Returned 97 matches (100 formulae, 48 docs)
    Lookup 1356.520 ms, Re-ranking 40255.016 ms
    Found 1729858 tuple postings, 206841 formulae, 22235 documents
[ formulas ] [ documents ] [ documents-by-formula ]

Doc 1
0.8590
-13.0000
58.0000
8.6262
testing/wikipedia/v3/21960.html
u 1 ( 𝐱 , z 1 ) = v 1 + u ˙ x By definition of  v 1 = - V x 𝐱 g x ( 𝐱 ) - k 1 ( z 1 - u x ( 𝐱 ) e 1 ) v 1 + u x 𝐱 ( f x ( 𝐱 ) + g x ( 𝐱 ) z 1 𝐱 ˙  (i.e.,  d 𝐱 d t ) ) u ˙ x  (i.e.,  d u x d t )
u 1 ( 𝐱 , z 1 ) = - V x 𝐱 g x ( 𝐱 ) - k 1 ( z 1 - u x ( 𝐱 ) ) + u x 𝐱 ( f x ( 𝐱 ) + g x ( 𝐱 ) z 1 )
u a 1 ( 𝐱 , z 1 ) = - V x 𝐱 g x ( 𝐱 ) - k 1 ( z 1 - u x ( 𝐱 ) ) + u x 𝐱 ( f x ( 𝐱 ) + g x ( 𝐱 ) z 1 )
u 1 ( 𝐱 , z 1 ) = 1 g 1 ( 𝐱 , z 1 ) ( - V x 𝐱 g x ( 𝐱 ) - k 1 ( z 1 - u x ( 𝐱 ) ) + u x 𝐱 ( f x ( 𝐱 ) + g x ( 𝐱 ) z 1 ) u a 1 ( 𝐱 , z 1 ) - f 1 ( 𝐱 , z 1 ) )
u i ( 𝐱 , z 1 , z 2 , , z i 𝐱 i ) = - V i - 1 𝐱 i - 1 g i - 1 ( 𝐱 i - 1 ) - k i ( z i - u i - 1 ( 𝐱 i - 1 ) ) + u i - 1 𝐱 i - 1 ( f i - 1 ( 𝐱 i - 1 ) + g i - 1 ( 𝐱 i - 1 ) z i )
u 2 ( 𝐱 , z 1 , z 2 ) = - V 1 𝐱 1 g 1 ( 𝐱 1 ) - k 2 ( z 2 - u 1 ( 𝐱 1 ) ) + u 1 𝐱 1 ( f 1 ( 𝐱 1 ) + g 1 ( 𝐱 1 ) z 2 )
u 3 ( 𝐱 , z 1 , z 2 , z 3 ) = - V 2 𝐱 2 g 2 ( 𝐱 2 ) - k 3 ( z 3 - u 2 ( 𝐱 2 ) ) + u 2 𝐱 2 ( f 2 ( 𝐱 2 ) + g 2 ( 𝐱 2 ) z 3 )
u i ( 𝐱 , z 1 , z 2 , , z i 𝐱 i ) = 1 g i ( 𝐱 i ) ( - V i - 1 𝐱 i - 1 g i - 1 ( 𝐱 i - 1 ) - k i ( z i - u i - 1 ( 𝐱 i - 1 ) ) + u i - 1 𝐱 i - 1 ( f i - 1 ( 𝐱 i - 1 ) + g i - 1 ( 𝐱 i - 1 ) z i ) Single-integrator stabilizing control  u a i ( 𝐱 i ) - f i ( 𝐱 i - 1 ) )
V ˙ 1 = V ˙ x ( 𝐱 ) + 1 2 ( 2 e 1 e ˙ 1 ) = V ˙ x ( 𝐱 ) + e 1 e ˙ 1 = V ˙ x ( 𝐱 ) + e 1 v 1 e ˙ 1 = V x 𝐱 𝐱 ˙ (i.e.,  d 𝐱 d t ) V ˙ x  (i.e., d V x d t ) + e 1 v 1 = V x 𝐱 ( ( f x ( 𝐱 ) + g x ( 𝐱 ) u x ( 𝐱 ) ) + g x ( 𝐱 ) e 1 ) 𝐱 ˙ V ˙ x + e 1 v 1
