Returned 98 matches (100 formulae, 76 docs)
    Lookup 7.920 ms, Re-ranking 1735.132 ms
    Found 102191 tuple postings, 57433 formulae, 13001 documents
[ formulas ] [ documents ] [ documents-by-formula ]

Doc 1
1.0000
1.4015
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Delay_spread.html
τ rms = 0 ( τ - τ ¯ ) 2 A c ( τ ) d τ 0 A c ( τ ) d τ
τ ¯ = 0 τ A c ( τ ) d τ 0 A c ( τ ) d τ

Doc 2
0.2411
0.2411
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Kirchhoff's_law_of_thermal_radiation.html
α sun = 0 α λ I λ sun ( λ ) d λ 0 I λ sun ( λ ) d λ

Doc 3
0.2339
0.4542
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Centroid.html
C k = z S k ( z ) d z S k ( z ) d z
C = x g ( x ) d x g ( x ) d x

Doc 4
0.2171
0.4192
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Xbar_and_s_chart.html
s = i = 1 n ( x i - x ¯ ) 2 n - 1
s ¯ i = j = 1 n ( x i j - x ¯ i ) 2 n - 1

Doc 5
0.2067
0.4061
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Opacity_(optics).html
1 κ = 0 κ ν - 1 u ( ν , T ) d ν 0 u ( ν , T ) d ν
1 κ = 0 ( κ ν , es + κ ν , ff ) - 1 u ( ν , T ) d ν 0 u ( ν , T ) d ν

Doc 6
0.1774
0.3302
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Root-mean-square_deviation.html
RMSD = t = 1 n ( y ^ t - y ) 2 n .
RMSD = t = 1 n ( x 1 , t - x 2 , t ) 2 n .

Doc 7
0.1751
0.3493
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/AB_magnitude.html
λ piv = e ( λ ) λ d λ e ( λ ) λ - 1 d λ
λ piv = e ( λ ) d λ e ( λ ) λ - 2 d λ

Doc 8
0.1726
0.5408
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Gabor_wavelet.html
( Δ k ) 2 = - ( k - k 0 ) 2 F ( k ) F * ( k ) d k - F ( k ) F * ( k ) d k
( Δ x ) 2 = - ( x - μ ) 2 f ( x ) f * ( x ) d x - f ( x ) f * ( x ) d x
μ = - x f ( x ) f * ( x ) d x - f ( x ) f * ( x ) d x
k 0 = - k F ( k ) F * ( k ) d k - F ( k ) F * ( k ) d k

Doc 9
0.1681
0.2984
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Residence_time_distribution.html
E ( t ) = C ( t ) 0 C ( t ) d t
σ 2 = 0 ( t - t ¯ ) 2 E ( t ) d t

Doc 10
0.1667
0.1667
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Proof_that_π_is_irrational.html
- x x ( x 2 - y 2 ) n cos ( y ) d y .

Doc 11
0.1618
0.1618
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Post-modern_portfolio_theory.html
d = - t ( t - r ) 2 f ( r ) d r

Doc 12
0.1590
0.1590
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Magnus_expansion.html
Ω 1 = 0 t A ( τ ) d τ

Doc 13
0.1573
0.1573
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Quantization_(signal_processing).html
d k = b k - 1 b k ( x - y k ) 2 f ( x ) d x

Doc 14
0.1553
0.1553
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Luminous_efficacy.html
0 y λ J λ d λ 0 J λ d λ ,

Doc 15
0.1538
0.1538
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Moment_(mathematics).html
μ n = - ( x - c ) n f ( x ) d x .

Doc 16
0.1514
0.1514
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Pitot_tube.html
u = 2 ( p t - p s ) ρ

Doc 17
0.1512
0.1512
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Sortino_ratio.html
D R = - T ( T - r ) 2 f ( r ) d r

Doc 18
0.1511
0.1511
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Cesàro_summation.html
lim λ 0 λ ( 1 - x λ ) α f ( x ) d x

Doc 19
0.1511
0.1511
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Improper_integral.html
lim λ 0 λ ( 1 - x λ ) α f ( x ) d x

Doc 20
0.1458
0.1458
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Omega_ratio.html
Ω ( r ) = r ( 1 - F ( x ) ) d x - r F ( x ) d x

Doc 21
0.1443
0.3436
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Logan_plot.html
0 t C p ( τ ) d τ ROI ( t )
0 t ROI ( τ ) d τ ROI ( t )
0 t A ( τ ) d τ = - 𝐔 n T 𝐊 - 1 𝐐 0 t C p ( τ ) d τ + 𝐔 n T 𝐊 - 1 𝐀
Doc 22
0.1429
0.1429
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Multiplier_(Fourier_analysis).html
1 2 π 0 2 π ( π - s ) f ( t - s ) d s

