Returned 98 matches (100 formulae, 76 docs)
    Lookup 7.920 ms, Re-ranking 845.291 ms
    Found 102191 tuple postings, 57433 formulae, 13001 documents
[ formulas ] [ documents ] [ documents-by-formula ]

Doc 1
1.0000
0.0000
29.0000
1.6302
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
0.6138
-19.0000
10.0000
1.1737
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Opacity_(optics).html
1 κ = 0 ( κ ν , es + κ ν , ff ) - 1 u ( ν , T ) d ν 0 u ( ν , T ) d ν
1 κ = 0 κ ν - 1 u ( ν , T ) d ν 0 u ( ν , T ) d ν

Doc 3
0.5598
-9.0000
11.0000
0.5598
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 4
0.5042
-22.0000
10.0000
1.6248
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 5
0.4893
-4.0000
7.0000
0.9081
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 6
0.4187
-17.0000
7.0000
0.4187
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 7
0.3679
-10.0000
6.0000
0.3679
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 8
0.3480
-5.0000
7.0000
0.6455
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 9
0.3480
-6.0000
6.0000
0.3480
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 10
0.3480
-7.0000
6.0000
0.3480
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Sortino_ratio.html
D R = - T ( T - r ) 2 f ( r ) d r

Doc 11
0.3480
-14.0000
8.0000
0.3480
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 12
0.3480
-30.0000
9.0000
0.3480
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 13
0.3327
-8.0000
6.0000
0.3327
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Moment_(mathematics).html
μ n = - ( x - c ) n f ( x ) d x .

Doc 14
0.3327
-15.0000
7.0000
0.3327
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 15
0.3327
-18.0000
6.0000
0.3327
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 16
0.3125
-7.0000
5.0000
0.3125
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 17
0.3125
-9.0000
6.0000
0.3125
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 18
0.3125
-9.0000
6.0000
0.3125
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
0.3125
-10.0000
6.0000
0.6250
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/AB_magnitude.html
λ piv = e ( λ ) d λ e ( λ ) λ - 2 d λ
λ piv = e ( λ ) λ d λ e ( λ ) λ - 1 d λ

Doc 20
0.3125
-27.0000
8.0000
0.3125
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 21
0.3014
-7.0000
7.0000
0.3014
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 22
0.2975
-4.0000
6.0000
0.8573
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Logan_plot.html
0 t C p ( 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
0 t ROI ( τ ) d τ ROI ( t )
Doc 23
0.2975
-5.0000
6.0000
0.5950
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 24
0.2899
-9.0000
7.0000
0.5797
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 25
0.2769
-10.0000
6.0000
0.2769
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 26
0.2769
-18.0000
7.0000
0.2769
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 27
0.2623
-2.0000
6.0000
0.2623
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Faraday's_laws_of_electrolysis.html
Q = 0 t I ( τ ) d τ

Doc 28
0.2623
-3.0000
7.0000
0.2623
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Magnus_expansion.html
Ω 1 = 0 t A ( τ ) d τ

Doc 29
0.2623
-4.0000
6.0000
0.2623
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Refinable_function.html
Φ ( t ) = 0 t φ ( τ ) d τ

Doc 30
0.2623
-5.0000
6.0000
0.2623
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Failure_rate.html
F ( t ) = 0 t f ( τ ) d τ .

Doc 31
0.2623
-5.0000
6.0000
0.2623
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/PID_controller.html
I out = K i 0 t e ( τ ) d τ