v 1 = - V x 𝐱 g x ( 𝐱 ) - k 1 e 1
V ˙ x = V x 𝐱 ( f x ( 𝐱 ) + g x ( 𝐱 ) u x ( 𝐱 ) ) - W ( 𝐱 )
V ˙ 1 = - W ( 𝐱 ) + V x 𝐱 g x ( 𝐱 ) e 1 + e 1 ( - V x 𝐱 g x ( 𝐱 ) - k 1 e 1 ) v 1
V ˙ 1 = V x 𝐱 ( f x ( 𝐱 ) + g x ( 𝐱 ) u x ( 𝐱 ) ) - W ( 𝐱 ) + V x 𝐱 g x ( 𝐱 ) e 1 + e 1 v 1 - W ( 𝐱 ) + V x 𝐱 g x ( 𝐱 ) e 1 + e 1 v 1
V 3 ( 𝐱 , z 1 , z 2 , z 3 ) = V 2 ( 𝐱 2 ) + 1 2 ( z 3 - u 2 ( 𝐱 2 ) ) 2
V ˙ 1 = - W ( 𝐱 ) + V x 𝐱 g x ( 𝐱 ) e 1 - e 1 V x 𝐱 g x ( 𝐱 ) 0 - k 1 e 1 2 = - W ( 𝐱 ) - k 1 e 1 2 - W ( 𝐱 ) < 0
V 1 ( 𝐱 , z 1 ) = V x ( 𝐱 ) + 1 2 ( z 1 - u x ( 𝐱 ) ) 2
V 1 ( 𝐱 , z 1 ) V x ( 𝐱 ) + 1 2 ( z 1 - u x ( 𝐱 ) ) 2
V i ( 𝐱 i ) = V i - 1 ( 𝐱 i - 1 ) + 1 2 ( z i - u i - 1 ( 𝐱 i - 1 ) ) 2
V 2 ( 𝐱 , z 1 , z 2 ) = V 1 ( 𝐱 1 ) + 1 2 ( z 2 - u 1 ( 𝐱 1 ) ) 2
V 2 ( 𝐱 , z 1 , z 2 ) = V 1 ( 𝐱 , z 1 ) + 1 2 ( z 2 - u 1 ( 𝐱 , z 1 ) ) 2
{ [ 𝐱 ˙ z ˙ 1 ] 𝐱 ˙ 1 = [ f x ( 𝐱 ) + g x ( 𝐱 ) z 1 0 ] f 1 ( 𝐱 1 ) + [ 𝟎 1 ] g 1 ( 𝐱 1 ) z 2  ( by Lyapunov function  V 1 ,  subsystem stabilized by  u 1 ( 𝐱 1 )  ) z ˙ 2 = u 2
{ [ 𝐱 ˙ z ˙ 1 z ˙ 2 ] 𝐱 ˙ 2 = [ f x ( 𝐱 ) + g x ( 𝐱 ) z 2 z 2 0 ] f 2 ( 𝐱 2 ) + [ 𝟎 0 1 ] g 2 ( 𝐱 2 ) z 3  ( by Lyapunov function  V 2 ,  subsystem stabilized by  u 2 ( 𝐱 2 )  ) z ˙ 3 = u 3
{ 𝐱 ˙ = f x ( 𝐱 ) + g x ( 𝐱 ) z 1 z ˙ 1 = u 1
{ 𝐱 ˙ = f x ( 𝐱 ) + g x ( 𝐱 ) z 1 z ˙ 1 = u a 1
{ 𝐱 ˙ = f x ( 𝐱 ) + g x ( 𝐱 ) z 1 z ˙ 1 = z 2 z ˙ 2 = u 2
{ 𝐱 ˙ = ( f x ( 𝐱 ) + g x ( 𝐱 ) u x ( 𝐱 ) ) + g x ( 𝐱 ) e 1 e ˙ 1 = v 1
{ 𝐱 ˙ = f x ( 𝐱 ) + g x ( 𝐱 ) z 1 z ˙ 1 = z 2 z ˙ 2 = z 3 z ˙ 3 = u 3
{ 𝐱 ˙ = ( f x ( 𝐱 ) + g x ( 𝐱 ) u x ( 𝐱 ) ) + g x ( 𝐱 ) e 1 e ˙ 1 = u 1 - u ˙ x