Doc 23
0.1423
0.1423
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/GEH_statistic.html
G E H = 2 ( M - C ) 2 M + C

Doc 24
0.1406
0.1406
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Calibration_curve.html
= ( y i - m x i - b ) 2 n - 2

Doc 25
0.1378
0.1378
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Numeric_precision_in_Microsoft_Excel.html
Σ ( x - x ¯ ) 2 n = Σ [ x - ( Σ x ) / n ] 2 n ,

Doc 26
0.1373
0.1373
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Degrees_of_freedom_(statistics).html
i = 1 n ( X i - X ¯ ) 2 σ 2

Doc 27
0.1346
0.1346
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Generation_time.html
T = x = 0 x ( x ) m ( x ) d x x = 0 ( x ) m ( x ) d x

Doc 28
0.1341
0.2682
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Zero_state_response.html
t 0 t f ( τ ) d τ
t 0 t f ( τ ) d τ

Doc 29
0.1340
0.1340
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Faraday's_laws_of_electrolysis.html
Q = 0 t I ( τ ) d τ

Doc 30
0.1330
0.2244
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Duhamel's_principle.html
= - t G ( t - τ ) F ( τ ) d τ
= 0 G ( τ ) F ( t - τ ) d τ

Doc 31
0.1330
0.2365
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Checking_whether_a_coin_is_fair.html
s p = p ( 1 - p ) n
= p ( 1 - p ) n = 0.5 × 0.5 n = 1 2 n

Doc 32
0.1321
0.2358
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Patlak_plot.html
0 t C p ( τ ) d τ / C p ( t )
R ( t ) C p ( t ) = K 0 t C p ( τ ) d τ C p ( t ) + V 0

Doc 33
0.1316
0.2250
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Short-time_Fourier_transform.html
- w ( τ ) d τ = 1.
- w ( t - τ ) d τ = 1 t

Doc 34
0.1300
0.1300
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Weight_function.html
Ω f ( x ) w ( x ) d x Ω w ( x ) d x

Doc 35
0.1283
0.3006
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Convolution.html
= - f ( t - τ ) g ( τ ) d τ .
= def - f ( τ ) g ( t - τ ) d τ
- δ ( τ ) g ( t - τ ) d τ = g ( t )
Doc 36
0.1262
0.1262
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Refinable_function.html
Φ ( t ) = 0 t φ ( τ ) d τ

Doc 37
0.1250
0.1250
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/PID_controller.html
I out = K i 0 t e ( τ ) d τ

Doc 38
0.1242
0.1242
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Lorenz_curve.html
L ( F ) = 0 F x ( F 1 ) d F 1 0 1 x ( F 1 ) d F 1

Doc 39
0.1226
0.1226
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Physics_of_magnetic_resonance_imaging.html
k ( t ) 0 t G ( τ ) d τ

Doc 40
0.1215
0.1215
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Failure_rate.html
F ( t ) = 0 t f ( τ ) d τ .

Doc 41
0.1192
0.1192
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Poisson–Boltzmann_equation.html
τ q U ( τ ) d τ

Doc 42
0.1189
0.1189
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Kinetic_scheme.html
d P d t = 0 t 𝐀 ( t - τ ) P ( τ ) d τ

Doc 43
0.1187
0.1187
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Signal-to-noise_ratio_(imaging).html
RMS noise = i = 1 n ( X i - i = 1 n X i n ) 2 n

Doc 44
0.1179
0.5690
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/P-chart.html
p ¯ ± 3 p ¯ ( 1 - p ¯ ) n
p ¯ ± 3 p ¯ ( 1 - p ¯ ) n
p ¯ ± 3 p ¯ ( 1 - p ¯ ) n ¯
p ¯ ± 3 p ¯ ( 1 - p ¯ ) n i
Z i = p ^ i - p ¯ p ¯ ( 1 - p ¯ ) n i

Doc 45
0.1179
0.1179
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Flight_dynamics_(spacecraft).html
v a = μ ( 1 - e ) a ( 1 + e )

Doc 46
0.1179
0.1179
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Linear_filter.html
y ( t ) = 0 T x ( t - τ ) h ( τ ) d τ

Doc 47
0.1159
0.1159
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/BKL_singularity.html
[ ( τ s - τ ¯ s ) 2 ] ¯ 1 2 = 1.4 s ,

Doc 48
0.1159
0.1159
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Millimeter_cloud_radar.html
W = 1 Z v m i n v m a x ( v d - V ) 2 S ( v d ) d v d

Doc 49
0.1149
0.1149
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Capacity_of_a_set.html
I [ u ] = D ( u ) T A ( u ) d x

Doc 50
0.1146
0.1146
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Master_equation.html
d P d t = 0 t 𝐀 ( t - τ ) P ( τ ) d τ .

