User:Maximilian Janisch/latexlist/latex/NoNroff/3

List

1.  ; $\sum _ { n = 0 } ^ { \infty } \{ \sum _ { m = 1 } ^ { \infty } [ \sum _ { k = m 2 ^ { n } } ^ { ( m + 1 ) 2 ^ { n } - 1 } | \Delta d _ { k } | ] ^ { 2 } \} ^ { 1 / 2 } < \infty$ ; confidence 0.350

2.  ; $2 ^ { n } \operatorname { exp } \{ - \left( \begin{array} { c } { n / 100 } \\ { 3 } \end{array} \right) p ^ { 3 } + O ( n ^ { 4 } p ^ { 5 } ) \} = o ( 1 )$ ; confidence 0.844

3.  ; $M ( S _ { n } ) \cong \left\{ \begin{array} { l l } { Z _ { 2 } } & { \text { if } n \geq 4 } \\ { \{ e \} } & { \text { if } n < 4 } \end{array} \right.$ ; confidence 0.301

4.  ; $\Phi ( u ) : = \sum _ { n = 1 } ^ { \infty } \pi n ^ { 2 } ( 2 \pi n ^ { 2 } e ^ { 4 \lambda } - 3 ) \operatorname { exp } ( 5 u - \pi n ^ { 2 } e ^ { 4 \lambda } )$ ; confidence 0.730

5.  ; $r s = \frac { n ( n ^ { 2 } - 1 ) - 6 \sum _ { i = 1 } ^ { n } ( R _ { i } - S _ { i } ) ^ { 2 } - 6 ( T + U ) } { \sqrt { n ( n ^ { 2 } - 1 ) - 12 T } \sqrt { n ( n ^ { 2 } - 1 ) - 12 U } }$ ; confidence 0.907

6.  ; $t \rightarrow \int _ { 0 } ^ { t } ( \partial _ { s } ^ { * } + \partial _ { s } ) 1 d s = S ^ { - 1 } ( \int _ { 0 } ^ { t } ( D _ { s } ^ { * } + D _ { s } ) \Omega d s )$ ; confidence 0.455

7.  ; $\frac { 1 } { n } \sum _ { k = 1 } ^ { n } f ( \lambda _ { k } ^ { ( n ) } ) = \frac { 1 } { 2 \pi } \int _ { 0 } ^ { 2 \pi } f ( a ( e ^ { i \theta } ) ) d \theta + o ( 1 )$ ; confidence 0.899

8.  ; $[ X ] \mapsto \chi _ { R } ( [ X ] ) = \sum _ { m = 0 } ^ { \infty } ( - 1 ) ^ { m } \operatorname { dim } _ { K } \operatorname { Ext } _ { R } ^ { m } ( X , X )$ ; confidence 0.116

9.  ; $T _ { \phi } = \operatorname { dim } \operatorname { Ker } T _ { \phi } - \operatorname { dim } \operatorname { Ker } T _ { \phi } ^ { * } = 0$ ; confidence 0.871

10.  ; $\operatorname { sup } _ { ( x , \xi ) \in R ^ { 2 n } , } | D _ { x } ^ { \alpha } D _ { \xi } ^ { \beta } \alpha ( x , \xi , h ) | h ^ { m - | \beta | } < \infty$ ; confidence 0.214

11.  ; $g _ { 1 } = | d x | ^ { 2 } + \frac { | d \xi | ^ { 2 } } { | \xi | ^ { 2 } } \leq g = \frac { | d x | ^ { 2 } } { | x | ^ { 2 } } + \frac { | d \xi | ^ { 2 } } { | \xi | ^ { 2 } }$ ; confidence 0.357

12.  ; $\operatorname { Sp } ( n + 1 ) / \operatorname { Sp } ( n ) , \quad \operatorname { Sp } ( n + 1 ) / \operatorname { Sp } ( n ) \times Z _ { 2 }$ ; confidence 0.901

13.  ; $T _ { n } = \frac { S _ { n } S _ { n + 2 } - S _ { n + 1 } ^ { 2 } } { S _ { n + 2 } - 2 S _ { n + 1 } + S _ { n } } = S _ { n } - \frac { \Delta S _ { n } } { \Delta ^ { 2 } S _ { n } }$ ; confidence 0.785

14.  ; $\frac { n ^ { 1 / 4 } } { ( \operatorname { log } n ) ^ { 1 / 2 } } \| \alpha _ { n } + \beta _ { n } \| \stackrel { d } { \rightarrow } \| B \| ^ { 1 / 2 }$ ; confidence 0.344

15.  ; $P _ { l } = \frac { \operatorname { exp } ( - \epsilon _ { l } / k _ { B } T ) } { \sum _ { l } \operatorname { exp } ( - \epsilon _ { l } / k _ { B } T ) }$ ; confidence 0.423

16.  ; $\sum _ { l = 0 } ^ { n } a _ { n - 1 } \left[ \begin{array} { c } { A _ { 1 } ^ { m - i } } \\ { A _ { 2 } A _ { 1 } ^ { m - i - 1 } } \end{array} \right] = 0 _ { m n }$ ; confidence 0.605

17.  ; $\phi \equiv ( x _ { 1 } \vee x _ { 2 } ) \wedge ( \overline { x _ { 2 } } \vee \overline { x _ { 3 } } ) \wedge ( \overline { x _ { 1 } } \vee x _ { 3 } )$ ; confidence 0.984

18.  ; $\frac { U _ { h } ^ { n + 1 } - U _ { h } ^ { n } } { k } = \frac { 1 } { 2 } F _ { h } ( t _ { n } , U _ { h } ^ { n } ) + \frac { 1 } { 2 } F _ { h } ( t _ { n } + 1 , U _ { h } ^ { n + 1 } )$ ; confidence 0.347

19.  ; $= \{ z \in D : \operatorname { liminf } _ { W \rightarrow X } [ K _ { D } ( z , w ) - K _ { D } ( z 0 , w ) ] < \frac { 1 } { 2 } \operatorname { log } R \}$ ; confidence 0.205

20.  ; $( c \frac { \hbar } { c } \vec { \alpha } . \vec { \nabla } + \vec { \beta } m 0 c ^ { 2 } ) \Phi = i \hbar \frac { \partial \Phi } { \partial t }$ ; confidence 0.531

21.  ; $\sum _ { k = 1 } ^ { \infty } e ^ { - \lambda _ { k } t } \approx \frac { A } { 4 \pi t } + \frac { L } { 8 \sqrt { \pi t } } + \frac { 1 } { 6 } ( 1 - r ) + O ( t )$ ; confidence 0.678

22.  ; $\frac { \partial u } { \partial t } = \frac { \partial ^ { 3 } } { \partial x ^ { 3 } } ( \frac { 1 } { \sqrt { u } } ) , - \infty < x < \infty , t > 0$ ; confidence 0.996

23.  ; $\equiv ( z - E _ { 0 } - \int _ { 0 } ^ { \infty } \frac { | ( V \phi | \lambda \rangle | ^ { 2 } } { z - \lambda } d \lambda ) ( \phi , G ( z ) \phi ) = 1$ ; confidence 0.869

24.  ; $( F f ) ( z ) = \sum _ { j = 1 } ^ { n } ( z _ { j } \frac { \partial f ( z ) } { \partial z _ { j } } + z _ { j } \frac { \partial f ( z ) } { \partial z _ { j } } )$ ; confidence 0.386

25.  ; $\operatorname { lim } _ { n \rightarrow \infty } P \{ \int _ { 0 } ^ { 1 } Z _ { n } ^ { 2 } ( t ) d t < \lambda \} = P \{ \omega ^ { 2 } < \lambda \} =$ ; confidence 0.694

26.  ; $\left\{ \begin{array}{l}{ ( T - z I ) x = K J \varphi _ { - } }\\{ \varphi _ { + } = \varphi _ { - } - 2 i K ^ { * } x _ { } }\end{array} \right.$ ; confidence 0.118

27.  ; $\frac { 1 } { i } ( A _ { 1 } - A _ { 1 } ^ { * } ) = \Phi ^ { * } \sigma _ { 1 } \Phi , \frac { 1 } { i } ( A _ { 2 } - A _ { 2 } ^ { * } ) = \Phi ^ { * } \sigma _ { 2 } \Phi$ ; confidence 0.964

28.  ; $\| \lambda \| = \operatorname { sup } _ { 0 \leq s < t \leq 1 } | \operatorname { log } \{ ( t - s ) ^ { - 1 } ( \lambda ( t ) - \lambda ( s ) ) \} |$ ; confidence 0.876

29.  ; $( X A _ { 1 } X ^ { \prime } , \ldots , X A _ { s } X ^ { \prime } ) \sim L _ { s } ^ { ( 1 ) } ( f _ { 1 } , \frac { n _ { 1 } } { 2 } , \ldots , \frac { n _ { s } } { 2 } )$ ; confidence 0.226

30.  ; $w ( m , l ) = \frac { d \Phi } { d z } = - \frac { i \Gamma } { 2 \pi } [ \operatorname { cotan } \frac { \pi z } { l } - \frac { 1 } { z - m l } ] \equiv 0$ ; confidence 0.991

31.  ; $\| H ( u , v ) \| _ { L } 2 _ { \langle R ^ { 2 n } \rangle } = \| u \| _ { L } 2 _ { \langle R ^ { n } } \rangle \| v \| _ { L } 2 _ { \langle R ^ { n } } \rangle$ ; confidence 0.089

32.  ; $0 \rightarrow \square _ { R } \operatorname { Mod } ( ? , A ) \rightarrow \square _ { R } \operatorname { Mod } ( ? , B ) \rightarrow$ ; confidence 0.807

33.  ; $CF ( \zeta - z , w ) = \frac { ( n - 1 ) ! \sum _ { k = 1 } ^ { n } ( - 1 ) ^ { k - 1 } w _ { k } d w [ k ] \wedge d \zeta } { \langle w , \zeta - z \rangle ^ { n } }$ ; confidence 0.453