{ 𝐲 ˙ = f y ( 𝐲 ) + g y ( 𝐲 ) z 2 ( where this  𝐲  subsystem is stabilized by  z 2 = u 1 ( 𝐱 , z 1 )  ) z ˙ 2 = u 2 .
{ 𝐱 ˙ = f x ( 𝐱 ) + g x ( 𝐱 ) z 1 z ˙ 1 = f 1 ( 𝐱 , z 1 ) + g 1 ( 𝐱 , z 1 ) u 1
{ 𝐱 ˙ = f x ( 𝐱 ) + g x ( 𝐱 ) z 1 + ( g x ( 𝐱 ) u x ( 𝐱 ) - g x ( 𝐱 ) u x ( 𝐱 ) ) 0 z ˙ 1 = u 1
{ x ˙ = ( f x ( 𝐱 ) + g x ( 𝐱 ) u x ( 𝐱 ) ) F ( 𝐱 ) + g x ( 𝐱 ) ( z 1 - u x ( 𝐱 ) ) z 1  error tracking  u x z ˙ 1 = u 1
{ [ 𝐱 ˙ 1 z ˙ 2 ] 𝐱 ˙ 2 = [ f 1 ( 𝐱 1 ) + g 1 ( 𝐱 1 ) z 2 0 ] f 2 ( 𝐱 2 ) + [ 𝟎 1 ] g 2 ( 𝐱 2 ) z 3  ( by Lyapunov function  V 2 ,  subsystem stabilized by  u 2 ( 𝐱 2 )  ) z ˙ 3 = u 3
{ 𝐱 ˙ = f x ( 𝐱 ) + g x ( 𝐱 ) z 1 z ˙ 1 = f 1 ( 𝐱 , z 1 ) + g 1 ( 𝐱 , z 1 ) 1 g 1 ( 𝐱 , z 1 ) ( u a 1 - f 1 ( 𝐱 , z 1 ) ) u 1 ( 𝐱 , z 1 )
{ 𝐱 ˙ = f x ( 𝐱 ) + g x ( 𝐱 ) z 1  ( by Lyapunov function  V x ,  subsystem stabilized by  u x ( 𝐱 )  ) z ˙ 1 = z 2 z ˙ 2 = z 3 z ˙ i = z i + 1 z ˙ k - 2 = z k - 1 z ˙ k - 1 = z k z ˙ k = u
{ 𝐱 ˙ 1 = f 1 ( 𝐱 1 ) + g 1 ( 𝐱 1 ) z 2  ( by Lyapunov function  V 1 ,  subsystem stabilized by  u 1 ( 𝐱 1 )  ) z ˙ 2 = u 2
{ 𝐱 ˙ 2 = f 2 ( 𝐱 2 ) + g 2 ( 𝐱 2 ) z 3  ( by Lyapunov function  V 2 ,  subsystem stabilized by  u 2 ( 𝐱 2 )  ) z ˙ 3 = u 3
u 1 ( 𝐱 , z 1 ) = 1 g 1 ( 𝐱 , z 1 ) ( u a 1 - f 1 ( 𝐱 , z 1 ) )
{ 𝐱 ˙ = f x ( 𝟎 𝐱 ) + ( g x ( 𝟎 𝐱 ) ) ( 0 z 1 ) = 0 + ( g x ( 𝟎 ) ) ( 0 ) = 𝟎  (i.e.,  𝐱 = 𝟎  is stationary) z ˙ 1 = 0 u 1  (i.e.,  z 1 = 0  is stationary)
Doc 2
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testing/wikipedia/v3/23338.html
V 1 ( 𝐱 , z 1 ) = V x ( 𝐱 ) + 1 2 ( z 1 - u x ( 𝐱 ) ) 2
V 2 ( 𝐱 , z 1 , z 2 ) = V 1 ( 𝐱 , z 1 ) + 1 2 ( z 2 - u 1 ( 𝐱 , z 1 ) ) 2

