Namespaces
Variants
Actions

User:Maximilian Janisch/latexlist/latex/NoNroff/5

From Encyclopedia of Mathematics
< User:Maximilian Janisch‎ | latexlist‎ | latex
Revision as of 23:13, 12 February 2020 by Maximilian Janisch (talk | contribs) (AUTOMATIC EDIT of page 5 out of 77 with 300 lines: Updated image/latex database (currently 22833 images latexified; order by Length, ascending: False.)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

List

1. c12028026.png ; $\operatorname { crs } ( A \otimes B , C ) \cong \operatorname { Crs } ( A , \operatorname { CRS } ( B , C ) )$ ; confidence 0.776

2. c12031031.png ; $e _ { N } ( C _ { d } ^ { k } ) \asymp n ^ { - k / d } \text { or } n ( \epsilon , C _ { d } ^ { k } ) \asymp \epsilon ^ { - d / k }$ ; confidence 0.172

3. d12019014.png ; $\operatorname { Dom } ( ( - \Delta _ { Dir } ) ^ { 1 / 2 } ) = \operatorname { Dom } ( E ) = H _ { 0 } ^ { 1 } ( \Omega )$ ; confidence 0.729

4. f120210106.png ; $= z ^ { \lambda } \sum _ { j = 0 } ^ { \infty } z ^ { j } [ \sum _ { i + k = j } c _ { k } ( \lambda ) p _ { i } ( \lambda + k ) ] =$ ; confidence 0.949

5. g13001058.png ; $\operatorname { Tr } _ { E / F } ( \beta _ { i } \gamma _ { j } ) = \delta _ { i j } \text { for } i , j = 0 , \dots , n - 1$ ; confidence 0.218

6. g120040186.png ; $\| u \| _ { T } ^ { 2 } = \sum _ { \xi \in Z ^ { n } } ( 1 + | \xi | ) ^ { 2 r } e ^ { 2 T | \xi | ^ { 1 / s } } | \hat { u } ( \xi ) | ^ { 2 }$ ; confidence 0.405

7. h13006045.png ; $( D \alpha D ) ( D \beta D ) = D \alpha D \beta D = D \alpha ( \cup _ { \beta ^ { \prime } } D \beta ^ { \prime } ) =$ ; confidence 0.896

8. i13005094.png ; $q \in L _ { 1,2 } : = \{ q : q = \overline { q } , \int _ { - \infty } ^ { \infty } ( 1 + x ^ { 2 } ) | q ( x ) | d x < \infty \}$ ; confidence 0.659

9. i13007054.png ; $( \nabla ^ { 2 } + \dot { k } ^ { 2 } 0 + \dot { k } ^ { 2 } 0 v ( x ) ) u ( x , y , k _ { 0 } ) = - \delta ( x - y ) \text { in } R ^ { 3 }$ ; confidence 0.122

10. k055840274.png ; $\sigma ( A | _ { ( I - E ( \Delta ) ) K } ) \subset \overline { ( R \backslash \Delta ) } \cup \sigma _ { 0 } ( A )$ ; confidence 0.327

11. k05584021.png ; $\kappa = \operatorname { min } ( \operatorname { dim } K _ { + } , \operatorname { dim } K _ { - } ) < \infty$ ; confidence 0.992

12. l120170255.png ; $B _ { 2 } \stackrel { d } { \rightarrow } B _ { 1 } \stackrel { d _ { 1 } } { \rightarrow } B _ { 0 } \rightarrow 0$ ; confidence 0.085

13. m12003098.png ; $M = \int ( \partial / \partial e ) \eta ( \vec { x } , e ) \vec { x X } ^ { t } d H _ { \vec { \theta } } ( \vec { x } , y )$ ; confidence 0.495

14. o13001043.png ; $\hat { f } ( \xi ) = \frac { 1 } { ( 2 \pi ) ^ { 3 / 2 } } \int _ { D ^ { \prime } } f ( x ) \overline { u ( x , \xi ) } d x : = F f$ ; confidence 0.825

15. p130070126.png ; $\delta ( z , w ) = \operatorname { inf } _ { f \in F } \{ \operatorname { log } | \xi | : f ( \xi ) = z , f ( 0 ) = w \}$ ; confidence 0.991

16. r130080126.png ; $B ( x , y ) = \sum _ { j = 1 } ^ { \infty } \lambda _ { j } ^ { - 1 } \varphi _ { j } ( x ) \overline { \varphi _ { j } ( y ) }$ ; confidence 0.973

17. r1301104.png ; $\zeta ( s ) : = \sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { s } } = \prod _ { p } \frac { 1 } { 1 - \frac { 1 } { p ^ { s } } }$ ; confidence 0.961

18. s08602018.png ; $\Phi ^ { + } ( t _ { 0 } ) + \Phi ^ { - } ( t _ { 0 } ) = \frac { 1 } { \pi i } \int _ { \Gamma } \frac { \phi ( t ) d t } { t - t 0 }$ ; confidence 0.421

19. s12022075.png ; $\operatorname { spec } ( M , \Delta ^ { ( 0 ) } ) , \ldots , \operatorname { spec } ( M , \Delta ^ { ( d i m M ) } )$ ; confidence 0.633

20. s13050029.png ; $\sum _ { k = 0 } ^ { n } \frac { f _ { k } } { \left( \begin{array} { l } { n } \\ { k } \end{array} \right) } \leq 1$ ; confidence 0.907

21. s12035027.png ; $P = \operatorname { lim } _ { N \rightarrow \infty } N \cdot \operatorname { Cov } ( \hat { \theta } N ) =$ ; confidence 0.274

22. t12005088.png ; $( p - n + i _ { 1 } ) \cdot \mu _ { i _ { 1 } , \dots , i _ { r } } - ( i _ { 1 } - i _ { 2 } ) \cdot \mu _ { i _ { 2 } , \dots , i _ { r } }$ ; confidence 0.578

23. t12006094.png ; $\operatorname { lim } _ { Z \rightarrow \infty } \frac { E ^ { TF } ( \lambda Z ) } { E ^ { Q } ( \lambda Z ) } = 1$ ; confidence 0.392

24. t12007027.png ; $\frac { 1 } { q } + a _ { 0 } + a _ { 1 } q + \alpha _ { 2 } q ^ { 2 } + \ldots , \quad q = \operatorname { exp } ( 2 \pi i z )$ ; confidence 0.614

25. t12013028.png ; $\oint _ { z = \infty } \tau _ { n } ( x - [ z ^ { - 1 } ] , y ) \tau _ { m + 1 } ( x ^ { \prime } + [ z ^ { - 1 } ] , y ^ { \prime } ) x$ ; confidence 0.671

26. w120090249.png ; $g = \sum _ { a \in \Phi ^ { - } } \oplus _ { g _ { a } } \oplus D _ { \gamma \in \Phi ^ { + } } \oplus _ { g _ { \gamma } }$ ; confidence 0.105

27. w120090342.png ; $\left( \begin{array} { c } { h } \\ { i } \end{array} \right) = \frac { h ( h - 1 ) \ldots ( h - i + 1 ) } { i ! }$ ; confidence 0.487

28. z13003027.png ; $( Z f ) ( t , w ) = ( 2 \gamma ) ^ { 1 / 4 } e ^ { - \pi \gamma t ^ { 2 } } \theta _ { 3 } ( w - i \gamma t , e ^ { - \pi \gamma } )$ ; confidence 0.985

29. a0100205.png ; $P = \cup _ { n _ { 1 } , \ldots , n _ { k } , \ldots } \cap _ { k = 1 } ^ { \infty } E _ { n _ { 1 } } \square \ldots x _ { k }$ ; confidence 0.192

30. a130060149.png ; $P _ { E } ^ { \# } ( n ) \sim \frac { 1 } { 468 \sqrt { \pi } } 4 ^ { n } n ^ { - 7 / 2 } \text { asn } \rightarrow \infty$ ; confidence 0.201

31. a11032022.png ; $A _ { j } ( z ) = \sum _ { l = 0 } ^ { \rho _ { i } } R _ { k + 1 } ^ { ( i ) } ( c _ { l } z ) c _ { i } ^ { l + 1 } \lambda _ { l j } ^ { ( l ) }$ ; confidence 0.263

32. a13032055.png ; $K = \operatorname { log } ( \frac { 1 - \beta } { \alpha } ) ( \operatorname { log } \frac { q } { p } ) ^ { - 1 }$ ; confidence 0.994

33. a13032056.png ; $J = \operatorname { log } ( \frac { 1 - \alpha } { \beta } ) ( \operatorname { log } \frac { q } { p } ) ^ { - 1 }$ ; confidence 0.996

34. b12003041.png ; $\| \operatorname { ltg } ( t ) \| _ { 2 } \| \gamma g ( \gamma ) \| _ { 2 } \geq ( 4 \pi ) ^ { - 1 } \| g \| _ { 2 } ^ { 2 }$ ; confidence 0.075

35. b13006013.png ; $| x | _ { 2 } = ( \sum _ { i } | x _ { i } | ^ { 2 } ) ^ { 1 / 2 } , \| x \| _ { \infty } = \operatorname { max } _ { i } | x _ { i } |$ ; confidence 0.344

36. b13006011.png ; $\| A \| = \operatorname { max } _ { x \neq 0 } \| A x \| / \| x \| = \operatorname { max } _ { | x | } \| = 1 \| A x \|$ ; confidence 0.050

