Returned 85 matches (100 formulae, 84 docs)
    Lookup 130.687 ms, Re-ranking 1807.120 ms
    Found 482112 tuple postings, 185962 formulae, 22095 documents
[ formulas ] [ documents ] [ documents-by-formula ]

Doc 1
0.9383
0.9383
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
0.6444
0.6444
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 3
0.6403
6.3378
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 4
0.6115
1.2077
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 5
0.6079
1.7176
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 6
0.5995
0.5995
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Asymptote.html
f ( x ) = { 1 x if x > 0 , 5 if x 0.

Doc 7
0.5588
0.5588
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 8
0.5192
0.5192
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 9
0.5135
1.0265
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Derivative.html
f ( x ) = { + 2 x , if x 0 - 2 x , if x 0.
f ( x ) = { + x 2 , if x 0 - x 2 , if x 0.

Doc 10
0.5049
0.9283
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 11
0.5017
0.5017
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Directed_infinity.html
a z = { z if a > 0 , - z if a < 0.

Doc 12
0.4966
1.4081
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 13
0.4942
0.4942
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Comparator.html
V o = { 1 , if V + > V - 0 , if V + < V -

Doc 14
0.4894
0.4894
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 15
0.4818
0.4818
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 16
0.4722
0.4722
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Diaconescu's_theorem.html
U = { { 0 , 1 } , if P { 0 } , if ¬ P

Doc 17
0.4633
0.4633
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 18
0.4507
0.4507
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 19
0.4502
0.4502
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 20
0.4486
0.4486
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Sigma_additivity.html
μ ( A ) = { 1 if 0 A 0 if 0 A .

Doc 21
0.4410
0.4410
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 22
0.4409
0.4409
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 23
0.4403
0.4403
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 24
0.4395
0.4395
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 25
0.4357
0.4357
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 26
0.4335
0.4335
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 27
0.4327
0.4327
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 28
0.4327
0.4327
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
0.4308
0.8606
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 30
0.4294
0.4294
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 31
0.4291
0.4291
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 32
0.4266
0.4266
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 33
0.4255
0.4255
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Homogeneous_distribution.html
x + α = { x α if x > 0 0 otherwise

Doc 34
0.4253
0.4253
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/RA_plot.html
a = { a + ϵ , if a = 0 a , if a > 0

Doc 35
0.4250
0.8472
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Many-valued_logic.html
u G v = { 1 , if u v 0 , if u > v
¬ G u = { 1 , if u = 0 0 , if u > 0

Doc 36
0.4245
0.4245
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 37
0.4244
0.8387
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Truncated_power_function.html
x + n = { x n : x > 0 0 : x 0.
x + = { x : x > 0 0 : x 0.

Doc 38
0.4244
0.4244
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Guard_(computer_science).html
f ( x ) = { 1 if x > 0 0 otherwise

Doc 39
0.4239
0.4239
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Kronecker_symbol.html
( a - 1 ) = { - 1 if a < 0 , 1 if a 0.

Doc 40
0.4235
0.4235
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 41
0.4231
0.4231
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 42
0.4226
0.4226
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Differential_coding.html
h ( k ) = { 1 , if k 0 0 , if k < 0

Doc 43
0.4226
0.4226
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 44
0.4226
0.4226
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 45
0.4226
0.4226
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Unit_function.html
ε ( n ) = { 1 , if n = 1 0 , if n 1

Doc 46
0.4225
0.4225
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Piecewise.html
| x | = { - x , if x < 0 x , if x 0

Doc 47
0.4215
0.8429
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 48
0.4207
0.4207
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Smoothness.html
f ( x ) = { x if x 0 , 0 if x < 0

Doc 49
0.4203
0.4203
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 50
0.4203
0.4203
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 51
0.4203
0.4203
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 52
0.4192
0.8227
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 53
0.4192
0.4192
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 54
0.4192
0.4192
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 55
0.4192
0.4192
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Direct_integral.html
𝐇 n = { n if n < ω 2 if n = ω

Doc 56
0.4187
0.4187
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 57
0.4171
0.4171
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 58
0.4169
0.4169
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Coalgebra.html
ϵ ( X n ) = { 1 if n = 0 0 if n > 0

Doc 59
0.4169
0.4169
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 60
0.4157
0.4157
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 61
0.4156
0.4156
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Bochner–Riesz_mean.html
( ξ ) + = { ξ , if ξ > 0 0 , otherwise .

Doc 62
0.4150
0.8246
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 63
0.4150
0.4150
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 64
0.4150
0.4150
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Depletion_force.html
V ( h ) = { 0 if h σ if h < σ

Doc 65
0.4150
0.4150
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Normal_distribution.html
F ( x ) = { 0 if x < μ 1 if x μ

Doc 66
0.4102
0.4102
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 67
0.4096
0.4096
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Artificial_neuron.html
y = { 1 if u θ 0 if u < θ

Doc 68
0.4096
0.4096
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 69
0.4094
0.4094
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 70
0.4077
0.4077
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
0.4076
0.8153
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 72
0.4073
0.4073
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 73
0.4073
0.4073
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 74
0.4073
0.4073
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Multiset.html
𝟏 A ( x ) = { 1 if x A , 0 if x A .

Doc 75
0.4073
0.4073
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 76
0.4057
0.4057
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Sorting_network.html
f ( x ) = { 1 if x > a i 0 otherwise.

Doc 77
0.4028
0.4028
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 78
0.4014
0.8028
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 79
0.3953
0.3953
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 80
0.3902
0.3902
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 81
0.3833
0.3833
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
0.3722
0.3722
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Iverson_bracket.html
[ P ] = { 1 if P is true; 0 otherwise.

Doc 83
0.3715
0.3715
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Conditioning_(probability).html
I = { 1 if Y 1 / 3 , 0 otherwise ,

Doc 84
0.2890
0.2890
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Microcanonical_ensemble.html
f ( x ) = { 1 , if | x | < 1 2 , 0 , otherwise .