Doc 3
0.1440
-37.0000
7.0000
0.1440
testing/wikipedia/v3/17507.html
A f ( x ) = i b i ( x ) f x i ( x ) + 1 2 i , j ( σ σ ) i , j ( x ) 2 f x i x j ( x ) .

Doc 4
0.1325
-36.0000
5.0000
0.1325
testing/wikipedia/v3/25461.html
f ′′′ ( x 0 ) - 1 2 f ( x - 2 ) + f ( x - 1 ) - f ( x + 1 ) + 1 2 f ( x + 2 ) h x 3 + O ( h x 2 )

Doc 5
0.1297
-27.0000
3.0000
0.6432
testing/wikipedia/v3/06206.html
= 𝔼 θ [ V ( x ( θ ) , θ ) - u ¯ ( θ 0 ) - 1 - P ( θ ) p ( θ ) V θ - c ( x ( θ ) ) ]
H = ( V ( x , θ ) - u ¯ ( θ 0 ) - 1 - P ( θ ) p ( θ ) V θ ( x , θ ) - c ( x ) ) p ( θ ) + ν ( θ ) x θ
ϕ 2 ( x ) ϕ 1 ( x ) ( V x ( x , θ ) - 1 - P ( θ ) p ( θ ) 2 V θ x ( x , θ ) - c x ( x ) ) d θ = 0
ν θ = - H x = - ( V x ( x , θ ) - 1 - P ( θ ) p ( θ ) 2 V θ x ( x , θ ) - c x ( x ) ) p ( θ )
𝔼 θ [ V ( x ( θ ) , θ ) - u ¯ ( θ 0 ) - θ 0 θ V θ ~ d θ ~ - c ( x ( θ ) ) ]

Doc 6
0.1297
-34.0000
4.0000
0.1297
testing/wikipedia/v3/16262.html
2 𝐱 i ( t ) t 2 m i = - 𝐱 i [ V ( 𝐱 i ( t ) ) + k = 1 n λ k σ k ( t ) ] ,  i = 1 N .

Doc 7
0.1244
-24.0000
3.0000
0.1244
testing/wikipedia/v3/00649.html
ψ ( 𝐫 1 ,  𝐫 2 ) = 1 2 ( u A ( 𝐫 1 ) u B ( 𝐫 2 ) + u B ( 𝐫 1 ) u A ( 𝐫 2 ) )

Doc 8
0.1198
-35.0000
4.0000
0.2287
testing/wikipedia/v3/29918.html
t E ( u ) + x F ( u ) = 0 where E ( u ) = S ( u ) - 1 2 κ ( u x , u ) ,  F ( u ) = 1 2 κ ( u t , u ) .
t I ( u ) + x G ( u ) = 0 where I ( u ) = 1 2 ω ( u x , u ) ,  G ( u ) = S ( u ) - 1 2 ω ( u t , u ) .

Doc 9
0.1198
-42.0000
5.0000
0.1198
testing/wikipedia/v3/00354.html
Π ( n , k ) n = 1 2 ( k 2 - n ) ( n - 1 ) ( E ( k ) + 1 n ( k 2 - n ) K ( k ) + 1 n ( n 2 - k 2 ) Π ( n , k ) )

Doc 10
0.1153
-25.0000
4.0000
0.1153
testing/wikipedia/v3/06475.html
d d s u ( x ( s ) , t ( s ) ) = u x d x d s + u t d t d s

Doc 11
0.1121
-41.0000
7.0000
0.1121
testing/wikipedia/v3/17975.html
ε x x = u x x = - z φ x ;   ε x z = 1 2 ( u x z + u z x ) = 1 2 ( - φ + w x )

Doc 12
0.1102
-31.0000
2.0000
0.1102
testing/wikipedia/v3/03194.html
Ψ ( x 1 , x n ) = 1 n ! | ψ 1 ( x 1 ) ψ n ( x 1 ) ψ 1 ( x n ) ψ n ( x n ) |

Doc 13
0.1102
-32.0000
5.0000
0.1102
testing/wikipedia/v3/01538.html
ρ t + 1 r r ( ρ r u r ) + 1 r ( ρ u ϕ ) ϕ + ( ρ u z ) z = 0.