34.  ; $\operatorname { lim } \{ \| x ^ { n } \| ^ { 1 / n } \} = \operatorname { max } \{ | \lambda | : \lambda \in \operatorname { sp } ( J , x ) \}$ ; confidence 0.370

35.  ; $H \equiv - \frac { \partial ^ { 2 } } { \partial \theta . \partial \theta } \int f ( \theta , \phi ) d \phi | _ { \theta = \theta ^ { * } }$ ; confidence 0.919

36.  ; $\operatorname { lim } _ { k \rightarrow \infty } \frac { S ( T ^ { k } , a f ( \epsilon ) ^ { k } ) } { k } = 2 H _ { \epsilon } ^ { \prime } ( \xi )$ ; confidence 0.824

37.  ; $\pi _ { v , p } ( d \theta ) = A ( m , p ) ( L _ { \mu } ( \theta ) ) ^ { - p } \operatorname { exp } \langle \theta , v \rangle \alpha ( d \theta )$ ; confidence 0.272

38.  ; $\operatorname { Tr } [ \operatorname { Aexp } ( - i \hbar ^ { - 1 } H ( t ) ) ] = \sum _ { k = 1 } ^ { N } a _ { 0 } ( x _ { k } ) d _ { k } e ^ { b _ { k } } + O ( h )$ ; confidence 0.385

39.  ; $\operatorname { lim } _ { r \rightarrow 0 } \frac { H ^ { m } ( \{ y \in E \cap B ( x , r ) : \quad > \text { dist } ( y - x , V ) > } { > s | y - x | } ) = 0$ ; confidence 0.092

40.  ; $N \rightarrow \infty , \sigma \rightarrow 0 , \frac { 1 } { \lambda } = \operatorname { lim } ( \pi \sigma ^ { 2 } N ) \in ] 0 , \infty$ ; confidence 0.979

41.  ; $\frac { J - W _ { \Theta } ( z ) J W _ { \Theta } ( w ) ^ { * } } { z - \overline { w } } = 2 i K ^ { * } ( T - z I ) ^ { - 1 } ( T ^ { * } - \overline { w } l ) ^ { - 1 } K$ ; confidence 0.826

42.  ; $J _ { n } = \frac { z ^ { n } } { 2 ^ { \pi + 1 } \pi i } \int _ { - \infty } ^ { ( 0 + ) } t ^ { - n - 1 } \operatorname { exp } ( t - \frac { z ^ { 2 } } { 4 t } ) d t$ ; confidence 0.985

43.  ; $\frac { \Gamma _ { p } [ \frac { \delta + n + p - 1 } { 2 } ] } { ( 2 \pi ) ^ { n } p / 2 | \Sigma | ^ { n / 2 } \Gamma _ { p } [ \frac { \delta + p - 1 } { 2 } ] }$ ; confidence 0.236

44.  ; $SH ^ { * } ( M , \omega , L _ { 1 } , L _ { 2 } ) \otimes SH ^ { * } ( M , \omega , L _ { 2 } , L _ { 3 } ) \rightarrow SH ^ { * } ( M , \omega , L _ { 1 } , L _ { 3 } )$ ; confidence 0.434

45.  ; $SH ^ { k } ( M , \omega , \phi _ { 1 } ) \otimes SH ^ { k } ( M , \omega , \phi _ { 2 } ) \rightarrow SH ^ { k } ( M , \omega , \phi _ { 2 } . \phi _ { 1 } )$ ; confidence 0.238

46.  ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { \operatorname { det } T _ { n } ( \alpha ) } { G ( \alpha ) ^ { N } } = E ( \alpha )$ ; confidence 0.614

47.  ; $( \int _ { - \infty } ^ { \infty } ( x - a ) ^ { 2 } | f ( x ) | ^ { 2 } d x ) ( \int _ { - \infty } ^ { \infty } ( y - b ) ^ { 2 } | \hat { f } ( y ) | ^ { 2 } d y ) \geq$ ; confidence 0.917

48.  ; $\operatorname { ln } ( 1 - \lambda ) = \frac { 1 } { \pi } \int _ { 0 } ^ { 1 } \frac { \theta ( s ^ { \prime } ) } { s ^ { \prime } } d s ^ { \prime }$ ; confidence 0.997

49.  ; $\beta \gamma = \gamma \beta + ( 1 - q ^ { - 2 } ) \alpha ( \delta - \alpha ) , \delta \beta = \beta \delta + ( 1 - q ^ { - 2 } ) \alpha \beta$ ; confidence 0.947

50.  ; $\frac { \partial v } { \partial t } - 6 v ^ { 2 } \frac { \partial v } { \partial x } + \frac { \partial ^ { 3 } v } { \partial x ^ { 3 } } = 0$ ; confidence 0.944

51.  ; $\sum _ { k = 1 } ^ { \infty } \frac { \zeta ( 2 k ) } { k ( 2 k + 1 ) 2 ^ { 4 k } } = \operatorname { log } ( \frac { \pi } { 2 } ) - 1 + \frac { 2 G } { \pi }$ ; confidence 0.948

52.  ; $\operatorname { lim } _ { n \rightarrow \infty } \operatorname { sup } f ( \sum _ { j \in I } \sum _ { j \in I } \sum _ { [ 1 , n ] } x _ { j } )$ ; confidence 0.657

53.  ; $\sum _ { i = 1 } ^ { k } \lambda _ { i } \geq \frac { n } { n + 2 } \frac { 4 \pi ^ { 2 } k ^ { 1 + 2 / n } } { ( C _ { n } | \Omega | ) ^ { 2 / n } } k = 1,2 , \ldots$ ; confidence 0.496

54.  ; $H _ { n + 1 } ^ { ( k ) } ( x ) = \sum \frac { ( n _ { 1 } + \ldots + n _ { k } ) ! } { n _ { 1 } ! \ldots n _ { k } ! } x _ { 1 } ^ { n _ { 1 } } \ldots x _ { k } ^ { n _ { k } }$ ; confidence 0.364

55.  ; $F + ( x ) = \sum _ { j = 1 } ^ { J } ( m _ { j } ^ { + } ) ^ { 2 } e ^ { - k _ { j } x } + \frac { 1 } { 2 \pi } \int _ { - \infty } ^ { \infty } r _ { + } ( k ) e ^ { i k x } d k$ ; confidence 0.334

56.  ; $\Delta = \frac { 1 } { 2 } \sum _ { A \neq B , A } \sum _ { B \neq \emptyset } E ( I _ { A } I _ { B } ) , \overline { \Delta } = \lambda + 2 \Delta$ ; confidence 0.546

57.  ; $\tau _ { n } = \frac { c - d } { c + d } = \frac { S } { \left( \begin{array} { l } { n } \\ { 2 } \end{array} \right) } = \frac { 2 S } { n ( n - 1 ) }$ ; confidence 0.400

58.  ; $m ( P ) = \int _ { 0 } ^ { 1 } \ldots \int _ { 0 } ^ { 1 } \operatorname { log } | P ( e ^ { i t } 1 , \ldots , e ^ { i t _ { n } } ) | d t _ { 1 } \ldots d t _ { n }$ ; confidence 0.291

59.  ; $\mu _ { k } = \operatorname { sup } \operatorname { inf } \frac { \int _ { \Omega } ( \nabla u ) ^ { 2 } d x } { \int _ { \Omega } u ^ { 2 } d x }$ ; confidence 0.951

60.  ; $( \sigma _ { 2 } \frac { \partial } { \partial t _ { 1 } } - \sigma _ { 1 } \frac { \partial } { \partial t _ { 2 } } + \tilde { \gamma } ) v = 0$ ; confidence 0.190

61.  ; $\left\{ \begin{array} { l } { d x ( t ) = A x ( t ) d t + B u ( t ) d t + d w ( t ) } \\ { d y ( t ) = C x ( t ) d t + D u ( t ) d t + d v ( t ) } \end{array} \right.$ ; confidence 0.850

62.  ; $\Gamma _ { 0 } ( p ) + = \langle \Gamma _ { 0 } ( p ) , \left( \begin{array} { c c } { 0 } & { - 1 } \\ { p } & { 0 } \end{array} \right) \rangle$ ; confidence 0.962

63.  ; $( a \circ b ) ( x , \xi ) = \sum _ { | \alpha | < N } \frac { 1 } { \alpha ! } D _ { \xi } ^ { \alpha } a \partial _ { x } ^ { \alpha } b + t _ { N } ( a , b )$ ; confidence 0.305

64.  ; $\left\{ \begin{array} { l } { \frac { d u } { d t } + A ( t , u ) u = f ( t , u ) , \quad t \in [ 0 , T ] } \\ { u ( 0 ) = u _ { 0 } } \end{array} \right.$ ; confidence 0.586

65.  ; $q _ { X } = \operatorname { lim } _ { s \rightarrow 0 + } \frac { \operatorname { log } s } { \operatorname { log } \| D _ { s } \| _ { X } }$ ; confidence 0.248

66.  ; $S _ { R } ^ { \delta } ( f ) ( x ) = \sum _ { m \backslash | \leq R } ( 1 - \frac { | m | ^ { 2 } } { R ^ { 2 } } ) ^ { \delta } e ^ { 2 \pi i x m } \hat { f } ( m )$ ; confidence 0.191

67.  ; $= \left\{ \begin{array} { l l } { I _ { n } , } & { p = q = 0 } \\ { 0 , } & { p \neq 0 \text { or } / \text { and } q \neq 0 } \end{array} \right.$ ; confidence 0.363

68.  ; $h . k = ( \theta \otimes \varphi - \varphi \otimes \theta ) \otimes ( \theta \otimes \varphi - \varphi \otimes \theta ) \in$ ; confidence 0.438

69.  ; $\operatorname { lim } _ { x \rightarrow \infty } f ( x _ { x } ) = f ( x ) = \operatorname { lim } _ { x \rightarrow \infty } f ( y _ { x } )$ ; confidence 0.428

70.  ; $f ( x ) = \left\{ \begin{array} { l l } { \operatorname { sin } \frac { 1 } { x } , } & { x \neq 0 } \\ { a , } & { x = 0 } \end{array} \right.$ ; confidence 0.571

