not halt
if
w
=
1
in
H
.
h
(
w
)
=
{
0
if
w
≠
1
in
S
undefined/does not halt
if
w
=
1
in
S
.
f
(
P
,
w
)
=
{
0
if
w
≠
1
in
H
undefined/does not halt
if
w
=
1
in
H
.
Doc 55
0.1262
0.1262
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Semi-continuity.html
f
(
x
)
=
{
sin
(
1
/
x
)
if
x
≠
0
,
1
if
x
=
0
,
Doc 56
0.1250
0.1250
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Beta_skeleton.html
θ
=
{
sin
-
1
1
β
,
if
β
≥
1
π
-
sin
-
1
β
,
if
β
≤
1
Doc 57
0.1228
0.1228
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Hodges'_estimator.html
θ
^
n
H
=
{
θ
^
n
,
if
|
θ
^
n
|
≥
n
-
1
/
4
,
and
0
,
if
|
θ
^
n
|
<
n
-
1
/
4
.
Doc 58
0.1223
0.1223
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Factorial.html
n
!
=
{
1
if
n
=
0
,
(
n
-
1
)
!
×
n
if
n
>
0
Doc 59
0.1205
0.1205
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Power_transform.html
y
i
(
λ
)
=
{
y
i
λ
-
1
λ
if
λ
≠
0
,
ln
(
y
i
)
if
λ
=
0
,
Doc 60
0.1205
0.1205
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Geometric_stable_distribution.html
Ω
=
{
tan
π
α
2
if
α
≠
1
,
-
2
π
log
|
t
|
if
α
=
1.
Doc 61
0.1174
0.1174
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Gaussian_period.html
P
=
{
-
1
+
p
2
,
if
p
=
4
m
+
1
,
-
1
+
i
p
2
,
if
p
=
4
m
+
3.
Doc 62
0.1173
0.1173
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Vandermonde_matrix.html
V
i
+
k
,
j
=
{
0
,
if
j
≤
k
;
(
j
-
1
)
!
(
j
-
k
-
1
)
!
α
i
j
-
k
-
1
,
if
j
>
k
.
Doc 63
0.1155
0.1155
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Sigma_additivity.html
μ
(
A
)
=
{
1
if
0
∈
A
0
if
0
∉
A
.
Doc 64
0.1140
0.1140
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Models_of_DNA_evolution.html
P
i
j
(
ν
)
=
{
1
4
+
3
4
e
-
4
ν
/
3
if
i
=
j
1
4
-
1
4
e
-
4
ν
/
3
if
i
≠
j
Doc 65
0.1111
0.1111
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Periodic_points_of_complex_quadratic_mappings.html
m
(
f
,
z
0
)
=
λ
=
{
f
c
′
(
z
0
)
,
if
z
0
≠
∞
1
f
c
′
(
z
0
)
,
if
z
0
=
∞
Doc 66
0.1095
0.2189
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/List_of_definite_integrals.html
∫
0
π
cos
m
x
cos
n
x
d
x
=
{
0
if
m
≠
n
π
2
if
m
=
n
m
,
n
positive integers
∫
0
π
sin
m
x
sin
n
x
d
x
=
{
0
if
m
≠
n
π
2
if
m
=
n
m
,
n
positive integers
Doc 67
0.1080
0.1080
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Preference_ranking_organization_method_for_enrichment_evaluation.html
P
j
(
d
j
)
=
{
0
if
d
j
≤
0
1
if
d
j
>
0
Doc 68
0.1078
0.1078
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Phase_detector_characteristic.html
φ
(
θ
)
=
{
1
+
2
θ
π
,
if
θ
∈
[
-
π
,
0
]
,
1
-
2
θ
π
,
if
θ
∈
[
0
,
π
]
.
Doc 69
0.1073
0.1073
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Carathéodory's_existence_theorem.html
H
(
t
)
=
{
0
,
if
t
≤
0
;
1
,
if
t
>
0.
Doc 70
0.1046
0.1046
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Self_number.html
D
R
*
(
n
)
=
{
D
R
(
n
)
2
,
if
D
R
(
n
)
is even
D
R
(
n
)
+
9
2
,
if
D
R
(
n
)
is odd
Doc 71
0.1028
0.1028
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/ATS_theorem.html
C
(
μ
)
=
{
1
,
if
f
′
(
a
)
<
μ
<
f
′
(
b
)
;
1
2
,
if
μ
=
f
′
(
a
)
or
μ
=
f
′
(
b
)
;
Doc 72
0.1016
0.1016
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Marchenko–Pastur_distribution.html
μ
(
A
)
=
{
(
1
-
1
λ
)
𝟏
0
∈
A
+
ν
(
A
)
,
if
λ
>
1
ν
(
A
)
,
if
0
≤
λ
≤
1
,
Doc 73
0.0993
0.0993
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Normally_distributed_and_uncorrelated_does_not_imply_independent.html
Y
=
{
X
if
|
X
|
≤
c
-
X
if
|
X
|
>
c
Doc 74
0.0954
0.0954
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Noncentral_t-distribution.html
E
[
T
k
]
=
{
(
ν
2
)
k
2
Γ
(
ν
-
k
2
)
Γ
(
ν
2
)
exp
(
-
μ
2
2
)
d
k
d
μ
k
exp
(
μ
2
2
)
,
if
ν
>
k
;
Does not exist
,
if
ν
≤
k
.
Doc 75
0.0948
0.0948
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Hinge_loss.html
ℓ
(
y
)
=
{
1
2
-
t
y
if
t
y
≤
0
,
1
2
(
1
-
t
y
)
2
if
0
<
t
y
≤
1
,
0
if
1
≤
t
y
Doc 76
0.0882
0.0882
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Gauss's_lemma_(number_theory).html
|
x
|
=
{
x
if
1
≤
x
≤
p
-
1
2
,
p
-
x
if
p
+
1
2
≤
x
≤
p
-
1.
Doc 77
0.0777
0.1555
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Mean_shift.html
F
(
x
)
=
{
1
if
∥
x
∥
≤
λ
0
if
∥
x
∥
>
λ
K
(
x
)
=
{
1
if
∥
x
∥
≤
λ
0
if
∥
x
∥
>
λ
Doc 78
0.0699
0.0699
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Filter_(large_eddy_simulation).html
G
(
s
y
m
b
o
l
x
-
s
y
m
b
o
l
r
)
=
{
1
Δ
,
if
|
s
y
m
b
o
l
x
-
s
y
m
b
o
l
r
|
≤
Δ
2
,
0
,
otherwise
.
Doc 79
0.0623
0.0623
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Matsubara_frequency.html
c
F
(
a
,
b
)
=
{
1
2
|
b
|
,
if
|
a
|
<
|
b
|
0
,
if
|
a
|
>
|
b
|
Doc 80
0.0387
0.0739
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/List_of_United_States_presidential_elections_by_Electoral_College_margin.html
absolute margin of victory
=
{
0
;
w
≤
c
2
w
-
max
{
r
,
c
2
}
;
w
>
c
2
normalized margin of victory
=
{
0
;
w
≤
c
2
w
-
max
{
r
,
c
2
}
c
2
;
w
>
c
2