tangent
Not Supported
*1*
=
{
*2*
if
*3*
>
1
2
*4*
if
*3*
≤
1
2
Search
Returned 85 matches (100 formulae, 84 docs)
Lookup 130.687 ms, Re-ranking 1014.395 ms
Found 482112 tuple postings, 185962 formulae, 22095 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
Doc 1
1.0000
-2.0000
13.0000
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
0.6826
-7.0000
8.0000
0.6826
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
Doc 3
0.6826
-11.0000
8.0000
0.6826
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
.
Doc 4
0.6567
-2.0000
7.0000
6.5672
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Tobit_model.html
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
*
>
0
0
if
y
i
*
≤
0
y
i
=
{
y
i
*
if
y
i
*
>
y
L
y
L
if
y
i
*
≤
y
L
.
Doc 5
0.6567
-2.0000
7.0000
0.6567
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 6
0.6567
-3.0000
7.0000
1.8230
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Binomial_regression.html
Y
n
=
{
1
,
if
U
n
>
0
,
0
,
if
U
n
≤
0
Y
n
=
{
1
,
if
U
n
>
0
,
0
,
if
U
n
≤
0
Y
=
{
0
,
if
Y
*
>
0
1
,
if
Y
*
<
0.
Doc 7
0.6567
-3.0000
7.0000
0.6567
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Asymptote.html
f
(
x
)
=
{
1
x
if
x
>
0
,
5
if
x
≤
0.
Doc 8
0.6567
-4.0000
7.0000
1.3134
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Non-analytic_smooth_function.html
f
(
n
)
(
x
)
=
{
p
n
(
x
)
x
2
n
f
(
x
)
if
x
>
0
,
0
if
x
≤
0
,
f
(
x
)
=
{
exp
(
-
1
/
x
)
if
x
>
0
,
0
if
x
≤
0
,
Doc 9
0.5422
-1.0000
5.0000
0.5422
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Homogeneous_distribution.html
x
+
α
=
{
x
α
if
x
>
0
0
otherwise
Doc 10
0.5422
-1.0000
5.0000
0.5422
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Guard_(computer_science).html
f
(
x
)
=
{
1
if
x
>
0
0
otherwise
Doc 11
0.5422
-1.0000
5.0000
0.5422
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Rectifier_(neural_networks).html
f
(
x
)
=
{
x
if
x
>
0
0.01
x
otherwise
Doc 12
0.5422
-2.0000
5.0000
0.5422
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Bochner–Riesz_mean.html
(
ξ
)
+
=
{
ξ
,
if
ξ
>
0
0
,
otherwise
.
Doc 13
0.5422
-2.0000
5.0000
0.5422
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Sorting_network.html
f
(
x
)
=
{
1
if
x
>
a
i
0
otherwise.
Doc 14
0.5422
-3.0000
5.0000
1.0843
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 15
0.5096
-2.0000
6.0000
1.0191
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 16
0.5096
-2.0000
6.0000
0.9944
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Absolute_value.html
|
a
|
=
{
a
,
if
a
≥
0
-
a
,
if
a
≤
0
|
x
|
=
{
x
,
if
x
≥
0
-
x
,
if
x
<
0.
Doc 17
0.5096
-2.0000
6.0000
0.5096
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 18
0.5096
-3.0000
6.0000
1.5040
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
ϕ
(
x
)
=
{
1
if
x
∈
R
0
if
x
∈
A
Doc 19
0.5096
-3.0000
6.0000
0.5096
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Directed_infinity.html
a
z
∞
=
{
z
∞
if
a
>
0
,
-
z
∞
if
a
<
0.
Doc 20
0.5096
-4.0000
6.0000
0.5096
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 21
0.5096
-4.0000
6.0000
0.5096
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Comparator.html
V
o
=
{
1
,
if
V
+
>
V
-
0
,
if
V
+
<
V
-
Doc 22
0.4848
0.0000
4.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Iverson_bracket.html
[
P
]
=
{
1
if
P
is true;
0
otherwise.
Doc 23
0.4848
-1.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Diaconescu's_theorem.html
U
=
{
{
0
,
1
}
,
if
P
{
0
}
,
if
¬
P
Doc 24
0.4848
-1.0000
4.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Conditioning_(probability).html
I
=
{
1
if
Y
≤
1
/
3
,
0
otherwise
,
Doc 25
0.4848
-2.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Pell_number.html
t
n
=
{
2
P
n
2
if
n
is even
;
H
n
2
if
n
is odd.