71.  ; $\operatorname { log } \int f ( \theta ^ { ( t + 1 ) } , \phi ) d \phi \geq \operatorname { log } \int f ( \theta ^ { ( t ) } , \phi ) d \phi$ ; confidence 0.976

72.  ; $( \Lambda ^ { \bullet } ( \mathfrak { g } / \mathfrak { k } ) , A ( \Gamma \backslash G ( R ) ) \otimes M _ { C } ) \rightleftharpoons$ ; confidence 0.119

73.  ; $I _ { \epsilon } ( X ) = \operatorname { lim } _ { n \rightarrow \infty } \frac { 1 } { n } H _ { \epsilon } ^ { \prime \prime } ( X ^ { n } )$ ; confidence 0.963

74.  ; $\sum _ { n \in Z } \frac { [ \lambda + \alpha ; n ] [ \mu - n + 1 ; n ] } { [ \mu - n + \beta ; n ] [ \lambda + 1 ; n ] } x ^ { \lambda + x } y ^ { \mu - x }$ ; confidence 0.249

75.  ; $\frac { d } { d t } A ( \sigma _ { t } ) | _ { t = 0 } = \frac { d } { d t } \int _ { N } \sigma ^ { k ^ { * } } \phi _ { t } ^ { k ^ { * } } ( L \Delta ) | _ { t = 0 } =$ ; confidence 0.198

76.  ; $P ( \theta , t , \nu ) ( d \omega ) = \frac { 1 } { L _ { \mu } ( \theta ) } \operatorname { exp } \{ \theta , t ( \omega ) \} \nu ( d \omega )$ ; confidence 0.534

77.  ; $\times \int _ { 0 } ^ { \alpha } [ K _ { i \tau } ( \alpha ) I _ { i \tau } ( x ) - I _ { i \tau } ( \alpha ) K _ { i \tau } ( x ) ] f ( x ) \frac { d x } { x }$ ; confidence 0.502

78.  ; $\Delta ( F ) : = \{ Y \in \left( \begin{array} { c } { [ n ] } \\ { k - 1 } \end{array} \right) : Y \subset \text { Xfor someX } \in F \}$ ; confidence 0.462

79.  ; $L ( x ) = x \operatorname { ln } 2 - \frac { 1 } { 2 } \sum _ { k = 1 } ^ { \infty } ( - 1 ) ^ { k - 1 } \frac { \operatorname { sin } 2 k x } { k ^ { 2 } }$ ; confidence 0.977

80.  ; $| u ( y ) | = | \sum _ { j = 1 } ^ { \infty } \lambda _ { j } ^ { 1 / 2 } v _ { j } \varphi _ { j } ( x ) | < c \Lambda \| v \| _ { 0 } = c \Lambda \| u \| _ { + }$ ; confidence 0.738

81.  ; $x ( t + ) = x ( t ) \text { for allo } \leq t < 1 , x ( t - ) = \operatorname { lim } _ { s \uparrow t } x ( s ) \text { exists for all } 0 < t \leq 1$ ; confidence 0.118

82.  ; $\nabla ( A ) : = \{ Y \in \left( \begin{array} { l } { [ n ] } \\ { l + 1 } \end{array} \right) : Y \supset \text { Xfor someX } \in A \}$ ; confidence 0.359

83.  ; $\operatorname { lim } _ { \tau \rightarrow \infty } \frac { \operatorname { det } ( I + W _ { \tau } ( k ) ) } { G ( a ) ^ { \tau } } = E ( a )$ ; confidence 0.634

84.  ; $M _ { 2 } = \operatorname { min } _ { z _ { j } } \operatorname { max } _ { k = 2 , \ldots , n + 1 } | s _ { k } | \leq 2 ( n + 1 ) ^ { 2 } e ^ { - \theta n }$ ; confidence 0.289

85.  ; $d S = \sum _ { 1 } ^ { M } T _ { n } d \hat { \Omega } _ { n } = \sum _ { 1 } ^ { M } T _ { n } d \Omega _ { n } + \sum _ { 1 } ^ { g } \alpha _ { j } d \omega _ { j }$ ; confidence 0.722

86.  ; $y = \Lambda ^ { N } ( w - \frac { 1 } { w } ) , P = \lambda ^ { N } - \sum _ { 2 } ^ { N } u _ { k } \lambda ^ { N - k } = \Lambda ^ { N } ( w + \frac { 1 } { w } )$ ; confidence 0.988

87.  ; $x ( \infty ) = \operatorname { lim } _ { n \rightarrow \infty } x ( n ) = \operatorname { lim } _ { z \rightarrow 1 } ( z - 1 ) Z ( x ( n ) )$ ; confidence 0.837

88.  ; $3 ^ { 2 } \cdot 5 ^ { 2 } \cdot 11,3 ^ { 5 } \cdot 5 ^ { 2 } \cdot 13,3 ^ { 4 } \cdot 5 ^ { 2 } \cdot 13 ^ { 2 } , 3 ^ { 3 } \cdot 5 ^ { 3 } \cdot 13 ^ { 2 }$ ; confidence 0.589

89.  ; $< x \operatorname { exp } ( - \frac { 1 } { 25 } ( \operatorname { log } x \operatorname { log } \operatorname { log } x ) ^ { 1 / 2 } )$ ; confidence 0.935

90.  ; $\frac { 1 } { p _ { 2 } ( \xi , \tau ) + \alpha i } = \frac { p _ { S } ( \xi , \tau ) } { 1 + \alpha ^ { 2 } } - \frac { \alpha i } { 1 + \alpha ^ { 2 } }$ ; confidence 0.385

91.  ; $A ^ { * } = \{ f : \| f \| _ { A } ^ { * } = \sum _ { k = 0 } ^ { \infty } \operatorname { sup } _ { k \leq p | < \infty } | \hat { f } ( m ) | < \infty \}$ ; confidence 0.134

92.  ; $\operatorname { lim } _ { t \rightarrow \infty } a ( t ) = \frac { \int _ { 0 } ^ { \infty } b ( u ) d u } { \int _ { 0 } ^ { \infty } u d F ( u ) }$ ; confidence 0.842

93.  ; $S _ { R } ^ { \delta } f ( x ) = \sum _ { \lambda _ { k } \leq R } ( 1 - \frac { \lambda _ { k } } { R } ) ^ { \delta } ( f , \phi _ { k } ) \phi _ { k } ( x )$ ; confidence 0.541

94.  ; $x = \sum _ { k \in P ^ { \prime } } \overline { \lambda } _ { k } x ^ { ( k ) } + \sum _ { k \in R ^ { \prime } } \overline { \mu } _ { k } x ^ { ( k ) }$ ; confidence 0.248

95.  ; $H ^ { \bullet } ( \partial ( \Gamma \backslash X ) , \tilde { M } ) = H ^ { 0 } \oplus H ^ { 1 } \rightleftarrows Q ^ { k } \oplus Q ^ { h }$ ; confidence 0.109

96.  ; $q \left( \begin{array} { l } { v } \\ { s } \end{array} \right) = r \left( \begin{array} { l } { v } \\ { t } \end{array} \right)$ ; confidence 0.717

97.  ; $P \{ F _ { \nu _ { 1 } , \nu _ { 2 } } < x \} = B _ { \nu _ { 1 } } / 2 , \nu _ { 2 } / 2 ( \frac { ( \nu _ { 1 } / \nu _ { 2 } ) x } { 1 + ( \nu _ { 1 } / \nu _ { 2 } ) x } )$ ; confidence 0.734

98.  ; $F = - \frac { k _ { B } T \operatorname { ln } Z } { N } , \quad Z = \operatorname { Tr } \operatorname { exp } ( - \frac { H } { k _ { B } T } )$ ; confidence 0.706

99.  ; $v = \frac { \partial } { \partial t } ( x ^ { 0 } + u ) | _ { x ^ { 0 } } = ( \frac { \partial u } { \partial t } ) | _ { x ^ { 0 } } = \frac { D u } { D t }$ ; confidence 0.932

100.  ; $\| \Delta _ { h _ { i } } ^ { 1 } f _ { x _ { i } } ^ { ( r _ { i } ^ { * } ) } \| _ { L _ { p } ( \Omega _ { W _ { i } } | ) } \leq M _ { i } | h _ { i } | ^ { \alpha _ { i } }$ ; confidence 0.057

101.  ; $( \xi _ { 1 } \frac { \partial } { \partial t _ { 1 } } + \xi _ { 2 } \frac { \partial } { \partial t _ { 2 } } ) \langle f , f \rangle _ { H } =$ ; confidence 0.977

102.  ; $\operatorname { lim } _ { r \rightarrow 1 } \int _ { 0 } ^ { 2 \pi } | f ( r e ^ { i \theta } ) - f ( e ^ { i \theta } ) | ^ { \delta } d \theta = 0$ ; confidence 0.920

103.  ; $T ( a ) = \operatorname { Ran } ( \alpha ) \cup \{ z \notin \operatorname { Ran } ( \alpha ) : \text { wind } ( \alpha - z ) \neq 0 \}$ ; confidence 0.339

104.  ; $\sigma ( T _ { \phi } ) = \operatorname { conv } ( R ( \phi ) ) = [ \operatorname { essinf } \phi , \operatorname { esssup } \phi ]$ ; confidence 0.775

105.  ; $\operatorname { inf } _ { z _ { j } } \operatorname { max } _ { k \in S } \frac { | \sum _ { j = 1 } ^ { n } b _ { j } z _ { j } ^ { k } | } { M _ { d } ( k ) }$ ; confidence 0.252

106.  ; $\frac { k = m + 1 , \ldots , m + | g ( k ) | } { \sum _ { j = 1 } ^ { N } | b _ { j } z _ { j } ^ { k } | } \geq \frac { 1 } { n } ( \frac { \delta } { 2 } ) ^ { n - 1 }$ ; confidence 0.341

107.  ; $R ( \theta ^ { * } ) = \sum _ { n = - \infty } ^ { \infty } \operatorname { cov } ( H ( \theta ^ { * } , X _ { n } ) , H ( \theta ^ { * } , X _ { 0 } ) )$ ; confidence 0.963