37. b12009040.png ; $p _ { 1 } ( \xi ) = 1 + \beta _ { 1 } \xi + \beta _ { 2 } \xi ^ { 2 } + \ldots ( \operatorname { Re } p _ { 1 } ( \xi ) > 0 )$ ; confidence 0.869

38. b12009091.png ; $f ( z ) = \{ \int _ { 0 } ^ { z } g ^ { \alpha } ( \xi ) h ( \xi ) \xi ^ { i \beta - 1 } d \xi \} ^ { 1 / ( \alpha + i \beta ) }$ ; confidence 0.544

39. b12009082.png ; $L ( r ) = \int _ { 0 } ^ { 2 \pi } | z f ^ { \prime } ( z ) | d \theta = O ( \operatorname { log } \frac { 1 } { 1 - r } )$ ; confidence 0.970

40. b110220243.png ; $\phi _ { i } : CH ^ { i } ( X ) ^ { 0 } \rightarrow \operatorname { Ext } _ { H } ^ { 1 } ( Z ( 0 ) , h ^ { 2 i - 1 } ( X ) ( i ) )$ ; confidence 0.139

41. b120430168.png ; $\partial _ { q } f ( x ) = \frac { f ( x ) - f ( q x ) } { x ( 1 - q ) } , \quad \partial _ { q } x ^ { n } = [ n ] _ { q } x ^ { n - 1 }$ ; confidence 0.833

42. b12043077.png ; $\Psi ( x _ { i } \otimes x _ { j } ) = x _ { b } \otimes x _ { k } R ^ { \alpha } \square _ { i } \square ^ { b } \square$ ; confidence 0.087

43. b12050048.png ; $= \operatorname { exp } ( - x \int _ { 0 } ^ { \infty } ( 1 - e ^ { - u v } ) \frac { 1 } { \sqrt { 2 \pi v ^ { 3 } } } d v ) =$ ; confidence 0.843

44. c12002048.png ; $\mathfrak { c } _ { \mathfrak { g } } = \int _ { 0 } ^ { \infty } g ( t ) \operatorname { log } \frac { 1 } { t } d t$ ; confidence 0.509

45. c12004062.png ; $f ( z ) = \operatorname { lim } _ { m \rightarrow \infty } \int _ { \Gamma } f ( \zeta ) [ CF ( \zeta - z , w ) +$ ; confidence 0.809

46. c13004016.png ; $Cl _ { 2 } ( z ) : = - \int _ { 0 } ^ { z } \operatorname { log } | 2 \operatorname { sin } ( \frac { 1 } { 2 } t ) | d t =$ ; confidence 0.745

47. c120080110.png ; $\Delta ( z _ { l } , z _ { 2 } ) = \operatorname { det } [ E z _ { 1 } z _ { 2 } - A _ { 1 } z _ { 1 } - A _ { 2 } z _ { 2 } - A _ { 0 } ] =$ ; confidence 0.932

48. c1202503.png ; $\tilde { \kappa } = \kappa | \nabla L | = L _ { y } ^ { 2 } L _ { x x } - 2 L _ { x } L _ { y } L _ { x y } + L _ { x } ^ { 2 } L _ { y y }$ ; confidence 0.661

49. d13013018.png ; $A _ { \phi } ^ { \pm } = \frac { g } { \operatorname { rin } \theta } ( \pm 1 - \operatorname { cos } \theta )$ ; confidence 0.472

50. d13017074.png ; $\lambda _ { 1 } ( \Omega _ { t } ) \leq t \lambda _ { 1 } ( \Omega _ { 1 } ) + ( 1 - t ) \lambda _ { 2 } ( \Omega _ { 2 } )$ ; confidence 0.998

51. e12002053.png ; $( X \wedge S ^ { 1 } , Y ) \approx \operatorname { map } _ { * } ( X , \operatorname { map } _ { * } ( S ^ { 1 } , Y ) )$ ; confidence 0.702

52. f12004035.png ; $f ^ { b ( \varphi ) } ( w ) = \operatorname { sup } _ { x \in X } \{ - [ - \varphi ( x , w ) \odot f ( x ) ] \} ( w \in W )$ ; confidence 0.466

53. f120110126.png ; $F ( z ) = - \frac { 1 } { 2 \pi i } \int \frac { \operatorname { exp } e ^ { \zeta ^ { 2 } } } { \zeta - z } d \zeta$ ; confidence 0.622

54. f12021041.png ; $u ( z , \lambda _ { 1 } ) = z ^ { \lambda _ { 1 } } + \ldots , \ldots , u ( z , \lambda _ { N } ) = z ^ { \lambda _ { N } } +$ ; confidence 0.410

55. h046010140.png ; $W \times S ^ { 1 } \approx M _ { 0 } \times S ^ { 1 } \times [ 0,1 ] \approx M _ { 1 } \times S ^ { 1 } \times [ 0,1 ]$ ; confidence 0.986

56. i13001022.png ; $d ( n ) ( A ) = \operatorname { per } ( A ) = \sum _ { \sigma \in S _ { n } } \prod _ { i = 1 } ^ { n } a _ { i \sigma ( i ) }$ ; confidence 0.067

57. i13009099.png ; $\operatorname { char } ( X ) = \prod _ { i = 1 } ^ { s } f _ { i } ( T ) ^ { l _ { i } } \prod _ { j = 1 } ^ { t } \pi ^ { m _ { j } }$ ; confidence 0.457

58. i130090226.png ; $X ^ { \omega } \chi ^ { - 1 } = \{ x \in X : \delta x = \omega \chi ^ { - 1 } ( \delta ) x f o r \delta \in \Delta \}$ ; confidence 0.193

59. j13004096.png ; $P _ { 4 _ { 1 } } ( v , z ) - 1 = ( v ^ { - 1 } - v ) ^ { 2 } - z ^ { 2 } = - v ^ { - 2 } ( P _ { 3 } ( v , z ) - 1 ) = - v ^ { 2 } ( P _ { 3 } ( v , z ) - 1 )$ ; confidence 0.445

60. j130040133.png ; $P ( i , i \sqrt { 2 } ) = ( - \sqrt { 2 } ) ^ { \operatorname { com } ( L ) - 1 } ( - 1 ) ^ { \operatorname { Arf } ( L ) }$ ; confidence 0.618

61. k05578012.png ; $\int _ { 0 } ^ { \infty } F _ { 1 } ( \tau ) F _ { 2 } ( \tau ) d \tau = \int _ { 0 } ^ { \infty } f _ { 1 } ( x ) f _ { 2 } ( x ) d x$ ; confidence 0.996

62. l12006033.png ; $\langle \lambda | G ( z ) \phi ) = \frac { 1 } { z - \lambda } \langle \lambda | V \phi ) ( \phi , G ( z ) \phi )$ ; confidence 0.515

63. l1201008.png ; $\sum _ { j \geq 1 } | e _ { j } | ^ { \gamma } \leq L _ { \gamma , n } \int _ { R ^ { n } } V _ { - } ( x ) ^ { \gamma + n / 2 } d x$ ; confidence 0.440

64. m130140141.png ; $\Delta _ { n } = \{ ( t _ { 2 } , \dots , t _ { n } ) : t _ { 2 } , \dots , t _ { n } \geq 0 , t _ { 2 } + \dots + t _ { n } \leq 1 \}$ ; confidence 0.383

65. n067520381.png ; $N _ { i } = \{ Q : \text { integers } \square q _ { j } \geq 0 , q _ { k } \geq - 1 , q _ { 1 } + \ldots + q _ { n } \geq 0 \}$ ; confidence 0.691

66. r13007030.png ; $\Lambda ^ { 2 } : = \sum _ { j = 1 } ^ { \infty } \lambda _ { j } < \infty , | \varphi _ { j } ( x ) | < c , \forall j , x$ ; confidence 0.905

67. s13041026.png ; $\langle p , q \rangle = \int _ { R } p q d \mu _ { 0 } + \lambda \int _ { R } p ^ { \prime } q ^ { \prime } d \mu _ { 1 }$ ; confidence 0.381

68. s12022069.png ; $\sum _ { k } ( z + \lambda _ { k } ) ^ { - s } , \operatorname { Re } ( s ) > \frac { 1 } { 2 } \operatorname { dim } M$ ; confidence 0.959

69. s12026055.png ; $\int _ { 0 } ^ { t } \phi ( s ) d B ( s + ) : = \int _ { 0 } ^ { t } ( \partial _ { s } ^ { * } + \partial _ { s + } ) \phi ( s ) d s$ ; confidence 0.926

70. s130620110.png ; $\operatorname { lim } _ { \epsilon \rightarrow 0 + } \operatorname { Im } m _ { + } ( \lambda ) = \infty$ ; confidence 0.934

71. s120340184.png ; $\operatorname { lim } _ { s \rightarrow \pm \infty } ( \sigma \cdot \varphi _ { i } ( s , t ) ) = x _ { i } ( t )$ ; confidence 0.765

72. t130130105.png ; $0 \rightarrow \Lambda \rightarrow T _ { 1 } \rightarrow \ldots \rightarrow T _ { n } \rightarrow 0$ ; confidence 0.946