Doc 26
0.4848
-2.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Symmetric_derivative.html
f
(
x
)
=
{
1
,
if
x
is rational
0
,
if
x
is irrational
Doc 27
0.4848
-2.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Chebyshev_filter.html
G
n
+
1
=
{
1
if
n
odd
coth
2
(
β
4
)
if
n
even
Doc 28
0.4848
-2.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Counting_measure.html
μ
(
A
)
=
{
|
A
|
if
A
is finite
+
∞
if
A
is infinite
Doc 29
0.4848
-2.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/List_of_limits.html
lim
x
→
0
-
1
x
r
=
{
-
∞
,
if
r
is odd
+
∞
,
if
r
is even
Doc 30
0.4848
-2.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Euler's_totient_function.html
φ
(
2
m
)
=
{
2
φ
(
m
)
if
m
is even
φ
(
m
)
if
m
is odd
Doc 31
0.4848
-2.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Symmetric_group.html
sgn
f
=
{
+
1
,
if
f
is even
-
1
,
if
f
is odd
.
Doc 32
0.4848
-3.0000
5.0000
0.9697
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Many-valued_logic.html
¬
G
u
=
{
1
,
if
u
=
0
0
,
if
u
>
0
u
→
G
v
=
{
1
,
if
u
≤
v
0
,
if
u
>
v
Doc 33
0.4848
-3.0000
5.0000
0.9697
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Spectral_sequence.html
(
C
i
,
j
I
I
)
p
=
{
0
if
j
<
p
C
i
,
j
if
j
≥
p
(
C
i
,
j
I
)
p
=
{
0
if
i
<
p
C
i
,
j
if
i
≥
p
Doc 34
0.4848
-3.0000
5.0000
0.9697
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Möbius_function.html
∑
d
|
n
μ
(
d
)
=
{
1
if
n
=
1
0
if
n
>
1.
∑
d
|
n
μ
(
d
)
=
{
1
if
n
=
1
0
if
n
>
1.
Doc 35
0.4848
-3.0000
5.0000
0.9697
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Kronecker_delta.html
δ
i
=
{
0
,
if
i
≠
0
1
,
if
i
=
0
δ
i
j
=
{
0
if
i
≠
j
,
1
if
i
=
j
.
Doc 36
0.4848
-3.0000
5.0000
0.9697
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Dirac_delta_function.html
H
(
x
)
=
{
1
if
x
≥
0
0
if
x
<
0.
δ
x
0
(
A
)
=
{
1
if
x
0
∈
A
0
if
x
0
∉
A
Doc 37
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Unit_function.html
ε
(
n
)
=
{
1
,
if
n
=
1
0
,
if
n
≠
1
Doc 38
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Differential_coding.html
h
(
k
)
=
{
1
,
if
k
≥
0
0
,
if
k
<
0
Doc 39
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Möbius_inversion_formula.html
ε
(
n
)
=
{
1
,
if
n
=
1
0
,
if
n
>
1
Doc 40
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Artificial_neuron.html
y
=
{
1
if
u
≥
θ
0
if
u
<
θ
Doc 41
0.4848
-3.0000
5.0000
0.4848
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 42
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Recursively_enumerable_set.html
f
(
x
)
=
{
1
if
x
∈
S
undefined/does not halt
if
x
∉
S
Doc 43
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Limit_of_a_function.html
f
(
f
(
x
)
)
=
{
1
if
x
≠
0
0
if
x
=
0
Doc 44
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Coalgebra.html
ϵ
(
X
n
)
=
{
1
if
n
=
0
0
if
n
>
0
Doc 45
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Set_(abstract_data_type).html
F
(
x
)
=
{
1
,
if
x
∈
S
0
,
if
x
∉
S
Doc 46
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Electromagnetic_reverberation_chamber.html
γ
=
{
1
if
p
≠
0
1
/
2
if
p
=
0
Doc 47
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Kronecker_symbol.html
(
a
-
1
)
=
{
-
1
if
a
<
0
,
1
if
a
≥
0.