108.  ; $\operatorname { cot } \omega = \operatorname { cot } \alpha + \operatorname { cot } \beta + \operatorname { cot } \gamma$ ; confidence 0.991

109.  ; $C ^ { n } ( C , M ) = \prod _ { \langle \alpha _ { 1 } , \ldots , \alpha _ { N } \rangle } M ( \operatorname { codom } \alpha _ { n } ) , n > 0$ ; confidence 0.202

110.  ; $\Lambda _ { n } ( \theta ) - h ^ { \prime } \Delta _ { n } ( \theta ) \rightarrow - \frac { 1 } { 2 } h ^ { \prime } \Gamma ( \theta ) h$ ; confidence 0.843

111.  ; $\hat { A } ( t | \beta ) = \int _ { 0 , t } \frac { 1 } { \sum _ { k = 1 } ^ { n } l _ { k } ( s - ) e ^ { Z _ { k } ^ { T } ( s - ) \beta } } d \overline { N } ( s )$ ; confidence 0.138

112.  ; $\int ( R _ { k } + \frac { 1 } { 2 } f ^ { - 2 } h ^ { \alpha \beta } \partial _ { \alpha } E \partial _ { \beta } \overline { E } ) d \mu _ { R }$ ; confidence 0.509

113.  ; $E _ { q } ( \alpha , \beta ) = [ \theta _ { x } + \alpha ] _ { q } [ \partial _ { y } ] _ { q } - [ \theta _ { y } + \beta ] [ \partial _ { x } ] _ { q }$ ; confidence 0.722

114.  ; $E ( \alpha , \beta ) = \partial _ { x } \partial _ { y } - \frac { \beta } { x - y } \partial _ { x } + \frac { \alpha } { x - y } \partial y$ ; confidence 0.825

115.  ; $\operatorname { inf } \{ \| \phi \| _ { \infty } : \phi \in L ^ { \infty } , \hat { \phi } ( j ) = \alpha _ { j } \text { for } j \geq 0 \}$ ; confidence 0.959

116.  ; $= \frac { 2 } { \pi ^ { 2 } x _ { 0 } } \int _ { 0 } ^ { \infty } K _ { i \tau } ( x _ { 0 } ) \tau \operatorname { sinh } \pi \tau F ( \tau ) d \tau$ ; confidence 0.854

117.  ; $\operatorname { IF } ( ( \vec { x } _ { 0 } , y _ { 0 } ) ; T , H _ { \vec { \theta } } ) = \eta ( \vec { x } _ { 0 } , e _ { 0 } ) M ^ { - 1 } \vec { x } _ { 0 }$ ; confidence 0.466

118.  ; $- \frac { \operatorname { sin } n \pi } { \pi } \int _ { 0 } ^ { \infty } e ^ { - n \theta - z \operatorname { sinh } \theta } d \theta$ ; confidence 0.965

119.  ; $E ( \alpha ) = \operatorname { exp } ( \sum _ { k = 1 } ^ { \infty } k [ \operatorname { log } a ] _ { k } [ \operatorname { log } a ] - k )$ ; confidence 0.720

120.  ; $\operatorname { max } _ { j = 1 , \ldots , n - m + 1 } | s _ { j } | \geq m ( \frac { 1 } { 2 } + \frac { m } { 8 n } + \frac { 3 m ^ { 2 } } { 64 n ^ { 2 } } )$ ; confidence 0.610

121.  ; $\Phi ( z ) = - \frac { i \Gamma } { 2 \pi } [ \operatorname { log } \operatorname { sin } ( \frac { \pi } { l } ( z - \frac { i b } { 2 } ) ) +$ ; confidence 0.830

122.  ; $d \omega _ { 1 } ( \lambda ) = \frac { \prod _ { i = 1 } ^ { g } ( \lambda - \alpha _ { i } ) } { \sqrt { R _ { g } ( \lambda ) } } d \lambda \sim$ ; confidence 0.401

123.  ; $= \{ \langle \alpha , b \rangle \in A ^ { 2 } : \epsilon ^ { A } ( \alpha , b ) \in \text { Ffor all } \epsilon ( x , y ) \in E ( x , y ) \}$ ; confidence 0.459

124.  ; $x \operatorname { exp } ( - 8 ( \operatorname { log } x \operatorname { log } \operatorname { log } x ) ^ { 1 / 2 } ) < A _ { 2 } ( x ) <$ ; confidence 0.852

125.  ; $\mathfrak { R } d _ { n } ( U ) = \{ \mathfrak { P } ( \square ^ { n } U ) , \mathfrak { c } _ { 0 } , \ldots , \mathfrak { c } _ { n } - 1 , Id \}$ ; confidence 0.077

126.  ; $\delta _ { T } = \operatorname { sup } _ { x \in X } \operatorname { dim } \operatorname { lin } \{ x , T x , T ^ { 2 } x , \ldots \} = N$ ; confidence 0.674

127.  ; $\int _ { 0 } ^ { 1 } \omega ( f ^ { \prime } ; t ) _ { p } ( \operatorname { ln } \frac { 1 } { t } ) ^ { - 1 / p ^ { \prime } } t ^ { - 1 } d t < \infty$ ; confidence 0.729

128.  ; $\frac { \partial u ^ { \prime } ( \xi ^ { \prime } ( \xi , \eta ) , \eta ^ { \prime } ( \xi , \eta ) ) } { \partial \eta ^ { \prime } } =$ ; confidence 0.993

129.  ; $\Delta ( \lambda , \mu ) = \operatorname { det } [ E \lambda - A \mu ] = \sum _ { i = 0 } ^ { n } a _ { i , n - i } \lambda ^ { i } \mu ^ { n - i }$ ; confidence 0.406

130.  ; $[ ( \varphi \rightarrow \psi ) \rightarrow ( ( \psi \rightarrow \chi ) \rightarrow ( \varphi \rightarrow \chi ) ) ] = 1$ ; confidence 0.997

131.  ; $u _ { - } = \left\{ \begin{array} { l } { e ^ { - i k x } + r _ { - } ( k ) e ^ { - i k x } } \\ { t - ( k ) e ^ { i k x } , \quad x } \end{array} \right.$ ; confidence 0.602

132.  ; $v _ { MAP } = \operatorname { arg } \operatorname { max } _ { v _ { j } \in V } \prod _ { i } P ( \alpha _ { i } | v _ { j } ) \cdot P ( v _ { j } )$ ; confidence 0.242

133.  ; $\frac { \pi ^ { n } } { n \operatorname { vol } ( D _ { 1 } ) } \int _ { \partial D _ { 1 } } f ( \zeta ) \nu ( \zeta - \alpha ) = f ( \alpha )$ ; confidence 0.405

134.  ; $\sum _ { l = 0 } ^ { k } \alpha _ { i } y _ { m + i } = h f ( \sum _ { i = 0 } ^ { k } \beta _ { i } x _ { m + i } , \sum _ { i = 0 } ^ { k } \beta _ { i } y _ { m + i } )$ ; confidence 0.166

135.  ; $f _ { j k l } = \frac { - i } { 4 } \operatorname { Tr } [ ( \lambda _ { j } \lambda _ { k } - \lambda _ { k } \lambda _ { j } ) \lambda _ { l } ]$ ; confidence 0.632

136.  ; $\operatorname { exp } [ \int _ { 0 } ^ { T } L ( \dot { \phi } ( s ) , \phi ( s ) ) d s - \int _ { 0 } ^ { T } L ( \dot { \psi } ( s ) , \psi ( s ) ) d s ]$ ; confidence 0.987

137.  ; $\frac { \partial ^ { 2 } f } { \partial t _ { 1 } \partial t _ { 2 } } = \frac { \partial ^ { 2 } f } { \partial t _ { 2 } \partial t _ { 1 } }$ ; confidence 0.999

138.  ; $p ( \lambda _ { 1 } , \lambda _ { 2 } ) = \operatorname { det } ( \lambda _ { 1 } \sigma _ { 2 } - \lambda _ { 2 } \sigma _ { 1 } + \gamma )$ ; confidence 0.998

139.  ; $\operatorname { Fun } _ { q } ( M ) \rightarrow \operatorname { Fun } _ { q } ( M ) \otimes \operatorname { Fun } _ { q } ( SU ( n ) )$ ; confidence 0.482

140.  ; $E [ W ] _ { \operatorname { exh } } = \frac { \delta ^ { 2 } } { 2 r } + \frac { P \lambda \dot { b } ^ { ( 2 ) } + r ( P - \rho ) } { 2 ( 1 - \rho ) }$ ; confidence 0.202

141.  ; $f ( x ) \mapsto ( S ^ { \alpha } f ) ( x ) = \int _ { | \xi | \leq 1 } \hat { f ( \xi ) } ( 1 - | \xi | ^ { 2 } ) ^ { \alpha } e ^ { 2 \pi i x . \xi } d \xi$ ; confidence 0.223

142.  ; $J _ { n } ( z ) = \frac { 1 } { \pi } \int _ { 0 } ^ { \pi } \operatorname { cos } ( n \theta - z \operatorname { sin } \theta ) d \theta +$ ; confidence 0.516

143.  ; $\frac { F _ { 1 } z } { 1 + G _ { 1 } z } \square _ { + } \frac { F _ { 2 } z } { 1 + G _ { 2 } z } \square _ { + } \frac { F _ { 3 } } { 1 + G _ { 3 } z } \square$ ; confidence 0.097

144.  ; $\geq 2 ( \frac { \delta _ { 1 } - \delta _ { 2 } } { 12 e } ) ^ { N } \operatorname { min } _ { j = k , \ldots , l } | b _ { 1 } + \ldots + b _ { j } |$ ; confidence 0.076

145.  ; $\psi _ { W } ( x , p , t ) = \int _ { R ^ { 3 N } } e ^ { i p z / \hbar } \overline { \psi } ( x + \frac { z } { 2 } , t ) \psi ( x - \frac { z } { 2 } , t ) d z$ ; confidence 0.345