73. t120200181.png ; $B = \frac { 1 } { 6 K } ( \frac { K } { 4 e ( m + 2 K ) } ) ^ { 2 K } | \operatorname { Re } \sum _ { j = 0 } ^ { n } P _ { j } ( 0 ) |$ ; confidence 0.890

74. v13011029.png ; $= - \frac { i \Gamma } { 2 \pi } \operatorname { log } [ \operatorname { sin } \frac { \pi z } { l } ] + const$ ; confidence 0.541

75. v13011064.png ; $U = \frac { \Gamma } { 2 l } \operatorname { tanh } \frac { \pi b } { l } = \frac { \Gamma } { 2 l \sqrt { 2 } }$ ; confidence 0.768

76. w13008031.png ; $\overline { u } ( x , t ) = \frac { 1 } { 2 } \sum _ { i = 0 } ^ { 2 g } \lambda _ { i } - \sum _ { j = 0 } ^ { g } \alpha _ { j }$ ; confidence 0.953

77. w130090108.png ; $\| \varphi \| _ { L ^ { 2 } ( \mu ) } ^ { 2 } = \sum _ { n = 0 } ^ { \infty } n ! | g _ { n } | _ { L } ^ { 2 } 2 _ { ( [ 0,1 ] ^ { n } ) }$ ; confidence 0.209

78. a1301302.png ; $\frac { \partial } { \partial t } P _ { 1 } - \frac { \partial } { \partial x } Q _ { 2 } + [ P _ { 1 } , Q _ { 2 } ] = 0$ ; confidence 0.971

79. a12016080.png ; $y _ { i } = \Delta \text { sales } = ( \frac { c _ { 1 } } { 1 - \lambda } ) \frac { I } { k } ( \text { in market } i )$ ; confidence 0.512

80. b12009070.png ; $\operatorname { Re } \{ \frac { z f ^ { \prime } ( z ) } { f ( z ) ^ { 1 - \beta } g ( z ) ^ { \beta } } \} > 0 ( z \in U )$ ; confidence 0.962

81. b1301708.png ; $d _ { 2 } = \frac { \operatorname { log } ( S ( t ) / K ) + ( r - \sigma ^ { 2 } / 2 ) ( T - t ) } { \sigma \sqrt { T - t } }$ ; confidence 0.952

82. b1301707.png ; $d _ { 1 } = \frac { \operatorname { log } ( S ( t ) / K ) + ( r + \sigma ^ { 2 } / 2 ) ( T - t ) } { \sigma \sqrt { T - t } }$ ; confidence 0.946

83. b12027076.png ; $\sum _ { n = 0 } ^ { \infty } ( | \overline { m } _ { n } ( h ) | + | m \underline { \square } _ { n } ( h ) | ) < \infty$ ; confidence 0.546

84. b12001020.png ; $\frac { d u } { d t } - i \frac { d v } { d t } = 2 e ^ { i \lambda } \operatorname { sin } ( \frac { 1 } { 2 } ( u + i v ) )$ ; confidence 0.975

85. c12002045.png ; $( I ^ { \alpha } f ) ( x ) = c _ { \mu , \alpha } \int _ { 0 } ^ { \infty } ( f ^ { * } \mu _ { t } ) ( x ) t ^ { \alpha - 1 } d t$ ; confidence 0.931

86. c13007095.png ; $f ( X ^ { \prime } , X ^ { \prime } Y ^ { \prime } ) = X ^ { \prime d } f ^ { \prime } ( X ^ { \prime } , Y ^ { \prime } )$ ; confidence 0.515

87. c02211035.png ; $X ^ { 2 } ( \theta ) = \sum _ { l = 1 } ^ { k } \frac { [ \nu _ { l } - n p _ { l } ( \theta ) ] ^ { 2 } } { n p _ { l } ( \theta ) }$ ; confidence 0.269

88. c13016015.png ; $P = \cup _ { k = 1 } ^ { \infty } \operatorname { DTIME } [ n ^ { k } ] = \operatorname { DTIME } [ n ^ { Q ( 1 ) } ]$ ; confidence 0.667

89. c120180198.png ; $A ( g ) = \frac { 1 } { n - 2 } ( \operatorname { Ric } ( g ) - \frac { 1 } { 2 } \frac { S ( g ) } { n - 1 } g ) \in S ^ { 2 } E$ ; confidence 0.397

90. c12026049.png ; $\| \Delta V ^ { n } \| ^ { 2 } \leq \| \Delta V ^ { 0 } \| ^ { 2 } + \sum _ { m = 1 } ^ { n } k \| ( L _ { h k } V ) ^ { m } \| ^ { 2 }$ ; confidence 0.486

91. d12028022.png ; $A _ { 0 } ( \overline { C } \backslash D ) = \{ f : f \in A ( \overline { C } \backslash D ) , f ( \infty ) = 0 \}$ ; confidence 0.965

92. e12012052.png ; $f _ { i } ( t + 1 ) = f _ { i } ( t ) \sum _ { j } ( \frac { h _ { i j } } { \sum _ { k } f _ { k } ( t ) h _ { k j } ) } ) g _ { j } , t = 1,2 ,$ ; confidence 0.176

93. e12010046.png ; $w ^ { em } = - \frac { 1 } { 2 } \frac { \partial } { \partial t } ( E ^ { 2 } + B ^ { 2 } ) - \nabla \cdot ( S - v ( P E ) )$ ; confidence 0.190

94. f13005030.png ; $\| \sum _ { j = 1 } ^ { m } w _ { j } \cdot \frac { p _ { j } - p _ { i } } { \| p _ { j } - p _ { i } \| } \| \leq w _ { i } , i \neq j$ ; confidence 0.297

95. g12005046.png ; $\frac { \partial A } { \partial \tau } = \frac { \partial \mu _ { 0 } } { \partial R } ( k _ { c } , R _ { c } ) A +$ ; confidence 0.480

96. i1300107.png ; $d _ { \chi } ^ { G } ( A ) : = \sum _ { \sigma \in G } \chi ( \sigma ) \prod _ { l = 1 } ^ { n } \alpha _ { \sigma ( l ) }$ ; confidence 0.240

97. i13002012.png ; $P ( A _ { 1 } \cap \ldots \cap A _ { n } ) = 1 - P ( \overline { A } _ { 1 } \cup \ldots \cup \overline { A } _ { n } )$ ; confidence 0.319

98. i13005037.png ; $| a ( k ) | ^ { 2 } = 1 + | b ( k ) | ^ { 2 } , r _ { - } ( k ) = \frac { b ( k ) } { a ( k ) } , r _ { + } ( k ) = - \frac { b ( - k ) } { a ( k ) }$ ; confidence 0.272

99. i12008072.png ; $\operatorname { exp } \{ \frac { 1 } { k _ { S } T } [ J S _ { i } S _ { + 1 } + \frac { H } { 2 } ( S _ { i } + S _ { + 1 } ) ] \} =$ ; confidence 0.764

100. i130090183.png ; $L _ { p } ( 1 - n , \chi ) = L ( 1 - n , \chi \omega ^ { - n } ) \prod _ { p | p } ( 1 - \chi \omega ^ { - n } ( p ) N p ^ { n - 1 } )$ ; confidence 0.497

101. j12002038.png ; $\varphi ( \vartheta ) = | \operatorname { log } | \operatorname { tan } \frac { 1 } { 2 } \vartheta \|$ ; confidence 0.558

102. k12008048.png ; $K _ { p } ( f ) = \sum _ { r = 0 } ^ { m } \int _ { [ p _ { 0 } \ldots p _ { r } ] } D _ { x - p _ { 0 } \cdots D _ { x } - p _ { r - 1 } f }$ ; confidence 0.151

103. m12013043.png ; $\frac { d N ^ { i } } { d t } = \lambda _ { ( i ) } N ^ { i } ( 1 - \frac { N ^ { i } } { K _ { ( i ) } } ) , \quad i = 1 , \ldots , n$ ; confidence 0.380

104. m13014085.png ; $\frac { \pi ^ { n } } { n \operatorname { vol } ( D ) } \int _ { \partial D } f ( \zeta ) \nu ( \zeta - a ) = f ( a )$ ; confidence 0.186

105. m12019011.png ; $F ( \tau ) = \frac { \tau \operatorname { sinh } ( \pi \tau ) } { \pi } \Gamma ( \frac { 1 } { 2 } - k + i \tau )$ ; confidence 0.763

106. n12002026.png ; $P ( \theta , \mu ) = \operatorname { exp } [ \langle \theta , x \rangle - k _ { \mu } ( \theta ) ] \mu ( d x )$ ; confidence 0.554

107. o1300605.png ; $\mathfrak { V } = ( A _ { 1 } , A _ { 2 } , H , \Phi , E , \sigma _ { 1 } , \sigma _ { 2 } , \gamma , \tilde { \gamma } )$ ; confidence 0.587

108. o13006050.png ; $\mathfrak { V } = ( A _ { 1 } , A _ { 2 } , H , \Phi , E , \sigma _ { 1 } , \sigma _ { 2 } , \gamma , \tilde { \gamma } )$ ; confidence 0.888

109. q12007096.png ; $\sum g ( 1 ) h _ { ( 1 ) } R ( h _ { ( 2 ) } \otimes g _ { ( 2 ) } ) = \sum R ( h _ { ( 1 ) } \otimes g _ { ( 1 ) } ) h _ { ( 2 ) } g ( 2 )$ ; confidence 0.130