Doc 32
0.2623
-6.0000
6.0000
0.2623
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 33
0.2623
-7.0000
6.0000
0.4893
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 34
0.2623
-10.0000
5.0000
0.2623
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
0.2623
-13.0000
6.0000
0.2623
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 36
0.2623
-17.0000
6.0000
0.2623
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 37
0.2535
-9.0000
6.0000
0.5070
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 38
0.2412
-7.0000
7.0000
0.4682
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 39
0.2412
-8.0000
7.0000
0.6246
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 40
0.2412
-8.0000
5.0000
0.2412
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 41
0.2412
-9.0000
7.0000
0.2412
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 42
0.2412
-13.0000
7.0000
0.2412
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
0.2412
-14.0000
7.0000
0.2412
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 44
0.2412
-17.0000
6.0000
0.2412
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 45
0.2270
-2.0000
5.0000
0.4541
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 46
0.2270
-4.0000
6.0000
0.4187
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 47
0.2270
-5.0000
5.0000
0.2270
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Feynman–Kac_formula.html
e - 0 t V ( x ( τ ) ) d τ

Doc 48
0.2270
-6.0000
5.0000
0.4541
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 49
0.2270
-10.0000
5.0000
0.4187
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 50
0.2270
-10.0000
5.0000
0.2270
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 51
0.2270
-10.0000
4.0000
0.4323
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 52
0.2270
-11.0000
6.0000
0.4187
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 53
0.2270
-12.0000
3.0000
0.2270
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Optical_autocorrelation.html
A ( τ ) = - + I ( t ) I ( t - τ ) d t

Doc 54
0.2270
-17.0000
6.0000
0.2270
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 55
0.2168
-7.0000
5.0000
0.2168
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 56
0.2168
-16.0000
6.0000
0.2168
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 57
0.2053
-5.0000
5.0000
0.2053
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Pitot_tube.html
u = 2 ( p t - p s ) ρ

Doc 58
0.2053
-8.0000
6.0000
0.2053
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/GEH_statistic.html
G E H = 2 ( M - C ) 2 M + C

Doc 59
0.2053
-10.0000
6.0000
0.2053
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Calibration_curve.html
= ( y i - m x i - b ) 2 n - 2

Doc 60
0.1917
-9.0000
3.0000
0.1917
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/LTI_system_theory.html
- h ( t - τ ) A e s τ d τ

Doc 61
0.1917
-10.0000
5.0000
0.1917
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 62
0.1917
-12.0000
6.0000
0.1917
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/BKL_singularity.html
[ ( τ s - τ ¯ s ) 2 ] ¯ 1 2 = 1.4 s ,

Doc 63
0.1917
-16.0000
4.0000
0.1917
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 64
0.1917
-18.0000
5.0000
0.1917
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 65
0.1917
-29.0000
5.0000
0.1917
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 66
0.1690
-4.0000
5.0000
0.1690
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Poisson–Boltzmann_equation.html
τ q U ( τ ) d τ

Doc 67
0.1690
-12.0000
5.0000
0.1690
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Semiperimeter.html
r = ( s - a ) ( s - b ) ( s - c ) s .

Doc 68
0.1690
-12.0000
5.0000
0.1690
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 69
0.1690
-12.0000
5.0000
0.1690
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Law_of_cotangents.html
r = ( s - a ) ( s - b ) ( s - c ) s .

Doc 70
0.1562
-11.0000
4.0000
0.1562
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Circular_convolution.html
- h ( τ ) x T ( t - τ ) d τ

Doc 71
0.1412
-5.0000
5.0000
0.2824
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 72
0.1412
-8.0000
5.0000
0.7059
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 i
p ¯ ± 3 p ¯ ( 1 - p ¯ ) n ¯
Z i = p ^ i - p ¯ p ¯ ( 1 - p ¯ ) n i

Doc 73
0.1412
-9.0000
5.0000
0.1412
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Flight_dynamics_(spacecraft).html
v a = μ ( 1 - e ) a ( 1 + e )

Doc 74
0.1412
-11.0000
5.0000
0.1412
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Statistical_hypothesis_testing.html
t = R 2 ( n - k - 1 * ) 1 - R 2

Doc 75
0.1412
-13.0000
5.0000
0.1412
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Histogram.html
σ g 1 = 6 ( n - 2 ) ( n + 1 ) ( n + 3 )

Doc 76
0.1322
-11.0000
5.0000
0.1322
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Lorentz_covariance.html
Δ τ = Δ s 2 c 2 , Δ s 2 > 0