146.  ; $\delta _ { k } ( n ) = \left\{ \begin{array} { l l } { 1 } & { \text { if } n = k } \\ { 0 } & { \text { if } n \neq k } \end{array} \right.$ ; confidence 0.980

147.  ; $= \frac { ( \alpha + 1 ) _ { k + l } } { ( \alpha + 1 ) _ { k } ( \alpha + 1 ) _ { l } } z ^ { k } z ^ { l } F ( - k , - l ; - k - l - \alpha ; \frac { 1 } { 2 z } )$ ; confidence 0.273

148.  ; $E ( \Gamma , \Delta ) = \{ \epsilon _ { i } ( \gamma , \delta ) : \gamma \approx \delta \in \Gamma \approx \Delta , i \in I \}$ ; confidence 0.992

149.  ; $S _ { P } = \langle P , \operatorname { Mod } _ { S _ { P } } , \operatorname { mng } _ { S _ { P } } , \operatorname { Fod } e l s _ { P } \}$ ; confidence 0.056

150.  ; $\Gamma \dagger _ { D } \varphi \text { iff } K ( \Gamma ) \approx L ( \Gamma ) \vDash _ { K } K ( \varphi ) \approx L ( \varphi )$ ; confidence 0.254

151.  ; $\| ( \lambda + A ( t _ { k } ) ) ^ { - 1 } \ldots ( \lambda + A ( t _ { 1 } ) ) ^ { - 1 } \| _ { L ( X ) } \leq \frac { M } { ( \lambda - \beta ) ^ { k } }$ ; confidence 0.617

152.  ; $B O _ { n } = \operatorname { lim } _ { r \rightarrow \infty } \operatorname { inf } \operatorname { Gras } _ { n } ( R ^ { r + n } )$ ; confidence 0.744

153.  ; $G _ { \delta } = ( 2 / \pi ) \operatorname { sup } _ { x > 0 } \int _ { 0 } ^ { 1 } ( 1 - t ^ { 2 } ) ^ { \delta } \operatorname { sin } x t d t / t$ ; confidence 0.931

154.  ; $\frac { \partial u ^ { \prime } ( \xi ^ { \prime } ( \xi , \eta ) , \eta ^ { \prime } ( \xi , \eta ) ) } { \partial \xi ^ { \prime } } =$ ; confidence 0.993

155.  ; $= ( 2 ^ { 2 t + 2 } \frac { 2 ^ { 2 t } - 1 } { 3 } , 2 ^ { 2 t - 1 } \frac { 2 ^ { 2 t + 1 } + 1 } { 3 } , 2 ^ { 2 t - 1 } \frac { 2 ^ { 2 t - 1 } + 1 } { 3 } , 2 ^ { 4 t - 2 } )$ ; confidence 0.940

156.  ; $E [ \gamma ( X ( t ) ) | \sigma ( Y ( u , u \leq t ) ] = \frac { E _ { \mu _ { X } } [ \gamma ( X ( t ) ) \psi ( t ) ] } { E _ { \mu _ { X } } [ \psi ( t ) ] }$ ; confidence 0.213

157.  ; $L ( \theta | Y _ { 0 b s } ) = \int _ { M ( Y _ { \text { aug } } ) = Y _ { \text { obs } } } L ( \theta | Y _ { \text { aug } } ) d Y _ { \text { aug } }$ ; confidence 0.135

158.  ; $H _ { \epsilon } ^ { \prime } ( \xi ) = \operatorname { inf } \{ I ( \xi , \xi ^ { \prime } ) : \xi ^ { \prime } \in W _ { \epsilon } \}$ ; confidence 0.589

159.  ; $J = \frac { 1 } { f } \left( \begin{array} { c c } { 1 } & { - \psi } \\ { - \psi } & { \psi ^ { 2 } + r ^ { 2 } f ^ { 2 } } \end{array} \right)$ ; confidence 0.916

160.  ; $f ^ { \Delta ( \varphi ) } ( w ) = \operatorname { sup } _ { x \in X } \operatorname { min } \{ \varphi ( x , w ) , - f ( x ) \} ( w \in W )$ ; confidence 0.403

161.  ; $U _ { n + 1 } ^ { ( k ) } ( x ) = \sum \frac { ( n _ { 1 } + \ldots + n _ { k } ) ! } { n _ { 1 } ! \ldots n _ { k } ! } x ^ { k ( x _ { 1 } + \ldots + n _ { k } ) - n }$ ; confidence 0.481

162.  ; $p _ { i } ( z ) z ^ { \lambda } = \sum _ { n = 0 } ^ { N } \alpha ^ { n _ { i } } z ^ { n } ( \frac { \partial } { \partial z } ) ^ { n } z ^ { \lambda }$ ; confidence 0.120

163.  ; $\Omega ( M ) = \oplus _ { k \geq 0 } \Omega ^ { k } ( M ) = \oplus _ { k = 0 } ^ { \operatorname { dim } M } \Gamma ( \bigwedge T ^ { * } M )$ ; confidence 0.683

164.  ; $\frac { \partial A } { \partial \tau } = A + ( 1 + i \alpha ) \frac { \partial ^ { 2 } A } { \partial \xi ^ { 2 } } - ( 1 + i b ) A | A | ^ { 2 }$ ; confidence 0.737

165.  ; $\operatorname { limsup } _ { k \rightarrow \infty } | \int _ { \Gamma } \frac { f ( \xi ) } { \xi ^ { k + 1 } } d \xi | ^ { 1 / k } \leq 1$ ; confidence 0.992

166.  ; $\operatorname { ind } _ { g } ( P ) = ( - 1 ) ^ { n } \operatorname { Ch } ( [ a | _ { T ^ { * } M ^ { g } } ] ) T ( M ^ { g } ) L ( N , g ) [ T ^ { * } M ^ { g } ]$ ; confidence 0.103

167.  ; $( N + 1 ) ^ { - 1 } \| \sum _ { k = 0 } ^ { N } c _ { k } D _ { k } \| _ { L } \leq \operatorname { max } _ { 0 \leq k \leq N } | \mathfrak { c } _ { k } |$ ; confidence 0.066

168.  ; $f ( z ) = \int _ { \partial D } f ( \zeta ) K _ { BM } ( \zeta , z ) - \int _ { D } \overline { \partial } f ( \zeta ) / K _ { BM } ( \zeta , z )$ ; confidence 0.838

169.  ; $F ( E ) = \{ t \in T : \text { there is an } \square \omega \in \Omega \square \text { such that } \square ( \omega , t ) \in F \}$ ; confidence 0.693

170.  ; $\operatorname { lim } _ { \varepsilon \rightarrow 0 } ( u ^ { * } \rho _ { \varepsilon } ) ( v ^ { * } \sigma _ { \varepsilon } )$ ; confidence 0.979

171.  ; $\zeta _ { \lambda } ^ { \lambda } = i ^ { ( n - r ( \lambda ) + 1 ) / 2 } \sqrt { ( \lambda _ { 1 } \ldots \lambda _ { r ( \lambda ) } ) / 2 }$ ; confidence 0.359

172.  ; $\sum _ { i , j = 1 } ^ { n } K ( x _ { i } , x _ { j } ) t _ { j } \overline { t } _ { i } \geq 0 , \forall x _ { i } , y _ { j } \in E , \forall t \in C ^ { n }$ ; confidence 0.693

173.  ; $\ldots \subset C _ { 3 } \subset \ldots \subset C _ { 2 } \subset \ldots \subset C _ { 1 } \subset \ldots \subset C _ { 0 } = R K$ ; confidence 0.609

174.  ; $\operatorname { Ker } D _ { A } / \operatorname { Ran } D _ { A } = \operatorname { Ker } A \oplus ( X / \operatorname { Ran } A )$ ; confidence 0.758

175.  ; $F = ( 2 \pi \hbar ) ^ { - 6 N } \int _ { R ^ { 3 N } \times R ^ { 3 N } } e ^ { i ( \sigma X + r P ) / \hbar } \phi ( \sigma , \tau ) d \sigma d \tau$ ; confidence 0.648

176.  ; $x _ { , j } = \left\{ \begin{array} { l l } { 1 , } & { \text { if } i + j = m + 1 } \\ { 0 } & { \text { otherwise } } \end{array} \right.$ ; confidence 0.156

177.  ; $V _ { 0 } = \emptyset ; V _ { \alpha } = \cup _ { \beta < \alpha } P ( V _ { \beta + 1 } ) ; \text { and } V = \cup _ { \alpha } V _ { \alpha }$ ; confidence 0.704

178.  ; $\frac { \partial u } { \partial t } + \sum _ { j = 1 } ^ { m } \alpha _ { j } ( t , u ) \frac { \partial u } { \partial x _ { j } } = f ( t , u )$ ; confidence 0.931

179.  ; $\left\{ \begin{array} { l l } { \frac { d u } { d t } + A ( t ) u = f ( t ) , } & { t \in [ 0 , T ] } \\ { u ( 0 ) = u _ { 0 } } \end{array} \right.$ ; confidence 0.432

180.  ; $\overline { \theta } _ { n } = \overline { \theta } _ { n - 1 } + \frac { 1 } { n } ( \theta _ { n - 1 } - \overline { \theta } _ { n - 1 } )$ ; confidence 0.827

181.  ; $\| x ^ { \prime } \| _ { X ^ { \prime } } = \operatorname { sup } \{ \int _ { \Omega } | x x ^ { \prime } | d \mu : \| x \| _ { X } \leq 1 \}$ ; confidence 0.746

182.  ; $( \phi \otimes \text { id } ) \Psi _ { V , W } = \Psi _ { V , Z } ( \text { id } \varnothing \phi ) , \forall \phi : W \rightarrow Z$ ; confidence 0.381

183.  ; $\frac { \partial u } { \partial t } + 6 u \frac { \partial u } { \partial x } + \frac { \partial ^ { 3 } u } { \partial x ^ { 3 } } = 0$ ; confidence 0.998