110. t12006083.png ; $H = - \sum _ { i = 1 } ^ { N } [ \Delta _ { i } + V ( x _ { i } ) ] + \sum _ { 1 \leq i < j \leq N } | x _ { i } - x _ { j } | ^ { - 1 } + U$ ; confidence 0.862

111. t12015057.png ; $A _ { 0 } \equiv \{ \xi \in A ^ { \prime \prime } : \xi \in \cap _ { \alpha \in C } D ( \Delta ^ { \alpha } ) \}$ ; confidence 0.479

112. t12020031.png ; $\operatorname { inf } _ { z _ { j } } \operatorname { max } _ { k \in S } \frac { | g _ { 1 } ( k ) | } { M _ { d } ( k ) }$ ; confidence 0.434

113. t12020073.png ; $\operatorname { inf } _ { z _ { j } } \operatorname { max } _ { j = 1 , \ldots , n } 2 | s _ { j } | \geq \sqrt { n }$ ; confidence 0.375

114. t12020097.png ; $P _ { m , n } = \sum _ { j = 0 } ^ { n - 1 } \left( \begin{array} { c } { m + j } \\ { j } \end{array} \right) 2 ^ { j }$ ; confidence 0.712

115. t12020032.png ; $\operatorname { inf } _ { z _ { j } } \operatorname { max } _ { k \in S } \frac { | g _ { 2 } ( k ) | } { M _ { d } ( k ) }$ ; confidence 0.382

116. w13005012.png ; $W ( G , K ) = \{ \bigwedge ( \mathfrak { g } / \mathfrak { k } ) ^ { * } \otimes S \mathfrak { g } ^ { * } \} ^ { K }$ ; confidence 0.169

117. w13017057.png ; $\int _ { - \pi } ^ { \pi } \operatorname { log } \operatorname { det } f ( \lambda ) d \lambda > - \infty$ ; confidence 0.999

118. z130100103.png ; $\downarrow \forall x \exists y \forall w ( w \in y \leftrightarrow \exists v ( v \in x / \varphi ) )$ ; confidence 0.744

119. z13011040.png ; $\frac { \mu _ { n } ( x ) } { \mu _ { n } } \approx \Delta \frac { 1 } { x } = \frac { 1 } { x ( x + 1 ) } , x = 1,2 , \dots$ ; confidence 0.338

120. a130050185.png ; $\zeta _ { A } ( z ) = \prod _ { r \geq 1 } \quad ( 1 - p ^ { - r z } ) ^ { - 1 } = \prod _ { r = 1 } ^ { \infty } \zeta ( r z )$ ; confidence 0.281

121. a12017017.png ; $F ( t ) = \int _ { t } ^ { + \infty } p _ { 0 } ( \alpha - t ) \frac { \Pi ( \alpha ) } { \Pi ( \alpha - t ) } d \alpha$ ; confidence 0.634

122. b12010031.png ; $( A ^ { * } f ) _ { n } ( X ) = \sum _ { i = 1 } ^ { n } f _ { n - 1 } ( x _ { 1 } , \dots , x _ { i } - 1 , x _ { i } + 1 , \dots , x _ { n } )$ ; confidence 0.118

123. b12010025.png ; $S _ { + } ^ { \nu - 1 } = \{ \eta \in R ^ { \nu } : | \eta | = 1 , \langle \eta , ( p _ { i } - p _ { n + 1 } ) \rangle > 0 \}$ ; confidence 0.766

124. b12003013.png ; $A \| f \| _ { 2 } ^ { 2 } \leq \sum _ { n \in Z } \sum _ { m \in Z } \| f , g _ { n } , m \} | ^ { 2 } \leq B \| f \| _ { 2 } ^ { 2 }$ ; confidence 0.277

125. b13002091.png ; $x ^ { * } : = 2 ( 1 | x ) 1 - \sigma ( x ) , \| x | ^ { 2 } : = ( x | x ) + ( ( x | x ) ^ { 2 } - | ( x | \sigma ( x ) ) | ^ { 2 } ) ^ { 1 / 2 }$ ; confidence 0.365

126. b12009042.png ; $= ( p _ { 0 } ( \xi ) - a i ) \frac { \tau } { \xi } + ( p _ { 1 } ( \xi ) + p _ { 0 } ( \xi ) ) \frac { \tau ^ { m + 1 } } { \xi }$ ; confidence 0.730

127. b110220165.png ; $\operatorname { ord } _ { s = m } L ( h ^ { i } ( X ) , s ) - \operatorname { ord } _ { s = m + 1 } L ( h ^ { i } ( X ) , s ) =$ ; confidence 0.454

128. b13019051.png ; $\sum _ { m = 1 } b ( m ) e ( \frac { m a } { q } ) g ( m ) = \sum _ { N } b ( n ) e ( - n \frac { \overline { a } } { q } ) L g ( n )$ ; confidence 0.068

129. b13020087.png ; $[ \mathfrak { g } ^ { \alpha } , \mathfrak { g } ^ { \beta } ] \subset \mathfrak { g } ^ { \alpha } + \beta$ ; confidence 0.789

130. c12008022.png ; $\operatorname { det } [ I _ { N } \lambda - A _ { 1 } ] = \sum _ { i = 0 } ^ { n } a _ { i } \lambda ^ { i } ( a _ { n } = 1 )$ ; confidence 0.152

131. c12008044.png ; $A = \left[ \begin{array} { l } { A _ { 1 } } \\ { A _ { 2 } } \end{array} \right] \in C ^ { ( m n + p ) \times m }$ ; confidence 0.801

132. c12008015.png ; $\operatorname { det } [ I _ { N } \lambda - A _ { 1 } ] = \sum _ { i = 0 } ^ { m } a _ { i } \lambda ^ { i } ( a _ { m } = 1 )$ ; confidence 0.473

133. c12008043.png ; $\sum _ { l = 0 } ^ { m } ( l _ { m } \otimes D _ { m - i } ) [ A _ { 1 } ^ { i + 1 } , A _ { 1 } ^ { i } A _ { 2 } ] = 0 ( D _ { 0 } = I _ { n } )$ ; confidence 0.213

134. c120180394.png ; $( \vec { \nabla } ^ { \psi _ { 1 } } R ( g ) \otimes \ldots \otimes \overline { \nabla } ^ { \psi m } R ( g ) )$ ; confidence 0.056

135. d1201409.png ; $D _ { N } ( x , a ) = ( \frac { x + \sqrt { x ^ { 2 } - 4 a } } { 2 } ) ^ { n } + ( \frac { x - \sqrt { x ^ { 2 } - 4 a } } { 2 } ) ^ { n }$ ; confidence 0.437

136. e12012086.png ; $L ( \mu , \Sigma | Y _ { aug } ) = \prod _ { i = 1 } ^ { n } f ( y _ { i } | \mu , \Sigma , \nu , q _ { k } ) f ( q _ { i } | \nu )$ ; confidence 0.649

137. f13010065.png ; $\lambda ^ { p } ( \mu ) [ \varphi ] = [ \varphi ^ { * } \Delta _ { G } ^ { 1 / p ^ { \prime } } \not \sim \rceil ]$ ; confidence 0.066

138. f120080150.png ; $f _ { k } \in L _ { p } ( G ) , g _ { k } \in L _ { q } ( G ) , \sum _ { k = 1 } ^ { \infty } \| f _ { k } \| \| g _ { k } \| < \infty$ ; confidence 0.421

139. f1201609.png ; $\chi _ { T } = \operatorname { dim } \operatorname { ker } T - \operatorname { dim } \text { coker } T$ ; confidence 0.572

140. f12021089.png ; $\pi ( \lambda ) = ( \lambda + 2 ) ( \lambda + 1 ) \alpha ^ { 2 } 0 + ( \lambda + 1 ) \alpha ^ { 1 } 0 + a ^ { 0 } =$ ; confidence 0.071

141. i12005091.png ; $\operatorname { log } \alpha _ { n } = o ( \operatorname { log } n ) \text { as } n \rightarrow \infty$ ; confidence 0.716

142. i13007014.png ; $v ( x , \alpha , k ) = A ( \alpha ^ { \prime } , \alpha , k ) \frac { e ^ { i k \gamma } } { r } + o ( \frac { 1 } { r } )$ ; confidence 0.638

143. i130090225.png ; $\Delta = \text { Gal } ( k _ { \infty } ^ { \prime } / k _ { \infty } ) \cong \text { Gal } ( k ^ { \prime } / k )$ ; confidence 0.471

144. j12002013.png ; $e ^ { i \vartheta } \mapsto k _ { \vartheta } ( z ) = \frac { 1 - | z | ^ { 2 } } { | z - e ^ { i \vartheta } | ^ { 2 } }$ ; confidence 0.913

145. l12001040.png ; $T = \left( \begin{array} { c c c c } { 1 } & { 1 } & { 1 } & { 0 } \\ { 1 } & { - 1 } & { 0 } & { 1 } \end{array} \right)$ ; confidence 0.985

146. l12006043.png ; $\int _ { 0 } ^ { \infty } \frac { | ( V \phi | \lambda \rangle ^ { 2 } } { \lambda } _ { d } \lambda < E _ { 0 }$ ; confidence 0.248