Doc 14
0.1102
-36.0000
3.0000
0.1102
testing/wikipedia/v3/16864.html
v 1 𝐞 1 + v 2 𝐞 2 = 𝐞 1 h 2 h 3 x 2 ( h 3 ψ 3 ) - 𝐞 2 h 3 h 1 x 1 ( h 3 ψ 3 )

Doc 15
0.1102
-38.0000
4.0000
0.1102
testing/wikipedia/v3/08059.html
e ˙ = d d t H ( x ) - d d t H ( x ^ ) = d d t H ( x ) - M ( x ^ ) sgn ( V ( t ) - H ( x ^ ( t ) ) ) ,

Doc 16
0.1051
-35.0000
3.0000
0.1051
testing/wikipedia/v3/16787.html
L u ( x ) = i , j = 1 n ( a i j ( x ) u x i ) x j + i = 1 n b i ( x ) u x i ( x ) + c ( x ) u ( x )

Doc 17
0.1051
-44.0000
3.0000
0.2963
testing/wikipedia/v3/23828.html
μ z z ( μ 1 , μ 2 ) + 1 2 { 2 z x 1 2 σ 1 2 + 2 z x 2 2 σ 2 2 } + z 2 x 1 x 2 σ 12    𝐄𝐪 ( 𝟏𝟒 )
( z - E [ z ] ) 2 ( z x 1 ) 2 ( x 1 - x ¯ 1 ) 2 + ( z x 2 ) 2 ( x 2 - x ¯ 2 ) 2 +    2 ( z x 1 ) ( z x 2 ) ( x 1 - x ¯ 1 ) ( x 2 - x ¯ 2 )
E [ 2 z x 1 x 2 ( x 1 - x ¯ 1 ) ( x 2 - x ¯ 2 ) ] = 2 z x 1 x 2 E [ ( x 1 - x ¯ 1 ) ( x 2 - x ¯ 2 ) ] = 2 z x 1 x 2 σ 1 , 2
Doc 18
0.1051
-59.0000
5.0000
0.1051
testing/wikipedia/v3/02611.html
V 1 = 2 R [ u ] ( x 1 x 2 [ p ( x ) u ( x ) v ( x ) + q ( x ) u ( x ) v ( x ) - λ u ( x ) v ( x ) ] d x + a 1 u ( x 1 ) v ( x 1 ) + a 2 u ( x 2 ) v ( x 2 ) ) ,

Doc 19
0.1051
-60.0000
3.0000
0.1051
testing/wikipedia/v3/09923.html
:= 1 2 μ ( w t ) 2 - 1 2 E I ( 2 w x 2 ) 2 + q ( x ) w ( x , t ) = μ 2 w ˙ 2 - E I 2 w x x 2 + q w ( x , t , w , w ˙ , w x x )

Doc 20
0.1045
-23.0000
4.0000
0.1045
testing/wikipedia/v3/14856.html
g t ( z ) t = g t ( z ) ζ ( t ) + g t ( z ) ζ ( t ) - g t ( z ) .

Doc 21
0.1045
-23.0000
4.0000
0.1045
testing/wikipedia/v3/01026.html
log ( x 0 ) + 1 x 0 ( x - x 0 ) - 1 x 0 2 ( x - x 0 ) 2 2 + .

Doc 22
0.1008
-42.0000
5.0000
0.2017
testing/wikipedia/v3/17512.html
A f ( x ) = i b i ( x ) f x i ( x ) + 1 2 i , j ( σ ( x ) σ ( x ) ) i , j 2 f x i x j ( x ) ,
𝒜 f ( x ) = i b i ( x ) f x i ( x ) + 1 2 i , j ( σ ( x ) σ ( x ) ) i , j 2 f x i x j ( x ) .