184.  ; $( L _ { h k } V ) _ { j } ^ { n + 1 } = \frac { V _ { j } ^ { n + 1 } - V _ { j } ^ { n } } { k } - \delta ^ { 2 } ( \frac { V _ { j } ^ { n + 1 } + V _ { j } ^ { n } } { 2 } )$ ; confidence 0.374

185.  ; $n ( \epsilon , F _ { d } ) \leq K . d ^ { p } . \epsilon ^ { - \gamma } , \quad \forall d = 1,2 , \dots , \forall \epsilon \in ( 0,1 ]$ ; confidence 0.163

186.  ; $\operatorname { lim } _ { x \rightarrow \infty } [ a _ { 0 } + \frac { n } { n + 1 } a _ { 1 } + \frac { n ( n - 1 ) } { ( n + 1 ) ( n + 2 ) } a _ { 2 }$ ; confidence 0.512

187.  ; $\sum _ { I \subseteq \{ 1 , \ldots , k \} , I \neq \emptyset } ( - 1 ) ^ { | | | + 1 } \operatorname { Bel } ( \cap _ { i \in I } A _ { i } )$ ; confidence 0.180

188.  ; $E _ { n } ( x , a ) = \sum _ { i = 0 } ^ { | n / 2 | } \left( \begin{array} { c } { n - i } \\ { i } \end{array} \right) ( - a ) ^ { i } x ^ { n - 2 i }$ ; confidence 0.153

189.  ; $( \varphi \rightarrow \varphi \left( \begin{array} { c } { x } \\ { \varepsilon x \varphi } \end{array} \right) ) = 1$ ; confidence 0.826

190.  ; $\overline { d } _ { \chi } ^ { G } ( A ) : = d _ { \chi } ^ { G } ( A ) / \chi ( \text { id } ) = d _ { \chi } ^ { G } ( A ) / d _ { \chi } ^ { G } ( I _ { n } )$ ; confidence 0.731

191.  ; $\{ \operatorname { Pred } ( x ) , x \in X _ { P } \} \cup \{ \operatorname { Pred } \operatorname { Succ } ( x ) , x \in X _ { P } \}$ ; confidence 0.274

192.  ; $\equiv - \operatorname { lk } ( L ) v ( \frac { v ^ { - 1 } - v } { z } ) ^ { \operatorname { com } ( L ) - 2 } \operatorname { mod } ( z )$ ; confidence 0.939

193.  ; $\frac { d T _ { 1 } } { d s } = [ T _ { 2 } , T _ { 3 } ] , \frac { d T _ { 2 } } { d s } = [ T _ { 3 } , T _ { 1 } ] , \frac { d T _ { 3 } } { d s } = [ T _ { 1 } , T _ { 2 } ]$ ; confidence 0.926

194.  ; $\Gamma _ { 0 } ( 2 ) ^ { + } : = \{ \Gamma _ { 0 } ( 2 ) , \left( \begin{array} { c c } { 0 } & { - 1 } \\ { 2 } & { 0 } \end{array} \right) \}$ ; confidence 0.769

195.  ; $( \sigma _ { 2 } \frac { \partial } { \partial t _ { 1 } } - \sigma _ { 1 } \frac { \partial } { \partial t _ { 2 } } + \gamma ) u = 0$ ; confidence 0.449

196.  ; $= \operatorname { sup } \{ h ( z ) : \quad h ( \zeta ) - \operatorname { log } \| \zeta - w \| = O ( 1 ) ( \zeta \rightarrow w ) \}$ ; confidence 0.779

197.  ; $\frac { \lambda _ { 2 } ( \Omega ) } { \lambda _ { 1 } ( \Omega ) } \leq \frac { j _ { \Re / 2,1 } ^ { 2 } } { j _ { \aleph / 2 - 1,1 } ^ { 2 } }$ ; confidence 0.243

198.  ; $\| f \| _ { k } = \operatorname { max } \{ \| D ^ { \alpha } f \| _ { L _ { \infty } } : \alpha \in N _ { 0 } ^ { d } , \alpha _ { i } \leq k \}$ ; confidence 0.553

199.  ; $W _ { n } = \operatorname { span } _ { C } \{ \frac { \partial ^ { k } \Psi _ { 1 , n } ( x , z ) } { \partial x _ { 1 } } : k = 0,1 , \ldots \}$ ; confidence 0.732

200.  ; $\epsilon x ^ { \prime } = y - x + \frac { x ^ { 3 } } { 3 } , \quad y ^ { \prime } = - x , \quad \square ^ { \prime } = \frac { d } { d \tau }$ ; confidence 0.539

201.  ; $\forall x \forall v _ { 1 } \ldots \forall v _ { n } \exists y \forall v ( v \in y \leftrightarrow ( v \in x / \not \varphi ) )$ ; confidence 0.115

202.  ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { F _ { n } + 1 } { F _ { n } } = \frac { 1 } { 2 } ( \sqrt { 5 } + 1 ) \simeq 1.618$ ; confidence 0.544

203.  ; $q ^ { ( l + 1 ) } = - ( q ^ { ( l ) } ) ^ { 2 } r ^ { ( l ) } + q ^ { ( l ) } \operatorname { log } ( q ^ { ( l ) } ) , r ^ { ( l + 1 ) } = \frac { 1 } { q ^ { ( l ) } }$ ; confidence 0.906

204.  ; $\frac { \partial } { \partial t _ { m } } P - \frac { \partial } { \partial x } Q ^ { ( m ) } + [ P , Q ^ { ( r ) } ] = 0 \Leftrightarrow$ ; confidence 0.156

205.  ; $\{ f ( t ) \} _ { ( k ; t _ { i } ) } = \sum _ { m = 0 } ^ { k } \frac { ( t - t _ { i } ) ^ { m } } { m ! } \frac { d ^ { m } f ( t ) } { d t ^ { m } } | _ { t = t _ { i } }$ ; confidence 0.370

206.  ; $( X _ { 0 } ^ { 1 - \theta } X _ { 1 } ^ { \theta } ) ^ { \prime } = ( X _ { 0 } ^ { \prime } ) ^ { 1 - \theta } ( X _ { 1 } ^ { \prime } ) ^ { \theta }$ ; confidence 0.985

207.  ; $\sum _ { 0 } ^ { \infty } | f _ { n } | \operatorname { sup } _ { U } | \varphi _ { n } ( z ) | \leq \operatorname { sup } _ { K } | f ( z ) |$ ; confidence 0.934

208.  ; $f \rightarrow \frac { 1 } { 2 \pi } \int _ { 0 } ^ { 2 \pi } \operatorname { Re } \frac { e ^ { i t } + z } { e ^ { t t } - z } f ( e ^ { i t } ) d t$ ; confidence 0.641

209.  ; $f ^ { \circ } ( x ; v ) : = \operatorname { liminf } _ { y \rightarrow x , t } \operatorname { lo } \frac { f ( y + t v ) - f ( y ) } { t }$ ; confidence 0.055

210.  ; $= g ^ { - 1 } \{ p _ { 1 } , p _ { 2 } ; \ldots ; p _ { 4 m - 1 } , p _ { 4 m } \} ( W ( g ) \otimes \ldots \otimes W ( g ) ) \in \in C ^ { \infty } ( M )$ ; confidence 0.307

211.  ; $\mu _ { R } ( M ) \leq \operatorname { max } \{ \mu ( M , P ) : P \in \operatorname { Spec } ( R ) \} + \operatorname { Kdim } ( R )$ ; confidence 0.743

212.  ; $\| \varphi \| = \operatorname { sup } _ { | \operatorname { maz } } | \varphi ( z ) | e ^ { \delta | \operatorname { Re } z | }$ ; confidence 0.125

213.  ; $\operatorname { lim } _ { i \rightarrow \infty } c _ { i } \int \phi ( \frac { y - x } { r _ { i } } ) d \mu ( y ) = \int \phi ( y ) d \nu$ ; confidence 0.860

214.  ; $\psi - \psi _ { 0 } = \varepsilon A ( \xi , \tau ) f _ { C } ( y ) e ^ { i ( \langle k _ { C } , x \rangle + \mu _ { C } t ) } + \text { c.c. } +$ ; confidence 0.057

215.  ; $\frac { \partial u } { \partial t } + u \frac { \partial u } { \partial x } + \frac { \partial ^ { 3 } u } { \partial x ^ { 3 } } = 0$ ; confidence 0.997

216.  ; $| \{ \vartheta \in I : | \varphi ( e ^ { i \vartheta } ) - \varphi _ { I } | \geq \lambda \} | \leq C e ^ { - \gamma \lambda } | I |$ ; confidence 0.547

217.  ; $\int _ { \partial D } \operatorname { exp } ( \varepsilon | \varphi ( e ^ { i \vartheta } ) - \varphi _ { I } | ) d \vartheta$ ; confidence 0.495

218.  ; $\frac { D v } { D t } = \frac { \partial v } { \partial t } + \frac { 1 } { 2 } \nabla v ^ { 2 } + ( \operatorname { curl } v ) \times v$ ; confidence 0.796

219.  ; $\frac { \partial u ( t , x ) } { \partial t } + \frac { 1 } { 2 } \| d _ { \chi } u ( t , x ) \| ^ { 2 } = 0 , \quad ( t , x ) \in ( 0 , T ) \times H$ ; confidence 0.545

220.  ; $\operatorname { lim } _ { \varepsilon \rightarrow 0 } ( u ^ { * } \rho _ { \varepsilon } ) ( v ^ { * } \rho _ { \varepsilon } )$ ; confidence 0.965

221.  ; $d _ { j k l } = \frac { 1 } { 4 } \operatorname { Tr } [ ( \gamma _ { j } \gamma _ { k } + \lambda _ { k } \lambda _ { j } ) \lambda _ { l } ]$ ; confidence 0.723

222.  ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { \operatorname { det } T _ { n } ( a ) } { G ( b ) ^ { n } n ^ { \Omega } } = E$ ; confidence 0.483

223.  ; $\rightarrow \pi _ { n } ( X , B , * ) \rightarrow \pi _ { n } ( X ; A , B , x _ { 0 } ) \stackrel { \partial } { \rightarrow } \ldots$ ; confidence 0.195