147. l12010025.png ; $L _ { \gamma , n } ^ { c } = 2 ^ { - n } \pi ^ { - n / 2 } \frac { \Gamma ( \gamma + 1 ) } { \Gamma ( \gamma + 1 + n / 2 ) }$ ; confidence 0.725

148. l13006069.png ; $W _ { 2 } ^ { * } = \frac { 1 } { D _ { 2 } ^ { * } } = \operatorname { min } _ { i } \sqrt { m _ { i } ^ { 2 } + p _ { 2 } ^ { 2 } }$ ; confidence 0.681

149. n13003027.png ; $\operatorname { exp } ( i \alpha ) = \operatorname { cos } \alpha + i \operatorname { sin } \alpha$ ; confidence 0.999

150. n12010033.png ; $\operatorname { Re } \langle f ( x , y ) - f ( x , z ) , y - z \rangle \leq \nu \| y - z \| ^ { 2 } , y , z \in C ^ { n }$ ; confidence 0.735

151. o13001026.png ; $\frac { A ( \alpha ^ { \prime } , \alpha , k ) - \overline { A ( \alpha , \alpha ^ { \prime } , k ) } } { 2 i } =$ ; confidence 0.939

152. p07548015.png ; $A \& B \Leftrightarrow \neg ( A \supset \neg B ) , \quad A \vee B \Leftrightarrow \neg A \supset B$ ; confidence 0.971

153. p12017029.png ; $\operatorname { ker } \delta _ { A , B } \nsubseteq \operatorname { ker } \delta _ { A } ^ { * } , B ^ { * }$ ; confidence 0.611

154. q12008064.png ; $+ \frac { R ( \rho - \sum _ { p \in E } \rho _ { p } ^ { 2 } + \sum _ { p \in G , L } \rho _ { p } ^ { 2 } ) } { 2 ( 1 - \rho ) }$ ; confidence 0.713

155. r13004058.png ; $\frac { 1 } { \mu _ { 2 } ( \Omega ) } + \frac { 1 } { \mu _ { 3 } ( \Omega ) } \geq \frac { 2 A } { \pi p _ { 1 } ^ { 2 } }$ ; confidence 0.999

156. r1200201.png ; $\frac { d } { d t } \frac { \partial L } { \partial \dot { q } } - \frac { \partial L } { \partial q } = \tau$ ; confidence 0.835

157. r13016036.png ; $R ^ { \infty } \rightarrow \ldots \rightarrow R ^ { m } \rightarrow \ldots \rightarrow R ^ { 0 }$ ; confidence 0.522

158. s0833607.png ; $P _ { n } ( z ) = \frac { 1 } { 2 \pi i } \int _ { - \infty } \frac { ( t ^ { 2 } - 1 ) ^ { n } } { 2 ^ { n } ( t - z ) ^ { n + 1 } } d t$ ; confidence 0.256

159. s12026048.png ; $\int _ { 0 } ^ { t } \phi ( s ) d B ( s ) : = \int _ { 0 } ^ { t } ( \partial _ { s } ^ { * } + \partial _ { s } ) \phi ( s ) d s$ ; confidence 0.986

160. s120320111.png ; $\operatorname { Ber } ( T ) = \operatorname { det } ( P - Q S ^ { - 1 } R ) \operatorname { det } ( S ) ^ { - 1 }$ ; confidence 0.973

161. t12005084.png ; $\Sigma ^ { i _ { 1 } , \ldots , i _ { r } } ( f ) = j ^ { r } ( f ) ^ { - 1 } ( \Sigma ^ { i _ { 1 } , \ldots , i _ { r } } ( V , W ) )$ ; confidence 0.594

162. t12005085.png ; $\Sigma ^ { i _ { 1 } } ( f ) = \{ x \in V : \operatorname { dim } \operatorname { Ker } ( d f _ { x } ) = i _ { 1 } \}$ ; confidence 0.763

163. t12007092.png ; $\sum _ { i > 0 } \left( \begin{array} { c } { m } \\ { i } \end{array} \right) ( u _ { Y } + i v ) _ { m + n - i } w =$ ; confidence 0.235

164. t120200123.png ; $\geq \frac { 1 } { 8 } ( \frac { n - 1 } { 8 e ( m + n ) } ) ^ { n } \operatorname { min } | b _ { 1 } + \ldots + b _ { j } |$ ; confidence 0.579

165. v0969104.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { 1 } { n } \sum _ { k = 0 } ^ { n - 1 } U ^ { k } h = \hbar$ ; confidence 0.817

166. w120070121.png ; $( I \frac { \partial } { \partial t } + \sum A _ { j } \frac { \partial } { \partial x _ { j } } ) E = I \delta$ ; confidence 0.847

167. w12007028.png ; $= ( p + p ^ { \prime } , q + q ^ { \prime } , t + t ^ { \prime } + \frac { 1 } { 2 } ( p q ^ { \prime } - q p ^ { \prime } ) )$ ; confidence 0.999

168. w130080170.png ; $\partial _ { \alpha } A = 0 \text { and } \partial \overline { A } = ( 1 / \kappa ) A \mu _ { \alpha } ^ { 0 }$ ; confidence 0.643

169. z13008054.png ; $= \frac { ( - 1 ) ^ { l } } { 2 } \Gamma ( \alpha + 1 ) ( \frac { 2 } { s } ) ^ { \alpha + 1 } J _ { k + l + \alpha + 1 } ( s )$ ; confidence 0.840

170. c02111012.png ; $\square \ldots \rightarrow H ^ { n } ( X , A ; G ) \rightarrow H ^ { n } ( X ; G ) \rightarrow H ^ { n } ( A ; G )$ ; confidence 0.853

171. a130040605.png ; $g _ { S _ { P } , \mathfrak { M } } ( \varphi ) = \operatorname { mng } _ { S } _ { P } , \mathfrak { M } ( \psi )$ ; confidence 0.071

172. a12008056.png ; $\alpha ( t , u , v ) = \langle A ( t ) u , v \rangle _ { \langle H ^ { 1 } \rangle } ^ { \prime } \times H ^ { 1 }$ ; confidence 0.284

173. a12013042.png ; $( h _ { \theta } ^ { * } - \frac { I } { 2 } ) V + V ( h _ { \theta } ^ { * } - \frac { I } { 2 } ) ^ { T } = R ( \theta ^ { * } )$ ; confidence 0.816

174. a1302206.png ; $0 \rightarrow A \stackrel { f } { \rightarrow } B \stackrel { g } { \rightarrow } C \rightarrow 0$ ; confidence 0.342

175. a13028022.png ; $c _ { k } = a _ { k } ^ { 2 } - b _ { k } ^ { 2 } , s _ { k } = s _ { k - 1 } - 2 ^ { k } c _ { k } , p _ { k } = 2 s _ { k } ^ { - 1 } a _ { k } ^ { 2 }$ ; confidence 0.487

176. a13032013.png ; $E _ { \theta } ( N ) = \sum _ { k = 0 } ^ { n - 1 } P _ { \theta } ( N > k ) = \sum _ { k = 0 } ^ { n - 1 } ( 1 - \theta ) ^ { k } =$ ; confidence 0.705

177. b13006098.png ; $1 \leq \operatorname { max } _ { i } ( \frac { 1 } { | \mu - b _ { i i } | } \cdot \sum _ { j \neq i } | b _ { i j } | )$ ; confidence 0.426

178. b13007058.png ; $\sigma : a \mapsto a b , b \mapsto b , \gamma _ { r } : \alpha \mapsto a ^ { r + 1 } b ^ { 2 } a ^ { - r } , r \geq 1$ ; confidence 0.205

179. b0163607.png ; $a d - b c = 1 , \quad c \equiv 0 ( \operatorname { mod } p ) , \quad d \equiv 1 ( \operatorname { mod } p )$ ; confidence 0.978

180. b120400102.png ; $0 \rightarrow G \times ^ { R } H _ { R } \rightarrow G \times ^ { R } V \rightarrow \xi \rightarrow 0$ ; confidence 0.991

181. c120180195.png ; $S ( g ) = g ^ { - 1 } \{ 1,2 \} \operatorname { Ric } ( g ) = g ^ { - 1 } \{ 1,4 ; 2,3 \} R ( g ) \in C ^ { \infty } ( M )$ ; confidence 0.983

182. c13019049.png ; $\lambda _ { 1 } \geq \ldots \geq \lambda _ { k } > 0 > \lambda _ { k + 1 } \geq \ldots \geq \lambda _ { n }$ ; confidence 0.909

183. d130080141.png ; $\operatorname { Ker } ( I - F ^ { \prime } ( c ) ) \oplus \operatorname { Im } ( I - F ^ { \prime } ( c ) ) = X$ ; confidence 0.757

184. e035000132.png ; $\epsilon ^ { 2 } = \sum _ { i = 1 } ^ { \infty } \operatorname { min } \{ \lambda _ { i } , f ( \epsilon ) \}$ ; confidence 0.980

185. e12023050.png ; $f ( t ) = A ( \sigma _ { t } ) = \int _ { x } ^ { b } L ( x , y ( x ) + t z ( x ) , y ^ { \prime } ( x ) + t z ^ { \prime } ( x ) ) d x$ ; confidence 0.261

186. f12009029.png ; $| F \mu ( \zeta ) | \leq C _ { \epsilon } \operatorname { exp } ( H _ { K } ( \zeta ) + \epsilon | \zeta | )$ ; confidence 0.990