Doc 23
0.1008
-42.0000
5.0000
0.1008
testing/wikipedia/v3/17534.html
A f ( x ) = i b i ( x ) f x i ( x ) + 1 2 i , j ( σ ( x ) σ ( x ) ) i , j 2 f x i x j ( x ) ,

Doc 24
0.0960
-35.0000
3.0000
0.0960
testing/wikipedia/v3/10729.html
d d x ( f 1 ( x ) f 2 ( x ) g ( t ) d t ) = g [ f 2 ( x ) ] f 2 ( x ) - g [ f 1 ( x ) ] f 1 ( x )

Doc 25
0.0960
-54.0000
5.0000
0.1864
testing/wikipedia/v3/02741.html
a b ¯ = ( d x + u x x d x ) 2 + ( u y x d x ) 2 = 1 + 2 u x x + ( u x x ) 2 + ( u y x ) 2 d x
e r s = 1 2 ( u r x s + u s x r - u k x r u k x s ) 1 2 ( u r x s + u s x r )

Doc 26
0.0960
-55.0000
5.0000
0.0960
testing/wikipedia/v3/22820.html
length ( a b ) = ( d x + u x x d x ) 2 + ( u y x d x ) 2 = d x 1 + 2 u x x + ( u x x ) 2 + ( u y x ) 2

Doc 27
0.0904
-21.0000
3.0000
0.0904
testing/wikipedia/v3/05933.html
2 ( x p ( x ) - C ( x ) ) 2 x = 2 π ( x , t ) x 2 ,

Doc 28
0.0904
-25.0000
4.0000
0.0904
testing/wikipedia/v3/30220.html
H z ( i ) ( z 1 , z 2 ) = A z ( i ) ( z 1 , z 2 ) B z ( i ) ( z 1 , z 2 )

Doc 29
0.0904
-30.0000
4.0000
0.3335
testing/wikipedia/v3/08430.html
| f ( z 1 ) - f ( z 2 ) 1 - f ( z 1 ) ¯ f ( z 2 ) | | z 1 - z 2 1 - z 1 ¯ z 2 |
| f ( z 1 ) - f ( z 2 ) f ( z 1 ) ¯ - f ( z 2 ) | | z 1 - z 2 | | z 1 ¯ - z 2 | .
| f ( z 1 ) - f ( z 2 ) 1 - f ( z 1 ) ¯ f ( z 2 ) | | z 1 - z 2 1 - z 1 ¯ z 2 | .
M ( z ) = z 1 - z 1 - z 1 ¯ z ,   φ ( z ) = f ( z 1 ) - z 1 - f ( z 1 ) ¯ z .

Doc 30
0.0904
-34.0000
4.0000
0.0904
testing/wikipedia/v3/14299.html
t Q i ( t ) = - 1 Δ x ( f ( q ( t , x i + 1 / 2 ) ) - f ( q ( t , x i - 1 / 2 ) ) ) ,

Doc 31
0.0904
-46.0000
3.0000
0.0904
testing/wikipedia/v3/01998.html
f ( ζ ) = 1 ( 2 π i ) n D 1 × × D n f ( z 1 , , z n ) ( z 1 - ζ 1 ) ( z n - ζ n ) d z 1 d z n

Doc 32
0.0901
-51.0000
4.0000
0.0901
testing/wikipedia/v3/23998.html
M 2 f = - n P ( f ) + n - 2 x n P ( f ) x n - ( n Q ( f ) - n - 2 x n Q ( f ) x n + n - 2 x n 2 Q ( f ) ) e n

Doc 33
0.0901
-64.0000
3.0000
0.0901
testing/wikipedia/v3/26549.html
M 11 = - D ( φ 1 x 1 + ν φ 2 x 2 ) ,   M 22 = - D ( φ 2 x 2 + ν φ 1 x 1 ) ,   M 12 = - D ( 1 - ν ) 2 ( φ 1 x 2 + φ 2 x 1 )

Doc 34
0.0862
-27.0000
3.0000
0.0862
testing/wikipedia/v3/05175.html
f ( x ) 2 u x 2 + g ( x ) u x + h ( x ) u = u t + k ( t ) u

Doc 35
0.0862
-35.0000
4.0000
0.0862
testing/wikipedia/v3/08334.html
( E c ( z ) - z 2 2 m c ( z ) z + 2 𝐤 2 2 m c ( z ) ) f k ( z ) = E f k ( z )