224.  ; $\operatorname { inf } _ { z _ { j } } \operatorname { max } _ { k \in S } \frac { \operatorname { Re } g _ { 2 } ( k ) } { M _ { d } ( k ) }$ ; confidence 0.419

225.  ; $x _ { 0 } ^ { - 1 } \delta ( \frac { x _ { 1 } - x _ { 2 } } { x _ { 0 } } ) = \sum _ { n \in Z } \frac { ( x _ { 1 } - x _ { 2 } ) ^ { n } } { x _ { 0 } ^ { n + 1 } } =$ ; confidence 0.587

226.  ; $\operatorname { diag } ( t _ { 1 } , \ldots , t _ { n } ) \mapsto t _ { 1 } ^ { \lambda _ { 1 } } \ldots t _ { n } ^ { \lambda _ { n } } \in K$ ; confidence 0.507

227.  ; $= \sum _ { k , l } A _ { k l } \int _ { R ^ { 3 N } } e ^ { i p z / \hbar } u _ { l k } ( x - \frac { z } { 2 } ) \overline { u } / ( x + \frac { z } { 2 } ) d z$ ; confidence 0.340

228.  ; $F _ { j k } = \frac { \partial } { \partial t _ { j } } \frac { \partial } { \partial t _ { k } } \operatorname { log } ( \tau )$ ; confidence 0.976

229.  ; $\operatorname { grad } \psi = ( \partial \psi / \partial \zeta _ { 1 } , \dots , \partial \psi / \partial \zeta _ { N } )$ ; confidence 0.302

230.  ; $\operatorname { lim } _ { \overline { A } } a _ { n } = \frac { \sum _ { 0 } ^ { \infty } b _ { j } } { \sum _ { 0 } ^ { \infty } j p _ { j } }$ ; confidence 0.177

231.  ; $0 \rightarrow \operatorname { Ext } _ { 2 } ^ { 1 } ( K _ { 0 } ( A ) , Z ) \rightarrow \operatorname { Ext } ( A ) \rightarrow$ ; confidence 0.466

232.  ; $H _ { + } ^ { - 1 } = ( I - \frac { s y ^ { T } } { y ^ { T } s } ) H _ { c } ^ { - 1 } ( I - \frac { y s ^ { T } } { y ^ { T } s } ) + \frac { s s ^ { T } } { y ^ { T } s }$ ; confidence 0.648

233.  ; $\frac { d ^ { 2 } u } { d t ^ { 2 } } = \operatorname { sin } ( u ) , \quad \frac { d ^ { 2 } v } { d t ^ { 2 } } = \operatorname { sinh } ( v )$ ; confidence 0.991

234.  ; $= \Lambda ^ { m } + D _ { 1 } \Lambda ^ { m - 1 } + \ldots + D _ { m - 1 } \Lambda + D _ { m } , D _ { k } \in C ^ { n \times n } , k = 1 , \ldots , m$ ; confidence 0.523

235.  ; $\Pi ^ { T } A \Pi = R ^ { T } R , \quad R = \left( \begin{array} { c c } { R _ { 11 } } & { R _ { 12 } } \\ { 0 } & { 0 } \end{array} \right)$ ; confidence 0.987

236.  ; $\mu ( x ) = \left( \begin{array} { l l } { \mu _ { 11 } } & { \mu _ { 12 } } \\ { \mu _ { 21 } } & { \mu _ { 22 } } \end{array} \right) =$ ; confidence 0.548

237.  ; $\frac { \partial ^ { 2 } u ( t , x ) } { \partial t ^ { 2 } } - a ^ { 2 } \frac { \partial ^ { 2 } u ( t , x ) } { \partial x ^ { 2 } } = f ( t , x )$ ; confidence 0.756

238.  ; $w _ { i } ^ { ( t + 1 ) } = E ( q _ { i } | y _ { i } , \mu ^ { ( t ) } , \Sigma ^ { ( t ) } ) = \frac { \nu + p } { \nu + d _ { i } ^ { ( t ) } } , i = 1 , \dots , n$ ; confidence 0.208

239.  ; $n \overline { H } ^ { 1 } = \operatorname { dim } C ^ { 0 } ( \Gamma , k + 2 , v ) + \operatorname { dim } C ^ { 0 } ( \Gamma , k + 2 , v )$ ; confidence 0.101

240.  ; $w ^ { em } = J . E + \frac { \partial P } { \partial t } E - M \cdot \frac { \partial B } { \partial t } + \nabla \cdot ( v ( P . E ) )$ ; confidence 0.154

241.  ; $= \varphi \wedge \psi \otimes [ X , Y ] + \varphi \wedge L _ { X } \psi \otimes Y - L _ { Y } \varphi \wedge \psi \otimes X +$ ; confidence 0.423

242.  ; $\sigma ( \Omega ( A ) ) \subseteq \cup _ { i , j = 1 \atop j \neq j } ^ { n } K _ { i j } ( A ) \subseteq \cup _ { i = 1 } ^ { n } G _ { i } ( A )$ ; confidence 0.105

243.  ; $\operatorname { exp } ( - \sum _ { p \leq x } \frac { 1 } { p } \cdot ( 1 - \operatorname { Re } ( f ( p ) p ^ { - i \alpha _ { 0 } } ) ) )$ ; confidence 0.700

244.  ; $s _ { r } ( \zeta , z ) = ( \partial r / \partial \zeta _ { 1 } ( \zeta ) , \ldots , \partial r / \partial \zeta _ { n } ( \zeta ) )$ ; confidence 0.465

245.  ; $( l + H _ { x } ) \Gamma _ { x } : = \Gamma _ { x } ( t , s ) + \int _ { 0 } ^ { x } H ( t - u ) \Gamma _ { x } ( u , s ) d u = H ( t - s ) , 0 \leq t , s \leq x$ ; confidence 0.293

246.  ; $\operatorname { exp } \{ \frac { 1 } { k _ { B } T } \sum _ { l = 1 } ^ { N } [ J S _ { i } S _ { + 1 } + \frac { H } { 2 } ( S _ { i } + S _ { + 1 } ) ] \} =$ ; confidence 0.367

247.  ; $\angle \operatorname { lim } _ { z \rightarrow \omega } F ( z ) = \omega , \text { and } \angle F ^ { \prime } ( \omega ) < 1$ ; confidence 0.668

248.  ; $q ( T ) p ( T ) \leq \operatorname { dim } \operatorname { ker } q ( T ) + \operatorname { dim } \operatorname { ker } p ( T )$ ; confidence 0.980

249.  ; $A = ( \frac { 1 } { \operatorname { sinh } r } - \frac { 1 } { r } ) \epsilon _ { i j k } \frac { x _ { j } } { r } \sigma _ { k } d x _ { i }$ ; confidence 0.768

250.  ; $\psi ( \gamma ) = \frac { 2 } { \pi ^ { 2 } \gamma } + O ( \frac { 1 } { \gamma ^ { 3 } } ) \text { as } \gamma \rightarrow + \infty$ ; confidence 0.633

251.  ; $\operatorname { det } ( \Delta + z ) = \operatorname { exp } ( - \frac { \partial } { \partial s } \zeta ( s , z ) | _ { s = 0 } )$ ; confidence 0.604

252.  ; $\frac { B _ { - } ( \delta + p - 1 ) / 2 ( \frac { 1 } { 4 } \Sigma T T ^ { \prime } ) } { \Gamma _ { p } [ \frac { 1 } { 2 } ( \delta + p - 1 ) ] }$ ; confidence 0.509

253.  ; $m _ { 0 } ( \lambda ) = A + \int _ { - \infty } ^ { \infty } ( \frac { 1 } { t - \lambda } - \frac { t } { t ^ { 2 } + 1 } ) d \rho _ { 0 } ( t )$ ; confidence 0.926

254.  ; $\square \ldots \rightarrow \pi _ { n + 1 } ( X ; A , B , * ) \stackrel { \partial } { \rightarrow } \pi _ { n } ( A , A \cap B , * )$ ; confidence 0.389

255.  ; $x = \frac { 1 - \lambda } { \pi } \operatorname { ln } \frac { 1 } { 2 } ( 1 + \operatorname { cos } \frac { \pi y } { \lambda } )$ ; confidence 0.782

256.  ; $k q ^ { \prime } s \frac { d } { d s } [ q ^ { \prime } s \frac { d \theta } { d s } ] + \operatorname { cos } \theta - q ^ { \prime } = 0$ ; confidence 0.975

257.  ; $\chi _ { \lambda } = \sum _ { \mu \in \Lambda ( n ) } \operatorname { dim } _ { K } ( \Delta ( \lambda ) ^ { \mu } ) _ { e _ { \mu } }$ ; confidence 0.461

258.  ; $e ^ { - t A _ { X } } = \operatorname { lim } _ { n \rightarrow \infty } ( I + \frac { t } { n } A ) ^ { - n } x = S ( t ) x , \forall x \in X$ ; confidence 0.189

259.  ; $\sum _ { | X | \geq n } \mu ( X ) \frac { T ^ { - 1 } ( \operatorname { time } _ { A } ( X ) ) } { | X | } \leq \sum _ { | X | \geq n } \mu ( X )$ ; confidence 0.387

260.  ; $+ O ( \frac { ( \operatorname { log } n ) ^ { 1 / 2 } ( \operatorname { log } \operatorname { log } n ) ^ { 1 / 4 } } { n ^ { 3 / 4 } } )$ ; confidence 0.631

261.  ; $P ( E _ { l } ) = \frac { \operatorname { exp } ( - E _ { l } / k _ { B } T ) } { \sum _ { l } \operatorname { exp } ( - E _ { l } / k _ { B } T ) }$ ; confidence 0.499

262.  ; $+ ( - 1 ) ^ { n + 1 } \operatorname { pr } ( \alpha _ { 2 } , \dots , \alpha _ { n + 1 } ) \} ( \alpha _ { 1 } , \dots , \alpha _ { n + 1 } )$ ; confidence 0.247