Doc 51
0.1145
0.1927
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Laplace_transform.html
0 t f ( τ ) d τ = ( u * f ) ( t )
( f * g ) ( t ) = 0 t f ( τ ) g ( t - τ ) d τ

Doc 52
0.1137
0.2275
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Quantum_LC_circuit.html
Q ( t ) = - t I ( τ ) d τ
ϕ ( t ) - t V ( τ ) d τ

Doc 53
0.1093
0.1093
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Incircle_and_excircles_of_a_triangle.html
r a = s ( s - b ) ( s - c ) s - a .

Doc 54
0.1084
0.1084
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Histogram.html
σ g 1 = 6 ( n - 2 ) ( n + 1 ) ( n + 3 )

Doc 55
0.1071
0.1071
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Gramian_matrix.html
G i j = t 0 t f i ( τ ) j ¯ ( τ ) d τ .

Doc 56
0.1067
0.1067
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Semiperimeter.html
r = ( s - a ) ( s - b ) ( s - c ) s .

Doc 57
0.1067
0.1067
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Law_of_cotangents.html
r = ( s - a ) ( s - b ) ( s - c ) s .

Doc 58
0.1059
0.1059
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Statistical_hypothesis_testing.html
t = R 2 ( n - k - 1 * ) 1 - R 2

Doc 59
0.1020
0.1020
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Fractional_calculus.html
D t - α a f ( t ) = I t α a f ( t ) = 1 Γ ( α ) a t ( t - τ ) α - 1 f ( τ ) d τ

Doc 60
0.1017
0.1017
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Initialized_fractional_calculus.html
𝔻 t q f ( t ) = 1 Γ ( n - q ) d n d t n 0 t ( t - τ ) n - q - 1 f ( τ ) d τ + Ψ ( x )

Doc 61
0.1016
0.1016
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Heterogeneous_random_walk_in_one_dimension.html
G i j ( t ; L ) = 0 Ψ i ( t - τ ) W i j ( τ ; L ) d τ ,

Doc 62
0.1016
0.2012
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Causal_system.html
y ( t ) = 0 sin ( t + τ ) x ( τ ) d τ
y ( t ) = - sin ( t + τ ) x ( τ ) d τ

Doc 63
0.1014
0.1014
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Feynman–Kac_formula.html
e - 0 t V ( x ( τ ) ) d τ

Doc 64
0.1000
0.1000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Volume.html
π r 2 h 2 0 h ( h - x ) 2 d x

Doc 65
0.0992
0.1819
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Dirac_delta_function.html
= - f ( τ ) δ ( τ - ( t - T ) ) d τ
= def - f ( τ ) δ ( t - T - τ ) d τ

Doc 66
0.0928
0.0928
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Airborne_particulate_radioactivity_monitoring.html
R s t a c k ( η ) = 0 η Q ( τ ) F s t a c k ( τ ) d τ

Doc 67
0.0924
0.0924
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Lorentz_covariance.html
Δ τ = Δ s 2 c 2 , Δ s 2 > 0

Doc 68
0.0814
0.0814
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Twin_paradox.html
Δ t = 0 Δ τ e ± 0 τ ¯ a ( τ ) d τ d τ ¯ ,

Doc 69
0.0800
0.1346
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Causal_filter.html
f ( t ) = 0 h ( τ ) s ( t - τ ) d τ
f ( t - 1 ) = - 2 0 s ( t + τ ) d τ = 0 + 2 s ( t - τ ) d τ

Doc 70
0.0800
0.0800
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Biot–Tolstoy–Medwin_diffraction_model.html
p ( t ) = 0 h ( τ ) q ( t - τ ) d τ

Doc 71
0.0731
0.0731
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Optical_autocorrelation.html
A ( τ ) = - + I ( t ) I ( t - τ ) d t

Doc 72
0.0717
0.0717
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Leak_noise_correlator.html
( f g ) ( t ) = def - f * ( τ ) g ( t + τ ) d τ ,

Doc 73
0.0711
0.0711
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Beta_wavelet.html
σ i 2 = - + ( τ - m i ) 2 p i ( τ ) d τ

Doc 74
0.0667
0.0667
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/LTI_system_theory.html
- h ( t - τ ) A e s τ d τ

Doc 75
0.0585
0.0585
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Order_of_integration_(calculus).html
1 ( 2 π i ) 2 L * g ( τ ) d τ ( L * d τ 1 ( τ 1 - t ) ( τ - τ 1 ) ) = 0 .

Doc 76
0.0583
0.0583
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Circular_convolution.html
- h ( τ ) x T ( t - τ ) d τ