187. f13019013.png ; $\frac { 1 } { 2 N } \operatorname { sin } N ( x - x _ { j } ) \operatorname { cot } \frac { ( x - x _ { j } ) } { 2 }$ ; confidence 0.995

188. i13003012.png ; $nd ( P ) : = \operatorname { dim } ( ker ( P ) ) - \operatorname { dim } ( \operatorname { coker } ( P ) )$ ; confidence 0.177

189. l12003057.png ; $\pi _ { 0 } \operatorname { Map } ( B E , X ) = [ B E , X ] = \operatorname { Hom } _ { K } ( H ^ { * } X , H ^ { * } B E )$ ; confidence 0.917

190. l1200502.png ; $\operatorname { Re } K _ { 1 / 2 + i \tau } ( x ) = \frac { K _ { 1 / 2 + i \tau } ( x ) + K _ { 1 / 2 - i \tau } ( x ) } { 2 }$ ; confidence 0.715

191. l13010060.png ; $\alpha \otimes \hat { f } : = \int _ { - \infty } ^ { \infty } \alpha ( x , \alpha , p - q ) \hat { f } ( q ) d q$ ; confidence 0.450

192. l12017051.png ; $n = \operatorname { max } ( \operatorname { dim } ( K _ { 0 } - L ) , \operatorname { dim } ( K _ { 1 } - L ) )$ ; confidence 0.910

193. l12019024.png ; $\sum _ { i = 1 } ^ { m } ( \sum _ { j = 1 } ^ { m } a _ { i j } x _ { j } ) \frac { \partial _ { v } } { \partial x _ { i } } = U$ ; confidence 0.813

194. m13014017.png ; $j _ { n } ( \zeta ) = \Gamma ( \frac { n } { 2 } ) ( \frac { 2 } { \zeta } ) ^ { ( n - 2 ) / 2 } J _ { ( n - 2 ) / 2 } ( \zeta )$ ; confidence 0.903

195. m130180148.png ; $\sum _ { X : X \in L } \mu ( 0 , X ) \lambda ^ { \operatorname { rank } ( L ) - \operatorname { rank } ( X ) }$ ; confidence 0.602

196. n12002092.png ; $V _ { F } ^ { \prime } ( m ) ( V ( m ) ( \alpha ) ) ( \beta ) = V _ { F } ^ { \prime } ( m ) ( V ( m ) ( \beta ) ) ( \alpha )$ ; confidence 0.851

197. p13007021.png ; $\operatorname { imsup } _ { j \rightarrow \infty } \frac { 1 } { j } \operatorname { log } | f _ { j } |$ ; confidence 0.905

198. p13007070.png ; $\rho _ { \lambda } ( z ) = \operatorname { limsup } _ { t \in C } ( u ( t z ) - \operatorname { log } | t z | )$ ; confidence 0.058

199. p12017058.png ; $\delta _ { A , B } ( X ) \in N _ { \epsilon } ^ { \prime } \Rightarrow \delta _ { A ^ { * } , B ^ { * } } ( X ) \in N$ ; confidence 0.249

200. r130070106.png ; $= \sum _ { j n , m _ { n } } ^ { J _ { n } } K ( y _ { m _ { n } } , y _ { j _ { n } } ) c _ { j _ { n } } \overline { c _ { m } n _ { n } } =$ ; confidence 0.113

201. r13011024.png ; $\Xi ( \frac { t } { 2 } ) : = \frac { 1 } { 8 } \int _ { 0 } ^ { \infty } \Phi ( u ) \operatorname { cos } ( u t ) d u$ ; confidence 0.981

202. s1304104.png ; $\langle p , q \rangle _ { s } = \sum _ { l = 0 } ^ { N } \lambda _ { i } \int _ { R } p ^ { ( l ) } q ^ { ( l ) } d \mu _ { l }$ ; confidence 0.190

203. s1304509.png ; $\overline { R } = \sum _ { i = 1 } ^ { n } R _ { i } / n = ( n + 1 ) / 2 = \sum _ { i = 1 } ^ { n } S _ { i } / n = \overline { S }$ ; confidence 0.629

204. s12022028.png ; $\operatorname { spec } ( M , \Delta ) = \operatorname { spec } ( M ^ { \prime } , \Delta ^ { \prime } )$ ; confidence 0.984

205. s13048018.png ; $C _ { k } = \Lambda ^ { k } T ^ { * } M \otimes R _ { m } / \delta ( \Lambda ^ { k - 1 } T ^ { * } M \otimes g _ { m + 1 } )$ ; confidence 0.144

206. s130510118.png ; $V ^ { \infty } = V \backslash V ^ { f } , \gamma ^ { \prime } ( u ) = \operatorname { mex } \gamma ( F ( u ) )$ ; confidence 0.994

207. s12024058.png ; $z ^ { N } = \{ z ^ { n } _ { i } , x _ { i } ^ { n + 1 } \} , z \square ^ { n } = \{ z _ { i } ^ { N } , x \square _ { i } ^ { n + 1 } \}$ ; confidence 0.077

208. s130620106.png ; $m _ { + } ( \lambda ) = \operatorname { lim } _ { \epsilon \rightarrow 0 + } m ( \lambda + i \epsilon )$ ; confidence 0.853

209. s120340111.png ; $\frac { \partial w } { \partial s } + J ( u ) \frac { \partial w } { \partial t } = \nabla H ( t , w ( s , t ) )$ ; confidence 0.982

210. w12001021.png ; $= \frac { m ! n ! } { ( m + n + 1 ) ! } \frac { 1 } { 2 \pi i } \oint _ { z = 0 } \alpha ^ { ( m + 1 ) } ( z ) b ^ { ( n ) } ( z ) d z$ ; confidence 0.719

211. w120110163.png ; $a _ { j } ( x , \lambda \xi ) = \lambda ^ { j } a _ { j } ( x , \xi ) , \text { for } | \xi | \geq 1 , \lambda \geq 1$ ; confidence 0.563

212. w12011076.png ; $\sigma = \left( \begin{array} { c c } { 0 } & { Id ( E ^ { * } ) } \\ { - Id ( E ) } & { 0 } \end{array} \right)$ ; confidence 0.613

213. w120110117.png ; $( \tau _ { x _ { 0 } , \xi _ { 0 } } u ) ( y ) = u ( y - x _ { 0 } ) e ^ { 2 i \pi \langle y - x _ { 0 } / 2 , \xi _ { 0 } \rangle }$ ; confidence 0.542

214. w12019041.png ; $\phi ( \sigma , \tau ) = \int _ { R ^ { 3 N } \times R ^ { 3 N } } e ^ { i ( \sigma x + r , p ) / \hbar } f ( x , p ) d x d p$ ; confidence 0.325

215. w12020036.png ; $( f , g ) = \sum _ { \nu = 1 } ^ { r } f ( x _ { \nu } ) g ( x _ { \nu } ) + \int _ { x } ^ { b } f ^ { ( y ) } ( x ) g ^ { ( y ) } ( x ) d x$ ; confidence 0.169

216. z13010059.png ; $\forall x \exists z \forall v ( v \in z \leftrightarrow \forall w ( w \in v \rightarrow w \in x ) )$ ; confidence 0.164

217. a13013078.png ; $q ^ { ( l ) } = 2 i \frac { \tau _ { l } + 1 } { \tau _ { l } } , r ^ { ( l ) } = - 2 i \frac { \tau _ { l } - 1 } { \tau _ { l } }$ ; confidence 0.315

218. a130050160.png ; $\sum _ { n = 0 } ^ { \infty } G ^ { \# } ( n ) y ^ { n } = \prod _ { m = 1 } ^ { \infty } ( 1 - y ^ { m } ) ^ { - P ^ { \# } ( m ) }$ ; confidence 0.346

219. a12023046.png ; $d w [ k ] = d w _ { 1 } \wedge \ldots \wedge d w _ { k - 1 } \wedge d w _ { k + 1 } \wedge \ldots \wedge d w _ { n }$ ; confidence 0.880

220. a13032025.png ; $E _ { \theta } ( S _ { N } ) = P _ { \theta } ( S _ { N } = 1 ) = 1 - P _ { \theta } ( S _ { n } = 0 ) = 1 - ( 1 - \theta ) ^ { n }$ ; confidence 0.647

221. b12003015.png ; $B ^ { - 1 } \| f \| _ { 2 } ^ { 2 } \leq \sum _ { n , m \in Z } | c _ { n , m } ( f ) | ^ { 2 } \leq A ^ { - 1 } \| f \| _ { 2 } ^ { 2 }$ ; confidence 0.552

222. b13010047.png ; $\tilde { \varphi } ( z ) = ( 1 - | z | ^ { 2 } ) ^ { 2 } \int _ { D } \frac { \varphi ( w ) } { | 1 - z w | ^ { 4 } } d A ( w )$ ; confidence 0.677

223. b12029044.png ; $\varepsilon _ { X } ^ { X \backslash V } ( R _ { S } ^ { X \backslash U } ) = R _ { S } ^ { X \backslash U } ( x )$ ; confidence 0.431

224. b120430118.png ; $\Psi ( \alpha \bigotimes \alpha ) = \alpha \otimes \alpha + ( 1 - q ^ { 2 } ) \beta \otimes \gamma$ ; confidence 0.158