263.  ; $V ( z _ { 0 } , \dots , z _ { r } - 1 ) ( \rho _ { 0 } , \dots , \rho _ { r - 1 } ) ^ { T } = ( \gamma _ { 00 } , \dots , \gamma _ { 0 , r - 1 } ) ^ { T }$ ; confidence 0.356

264.  ; $\nabla ( \Theta \otimes \Phi ) = \nabla \Theta \otimes \Phi + \tau _ { p + 1 } ( \Theta \varnothing \nabla \Phi ) \in$ ; confidence 0.260

265.  ; $= g ^ { - 1 } \{ 1,4 \} \nabla C ( g ) - g ^ { - 1 } \{ 1,3 ; 2,5 \} ( A ( g ) \otimes W ( g ) ) \subset \subset \otimes \square ^ { 2 } E$ ; confidence 0.099

266.  ; $f _ { \nu _ { 1 } , \nu _ { 2 } } ( x ) = \frac { 1 } { B ( \nu _ { 1 } / 2 , \nu _ { 2 } / 2 ) } ( \frac { \nu _ { 1 } } { \nu _ { 2 } } ) ^ { \nu _ { 1 } / 2 }$ ; confidence 0.967

267.  ; $[ \left( \begin{array} { c c } { Id } & { 0 } \\ { 0 } & { - Id } \end{array} \right) , L _ { \ell } ] = i L _ { i } ( - 2 \leq i \leq 2 )$ ; confidence 0.301

268.  ; $\operatorname { per } ( A ) \geq \operatorname { per } ( B ) \operatorname { per } ( D ) \geq \prod _ { i = 1 } ^ { n } a _ { i i }$ ; confidence 0.696

269.  ; $\angle \operatorname { lim } _ { z \rightarrow \omega } ( F ( z ) - \eta ) / ( z - \omega ) = \angle F ^ { \prime } ( \omega )$ ; confidence 0.912

270.  ; $\alpha _ { 0 } : \cup _ { \mathfrak { p } ^ { \prime } \in S ^ { \prime } } G ( K _ { \mathfrak { p } ^ { \prime } } ) \rightarrow G$ ; confidence 0.239

271.  ; $a ( f ) = \int _ { M } a ( x ) f ( x ) d \sigma ( x ) , \quad \alpha ^ { * } ( f ) = \int _ { M } a ^ { * } ( x ) \overline { f } ( x ) d \sigma ( x )$ ; confidence 0.180

272.  ; $\left.\begin{array} { c c } { T } & { ( I - T T ^ { * } ) ^ { 1 / 2 } } \\ { ( I - T ^ { * } T ) ^ { 1 / 2 } } & { T ^ { * } } \end{array} \right\}$ ; confidence 0.169

273.  ; $S ( \lambda ) = I _ { E } - i \Phi ( \xi _ { 1 } A _ { 1 } + \xi _ { 2 } A _ { 2 } - \xi _ { 1 } \lambda _ { 1 } - \xi _ { 2 } \lambda _ { 2 } ) ^ { - 1 }$ ; confidence 0.459

274.  ; $\mathfrak { E } ( \lambda ) = \operatorname { ker } ( \lambda _ { 1 } \sigma _ { 2 } - \lambda _ { 2 } \sigma _ { 1 } + \gamma )$ ; confidence 0.252

275.  ; $J ( \rho ) = J ( \rho ; x _ { 0 } , u ) = \frac { 1 } { \sigma _ { N } ( \rho ) } \int _ { S _ { R } ( x _ { 0 } , \rho ) } u ( y ) d \sigma _ { N } ( y )$ ; confidence 0.275

276.  ; $\operatorname { Vol } ( \overline { U M } ) = C _ { 1 } ( n ) \int _ { U ^ { + } \partial N } l ( v ) \langle v , N _ { x } \rangle d v d x$ ; confidence 0.421

277.  ; $= \frac { 1 } { 2 } ( \frac { \Theta _ { \Delta } ( q ) } { \eta ( q ) ^ { 24 } } + \frac { \eta ( q ) ^ { 24 } } { \eta ( q ^ { 2 } ) ^ { 24 } } ) +$ ; confidence 0.904

278.  ; $R ( \phi ) \subset \sigma _ { e } ( T _ { \phi } ) \subset \sigma ( T _ { \phi } ) \subset \operatorname { conv } ( R ( \phi ) )$ ; confidence 0.936

279.  ; $\operatorname { max } _ { k = 1 , \ldots , n } ( \frac { 1 } { n } | s _ { k } | ) ^ { 1 / k } > \frac { 1 } { 5 } > \frac { 1 } { 2 + \sqrt { 8 } }$ ; confidence 0.635

280.  ; $\operatorname { min } _ { r = m + 1 , \ldots , m + K } | G _ { 1 } ( r ) | \geq \frac { 1 } { P _ { m , K } } | \sum _ { j = 1 } ^ { n } P _ { j } ( 0 ) |$ ; confidence 0.350

281.  ; $g x ( T ) = \frac { G _ { X } ( T ) } { H ( X ) [ 1 + \alpha ( X ) + H ( X ) ^ { 2 } \| \alpha ^ { \prime \prime } ( X ) \| ^ { 2 } G _ { X } ] ^ { 1 / 2 } }$ ; confidence 0.162

282.  ; $| \frac { n } { 2 } | \lfloor \frac { n - 1 } { 2 } \rfloor \lfloor \frac { m } { 2 } \rfloor \lfloor \frac { m - 1 } { 2 } \rfloor$ ; confidence 0.206

283.  ; $+ \frac { d } { d m } \operatorname { ln } g ( R ; m , s ) \frac { d m } { d s } + \frac { d } { d s } \operatorname { ln } g ( R ; m , s ) = 0$ ; confidence 0.979

284.  ; $p ^ { * } ( \alpha , t ) = \omega e ^ { \lambda ^ { * } ( t - \alpha ) } \Pi ( \alpha ) = e ^ { \lambda ^ { * } t _ { w } ^ { * } ( \alpha ) }$ ; confidence 0.131

285.  ; $\mathfrak { p } _ { i } ( t ) = q _ { i } ( t ) \prod _ { m = 1 , m \neq i } ^ { n } ( t - t _ { m } ) ^ { \gamma _ { m } } \quad ( i = 1 , \ldots , n )$ ; confidence 0.353

286.  ; $L ^ { * } ( h ^ { i } ( X ) , s ) _ { s = m } \equiv \operatorname { det } ( \Pi ) \cdot \operatorname { det } \langle . . \rangle$ ; confidence 0.138

287.  ; $X ^ { \prime } = \sqrt { X ^ { 2 } + \hat { y } ^ { 2 } } e ^ { ( \operatorname { arctan } y / X + k \pi ) \rho / \omega } - X _ { H } + \Re$ ; confidence 0.068

288.  ; $b _ { j } ^ { n } ( x ) : = \left( \begin{array} { c } { n } \\ { j } \end{array} \right) x ^ { j } ( 1 - x ) ^ { n - j } , j = 0 , \ldots , n$ ; confidence 0.444

289.  ; $\forall x _ { 1 } \ldots \forall x _ { N } ( P _ { X 1 } \ldots x _ { N } \leftrightarrow \varphi ( x _ { 1 } , \ldots , x _ { N } ) )$ ; confidence 0.198

290.  ; $\partial _ { t } \int f \operatorname { ln } f d v + \operatorname { div } _ { X } \int v f \operatorname { ln } f d v \leq 0$ ; confidence 0.472

291.  ; $S ^ { * } ( \frac { \alpha } { q } ) = \sum _ { k } e ( x ( h ) y ( \frac { \alpha } { q } ) ) \gamma ( h ) \delta ( \frac { \alpha } { q } )$ ; confidence 0.317

292.  ; $\mathfrak { h } _ { R } \rightarrow \mathfrak { h } _ { R } ^ { * } : = \operatorname { hom } _ { R } ( \mathfrak { h } _ { R } , R )$ ; confidence 0.571

293.  ; $\psi ( z ) : = \frac { d } { d z } \{ \operatorname { log } \Gamma ( z ) \} = \frac { \Gamma ^ { \prime } ( z ) } { \Gamma ( z ) }$ ; confidence 0.998

294.  ; $0 < C _ { \psi } = 2 \pi \int _ { 0 } ^ { \infty } \frac { | \hat { \psi } ( \alpha \omega ) | ^ { 2 } } { \alpha } d \alpha < \infty$ ; confidence 0.655

295.  ; $( M _ { t } f ) ( s ) = \frac { 1 } { 2 } \operatorname { sup } _ { t } f ( s , t ) + \frac { 1 } { 2 } \operatorname { inf } _ { t } f ( s , t )$ ; confidence 0.930

296.  ; $( M _ { s } f ) ( t ) = \frac { 1 } { 2 } \operatorname { sup } _ { s } f ( s , t ) + \frac { 1 } { 2 } \operatorname { inf } _ { s } f ( s , t )$ ; confidence 0.838

297.  ; $( y - x ) ^ { \alpha + \beta } ( \frac { \partial u } { \partial y } - \frac { \partial u } { \partial x } ) | _ { x = y } = \nu ( x )$ ; confidence 0.989

298.  ; $\| u \| A _ { 2 } ( G ) = \operatorname { inf } \{ N _ { 2 } ( k ) N _ { 2 } ( l ) : k , l \in L _ { C } ^ { 2 } ( G ) , u = \overline { k } ^ { * } t \}$ ; confidence 0.142

299.  ; $u _ { i l } = z ^ { \lambda _ { i } } \sum _ { j = 0 } ^ { l } \sum _ { k = 0 } ^ { \infty } b _ { j k } ( \operatorname { log } z ) ^ { j } z ^ { k }$ ; confidence 0.664

300.  ; $F ( x ) : = \sum _ { j = 1 } ^ { J } s _ { j } e ^ { - k _ { j } x } + \frac { 1 } { 2 \pi } \int _ { - \infty } ^ { \infty } [ 1 - S ( k ) ] e ^ { i k x } d k$ ; confidence 0.646