Doc 48
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Smoothness.html
f
(
x
)
=
{
x
if
x
≥
0
,
0
if
x
<
0
Doc 49
0.4848
-3.0000
5.0000
0.4848
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 50
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Subobject_classifier.html
χ
A
(
x
)
=
{
0
,
if
x
∉
A
1
,
if
x
∈
A
Doc 51
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/P-adic_order.html
|
x
|
p
=
{
p
-
ν
p
(
x
)
if
x
≠
0
0
if
x
=
0
Doc 52
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Depletion_force.html
V
(
h
)
=
{
0
if
h
≥
σ
∞
if
h
<
σ
Doc 53
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Direct_integral.html
𝐇
n
=
{
ℂ
n
if
n
<
ω
ℓ
2
if
n
=
ω
Doc 54
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/RA_plot.html
a
=
{
a
+
ϵ
,
if
a
=
0
a
,
if
a
>
0
Doc 55
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Integer.html
f
(
x
)
=
{
2
|
x
|
,
if
x
≤
0
2
x
-
1
,
if
x
>
0.
Doc 56
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Normal_distribution.html
F
(
x
)
=
{
0
if
x
<
μ
1
if
x
≥
μ
Doc 57
0.4848
-3.0000
5.0000
0.4848
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 58
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Sigma_additivity.html
μ
(
A
)
=
{
1
if
0
∈
A
0
if
0
∉
A
.
Doc 59
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Spline_wavelet.html
δ
i
j
=
{
1
,
if
i
=
j
0
,
if
i
≠
j
Doc 60
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Piecewise.html
|
x
|
=
{
-
x
,
if
x
<
0
x
,
if
x
≥
0
Doc 61
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/String_operations.html
(
s
a
)
/
b
=
{
s
if
a
=
b
ε
if
a
≠
b
Doc 62
0.4848
-3.0000
5.0000
0.4848
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 63
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Radial_basis_function_network.html
δ
i
j
=
{
1
,
if
i
=
j
0
,
if
i
≠
j
Doc 64
0.4848
-3.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Ramanujan's_sum.html
η
q
(
n
)
=
{
0
if
q
∤
n
q
if
q
∣
n
Doc 65
0.4848
-4.0000
5.0000
0.9697
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 66
0.4848
-4.0000
5.0000
0.4848
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 67
0.4848
-4.0000
5.0000
0.4848
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 68
0.4848
-4.0000
5.0000
0.4848
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 69
0.4848
-4.0000
5.0000
0.4848
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 70
0.4848
-4.0000
5.0000
0.4848
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 71
0.4848
-4.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Davenport–Schmidt_theorem.html
C
=
{
C
0
if
|
ξ
|
<
1
C
0
ξ
2
if
|
ξ
|
>
1.
Doc 72
0.4848
-4.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Discrete_measure.html
δ
s
i
(
X
)
=
{
1
if
s
i
∈
X
0
if
s
i
∉
X
Doc 73
0.4848
-4.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Multiset.html
𝟏
A
(
x
)
=
{
1
if
x
∈
A
,
0
if
x
∉
A
.
Doc 74
0.4848
-4.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Hamiltonian_optics.html
n
(
x
3
)
=
{
n
A
if
x
3
<
0
n
B
if
x
3
>
0
Doc 75
0.4848
-4.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Cebeci–Smith_model.html
μ
t
=
{
μ
t
inner
if
y
≤
y
crossover
μ
t
outer
if
y
>
y
crossover
Doc 76
0.4848
-4.0000
5.0000
0.4848
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 77
0.4848
-5.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Neural_cryptography.html
θ
N
(
x
)
=
{
0
if
x
≤
N
/
2
,
1
if
x
>
N
/
2.
Doc 78
0.4848
-5.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Instantaneously_trained_neural_networks.html
y
=
{
1
if
∑
x
i
≥
0
0
if
∑
x
i
<
0
Doc 79
0.4848
-6.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Convolution_for_optical_broad-beam_responses_in_scattering_media.html
S
(
r
′
)
=
{
S
0
,
if
r
′
≤
R
0
,
if
r
′
>
R
(
8
)
Doc 80
0.4848
-6.0000
5.0000
0.4848
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 81
0.4848
-7.0000
5.0000
0.4848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Valuation_(measure_theory).html
δ
x
(
U
)
=
{
0
if
x
∉
U
1
if
x
∈
U
∀
U
∈
𝒯
Doc 82
0.4848
-8.0000
5.0000
0.4848
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 83
0.4317
-4.0000
5.0000
0.8633
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Truncated_power_function.html
x
+
=
{
x
:
x
>
0
0
:
x
≤
0.
x
+
n
=
{
x
n
:
x
>
0
0
:
x
≤
0.
Doc 84
0.2932
-3.0000
3.0000
0.2932
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Microcanonical_ensemble.html
f
(
x
)
=
{
1
,
if
|
x
|
<
1
2
,
0
,
otherwise
.