225. b12052075.png ; $u _ { n } = \frac { y _ { n } } { \| s _ { n } \| _ { 2 } } \text { and } v _ { n } = \frac { s _ { n } } { \| s _ { n } \| _ { 2 } }$ ; confidence 0.947

226. c12002063.png ; $\int _ { S O ( n ) } d \gamma \int _ { 0 } ^ { \infty } \frac { f ^ { * } \mu _ { \gamma , t } } { t } d t = c _ { \mu } f$ ; confidence 0.502

227. c13008012.png ; $\sigma _ { \mathfrak { P } } \equiv x ^ { N ( \mathfrak { p } ) } \operatorname { mod } \mathfrak { P }$ ; confidence 0.437

228. c1202908.png ; $\mu ( \square ^ { g } m ) = g \mu ( m ) g ^ { - 1 } , \square ^ { \mu ( m ) } m ^ { \prime } = m m ^ { \prime } m ^ { - 1 }$ ; confidence 0.943

229. d1300303.png ; $f ( x ) = \sum _ { j = - \infty } ^ { \infty } \sum _ { k = - \infty } ^ { \infty } a _ { j , k } \psi ( 2 ^ { j } x - k )$ ; confidence 0.970

230. d13008018.png ; $D _ { \xi } = D ( \xi , R ) : = \{ z \in \Delta : \frac { | 1 - z \overline { \xi } | ^ { 2 } } { 1 - | z | ^ { 2 } } < R \}$ ; confidence 0.960

231. e120010111.png ; $e : X \rightarrow G A \in E \text { and } M = ( m _ { i } : A \rightarrow A _ { i } ) _ { I } \in \mathfrak { M }$ ; confidence 0.525

232. e12016028.png ; $f ( d t ^ { 2 } - \omega d \theta ^ { 2 } ) - r ^ { 2 } f ^ { - 1 } d \theta ^ { 2 } - \Omega ^ { 2 } ( d r ^ { 2 } + d z ^ { 2 } )$ ; confidence 0.989

233. f13005026.png ; $\| \sum _ { j = 1 } ^ { m } w _ { j } \cdot \frac { p _ { j } - p _ { i } } { \| p _ { j } - p _ { i } \| } \| > w _ { i } , i \neq j$ ; confidence 0.389

234. f120110157.png ; $G ( \zeta ) = O ( e ^ { \varepsilon | \zeta | + H _ { K } \langle \operatorname { lm } \zeta \rangle } )$ ; confidence 0.379

235. f12023012.png ; $+ ( - 1 ) ^ { k } ( d \varphi \wedge i _ { X } \psi \otimes Y + i \gamma \varphi \wedge d \psi \otimes X )$ ; confidence 0.246

236. g12005058.png ; $E ( A ) = \frac { 1 } { 2 } \int _ { G } | \nabla A | ^ { 2 } d x + \frac { 1 } { 4 } \int _ { G } ( | A | ^ { 2 } - 1 ) ^ { 2 } d x$ ; confidence 0.993

237. j13002019.png ; $P ( X = 0 ) \leq \operatorname { exp } \{ \frac { \Delta } { 1 - \epsilon } \} \prod _ { A } ( 1 - E I _ { A } )$ ; confidence 0.421

238. k055840397.png ; $S _ { f } ( z , \overline { \rho } ) = \frac { 1 - f ( z ) \overline { f ( \rho ) } } { 1 - z \overline { \rho } }$ ; confidence 0.576

239. l12010080.png ; $\rho ( x ) = N \int _ { R ^ { n ( N - 1 ) } } | \Phi ( x , x _ { 2 } , \ldots , x _ { N } ) | ^ { 2 } d x _ { 2 } \ldots d x _ { N }$ ; confidence 0.454

240. l12015052.png ; $\times \alpha ( x 0 , \dots , x _ { i } - 1 , [ x _ { i } , x _ { j } ] , x _ { i } + 1 , \dots , x _ { j } , \dots , x _ { x } )$ ; confidence 0.060

241. m1300902.png ; $+ c ^ { 2 } ( \nabla - i \frac { q e } { \hbar } A ) ^ { 2 } + \frac { c ^ { 4 } m ^ { 2 } } { \hbar ^ { 2 } } ] \psi ( t , x )$ ; confidence 0.533

242. m12013029.png ; $= f ( N _ { * } ) + f ^ { \prime } ( N _ { * } ) n + \frac { f ^ { \prime \prime } ( N _ { * } ) } { 2 } n ^ { 2 } + \ldots$ ; confidence 0.619

243. m1202309.png ; $f _ { t } ( x ) = \operatorname { inf } _ { y \in H } ( f ( y ) + \frac { 1 } { 2 t } \| x - y \| ^ { 2 } ) , \quad x \in H$ ; confidence 0.697

244. m12027020.png ; $d w [ k ] = d w _ { 1 } \wedge \ldots \wedge d w _ { k - 1 } \wedge d w _ { k + 1 } \wedge \ldots \wedge d w _ { n }$ ; confidence 0.876

245. m13025083.png ; $\operatorname { lim } _ { \varepsilon \rightarrow 0 } u ( , , \varepsilon ) v ( , , \varepsilon )$ ; confidence 0.604

246. o13001095.png ; $S = \frac { k ^ { 2 } V } { 4 \pi } \cdot \left( \begin{array} { c } { A B } \\ { C D } \end{array} \right)$ ; confidence 0.772

247. q13004027.png ; $\operatorname { l(f } ^ { \prime } ( x ) ) = \operatorname { min } \{ | f ^ { \prime } ( x ) h | : | h | = 1 \}$ ; confidence 0.202

248. r13007043.png ; $B ( x , y ) = \sum _ { j = 1 } ^ { \infty } \lambda _ { j } \overline { \varphi _ { j } ( x ) } \varphi _ { j } ( y )$ ; confidence 0.817

249. r130080104.png ; $K ( x , y ) = \sum _ { j = 1 } ^ { \infty } \lambda _ { j } \varphi _ { j } ( y ) \overline { \varphi _ { j } ( x ) }$ ; confidence 0.694

250. s13002033.png ; $\int _ { Q } f ( u ) d u = \int _ { \gamma \in \Gamma l ( \gamma ) } f ( \gamma ^ { \prime } ( t ) ) d t d \gamma$ ; confidence 0.891

251. s08602013.png ; $\Phi ( z ) = \frac { 1 } { 2 \pi i } \int _ { \Gamma } \frac { \phi ( t ) d t } { t - z } , \quad z \notin \Gamma$ ; confidence 0.985

252. s13058017.png ; $V = 2 \xi _ { l } ^ { 0 } \xi _ { r } ^ { 0 } \operatorname { sin } ( \varepsilon _ { l } - \varepsilon _ { r } )$ ; confidence 0.975

253. s13058016.png ; $U = 2 \xi _ { l } ^ { 0 } \xi _ { r } ^ { 0 } \operatorname { cos } ( \varepsilon _ { l } - \varepsilon _ { r } )$ ; confidence 0.979

254. s12028012.png ; $E _ { n } ( X ) = \operatorname { lim } _ { k } \pi _ { n + k } ( X \wedge E _ { k } ) = \pi _ { n } ^ { S } ( X \wedge E )$ ; confidence 0.683

255. v0969109.png ; $\operatorname { lim } _ { T \rightarrow \infty } \frac { 1 } { T } \int _ { 0 } ^ { T } U _ { t } h d t = \hbar$ ; confidence 0.974

256. w12001028.png ; $[ L _ { n } , L _ { m } ] = ( n - m ) L _ { n + m } + \frac { 1 } { 12 } ( n ^ { 3 } - n ) \delta _ { n , - m } \cdot C ^ { \prime }$ ; confidence 0.231

257. w12002025.png ; $\operatorname { l } _ { p } ^ { p } ( P , Q ) = \int _ { 0 } ^ { 1 } | F ^ { - 1 } ( u ) - G ^ { - 1 } ( u ) | ^ { p } d u , p \geq 1$ ; confidence 0.201

258. w12007020.png ; $[ P _ { j } , P _ { k } ] = [ Q _ { j } , Q _ { k } ] = 0 , \quad [ P _ { j } , Q _ { k } ] = \frac { \hbar } { i } \delta _ { j k } I$ ; confidence 0.831

259. a13013046.png ; $\frac { \partial } { \partial t _ { k } } F _ { i j } = \frac { \partial } { \partial t _ { i } } F _ { j k }$ ; confidence 0.932

260. a130040646.png ; $\operatorname { Th } _ { S _ { P } } \mathfrak { M } = \operatorname { Th } _ { S _ { P } } \mathfrak { N }$ ; confidence 0.689

261. a130050196.png ; $Z _ { A ( p ) } ( y ) = \prod _ { r = 1 } ^ { \infty } ( 1 - y ^ { r } ) ^ { - 1 } = \sum _ { n = 0 } ^ { \infty } p ( n ) y ^ { n }$ ; confidence 0.525

262. a120050109.png ; $\| U ( t , s ) \| _ { Y } \leq \overline { M } e ^ { \overline { \beta } ( t - s ) } , \quad ( t , s ) \in \Delta$ ; confidence 0.913

263. a13008051.png ; $= \frac { d \operatorname { ln } g ( R ; m , s ) } { d m } \frac { d \operatorname { ln } g ( L ; m , s ) } { d s }$ ; confidence 0.759