Doc 36
0.0862
-42.0000
4.0000
0.2389
testing/wikipedia/v3/03795.html
σ x = 2 μ ε x + λ ( ε x + ε y + ε z ) = 2 μ u x x + λ ( u x x + u y y + u z z )
( λ + μ ) x ( u x x + u y y + u z z ) + μ ( 2 u x x 2 + 2 u x y 2 + 2 u x z 2 ) + F x = 0
x ( 2 μ u x x + λ ( u x x + u y y + u z z ) ) + μ y ( u x y + u y x ) + μ z ( u z x + u x z ) + F x = 0
Doc 37
0.0817
-38.0000
3.0000
0.0817
testing/wikipedia/v3/14293.html
y ˙ = d h ( x ) d t = d h ( x ) d x x ˙ = d h ( x ) d x f ( x ) + d h ( x ) d x g ( x ) u

Doc 38
0.0763
-30.0000
3.0000
0.0763
testing/wikipedia/v3/05668.html
g x j ( x ) = - ( f y ( x , g ( x ) ) ) - 1 f x j ( x , g ( x ) )

Doc 39
0.0763
-34.0000
3.0000
0.0763
testing/wikipedia/v3/05547.html
2 F ( z , w ) z w = f ( z ) f ( w ) ( f ( z ) - f ( w ) ) 2 - 1 ( z - w ) 2 ,

Doc 40
0.0763
-35.0000
3.0000
0.0763
testing/wikipedia/v3/14309.html
u ( x ) = u i + ( x - x i ) ( x i + 1 - x i ) ( u i + 1 - u i )    x ( x i , x i + 1 ] .

Doc 41
0.0763
-43.0000
4.0000
0.0763
testing/wikipedia/v3/23918.html
x x x = C e ζ ( - 1 , x ) - ζ ( - 1 ) = C e ψ ( - 2 ) ( z ) + z 2 - z 2 - z 2 ln ( 2 π ) = C K ( x )

Doc 42
0.0672
-39.0000
2.0000
0.0672
testing/wikipedia/v3/13787.html
ρ ( u x t + y u x u y ) = - x p + ν y ( x ( ρ u y ) + y ( ρ u x ) )

Doc 43
0.0672
-61.0000
4.0000
0.0672
testing/wikipedia/v3/23214.html
L = - ρ { - h ( x , y ) ζ ( x , y , t ) [ Φ t + 1 2 ( ( Φ x ) 2 + ( Φ y ) 2 + ( Φ z ) 2 ) ] d z + 1 2 g ( ζ 2 - h 2 ) } ,

Doc 44
0.0622
-18.0000
3.0000
0.0622
testing/wikipedia/v3/14685.html
( z x ) y = - ( z y ) x ( y x ) z

Doc 45
0.0622
-20.0000
3.0000
0.1866
testing/wikipedia/v3/04601.html
( y x ) z = - ( z x ) y ( z y ) x .
d z = [ ( z x ) y ( x y ) z + ( z y ) x ] d y + ( z x ) y ( x z ) y d z ,
[ 1 - ( z x ) y ( x z ) y ] d z = [ ( z x ) y ( x y ) z + ( z y ) x ] d y .
Doc 46
0.0622
-51.0000
3.0000
0.0622
testing/wikipedia/v3/27863.html
ξ = f 3 ( x ) E 2 d x , u = ( y + f 2 ( x ) 3 f 3 ( x ) ) E - 1 , E = exp ( ( f 1 ( x ) - f 2 2 ( x ) 3 f 3 ( x ) ) d x )

Doc 47
0.0480
-23.0000
2.0000
0.0480
testing/wikipedia/v3/04243.html
x 1 = f 1 ( t ) g 1 ( t ) x n = f n ( t ) g n ( t ) ,

Doc 48
0.0480
-45.0000
3.0000
0.0480
testing/wikipedia/v3/25912.html
{ z 1 = 1 2 ( x 1 - i y 1 ) z n = 1 2 ( x n - i y n ) ,