264. a1301804.png ; $L = \{ Fm _ { L } , \operatorname { Mod } _ { L } , \vDash _ { L } , \operatorname { mng } _ { L } , t _ { L } \}$ ; confidence 0.094

265. b12042056.png ; $b _ { i } b _ { i } + 1 b _ { i } = b _ { i } + 1 b _ { i } b _ { i } + 1 , b _ { i } b _ { j } = b _ { j } b _ { i } , \quad | i - j | \geq 2$ ; confidence 0.362

266. b12052091.png ; $w _ { n - 1 } = ( \| s _ { n } - 1 \| _ { 2 } + v _ { n - 1 } ^ { T } w ) ^ { - 1 } w , s _ { n } = - ( I - w _ { n - 1 } v _ { n - 1 } ^ { T } ) w$ ; confidence 0.164

267. c13009016.png ; $C _ { j } = ( 1 - x ^ { 2 } ) \frac { T _ { N } ^ { \prime } ( x ) ( - 1 ) ^ { j + 1 } } { [ \tau _ { j } N ^ { 2 } ( x - x _ { j } ) ] }$ ; confidence 0.370

268. c02211041.png ; $X ^ { 2 } ( \tilde { \theta } _ { N } ) = \operatorname { min } _ { \theta \in \Theta } X ^ { 2 } ( \theta )$ ; confidence 0.615

269. c13015010.png ; $\varphi _ { \varepsilon , x } ( y ) = \varepsilon ^ { - n } \varphi ( \frac { y - x } { \varepsilon } )$ ; confidence 0.791

270. c120180504.png ; $R ( \mathfrak { g } ) = W ( \mathfrak { g } ) \in A ^ { 2 } \mathfrak { E } \otimes A ^ { 2 } \overline { E }$ ; confidence 0.073

271. c12019049.png ; $\phi * ( \operatorname { ind } ( D ) ) = c _ { q } ( \operatorname { Ch } ( D ) T ( M ) f ^ { * } ( \phi ) ) [ T M ]$ ; confidence 0.154

272. c12026012.png ; $\frac { U _ { l } ^ { n + 1 } - U _ { l } ^ { n } } { k } = \delta ^ { 2 } ( \frac { U _ { l } ^ { n + 1 } + U _ { l } ^ { n } } { 2 } )$ ; confidence 0.315

273. d11008067.png ; $= d ( w ^ { H _ { i } } | v ^ { H _ { i } } ) \cdot e ( w ^ { H _ { i } } | v ^ { H _ { i } } ) . f ( w ^ { H _ { i } } | v ^ { H _ { i } } )$ ; confidence 0.435

274. d13017045.png ; $\lambda _ { k } \geq \frac { 4 \pi ^ { 2 } k ^ { 2 / n } } { ( C _ { n } | \Omega | ) ^ { 2 / n } } \text { for } k = 1,2$ ; confidence 0.885

275. d120280140.png ; $g _ { \lambda } = \sum _ { k = 1 } ^ { n } ( - 1 ) ^ { k - 1 } \frac { \partial u } { \partial z _ { k } } d z [ k ] / d z$ ; confidence 0.270

276. e12015031.png ; $\frac { d ^ { 2 } \xi ^ { i } } { d t ^ { 2 } } + g _ { i } ^ { i } \frac { d \xi ^ { r } } { d t } + g _ { r } ^ { i } \xi ^ { r } = 0$ ; confidence 0.142

277. e120230161.png ; $\frac { d } { d t } A ( \sigma _ { t } ) | _ { t = 0 } = \int _ { M } \sigma ^ { k ^ { * } } ( Z ^ { k } _ { - } d L \Delta ) =$ ; confidence 0.430

278. f12011027.png ; $\langle f , \varphi \rangle = \sum _ { j = 1 } ^ { N } \int _ { \gamma _ { j } } F _ { j } ( z ) \varphi ( z ) d z$ ; confidence 0.957

279. f12021022.png ; $\pi ( \lambda ) = \sum _ { n = 0 } ^ { N } ( \lambda + n ) ( \lambda + n - 1 ) \ldots ( \lambda + 1 ) a ^ { n } 0 =$ ; confidence 0.798

280. f1202307.png ; $[ K _ { 1 } , [ K _ { 2 } , K _ { 3 } ] ] = [ [ K _ { 1 } , K _ { 2 } ] , K _ { 3 } ] + ( - 1 ) ^ { k _ { 1 } k _ { 2 } } [ K _ { 2 } , [ K _ { 1 } ]$ ; confidence 0.250

281. f12024030.png ; $y ( t ) = f ( t , x ( t - h _ { 1 } ( t ) ) , \ldots , x ( t - h _ { k } ( t ) ) , y ( t - g _ { 1 } ( t ) ) , \ldots , y ( t - g ( t ) ) )$ ; confidence 0.557

282. g13003061.png ; $E _ { M } = \{ ( u _ { \varepsilon } ) _ { \varepsilon > 0 } \in C ^ { \infty } ( \Omega ) ^ { ( 0 , \infty ) }$ ; confidence 0.773

283. g04339014.png ; $\delta f ( x _ { 0 } , h ) = f _ { G } ^ { \prime } ( x _ { 0 } ) h , \quad f _ { G } ^ { \prime } ( x _ { 0 } ) \in L ( X , Y )$ ; confidence 0.752

284. k13002048.png ; $\tau = 4 \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { 1 } C _ { X , Y ^ { \prime } } ( u , v ) d C _ { X , Y ^ { \prime } } ( u , v ) - 1$ ; confidence 0.227

285. k0558404.png ; $[ \alpha _ { 1 } x _ { 1 } + \alpha _ { 2 } x _ { 2 } , y ] = \alpha _ { 1 } [ x _ { 1 } , y ] + \alpha _ { 2 } [ x _ { 2 } , y ]$ ; confidence 0.596

286. k1300602.png ; $\left( \begin{array} { c } { [ n ] } \\ { k } \end{array} \right) : = \{ X \subseteq [ n ] : | X | = k \}$ ; confidence 0.505

287. m12023032.png ; $\partial f ( x ) = \partial _ { c } ( f + ( 2 T ) ^ { - 1 } \| \| \cdot \| ^ { 2 } ) ( x ) - T ^ { - 1 } x , \quad x \in H$ ; confidence 0.657

288. m13025016.png ; $( f , g ) \rightarrow f g : L ^ { p } ( \Omega ) \times L ^ { Y } ( \Omega ) \rightarrow L ^ { 1 } ( \Omega )$ ; confidence 0.463

289. n067520477.png ; $S = ( s _ { 1 } , \dots , s _ { k } ) , \quad Y = ( y _ { 1 } , \dots , y _ { l } ) , \quad Z = ( z _ { 1 } , \dots , z _ { m } )$ ; confidence 0.311

290. p12017041.png ; $\overline { X } \in \operatorname { ker } \delta _ { \overline { H } } ^ { * } , \overline { B } ^ { * }$ ; confidence 0.077

291. r130080125.png ; $( u , v ) + = \int _ { D } \int _ { D } B ( x , y ) u ( y ) \overline { v ( x ) } d y d x \text { if } H _ { 0 } = L ^ { 2 } ( D )$ ; confidence 0.576

292. s12016031.png ; $e ( A ( q , d ) , f ) \leq C _ { d } n ^ { - k } ( \operatorname { log } n ) ^ { ( \alpha - 1 ) / ( k + 1 ) } \| f \| _ { k }$ ; confidence 0.052

293. s12022058.png ; $\operatorname { det } ( \Delta ) = \operatorname { exp } ( - \frac { d } { d s } \zeta ( s ) | _ { s = 0 } )$ ; confidence 0.960

294. s120320128.png ; $\operatorname { ev } _ { x } ( \varphi ^ { * } ( a ) ) = \operatorname { ev } _ { \varphi _ { 0 } ( x ) } ( a )$ ; confidence 0.243

295. t12006026.png ; $E ^ { TF } ( N ) = \operatorname { inf } \{ E ( \rho ) : \rho \in L ^ { 5 / 3 } , \int \rho = N , \rho \geq 0 \}$ ; confidence 0.641

296. t120140167.png ; $B f = \Psi _ { 2 } ^ { - 1 } P _ { + } \overline { \Lambda } P _ { + } \overline { \Psi } _ { \square } ^ { - 1 } f$ ; confidence 0.704

297. w120110127.png ; $( a \circ b ) ( x , \xi ) = \int \int e ^ { - 2 i \pi y \cdot \eta } a ( x , \xi + \eta ) b ( y + x , \xi ) d y d \eta$ ; confidence 0.175

298. w120110206.png ; $G _ { X } ^ { g } = \sum _ { 1 \leq j \leq n } h _ { j } ^ { - 1 } ( | \alpha q _ { j } | ^ { 2 } + | \alpha p _ { j } | ^ { 2 } )$ ; confidence 0.277

299. w13008041.png ; $\psi ( P ) = \operatorname { exp } ( \sum t _ { n } \Omega _ { n } ) \phi ( \sum t _ { n } \vec { V } _ { n } , P )$ ; confidence 0.447

300. w13008015.png ; $\frac { \partial d \omega _ { 1 } } { \partial T } = \frac { \partial d \omega _ { 3 } } { \partial X }$ ; confidence 0.987

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/5. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/5&oldid=44493